Remington, The Science & Practice of Pharmacy. (Joseph P. Remington).

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E D~ I T I O~ N

Remington The Science and Practice of Pharmacy

2 1 S T

EDITION

The Science and Practice of Pharmacy

L r p m ~ c a rWILLW r G WILKINS A Wolters Kluwer Company Philadelphia Baltimore New York London Buenos Aires Hong Kong Sydney Tokyo

Lditor. Uarid Troy Manag-kg-Editor: klatthew J . IIauber Lippincutt Williams k Williins 351 West Camden Street Baltimore. Maryland 21201-2436 USA 227 East Washington Square Wiladelpl~ia.PA 19106

1111 rights reserved This book is protected by copyright No part of this book may be reproduced in any form or by any means. illcludulg photocopying, or utilized by any inforrnatioll storage and retrieval system without written permissiol~from t h e copy

right owner, T11c pubhsher is not responsible (3s a matter of product liabilitv. ncgligellcc or uthcrwise) fur any injury resultine frum any material contained herein '[his publicatiol~contains infurmation relating to general prillciples of medical care which should not be cunstrued as specific instructions for individual patients ,\.lanufacturer's product ulformatioll and pacliav inserts shuuld be reviewed for current informatiun. ineludule contraindications, dusages and precautiolls Printed in t h e United States of r h e r i e a Entcred according to Act of Congress, 111 the year 1885 by Joseph P Herni~lgon.111 t h e Office of the Librarian of Congress, at Washington UC' Copyright 1889,1894.1905.1907. 1917. by J o s e p l ~P Hernin@on Copyright 1926. 1936. bp the Joseph P It~mingtonEstate Copyrigl~t1948. 1951. by the Philadelphia Culleg-e of Pharmacy and Science C o p y r i ~ h 1956. t 1960. 1965. 1970. 1975. 1980. 1985. 1990. 1995. by the Wiladelphia College of Pharmacy a n d Science C o p y r i ~ h 2000. t 2005. by the University of t h e Sciences in Philadelphia All Itights Itesen~ed Library of Congress Catalog- Card lnformatiol~is available lSUN 0-683-306472

Th.? prl hJisht,rs tr.ni~bllladr Prwy tbffnrt to trarr t h . rol~>~rr.h,trt ~ holclprs fir horrorr:rd ~ilntrl-iol.I f t h ~ hh.n > ~r), t h ~ will > ~ hp plrasrd to lllahr thr Yrrrrssnrj nl-m rrgt7iilrrrts a f fhp first opportr~rlits. Tltr usr cfsil-urtulnl firnil rrlas firlnl USAN n I L th.r ~ LTASPD i c f i o n a ~(if : ~ Drug Nrr~ilcsis hy p~r)i7isston( i f ' T l i , ~LTSP C n r ~ r ~ ~ r t i Tr >l ~n r C'(inrnrp ~ or rEisrl-rpo~rc:yhvtrveen tlrt rrr rrtbnt clfficiol LTSP o r ATF stondo rds o f strwrgtJr., clr/oIit,tt,purity, porkogi~?go n,d lo heling fill- drugs n ~ r drryrcbsrn,totinn,sof f/irfil hrlrin,, t J wcorrtrmf a7r.d ebffirt of thw nffictol cnrllprbrrdio sh.oll p r r w il. To purchase additional eupies of this book call our customer service departmel~tat (800) 638-3030 or fax urders to (301 1 824-7390. lnternatiollal custo~nersshould call (301) 714-2324.

Remington: The Science and Practice of Pharmacy . . . A treatise on the theory and practice of the pharmaceutical sciences, with essential in formation about pharmaceutical and medicinal agents; also, a guide to the professional responsibilities of the pharmacist as the drug information specialist of the health team . . . A textbook and reference work for pharmacists, physicians, and other practitioners of the pharmaceutical and medical sciences.

EDITORIAL BOARD

AUTHORS

Paul Beringer

Pardeep K. Gupta

Ara DerMarderosian

John E. Hoover

Linda Felton

Nicholas G. Popovick

Steven Gelone

William J. Reilly, Jr

Alfonso R. Gennaro

Randy Hendrickson, Chair

The 133 chapters of this edition of Remington were written by the editors, by members of the Editorial Board, and by the authors listed on pages xi to xv.

Director

Philip P Gerbino 1995-2005

Twenty-first Edition-2005

Published in the 185th year of the PHILADELPHIA COLLEGE OF PHARMACY A N D SCIENCE

Remington HistoricallBiographical Data The fon~wingis a record of the editors and the dates of publication of successive editiom of this b o k , prior to the 13th Edition known as Remington's Practice of Pharmacy and subsequently a~ Remington's Pharmadeutical Sciences trhough the 20th editim.

Herald R. Cox Richard A Deno Alfomo R. Gennaro Stewart C .Harvey

Firrt Edition, 1886 Second Edition, 1889 Third Edition, 1897 Fourth Edition, 1905 Joseph P. Remington Fifth Edition, 1307 Sixth Edition, 1917 Joseph P. Remington

Assisted by E. Fullerton C&

Associated Editors Ivar Gri5th Adley B. Nichols Arthur OBol

Ninth Edition, 1948 Tenth Edition, 1951 Editors E. Nlerton Cook Eric W. Martin

Twelfih Edition, 1361 Editors

Eric W.Martin E. Fullerton Cook E. Emerson Leuden Arthur Osal Linwml F.Tioe Clarence T. Van Meter

Editors GraRon D. Chase Richard A Deno Alf0m0 R. G ~ M I ~ M Melvin R. Gibson Stewart C. Harvey

Charles H. LaWall

Eleventh Edition, 1956 Editors Eric W.Martin E. Nlerton Cook

Managing Editor John E. Hoover

Robert E. King E.Emerson Leuallen

Author 0801 Ewart A Swinyard Clarence T. Van Meter

Fourteenth Edition, 1970 Chairman, Editorial Board Managing Editor Arthur 0501 John E. Hoover

Seventh Edition, 1926 Editors E. Nlerton Cook Eighth Edition, 1936 Editors E. Fullerton Cook Charle~H. LaWalI

Thirteenth Edition, 1M5 Editor-in-Chief Eric W.Martin Editors GraRw D. Chase

Associated Editors E.Emerson Leuallen Arthur 0801 L i n w d F. Tice Clarence T. Van Meter Assistant to the Editors John E . Hoover

Robert E.King WN.Martin Ewart Clarence A T. Swinyd Van Meter

Fifteenth Edition, 1975 Chairman, Editorid B o d Managing E&tor Arthur Osol John E. Hoover Editors John T.Anderson C. Boyd Granberg Cecil L.Bendush Stewart C. Harvey Gr&on D. Chase Robert E. King Alfonso R. G e m a m Alfred N.Martin Melvin R. Gibson Ewart A Swinyard Sixteenth Edition, 1980 Chairman, EditoriaE Bowd C . Boyd Granberg Arthur Osol Stewart C . Harvey Edztors Robert E . King Grafton D. Chase A E d N.*tin Alfonso R. G e m a m Ewart A 8winyard Melvin R. Gibson GWL.Zinlr Seventeenth Edition, 1985 Chairman, EditoriaE Bowd

Alfonso R. G e ~ a r o Edztors Grafton D. Chase h a H.DerMarderosian Stewart C. Harvey Daniel A. Hwsm Thomas Medwick

Managing E&tur John E. Hoover

Edward G.Rippie Joseph B. Schwartz Ewart A Swinyard Gilbert L. Zink

Eighteenth Edition, 1990 Chairman, Editorial Board Managing Editor Alfomo R. Gennaro John E. Hoover Editorial Assistant Bonnie Packer Editors GraRw D. Chase E d w d G.Rippie Ara H. D e r M a r d e h Joseph B. Schwartz Skwmt C . Harvey Ewart A 8winyard Daniel A H u a w GWL.Zinlr Thoma$ Meotwick

vii

REMINGTON Hl5TORICAL/BIOGRAPHlCAL DATA

Twentieth Edition, 2000

Nineteenth Edition. 1995

Phail-nln~r,Erfr tol-iol Ronld Alfonso It Gennaro

Arlo ~r.agiugEditor

John E.IIoover Editorial Assiston t Bonnie Packer

Bonnie Packer Editors

Editnl-s

Grafton U.Chase rlra 11. Uerklarderosian Glen K.IIallson Daniel A. IIussar Thomas Med~vick

Chairman, Editorial Board Managing Editor John E. Harmer Alfomo R. Geman, Editorid Assistant

Edward G. Ilippie Joseph HU. Schwartz 11. Steve White Gilbert L.Zink

Am DerMarderosian Glen R. Hanson

Thomae Medwick Nicholas G.Popovich

Roger L. Schnmre JosephB. Schwmtz H.Steve White

Editorial Board Paul Beringer, PharmD, BCPS

Pardeep K Gupta, PhD

Associate Pmfessor, Department of Pharmacy USC School of Pharmacy Los Angeles, CA Section Editor for Part 6

Associate Professor of Pharmaceutics Director of BS Program in Pharmaceutical Sciences University of the Sciences in Philadelphia PhiladeIphia, PA Section Editor for Parts 3 and 4

Ara Derllllardemsian, PhD

Professor ofPharmacagnasy Research Professor af Medicinal Chemistry University of the Sciencea in Philadelphia Philadelphia, PA Section Editor for Part 1

John E Hoover, BSc (Pharm)

Linda Felton, PhD, BSPharm, RPh

Professor and Head Department of Pharmacy Administration University of Illinois at Chicago College of Pharmacy

Associate Pmfessor of Pharmaceutics University of New Mexico College of Pharmacy Albuquerque, NM Section Editor for Part 5

Consultant, Biomedical Communications Swarthmore, PA Consulting Editor and Indexer Nicholas G Popovich, PhD

Chicago,IL Section Editor for Part 8

Steven Gelone, PharmD

Consultant AGE Consultants Wyndmoor, PA Section Editor for Part 7

William J Rellly, Jr, MBA

KW. Tunnel1 Consulting King of rlrussia, PA Section Editor for Part 2

Alfonso R Gennaro, PhD

Randy Hendrickson, MPP

Professor Emeritus of Chemistry University of the Sciences in Philadelphia Philadelphia, PA Section Editor for Part 7

Advanced Concepts Institute University of the Sciences in Philadelphia Philadelphia, PA Editor

Authors Marie Abate, BS, PharmD / Professor of Clinical Pharmacy and Director, West Virginia Center for Drug and Health Information,S h l of Pharmacy, West Virginia University. Chapter 9, Clinical Drug Literature Steven R Abel, PharmD, FASHP / Professor and Head, Department of Pharmacy Practice, Purdue University W m l of Pharmacy and PbrmacaI Sciences. Chapter 100,

Michael R b r e d i n , RPh,PhD Illsscciate Professor and Chairman, Department of Pharrn aceutical Sciences, Temple University School of Pharmacy. Chapter 78, General Anesthetics; Chapter 85, Central Nemous System Stimulants

Jomph I BouIlata, PharmD, BCNSP I Professor of Pharmacy Practie, Temple University School of Pharmacy.

Bradley L Ackarmann, PhD / Research Advisor, Lilly

Chapter 92, Nutrients and Associated Substances Bill J Bowman, PhD, RPh / Assistant Professor of

Research Laboratories, Eli Lilly & Co. Chapter 34, Instrumental Methods ofAnalysis Mignon S Adam, MSLS / Associate Professor of Information Science; (;?lair of the Department of Information Science; D h c t a r of Library and Information Services, University of the Sciences in Philadelphia. Chapter 8, Information Resources in Pharmacy and the Pharmaceutical Sciences Michael J Akers, PhD / Director of Pharmaceutical Research and Development, Baxker Pharmaceutical Solutions, LLC. Chapter 41, Parenteral Solutions Adam W G Alani, MSc / Research Assistant, School of Pharmacy, University of Wkconsin-Madison. Chapter 47, Extended-Release and Targeted Drug Delivery Systems Loyd V Allen, Jr, PhD / Professor Emeritus,Department of Medicinal Chemistry and Phmnaceutics, College of Pharmacy, University of Oklahoma and Editor-In-Chief, International Journal of Pharmaceutical Compounding. Chapter 105,Eztemporaneous Prescription Compounding Heidi M Andermn, PhD / Pmfeesor and Assistant Dean, Education Innovation, College of Pharmacy, University of Kentucky. Chapter 97, Patient Communication Howard Y Ando, PhD 1 Director of Candidate Enabling and Development, Wuer GlobaI Research and Development. Chapter 38, Property-Based Drug Design and Preformulation R Jayachandra Babu, PhD / Research Assmiate, College of Pharmacy, Florida A&M University. Chapter 33, Chromatography Thomas A Barbolt, PhD, DABT / Senior Research Fellow, ETHICON, S o m e d e , NJ.Chapter 109, Surgicd SuppZies Kenneth N Barker, PhD I Distingukhed Sterling Profemor and Director, Center for Pharmacy Operations and Design, Harrison School of Pharmacy, Auburn University. Chapter 95, Technology anddutomation Sara J Beis, MS,RPh / Consultant, Akron, OH. Chapter 112, Re-Engineering Pharmacy Practice Robert W Bennett, MS, RPh / Asm5ate Professor of Clinical Pharmacy; Director, Pharmacy Continuing Education, Depwtment of Pharmacy Practice, Purdue University School of Pharmacy. Chapter 112, Re-Engineering Pharmacy Practice Paul M Beringer, PharmD 1 Assmiate Professor of Clinical Pharmacy, Sdhml of Pharmacy, University of Southern California. Chapter 69, Clinical Pharrnacokznetics and Pharmacodynamics Richard J Bertin, PhD, RFh / Executive Director, B o d of Pharmaceutical Bpcialties, W d i n g t o n , DC.Chapter 120, Specialization in Pharmacy Practice Lawrence H Block, PhD / Professor of Pharmaoeutics, Mylan School of Pharmacy, Duquesne University. Chapter 23, Rheologg, and Chapter 44, Medicated Topicals Allan D Bokser, PhD / Assmiate Director of Analytical Development, Neurouine Biasciences, Inc. Chapter 52, Stability of Pharmaceutical Products Sanford Bolton, PhD / Visiting Professor, College of Pharmacy, Univer8ity of Arizona. Chapter 12, Statistics

Pharmaceutical Sciences, College of Pharmacy-Glendale, Midwestern University. Chapter 21, Colloidal Dispersions; Chapter 26, Natural Products L ~ l i eAnn Bowman, AMLS / Assmiate Pmfesgor of Information Science and Coordinator of Instructional Services, Joseph W England Library, University of the Sciences in Philadelphia. Chapter 8, Information Resources in Pharmacy and the Phrarmaceutical Sciences Cynthia A Burman, BS, PharmD / Medical Information Scientist, GhxoSmithKLine, Philadelphia, PA. Chapter 75, Diuretic Drugs Paul M Bummer, PhD /Associate Professor of Pharmaceutic d Sciences, College of Pharmacy,University of Kentucky. Chapter 20, Interfacial Phenomena Daniel J Canney, PhD I Associate Professor of Medicinal Chemistry, Department of Pharmaceutical Sciences, Temple University School of Pharmacy. Chapter 71, Cholinomimetic Drugs and Chapter 73,Antimuscarinic and Antispasmodic B u g s Bradley C Cannon, PharmD / Clinical Assistant Professor, University of Illinois at Chicago,College of Pharmacy. Chap ter 122, Development of a Pharmacy Care Plan and Patient Problem Solving F Lee Cantrell, PharmD / Assistant Clinical Professor of Pharmacy, SGhcml of Pharmacy, University of California, San Francisco, San Diego Program; Assistant Director, San Diego Division, California P o k n Control System, University of California San Diego Medical Center. Chapter 103, Poison Control qjai Chaudhary, MPharm, PhD / Head, Drug Disposition, Lilly Research Laboratories, Eli Lilly & Co. Chapter 34, Instrumental Methods of Analysis Amy Christopher, MS / Assistant Professor of Information Science and Web Manager, UniversiQ of the Sciences in Philadelphia. Chapter 8, Information Resources in Phannacy and the Pharmaceutical Sciences Michael M Crowley, PhD / Vice President, Drug Delivery Technology and Manufacturing Services, PharmaForm, LLC . Chapter 39, Solutions, Emulsions, Suspensions, and Extracts Ara H DerMarderdan, PhD /Professor of Pharmacognmy; Research Pmfessor of Medicinal Chemistry, University of the Sciences in Philadelphia. Chapter 7, Pharmacists and Public Health; Chapter 49, Biotechnoiogy and Drugs; Chapter 93, Pesticides; Chapter 132, Compkmentaiy and Alternative Medical Hedth Care Xuan Ding, PhD / School of Pharmacy, University of Wisoonsin-Madison. Chapter 47, Extended-Release and Targeted Drug Delive~yS y s t e m Clarence A Dimher, PhD / Deceased.Chapter 24, Inorganic Pharmaceutical Chemistry William R Douwtte, PhD / Assmiate Professor, Director for the Center to Improve Medication Use in the Community, College of Pharmacy, The UniversiQ of Iowa. Chapter 116, Marketing Phannrmceuticd Care Services

Professional Communications

xi

T e r e s a P e t e Dowling, PharmD 1 Uirector. P r o m o t i o ~ ~ a l Donald E Hagman PhD / Vice President, Scientific Affairs. Iicgulatory rlffairs. rlstraZeneca LP. Chapter 5 . P1~orn1ncist.s CardinalIIealth. hlc. C h a p t ~ 40. r Sttbri!izotio~r iri T r d rt,str>~ WilIiam A Heas, BSc Pharm / Captain a n d Pharmacist G 1, Drusano, MII / Co-Uireetor. Ordway Iteseareh institute. Director. FDA Center Consultant. United States Public I I I ics in Drr1,g IIealth Service. Chapter 6. Pl'o r - i ~t'ists n in C;or~c~rrtn~r~t t Chapter 6 3 . Pho rrl~omkinrtirs/ Phn nl~acod.y~z(~ n ( ~ i ~ ( ~ l o ] tl l ? l ~ ~ n Gregory J Higby, Phn / Uirector, rlmeriean institute of the John E Endera, PhD, MBA / Uircctor of Quality rlssuranee. IIistory of Pharmacy, School of W a r m a e y , University of Wisconsin-Madison. Chapter 2. B r ~ ~ l u t i oof'n Pho n11o(:1' Uelrnont Laboratories. Swarthmore, Pri. Chapter 51. James R Hildebrand III, B S , P h a r m n / Llirector of Clinical Q~rolityA s s u l n r t r ~on T1rr1,g.s: Chapter 81. A n t i q ~ i l ~ p t iDrugs. r Chapter 81.

Histo111inw rr~rtlA~rtilristoll~ in,ic Drrtgs Corporate Itelations and Eco~lomieOutreach, Professor of Daniel A Hussar, PhD / Hen~ingtollPrufessur of Warmaey. Wnrmacy. C'olleee of Warmacv. L'niversity uf Kentucky. Chaptcr 1. Scopr o f Phal-~llot:l'; Chapter 111, Lnri:s Philadelphia College of W a r m a c y . Cniversity of t h e Sciences in Philadelpl~ia.Chapter 98. Pofient C'(i113plin~~r~ Gor~cmzi~tg Pllrrl-lilnt:l' Michael R Franklin, PhD / Professor. Department of and Chapter 104. IIrr~,gIrrtrlnrtio~rs Michael F Imperato. PharmD / eseelleRx lnc.. Wiladelpl~ia, Warmaeolog?l and Toxicology, University of Utah. Chapter 57. Tlrrq Absorption,. Actin~r,a ~ t dDispnsitio~r: CXapter 91. Prl. Chapter 4, Tlrt. P r a r t i r ~nf C o ~ i ~ ~ i ~P~lri ai irti j~ ~ o r ~ ~ R~~ZJ/~IC~~' Matthew K Ito, PharmD, F C C P , B C P S / Professor a n d Vice Donald N Franz, PhD / Professor Lmeritus. Uepartnlent of Chair of Warmacy Practice. TJ Long School of Pharnlacp Warmacolog?r and Toxicolog7r.. University of Utah. Chapter a n d IIealth Sciences. Cniversity of t h e Pacific; Uirector. 57. Dl-r~gAbsorption, Acf inn, o rrd Tlispc>sitio~r Cardiac Iiehabilitatiun Cholesterol Clinic. Sari Uieeu Vrl Raymond E GaIinaky, PharmD / Professor of WarmaeeuIIealtheare System. Chapter 121, Pho rwo(.ists o vd T ~ ~ S ~ ~ C I S P Astrrt6bA9n' 7!lT'q~)i7(77?t tics. School uf Warmacy and Warnlaeal Sciences. Purdue T i m o t h y J Ives, P h a r m n , M P H , RCPS, FCCP / rlssoeiate Cniversity. Chapter 58. Rasic P l t a r i ~ ~ o r i ~ k i n r f ia~rrl cs Pho mlocncljn o l l ~ i c s hofessor of Warmacy a n d Medicine. Sehoul of Warmacy, Daniele K Gelone, PharmD / rlssistant Professor of Clinical Lniversity of North Carolina at Chapel IIill. Chapter 7. Plrnl-~l~nrlsts nn,d Pr1,hIic Hrolfh. Warmaey. Department ofPharmaey Practice and Warmaey Rajni Jani, PhD / Senior Uirector. Uepartnlcnt uf Warrnahdministratiun. Philadelphia College uf Pharmacy. Universit? of the Sciences in Philadelphia. Chapter 87. I / I I I I I I L I I ~ O C I ~ceutics. rilcon Research. Ltd. Chapter 43, O p h t l l a l n ~ i r A-pp" 1 n t i 0 7 ~ ~ tit'(,Drr1,gs Steven P Gelone, PharmD / Consultant. AGE Consultants, T a r a M J e n k i n s , MS, PharmD / rissistant Professur of Wyndmoor. PA. Chapter 88. Pal-asitiridrs. Chapter 89. Phnrnlaey Practice. School of Pharmacy. IIampton ~/111111~1li~~ll,g A g m t s : Chapter 90. A l l t i - T ~ t f i r t i r ~ ~ s L'niversity . Chapter 125. Diag~rnsfir S ~ l f - C a w Alfonso R Gennaro, PhD 1 Emeritus Professvr. Department Steven B Johnson, PharmD 1 Uivision of Warnlaeeutical uf C h e m i s t q and Hivehemistry. University of the Sciences Evaluation 11. Food a n d Drug Administration. Itockville. MU.Chapter 53. Rioorwilo hi lit^^ a a#.dRiorc~rtir~oIc~~rr>~ T~sfirig in Philadelphia. Chapter 25. Ol-grrn,ir Phar/ilocrrtfirol Chr'n~i s t ~ : ~ Robert J o r d a n , PharmD C a n d i d a t e / College uf Warmaey-Glendale, Midwestem University. Chapter 26. Doug Geraeta, PharmD, F C C P , BCPS / Clinical Pharmacy Xn frrlnl Arjdr1,rt.s Specialist-rlmbulatory Care, luwa City VA Medical Center: Calvin H KnowIton, RPh, MDiv, PhD, FACA / exeelleHx Adjunct rissociate Prufessor, Clinical a n d Administrative Wnrmaev. Cullege of Warmaey. The University of iowa. lne.. Philadelphia. Prl. Chapter 4. T h v Plnrticr o f ' C ' n r ~ ~ l ~ ~ r ~ , Chapter 121. Phrrr/llnr.ists on,d Dispasp Stat(' :Irla~tagr)l~r~tt 7tif.v Ph.arlllor>~ David J KroI1, PhD / Senior Research Warmacologist. NatuSteven J Gilbert, RPh, PharmD(c)/ excelleIh Ine.. Philadelphia. PA. Chapter 4 . T h r A n r t i c r n f ' C ' o ~ i ~ i i ~ r ~Phnr111nrj niQ ral Products Laborator?;. Research Triangle institute (ItT1). Martin C Gregory, B M , BCh, DPhil / Professor of kledici~le. Chapter 49. R i o t ~ c hno log)^ rrnd Drr~gs V i j a y K u m a r , MS, MBA / Chief Operating Officer. h c u r a Division uf Nephrology. University uf Utah School uf n ~ r dPathnMedicine. Chapter 56, Disrbnses: IlIo~tifi.stc~tions P~~armaceuticals. Chapter 35. Tlissolrt tion plysiolr~g?' John C Lang, PhD / Director of Emerging Technologies. Alcon Purdeep K Gupta, PhD / rlssoeiate Professor. Wiladelpl~ia Itesearch. Ltd. Chapter 43. O ~ ~ ~ t h n Pwprrratin~~s li~~ic Arthur J Lawrence, PhD, RPh / Ilearridmiral a n d Assistant Cullege of W a r m a c y . University of t h e Sciences in Philadelphia. Chapter 16. Solutiorrs nrtcl Phnsr Equilibl-ia; Surgeon General. Ueputp rlssistant Secretary for IIenlth Chapter 27. Tl1-r~gXn/i~t.n,rlotuwITSAN Operations, G'nited States Public IIealth Service. Chapter 6. Amy Marie Haddad, PhD / Professor. School of W a n n a c y P h a r ~ ~ l o r i sin t s C;or>ebr~rll~rv~t Erie J Lien, PhD / Professor of Warn~acyl./Warmaceuticsand and IIealth Professions. Creigl~tonUniversity. Chapter 84. Appliro tion o f Ethical Prinwipl~stn Pmctice Dilr/il H I U S Uiomedicinal C h e m i s t q . School of Wnimaey. University of Dennis D Hager, RPh, PharmD(c) / exeelleIh lnc.. Wiladelr M o l ~ c ? ~ , l o l - S t r u c t ~Pro)>~r-r, Southern California. C h a p t ~ 13, phia. Prl. Chapter 4. Thtb Prartivcb c)f C O I I I rt~l.ity I H PPIia rnlnt:t' rl-tips, U I E Stntrs ~ of~Vottrr

AUTHORS

Hetty A Lima, RPh, FASHP / Vice President, Marketing, Caremark, Inc. Chapter 130, Aseptic Processing for Home Infusion Pharmaceuticals Sylvia H Liu, BVM, DACVP / Vice President, Research and Development, ETHICON, Somerville, NJ. Chapter 109, Surgical Supplies Stan G Louie, PharmD / Associate Professor of Pharmacy, University of Southern California. Chapter 60, Principles of Immunology Eva Lydick, PhD / Chief Research Officer, Lovelace Clinic Foundation. Chapter 118, Pharmaceutical Risk Management Elaine Mackowiak, PhD, RPh /Professor of Pharmaceutical Chemistry (School of Pharmacy) and Clinical Assmiate Professor of Diagnostic Imaging (School of Medicine), Temple University. Chapter 64, Diagnostic Drugs and Reagents Henry JMalinow~ki,PhD /Division of Pharmaceutical Evaluation Lt, Food and Drug Administration, Rockville, MD. Chapter 53, Bioavailability and Bioeq uiualency Testing Michael A Mancano, PharmD / A s k a t e Professor of Clinical Pharmacy, Temple University School of Pharmacy. Chapter 77, Hormones and Hormone Antagonists Laura A Mandos, BS, PharmD / Associate Professor of Clinical Pharmacy, Philadelphia College of Pharmacy, University of the Sciences in Philadelphia. Chapter 80, Antianxiety Agents and Hypnotic Drugs Anthony S Manoguerra, PharmD / Professor of Clinical Pharmacy, School of Pharmacy, University of C alifornia, San Francisco, San Diego Program; Director, San Diego Division, California Poison Control System, University of California San Diego Medical Center. Chapter 103, Poison Control Robert W Martin 111, MD / Chairman, Department of Dermatology; Chief, Division of Dermatopathology, Arnett Clinic, Lafayette, Indiana; Clinical Assistant Professor, Department of Dermatology, Indiana University School of Medicine. Chapter 133, Chronic Wound Care Robert L Mc Carthy, PhD / Dean and Professor, School of Pharmacy, University of Connecticut. Chapter 3, Ethics and Professionalism Michael R McConnell, RPh / Founder and Consultant, National Notification Center. Chapter 115, Product Recalls and Withdrawals Randal P McDonough, PharmD, MS / Associate Professor (Clinical), Director of Practice Development and Educational Programs, College of Pharmacy, The University of Iowa. Chapter 116, Marketing Pharmaceutical Care Seruices William F McGhan, PharmD, PhD / Professor of Pharmacy and Health Policy, Department of Pharmacy Practice and Pharmacy Administration, Philadelphia College of Pharmacy, University of the Sciences in Philadelphia. Chapter 113, Pharmacoeconomics Howard L McLeod, PharmD / A s k a t e Professor, Department of Medicine, Washington University School of Medicine. Chapter 62, Pharmacogenomics Mary Lynn McPherson, PharmD / Associate Professor, Pharmacy Practice and Science Department, School of Pharmacy, University of Maryland. Chapter 110, Health Accessories Thomas Medwick, PhD / Emeritus Professor of Pharmaceutical Chemistry, School of Pharmacy, Rutgers University. Chapter 24, Inorganic Pharmaceutical Chemistry Robert Middleton, PharmD / Department of Pharmacy, Beebe Medical Center, Lewes, DE. Chapter 61, Adverse Drug Reactions Clinical Toxicology Michael Montagne, PhD / Professor of Social Pharmacy, Massachusetts College of Pharmacy-Boston. Chapter 3, Ethics and Professionalism and Chapter 99, Drug Education Louis A Morris, PhD / President, Louis A Morris and A s k ates, Inc. Chapter 118, Pharmaceutical Risk Management Michael D Murray, PharmD, MPH I Professor and Chair, Pharmaceutical Policy and Evaluative Sciences, School of Pharmacy, The University of North Carolina at Chapel Hill. Chapter 108, Pharmacoepidemiology

xiii

Gail D Newton, PhD, RPh /Associate Professor of Pharmacy Practice, School of Pharmacy and Pharmacal Sciences, Purdue University. Chapter 123, Ambulatory Patient Care

Jeffrey P Norenberg, MS, PharmD, BCNP, FASHP, FAPhA / A s k a t e Professor and Director, Radopharmaceutical Sciences, College of Pharmacy, University of New Mexico Health ScienoesCenter. Chapter 29, Fundamentals of Medical Radionucl ides Robert E O'Connor, PhD /Senior Director, European Technical Operations,Janssen Pharmaceutica. Chapter 3 7, Powders Judith A O'Donnell, MD / Assmiate Professor of Medicine and Public Health, Drexel University Schools of Medicine and Public Health.Chapter 90, Anti-Infectiues Patrick B O'Donnell, PhD / Assmiate Director of Product Development, Neurocrine Biosciences, Inc. Chapter 52, Stability of Pharmaceutical Products Clyde M Ofner Ill, PhD / kssociate Professor and Director, Graduate Program in Pharmaceutics, Philadelphia College of Pharmacy, University of the Sciences in Philadelphia. Chapter 2 1, Colloidal Dispersions Carol Ott, PharmD, BCPP / f i l i a t e Assistant Professor of Pharmacy Practice, School of Pharmacy, Purdue University. Chapter 129, Long-Term Care James A Palmieri, PharmD / Assistant Professor of Pharmacy Practice, TJ Long School of Pharmacy and Health Sciences, University of the Pacific; Clinical Pharmacy Specialist, Cardiovascular Disease Management, The Mercy Heart Institute, Sacramento, CA. Chapter 121, Pharmacists and Disease State Management Susie H Park, PharmD / Assistant Professor of Clinical Pharmacy, University of Southern California. Chapter 60, Principles of Immunology John H Parker,PhD / President, Tech Manage Asmiates, Clarks Summit, PA. Chapter 51, Quality Assurance and Control Payal Patel, BSc (Pharm), PharmD / Evidence-Based Pharmacy Consultant, London Health Sciences Centre, London, Ontario, Canada. Chapter 128, Emergency Medicine Pharmacy Practice Garnet E Peck, PhD / Professor Emeritus of Industrial and Physical Pharmacy, School of Pharmacy and Pharmacal Sciences, Purdue University. Chapter 36, Separation Thomas G Pettinger, BSP, BOCO / Staff Orthotist, Great Plains Health Company, Fargo, North Dakota. Chapter 110, Health Accessories Peggy Piascik, PhD / Associate Professor of Pharmacy Practice, University of Kentucky. Chapter 97, Patient Communication James A Ponto, MS, BCNP / Chief Nuclear Pharmacist and Professor (Clinical), University of Iowa Hospitals & Clinics and College of Pharmacy University of Iowa. Chapter 106, Nuclear Pharmacy Practice Cathy Y Pmn, PharmD / A s k a t e Professor of Clinical Pharmacy Philadelphia College of Pharmacy, University of the Sciences in Philadelphia. Chapter 18, Tonicity, Osmoticity, Osrnolality, and Osmolarity; Chapter 32, Clinical Analysis Stuart C Porter,PhD /President, PPT, Hafield, PA. Chapter 46, Coating of Pharmaceutical Dosage Forms W Steven Pray, BS (Pharm), MPH, PhD / Bernhardt Professor of Nonprescription Drugs and Devices, College of Pharmacy, Southwestern Oklahoma State University. Chapter 124, Self-Care Shelly J Prince, PhD / Assmiate Professor of Pharmaceutics, College of Pharmacy, Southwestern Oklahoma State University. Chapter 11, Metrology a n d Pharmaceutical Calculations Barrett E Rabinow, PhD /Senior Director, Strategic Technical Development, Baxter Healthcare Corporation, Round Lake, IL. Chapter 54, Plastic Packaging Materials Gden W Radebaugh, PhD / Vice President of Analytical Development, Schering-PloughResearch Institute. Chapter 38, Property-Based Drug Design and Prefomzulation

Robert B R a f f a , PhD / Professor of Pharmacology. Temple the Sciellces in Philadelphia. Chapter 37. Porud(brs; Chapter University School uf Pharmacy. Chapter 83. Analg(~sic, 4 5 . O w l Solid Tlosogv Fol-fils r\rttil>>~wtic, o nd An ti-l~r,j7rr/il/ilo f o ~ Tlrr~gs y Christopher J Sciarra, MS (Industrial P h a r m a c y ) / \'ice n e n n i s W Raisch, RPh, PhD / Associate Center Director. President. Sciarrn Laboratories. lnc. Chapter 50. A(,lrls(ils John J Sciarra, PhD / President. Sciarra Laboratories, lnc. Scientific rlffairs, VA Cooperative Studies Program Clinical Chapter 50. Avl-osols Iteseareh Pharnlacy Courdinating Center, rllbuquerque. Chapter 48. Tlip Arcbrr: Tlrrq Applnrwl P r i ~ r ~ and s s Clirlirricol B r u c e E S c o t t , M S / Chief Operating Officer, kleKesson Trinl Tlpsign, Medication Management. Brooklyn Park. M Y . Chapter 127. Hospifol Ph.nl-iiiur>~A n c t i r ~ William J Reilly, J r , RPh, MBA / Managing- Consultant. Tunnel1 Consulting. King of Prussia. Pr'l. Chapter 5 5 . Steven A Scott, PharmD / rlssociate Professor of Pharmacy Plro nilrrr~utirolX r c r s s i t i ~ s Practicc. Schoul of Warmncy. Purdue Lniversity. Chapter 101.Tlztb Prc>.sr.l-iptiov J u n e E RiedIinger, RPh, PharmD / Adjunct Assnciatc Bonnie L Senst, M S / Uirector uf Phamlacy. Mercy and Unity Professor. Southwest College of Naturopathic Medicine and Adjunct ~lssoeiateProfessor of Warmaey Practice. Schonl of IInspitals. Fridley. >IN.Chapter 127. Hospitol Pl'ol-mut:v Plncticr Warmnev-Boston. Massachusetts Cullege of Wnrmaev Nancy L Shapiro, PharmD, BCPS / Clinical Assistant Proand IIealth Sciences. Chapter 132. P o r ~ l p l c ~ l l ~ n t orld n~-j Altcbl-n,otirl~,vsiol(g~~ s hdministratiun. College of Warmacy. Midwestern LniverBonnie L Svartitad, PhD / Prufessor Emerita uf Sucial Pharsity-Glendale. Chapter 117. D o r r ~ u ~ l r ~ t t i nRgi l, l i ~ t g ,n ~ t d macy. School of Pharmacy. University of WisconsinR ~ i r nburs~nltvrt for P l ~ ~ ~ r ~r~,ticaI i ~ n rf ir r e S ( , r r < i r ~ s Madison. Chapter 96. Tl~wPn tirnf: Rrhr! viol-al Dc'tr1711 i ~ t ~ l ~ i . t s Mandip Singh Sachdeva, PhD /Professor of Warmaceutics, Craig K Svensson, PharmD, PhD / Lyle & Sharon Uighley hofessor in Warnlaeeutical Sciences. College of Pharmacy, Cullege of Pl~nrmaey.Florida r l k k l University. Chapter 33, Clrlnlllo tograp h,>~ 'l'he University of lowa. CXapter 58. Rosic PITor~lluci~k i~t~tirs o n,tlPlra~-~ilo~o~Ejn.o 1 1 1 ivs Roger Schnaare, PhD / Professor Emeritus of Warmaey. James Swarbriek, J3Se. PhJ3 / President. Pl~armaceu'l'ech. Philadelphia College of Pharmacy. U n i v e r s i t ~ of t h e Sciences in Philadelphia. Senior Pharmaceutics Fellow. Chapter 22. Conrsr Tlisp~,rsiun,s Uiosyn lnc. Chapter 11. !M~tl-ologya ~ t dP l ~ ~ l ~ - ~ i l r r r ~ ~ r ~Ttiimr oo lt h y W SynoId, PharmD / Assistant Prufessor. UepartCalrulrrtio~tsand Chapter 23. Rlrf~o1ng.v m m t of Medical Onculogy, City of IIope Cnmprehensive J e a n M Scholtz, B S , PharmD, BCPS /Associate Professor of Cancer Center. Chapter 62. P h o r n l a t . c g ~ n ~ ( i ~ ~ ~ i c s Robert L Talhert, PharmD, R C P S , F C C P / Professor and Clinical Pharmacy. Uepai-tm~ntof W a r m a e y Practice. Uivisivn IIead. Uivisiun of Warmacothempy, College of Wilndelphin College uf Wnrmacy, Cniversitg uf the Seiences in Pl~iladelpl~ia. Chapter 86. Antirrroplnstir Tlrrtgs Pllarmacy. ' I ~ I cUl~iversitpnf Texas at Austin: Professor of Hans Schott, PhD / Professor Emeritus of Warmaceuties and Pharn~aeolog?: and Medicine. The Lniversity of Texas Culloidal Chemistry. Temple University. Chapter 21. IIealth Science Ccnter at San rlntonio. Chapter 120. ~ o l l o i d o Tlis/>~rsions l S p ~ c i o l i z tiori o in Plr rrl-~lln,:l' Pint. tic? J o s e p h B Schwartz, P h n / Burroughs-M:ellcome Fund ProM a t h e w T h a m h i , P h a r m D , BCPS / Clinical Assistant fessor of Phnrmaeeutics. Director of industrial Pharmacy Professor, College of Warmacy. Cniversity of Illinois at Iteseareh. Pllilndelpl~iaCollege of Pharmacy. Cniversity of C h i c a p . Chapter 133. Clrlr)n,ic Wortnrl Col-cb

AUTHORS

Mark Thomas, MS / Director of Pharmacy, Children's Hospitals and Clinics, Minneapolis, MN. Chapter 127, Hospital Pharmacy Practice Mark A Touchette,PharmD,BmS/ Sr. Manager, Inpatient Pharmacy Semice~,Henry Ford Hospital, Detroit, MI. Chapter 119, Integrated Health Care D e S v e q Systems Salvatom J Turco, PharmD, FASHP / Professor of Pharmacy, Temple University W w l of Pharmacy. Chapter 42, Intmvenous Adm&ures Deepika Vadher, PharmD, BCPS / Assistant Professor of Clinical Pharmacy, Philadelphia College of Pharmacy and Science,University of the Sciences in Philadelphia. Chapter 122, D e ~ e l o ~ m e noft a Pharntacj Care Plah and Patieht ProbZem Salving Jesse C Vivian, BS Pharm, JD / hofessor of Pharmacy Law, Department of Pharmacy Practice, Eugene Applebaum College of Pharmacy and Health Sciences, Wayne State University. C b p b r 111, Laws Governing Pharmacy Ronnie A Weathermon, PharmD / Clinical Education Consultant, P h e r Inc.Chapter 131, The Pharmacist's Role in Substance Use Disorders Maria L Webb,PhD / VP Drug Discovery, Pharmaoopeia, Inc. Chapter 10, Research Timothy S Wiedmann, PhD / Professor of Pharmaceutia, College of Pharmacy, University of Mkwsota. Chapter 15, Thennodynamics R d n e y J Wigent, PhD / Professor of Chemisixy, Resew& Professor of Pharmceutics; Dean, College of Graduate

XY

Studies, University of the Sciences in Philadelphia. Chapter 19, Chemical Kinetics Lori A Wilken, PharmD, CDE, AE-C / ClinicaI Assistant Professor, College of Pharmacy, University of Illinois at Chicago. Chapter 131, The Pharmacist's Role in Substance Use Disorders S w a n R Winkler, PharmD, BCPS / Clinical Associate hofessor, College of Pharmacy, University of Illinois at Chicago. Chapter 131, The Pharmacist's Role in Substance Ue Disorders Michael E Winter,PharmD / Professor of ClinicalPharmacy, School of Pharmacy, University of California San Francisco. Chapter 59, Clznicral Phamrmcokinetics and Pharmacodynamics h a M Wodlinger, PharmD,BCPS /Assistant Professor of Clinical Pharmacy, Temple University School of Pharmacy. Chapter 68, Cardiovascular Drugs Olivia Bennett Woo& MPEI, BD I A s ~ ~ 5 aProfcmor te of Foods and Nutrition, School of Consumer and Family Sciences,hrrdue Univer*. Chapter 107, Nutrition in Pharmacy h t i c e Barbara J Zarowitz, PharmD, FCCP, BCPS / Vice Pregident, Pharmacy Care Management, Henry Ford Health System, Detroit, MT. Chapter 119, Integrated Health Care Delivery Systems Randy J Zauhar, PhD / hixiate Professor of Biochemistry, Dep&ment of Chemistry & Biochemistry, UniversiQ of the Sciences in Philadelphia. Chapter 2 8, Structure-Activity ReZ&ionship and Drug Design

Preface to the Twenty-First Edition For aver 100 years and throu&out 20 previous editions, Remington: The Science and Practice of Pharmacy has shod aa the deFdiive text m d reference murce of an aspects of the science and practice of pharmacy. In t h i ~ new edition, you will End a text that is practice-oriented while m&nt&hg its tradition-

ally reliable coverage of scientific ape&. The 2Ist edition keeps pace with the change8 in pharmacy curriculum and p m fessional pharmacy practice in general. In the years since the fist publication of Remington's Pharnaaceutid Sciences, there have been many changes in the &Id of pharmacy and pharmacy practice. Although this edition of Remdngton maintains the general philo~ophyof previom editions, several change8 have been made to present fresh and new information and to take advantage of the advances made in recent years. Each section of the h k has been critically reviewed and revised to reflect the emerging trends in the field. The overall organization of the b k G the m e as the previous editions. The biggest change h the 21st edition k in the Pharmacy Practice section. This section has been reorganized and expanded to reflect the changing realities of corntemporary practice. The integration of new scientEc information into clinical practice is oRen diiEcult, and one of the key purposes of this section is to help c l i n i c h u translate theae SCienWu:advances into clinical practice and care of patients. This seGtion brings the reader up to date on the latest trends and approaches. New chapters have been added that wver the areas of: The application of ethical principle^ to practim dilemmas Statietics applied to pharmacy p r h e Technology a d automation Professional communication Medication errore - h g p+nay prn""+ Management ofspenal nsH d c l a e s Specialization of pharmacy practice D h e state management Emergericy patient care Woundcare

The Pharmaceutical and Medicinal Agents section is the most very useful part of the b k in terms of core drug information. For this edition, we've added more than 100 new dnrg monograph, and the previod y existing material has been u p

dated. We realize that this is a section that is nearly impossible to keep current, and we've tried to include as many new drugs as possible.Because of space constraints,we were limited to the most important or most widely used drugs. Another sign5cant addition to this edition is the expamion of the Phamocodynamics and Phramacokinetics W o n t o include the new, growing area of Pharmaoogenomics. This chap ter highlighb many of the important advmces including:practical applications and technological considerations, molecular diagnostics for optimizing drug therapy, and pharmacogenamics and drug development. Many people were involved in creating this edition. I am grateful to all the Section Editors md authors for their skillful review of the literature and for incorporating their own unique perspectives and experience into their chapters. With this sdition, we welcome five new Section Editors. T h y represent a wide geographic diversity and spectrum of experience. We a h have approximately 100 new authors who represent over 32 universities as well as positions in governmental agencies and privateindmtry. I also gratefully acknowledge the extensive oontribution~of the authors rtnd Section Editors of previous editions ofRernington for laying the foundation for the current voIume. I recognize tbat we dl stand upon the shoulders of giants and are s u p ported by W e leaders who tataught and inspiredmany previous generations. I especiallythank Alfomo R Gemam, PhD for his oontinued support. Dr. Gennaro was Remington editor for the p a t four editions. No one is more familiar with Remington than he is. Dr. Gemam has been instrumental in the creation and review of the drug monographs. Ensuring scienmc a m r a c y is criticd in a h k such ws Remington, and he has been very generous with his time and expert& in this area. A heartfelt thanks &o goes to Mr. John Hoover, author and indexer, who has been involved with Remington since the 19608 and h~ provided editorial guidance at every step of the pmess. It is a plwm m dhonor ta work on a book with such a long md rich tradition.

Randy Hendrickson Editor

xvii

Preface to 1st Edition The sapid and substantial progress made in Pharmacy within the k t decade has creabd a necessity for a work treatingof the improved appmtm, the revised processes,and the recently intraduced prepmatiom of the ap. The v& advances made in theoretical and applied &emistry and physics have much to do with the development of phmrtceutid science, and thesehave h n reflected in dI the revked editiona of the Phrmacopoeias which have h e n recently published When the author ww elected in 1874 to the chair of Theory and Practice of Pharmacy in the Philadelphia College of Pharmacy, the outlines of stody which had been so carefully prep& far the classesby his eminent p r e d e w s m , Professor William Proctor, Jr, and Profernor Edward Parrish, were found to IE not strictly in accord, either in their mmg+ ment of the ~ubje& or in their method of treahnent. Desiring to p r e m e the distinctive characteristic8 of e d , an effort wrts at once made to frame a sy8Bm which should e m l d y their valuable features, embram new subjects, and still rethat harmony of plan and prop@ sequence which are abmlutely e s sentid to the w m w of any system. The strictly alphabetid classi5cation of subjects which is now nnivermlly adopted by pharmacopwias and dhpensat* r i a , although admirable in works of reference, presenb an eff e c b l stumbling block to the acquisition of pharmaceutical knowledge through systemati~study; the vast accumulation of facts collected nnder each head arranged lexically, they n e c e s s d y have no connection with me another, and thus the saving of labar effected by considering similar groups together, and the value of the association of kindred subjects, are lost to the student. In the method ofgrouping the subject8 which k herein adopted, the constant aim has been to arrange the htter in such a manner that the reader s h d lx gradually led from the consideration of elementary subjects to those which involve more advanced howledge, w W t the p u p s themselves are so placed as to follow one another in a nataral sequence.

The wark is divided into six p a . Part I is devated to detailed descriptions of apparatus and defmitiom and comments on general phmaceutical processes. The Official Preparations alone me conaidered in Part LI. Due weight and prominence are thw given to the Phttrmaoopoiea, the National authority, which is now so thoroughly recognized. In order to suit the oonpenienmof pharmacists who prefe~ to weigh solids and measut-e liquids, the official formulas are expressed, in addition to p a by weight, inavoirdupois weight and apothecaries' measure. These equivdents are printed in

boid type near the margin, and arranged so a~ to fit them for quick and accurate reference. Part m treats of Inorganic Chemical Substances. Precedence is of coarse given to o f k i a l prepmation in these.The de=riptiom, solubilitie~,and tmts far identity and impuritiw of each substance m systematically tabnlated under ita proper title. It 6 ooddentIy believed that by this method of arrange ment the valuable descriptive features of the Pharmmp&a will be more prominently developed, read reference facilitated, and do88 study afthe d e w rendered easy. Each chemical o p eration is ~ m by equatiom, ~ w m tdthe reaction is, in addition, explain& in words. The Cmhn Componnds, or Organic Chemical Substttnces, are considered in Part IV.These are naturally gmuped according to the physical and medical propertics of their principal canstituenb, M g with simpleb&e8 like cell&, gum,et., and m i n g to the most highly organized akaloids, etc. Parb V IB devoted to Extemporaneous Pharmacy. Care has h e n taken to treat of the practice which would be best adapipted for the n& of the many pharmacist8 who oonduct opratiom upon a moderate scale, rather than for those of the few who manage very large establishments. In thh, m wen ~tein other parts of the work, operations are illmtrated which are conducted by manufacturingpharmacists. Part VI cantains a formulary of Pharmaceutical Preparatiom which have not been recognized by the Pharmacopoeia. The recipes eel* are chiefly those which have been heretofare rather difEcult of acwss to mast pharmacists, yet such me likely to IM in q u e s t . Many private f o r m u b are embramd in the collection; and such of the preparations of the old Phwmacopc4as as have not been included in the new edition, bnt am &i in lIuse,have bsen insert&. In conclusion, the author ventures to expms the hope that the work will p m e an efficient he4 to the pharmaot!utical student as well a s to the phmacist and the phpician. Although the labor has k e n mainly performed m i d s t the hamsing cares of active pmfe8sional duties, and perfedion k h o r n to be ~ ~ b lno pains e ,have been spared to discover and correct errors and omissions in the text. The author's warmest a& howledgments, are tendered to Mk A B Taylor, Joseph McCreery, and Mr George M Smithfor their vdwble assistancein revising the proof sheets, and t o the ktter especially for his work on the index. The outline illmtratione, by Mr John Collins, were drawn either fmm the actual objects or h n photographs taken by the author.

=

Philadelphia, October, 1885

JPR

xix

Contents

Part 1 1

2 3 4

5 6 7

8 9 10 Part 2

Orientation

49

Scope of Pharmacy ............................... 3 EvolutionofPharrnacy ............................7 Ethics and Professionalism .........................20 The Practice of Community Pharmacy . . . . . . . . . . . . . . . . 30 Pharmacits in Indatry ...........................35 Pharmacists in Government ........................40 Pharmackts and Public Health ...................... 51 Information ReSOUKes in Pharmacy and the pharrna~euticalSciences ..........................ti4 Clinical Drug Lilrature ........................... 74 Research ...................................... 87

50 51 52 53 54 55 p aE

56 57 58

59

P)wms#srrth

60

11 12

..........-99 Statistics ..................................... 127

I3

Molecular Sbudure. Properties. and States of Matter ... 162 CamplexFarmation ............................186 Thermodymamio ............................... 201

63

14 15 16 17 18 19 20 21 22 23

-3

24 25 26 27 28 29

M&rolo& and Pharma~@lLt~al Calcub'tions

blutiomandPhaseEquilibria

.................... 211

Ionic Solutidns and El~trolyticEquilibria .............231 Tonici@. Osmoticiv. @[email protected] Osmobriv .......z50 Ckmical Kinetics ............................. 266 Interfacial Phenomena .......................... 280 Colloidal Dispersions ............................293 CoarseDispersions .............................319 Rheology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 338 ?hrmKluthiBHmk&y

Inorganic Pbrmaceutical Chemirw ................361 Organic Pharrnacelrtical C k m istry .................386 MaturalProducts ............................. ..41U Drlmg ~omenclature4nitedSWes Adopted Names ....443 StrucbreActivity Relationship and Drug Deign .......468 Fundamentals of Medical Radionuclides ............. 479

Art 4 PhrrmKHltkrl Tmrtinp, A r u l y r b md -1 30 31 32 33 34 35 h.5

36 37 38 39

40 41 42 43 44 45 46 47 48

Analysis of Medicinals . . . . . . . . . . . . . . . . . . . . . . . . . . . 495 Biological T&ing ..............................553 CliflicalAnahis ...............................565 Chromatogtaphy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599 Instrumental Mtbds of Attabis ..................633 Dissolution ................................... 672

P h r r m ~ . u t h I#nufrctUtinp l Separation ................................. ..691 Powders ..................................... 702 Property-BasedDrug &sign and Preformulation .......720 Solutions. Emulsions. Suspensions. and Extracts .......745 Steriliratian . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776 Parenteral Preparations ..........................802 lntrayenaus Admixtures .........................837 Ophthalmic Preparations . . . . . . . . . . . . . . . . . . . . . . . . . 850 Medicated T o ~ K ............................. ~~s 871 Ord5olidDosageFoms .........................889 Coating af Pharmacetrtical Dosage Fwms ............ 929 Extended-Releme and Targeted Drug Delivery Sptems . .939 The New Drug Approml Process and Clinical Trial Design ............................-965

61

62

Biokchnology and Drugs ........................ 976 Aerosols .................................... 1000 Quality Asutance and Control ................... 1018 Stability of Pharmaceutical Produrb ............... 1025 Biowailabilityand Bioequivalency Testing ...........1037 Plastic Packaging [email protected] PharmaceuticalNecessities ...................... 1058 P ) L m e r t l Qa d v

y

n

&

Diseases: Manifatations and Pathophysiology .......1095 Drug Absorption. Action. and Dispwition ........... 1142 Basic Pharmxokinetics and PharmacodyraamLs ......1171 Clinical Pbrrnacobnetics and Pharmacodynamics ..... 1191 Priniciplesof Immunology ....................... 1206 Adverse Drug Reactions and C l i n d Toxicology ......1221 Pharmxogenomics ............................ 1230 Pharmacoki~tiWharmacodymmicsin Drug Development . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1249

P a 7 H % m m a a u i h rrd l Medirkul Aprntr 64

65 66 67 69

71 72 73 74

75 76

n

78 79 80

81 82 8J 84

85 86 87 88

Diagnatic Drug and Reagents . . . . . . . . . . . . . . . . . . . 1261 -,-apical Dnrgs ................................1277 Gastroint&ti~Iand Liver Dmgs .................-1294 Blood. Fluids. El~trolytes.and Hematological Drugs . . .13 18 Cardidvascular Drugs ..........................1350 Respiratory Drugs ............................ 371 Sympathomirnefic Drugs 1379

........................

CholinomimeticDrugs ......................... 1389 Adrenergic Antagonists and A d ~ w r g i c Neuron Blocking Drugs ......................... 1399 Antimmarinic and Arrtispasmodic Drugs . . . . . . . . . . . 1405 Skeletal Musde R@bxants....................... 1411 DiureticDrugs ................................1422 Uterine and Antimigraine Drugs .................. 1432 Hormones and Harmone Anlagonis& ..............1437 General Anesthetia ........................... 1474 Local Anathetics ............................. 1479 Antianxiety Agents and Hypnotk Drugs ............1486 Antiepileptic Drugs ............................ 1501 PsychopharmacologicAgents .................... 1509 halgaic.Anti~r&ic.adAnti.lnflammator~Drugs...1524

Histamine and Antihistaminic Dru$ ...............1543 Cerrtrd Nervous System S~mulants..,....,....,...1551 Antinmpb.~Dru~ . . . . . . . . . . . . . . . . . . . . . . . . . . . 1556 Immunoarti~Drugs ...........................1588 Parmiticdes .................................1595

..........1600 ................................1626 Enzymes .................................... 1685 Nutrients and Assaciated Substanca .............. 1688

89

lmmunizingAgentsandAllergenicExtracts

90

Anti-lnfedives

91 92 93 PmdI

Pesticides ...................................1719 Ph-Pnctfm A Fundamentals of Pharmacy Practice

Application of Ethical Principlest6 Practice Dilemmas . .1745 Technology and Automation .....................1753 The Patient: Behaviaral Determinants .............. 1762 Patient Communication ........................1770 Patient Compliance ............................ 1782 Drug Education ............................... 1796 mi

xxii

CONTENTS

1 00 101 1G2

The Pracription

103 1G4 Io5 1 0G 1C7 O8

1 Og 110

111 1 12 1 13 1 13 11 5 116

....................I808 .............................. 1823

Professioml Communications

117

Providinga Framework for Ensuring 118 Medication Use safety ......................... 1840 1 I9 Poison Control ............................... 1881 Dnrg Interactions .............................1889 120 k~e~praneousPrescrip~anCorflpunding4+...4+..1903121 Mudear Pbrmacy Practie ...................... 1913 122 Nufrition in Pharmacy Practice . . . . . . . . . . . . . . . . . . . . 1925 PharmxmpaemidoW ~ 1 9 ~ 8 123 Surgical S u p p l i ~..............................I968 124 HealthAccessories ............................ 1979 125 B Social. Behavioral, komrnic. and 126 Adminktratlve Sciences 127 bwsGoverningPbrmacy ...................... 2015 128 ~e-engineringPharmacy practice ................. 2055 129 Pharmxmconomid '2070 130 Community Pharmxy Economics and Management . . .2082 131 Product Recalls and Withdrawals . . . . . . . . . . . . . . . . . . 2098 132 Marlce~ngPharmaceuticalCareServices............2107 133

Index

........................

..........................

Documenting. Billing. and Reirnbumment for ..

When organized settlenlel~tsarose in the great fertile valleys of the Nile, the Tigris and Euphrates, t h e Yellow and Ynngtze, a n d t h e lndus Rivers. changes occurred that gradually influenced the col~ceptsof disease a n d healing As men and women learned how to c o ~ ~ t r aspects ol of nature through farming. pernlanent shelter, and large-scale building projects. the powers of the gods in day-to-day l i f ~started to decline These changes are evidcnt among the remains of the great civilizatiol~s of Llesoputamia and Egypt of the second nlillel~niumnrr:, whose clay tablets a n d papyri document the beeinnings uf rational d r u e use in the West I ~ examination I of these allcient records reveals a gradual separation of empirical healing (based on experience) from the purely spiritual For the Babylonians, medical care was pro~ i d e dby two classes of practitioners t h e rrsipu (nlngicalhealer) a n d thc as?/(enlpirical healer) The osrprt relied more heavily on spells a n d used maeical stones far more t h a n plant materials. the nsrt drew upon a large collection of drugs a n d manipulated them intu severill dosaeeforms t h a t a r e still basic todav. such as suppositories, pills. wishes. enemas. a n d ointnlents ?he asrprr a n d t h e as?]were not in direct competitio~land sometimes coogerated on difficult cases rlpparently t h e 111 often went back and forth between t h e two types of h e a l ~ r slooking for a cure The extensive records t h a t survive of Lgyptian ~ n c d i c a l practices denlo~lstrateeve11 g-reater pl~armaceuticalsophistication, with mure dosage forms compounded from more detailed formulas The Egyptian nledical tests, like those from Babylon. show a cluse connection between supernatural a n d empirical healing. Suggested recipes usually began with a prayer or incantation. Plant drugs. of which laxatives and enemas were the most prominent, were t h e main vehicle of healing power, 11s was t h e case with healing practices in ~lesopotamia.certain indir~idualsspecialized in the preparation and sale uf drugs. Were these early nledici~lemakers t h e forebears of today's pharmacists? No, because pl~ysiciansand other healers again took on t h e duties uf medicine nrenarntion as these two ereat river THE MIDDLE AGES civilizations declined rl fully separate pharmaceutical calling Traditionally, t h e Middle Ages are defined a s the period from would be centuries away t h e first fall uf Itome (ro 400 A r ) ) to the fall of Constantinople During t h e millennium that followed, the roots of the mod( 1453) The first half of this millelll~iunlwas once referred to as ern medical professiol~in the West arose out of the flowering of t h e "Uark Ages" by historians because of the political and social Greek cir~ilizationin the basin of the Aegean Sea In t h e earliest records of ancient Greece. one finds a similar mixed concept chaos that existed 111 the lands t h a t h a d once been part of t h e of drug o r l ~ h a r ~ ~ ~ ~al kword western half of t h e Human Empire Modern historians have o w , that meant magic spell, remedy, ~. 1r.u 800 rrrm refers to the esor noison In the O d v s s ~ l IIomer revealed, however. t h a t m a n y advances were made during t h e eentiiries between 400 a n d 900 A[). ulcluding a new. indet e e k e d rnedical wisdom'of ~ g y ~thus t , illustrating the ebb and flow of ancient knowledge long before the pril~tedword. 'rhe pendent calling t h a t emerged out of the flourishing lslamic civilization-pharmacy early Greek physicians described by IIomer. the rlrlil iourgol. h a d adrallced to where they diagnosed rrrrtr~,lnlcauses for 'I'l~estory of how Greco-Itoman p ~ ~ i l o s o p science. ~ ~ y . and a r t returned to western Lurupe a n d sparked the creative periud i l h c s s , while still not rejecting the use of supcr~laturalhealing in culljunctiol~with empirical remedies. Some people beset with known as the Ite~laissal~ce is one of the most fascinating of h u persistent afflictions traveled to a temple of the god rlsklepios. man history It began wit11 the crumbling of civil authority in where they would sleep with the hope of being visited during t h e western half of the Homan Empire during the 4th and 5th t h e night by t h e god or his daughter IIygeia, who carried a centuries. Greco-Itoman culture survived in t h e Eastern magical serpent a n d a bowl of healine medicine. (Byzantine) half of t h e empire. but with considerably less The ratiollal tradition within Greek medicine t h a t was creative e n e r E . With Roman authority gone in the West. the evident in IIomer's work was refined and codified in t h e body of Church became the stabilizing cultural force. and local feudalliterature connected with t h e name of IIippocrates of Cos (co ism arose to replace centralized government. 425 r!t:r.:l. Uuilding on the foundations laid by previuus natural 'l'he use uf drues tu treat illness undenvent another shift, as paean temples, some of which h a d operated in conjul~ctio~l with philosophers such as Thales (co 590 rwt?),Anaximander (ca 550 nt.r:i. Parmenides rrn 470 rrrsl. and Empedoeles rra 450 rrrs). Greco-Itoman healing- methods. were closcd. Iiational d r u g the I I i ~ ~ o c r a twriters ic constructed a rational e x ~ l a n n t i o nof therapy declined in t h e West, to be replaced by the Church's teaching that sin and disease were related intimately. The cult illness 'l21ey accu~nplishedthis by furging a co~lceptuallink between the environment and humanity by connecting the four surroundine the healing- saints of Cosmas a n d Uamian exemelenlents of earth. air. fire. a n d water to four p v e r ~ ~ i ~ g h u n l o r splifies this attitude. Monasteries became centers for healing. both spiritual and corporal, because the two were not viewed as of the body black bile. blood. yellow bile. a n d phlegm The

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CHAPTER 2: EVOLUTION OF PHARMACY

essentially separate. Cast to their own devices, monks put together their own short versions of classical medical texts {epitomes)and planted gardens to grow the medichd herbs that were no longer available afbx the collapse of trade and commerce. Strong in their faith, these amateur healers tended to ascrib their cures to the will of Gcd, rather than to their meager medical mu~es. As WesteTn Europe struggled, a new civilization arose among those who followed the teachings of Mohammed (570-632). The formerly nomadic peoples who united into the nations of Islam wnquered huge areas of the Middle East and M i c a , eventually expandinginto Spain,S i d y , and Eastern Europe. Because their faith taugbt them to respect the written word and those who studied it, they tolerated the scholar&ip of the Chrhtian sectarians who had fled persecution in the Eastern Roman Empire; the N e s t o h , for example, eshhlished a famous school in Gondeshapur in the 6th century. Among the Islamic nations, Greek writing&,including those dealing with medicine, were translated intoArabic. At -first the Arabs accepted tbe authority of Greek medical writings totally, especially those of Galen and Diosoorides. But as their sop& tication grew,Islamic medical men like Rhazes (860-9321 and Avioenna (980-10631 added to the writings of the Greeb. The fx-flung trading outposts of the mnqueringArabs also brought new drugs and spices to the centers of learning. Morermer, Arab physicians rejected the old idea that foul-tasting medicines worked best. Imtead, they devoted a great deal of effort to making their dosage forms elegant and palatable, through the silvering and gilding of pills and the use of syrups. The new, more sophisticated medicine8 rsquired elahrate prepmatioh In the oosmopolib city of Baghdad of the 9th oentury, th6 work was taken over by specialists,the occupational a n w t o r s of today's pharmacists. In places such as Spain and southern Italy where the Ishmic world interacted mmt with recavering we~ternEurope, several of the institutions and developments of the more highly developed Arabic culture-such rn the sepmation of pharmacy and m e d k i n e p w e d over to the West. By the mid-13th century, when Frederick 11, the ruler of the Kingdom of the Two Sicilies, di!M the separate practice of pharmacy for the f i s t time in Europe, public pharmacies had b m e relatively common in southern Europe. Practitioners of pharmacy had joined topther within guilds, which sometimes included dealers in similar goods, such aa spicers or grocers, or physic+. Arabic culture had returned classical scientist and m e d i d knowledge to Europe. At centers such as Toledo and Salemo, the writings of the Greeks, which had h e n translated into Arabic centuries before on the fringes of the old easteTn half of the Roman Empire, were translated intD Latin for the use of European s c h o k s . Thus, a t the emerging universities of Europe such as Paris (11501, Oxford (11671, and Salerno{1180), scholar^ discussed the works of the great medical authorities such as D i m r i d e s , Galen, and Avicenna. However, the debates on medicine among European academics were based on speculation, not obeervatioa Theirs w a a philosophical pursuit, with no great impact on medical pra+ tie. For significant change to occur in the use of drugs, the schohtic approach had to be set aside and a more skeptical, observrttional methodology adopted. This new, experimental age we n,ow cap the Rey$,epce.

THE RENAISSANCE AND EARLY MODERN EUROPE The Renaissance, simply put, was the beginning of the mcdern period. Changes that had bgun during the European Middle Ages, and were stimulated further by contact8 with other cultures, gained momentum. The burst of creative energy that would result in our present shared culture of the West stemmed not from a single episde, but from a series of events.

In 1453 Constantinople (Istanbul) fell t o the conquering Turks, and the remnants of the Greek scholarIy community there fled west, carrying their books and knowledge with them. About that same time,Jobann Gutenberg began printing with movable type, starting an information revolution. Within a half century, Columbw discovered the New World, Vasm da Gama found the sea route to India that Columbus had sought, mmmerce b a e d on money and banking was estabWed, and syphilig r a p d through Europe. It was a time for new ideas through reinterpretation of the old W i c a l themes, and through exploration on the high sea and in the Iahratory. The time was ripe for casting off the old wncepb of disem8 and drugs of Galen. The new drug8 that were miving from faroff lands were &own to the ancients.Printers, after W n g the demand for religious bob such as bibles and hymnals, turned to pcducing medical and pharmaceutical works, cially those that could benefit from profuse and detailed illustrations. On the medical side, for example, this trend is exempl3ied in the matomid masterworks of And- Vesalim (1514-1664). For pharmacy, printing had a profound effect on the study of plant drugs, became illu8trations of the plants wuld be reproduced easily. Medical botanists such as Otto Brunfels (1500-15341, Leo&& hr~hs(1501-15661, and John Gerard (1545-1612) illustrated their works with reahtic renditiom of plants, allawing readers to do serious field work or h d the drugs needed for their practices. Among the most g i f M of these invmtigators was Vderius Cordus (1515-16441, who dm wmte a work in another popular genre-formula h k s . H% Dispensatodum (15461became the o f i i a l standard for the preparation of medicines in the city of Nuremberg and generally is considered the fist pharmacopeia. Although they were critical to the advancement of medical science, the nearly mcdern, precise works of hrcb ad Vesaliusl did not influence the treatment of disease much as the speculative, mystically tinged writing8 of an itinerant Swiss surgeon who dubbed himself "Paracelsus." Born Philippus Aureolus Theophrastus Bombastus von Hohenheim in 1493, the year Columbus went on his second trip, this medial rebel represents well the combined attitudes of the common man, the scholarly physician, the practical surgeon, and the alchemist. The battles of Paracelsus against the static i d w of Galen, Avicema, and other traditional authorities opened a window into the complicated mind of the Renaissance. As Erwin Ackerknecht observed in A Short History of Medicine, "Paracelaw ia one of the most contradictory &re8 of a contrad i c k y age. He was more modern than most of hb oantemporaries in his relentless and uncompromking b v e for the new and in his opposition to b h d obedience to authoritariadm and boob. On the other hand, he was more medieval than most of his contemporariesin his all-pervading mystic religiosity. Hia writings are a strange mixture of intelligent ohemation and mytical nonsense, of humble sinceritgr and boasting megalomania.'

Pmace18us was the most imporbnt advwte of chemically prepared drug5 from crude plant and mineral substances, yet he believed fimly that the collection of those gubgtances should be determined by astrology. He stated, again and again, his total faith in obwrvation while at the same time preaching the "dwtrine of signatme," a belief that God had placed a sign on healing substances indicating their use against disease Ieg, liverwort resembles a liver, $0 it must be gmd for liver ailments). An outspoken enemy of university-educated physicians, Pmaoelsus denigrated their scholasticism ad wrote his own works in his native language rather than in the traditional Latin. He harshly criticized pharmacy practitioners as well, even though bis advocacy of chemically prepared medicines was ta 8pmk the growth of the modern pharmaceutical sciences. Chemical p m s e s , especially &tillation, empowered the follower of Paraoelsus to &late the healing principles of a drug, its quintessence. Eventually, as the effmcy of some of these dmgs became h o r n , they entered professional medical

PART I: ORIENTATION

as well a s becoming firmly established as a profession on the practice and appeared in books on medicines. 'rh~lus.a great leap in t h e h i s t o v of pl~armacy.t h e preparation of medicu~es. European c o n t u ~ e l ~11s t , chemicalnledici~~es became more prevalent il] medical practice. pharn~acistswere forced to learn the emerged when a tool of science, chemistry, was adopted to make one of humanity's most alleiel~tof tools. drugs. new methods of preparatiun and manipulatiun. To do so they turned to the most populartestbooks on chemistry. which were Paracelsus and his followers. who chastised practitioners of conlposed by pharmacists such as Nicaise LeFebvre (Trnitk dr pharmacy. soon took a position on the forefront of chemistry during the 16th century 'rhe apothecary Johann IIartmann rh.v/llip. 1660 1 and Nicolns Lemeiy (C'or~,l:.;c l ~( . / I . J J / I I ~ P1675). , (1568-163 1).for example. was the first professor of chemistry 'I'l~evolume of chemical discuveries made by pharmacists at a Europeal~university. This trend contu~ucdthrough the would fill a chapter twice this size. Carl Wilhelnl Scheele 17th, 18th, and into the beginning of the 19th century as chem(1742-17861, for example. discovered oxygen in 1773. a year istry emerged as a separate prufessiun. Fur a periud uf abuut before Priestley. as well as chlorine, glycerin, and several inorganic acids. Martin Klaproth ( 1743-1817) was a pl~armacist 300 years, a small minority of practicing pharmacists made significant investigations into t h e chemistry of drugs, and alongwho pioneered the field uf analytical chemist^. Like Scheele. the way isolated many drugs t h a t are still used today and cum he made his discuveries using t h e equipment of the pharmacy in which h e worked. Other pharmacists, such a s h n d r e a s tributed much tu general chenlical knowledge. During t h a t same period. when men and their ships sailed t h e seas looking Marggraf (1709-1782). became such proficient chemists t h a t for new lands. and returned with new druys, practitioners of they pursued chemical work full-time, Along the way pharnlapharnlacy explored a much smaller. but equally exciting. world cists contributed much to the development of chemical apparatus. especially analytical chenlists such as Klaproth. Marggraf. in their laboratories. Mluch of the stimulation for t h e carly research came out uf rlntoine Uaumk ( 1728-1801). Carl Freidrich Mohr (1806-1879). the discovery of drugs in recently explored lands. J u s t as Galen and IIellri Moissan (1852-1907). Moissan. a French pl~armadid nut know all the diseases in the world. Uioscorides and his cist. received t h e Yobe1 prize in chemistry in 1906 for his Arab elaborators did not know all the drugs in the world. Toisolation of fluorine. bacco, guaiac. cascara sagrada, ipecac. and cinchona bark were Sincr. most drugs before 1900 were derived f r u ~ nthe plant anlong the scores of new plant drugs from the New It'orld. liingdom. it is not surprising that pl~arrnacistsdominated the investigation of botanical drugs during the 1700s and 1800s. Cillchona bark, from which q u i n i ~ ~was e extracted in 1820. 111 collaboratiol~with interested physicians. pharmacists docufirst came to Europe around 1640. a t which point it created a crisis within scholastic medicine. Galen's elaborate system of mented the sources of plant drugs around the elobe, making balancing h u ~ n o r by s using drugs uf opposite qualities could not significant contributions to t h e llascellt science of botany. explain cinchona bark's efficacy against malaria. Nnt only did Combining this proficiency with their skills in manipulative chemistry. pl~armacistscol~til~ued the bark cure malarial fevers, but also it h a d little effect on the search begun by the other fevers. IIere was somethine Galen said could tot exist. P a r a c e l s i a ~ ~tos find pure healing principles within rnediclllal t s~ecificre~nedvfur a disnlants. but Paraeelsus insisted ~ l l u s exist-a ease This conceptual crisis. plus t h e efforts of thnse i d r ~ o c a t l l ~ ~ rlpproachillgpharnlacy with a more nlodernviewpoint. these chemical medicines. displaced the therapeutic ag-reenlent of men sought to isolate pure. crystalline chemicals that could be Galenism. which had lasted nearly 1500 years '[he followu~g measured accurately and identified che~nically Medicinal period, about 250 pears, was a tlme of therapeutic chaos that preparations of crude drugs, no matter how carefully made. fluclasted until the present era of mudern pharnlacology tuated considerably in potency because of the natural variation Uuring the time ofturmoil for therapeutics while the followof active constituents in botanicals Thus, the pursuit of active ers of Paracelsus and Galen argued, the calling vf pllannacv prillciples was no easy task, and it fascinated pl~armaeeutical established t h e leeal and scientific foundations of the modern investigators for nearly 300 years T o search, separate, characterize, and identify the scores of chemicals contained u1 the profession Uut o f k e medieval complex uf guilds on the Eurogrew organizations t h a t represented pl~armacy pean col~tinel~t simplest plant drugwas a challenge as great as any exploration Discoveries came ~ r a d u a l l ythrough 11it and miss research As t h e occupational divisiol~from medicine spread north. until the late 1700s. when Scheele. for example, extracted sevpI!armacy practitiuners joined tugether or aligned themselves with similar g-roups, such as the sellers of spices ur pl~ysicians eral plant acids illeludll~gcitric acid (1784) 'Lhe single, most and surgeons The guilds of t h e late Middle Ages and early inlportnnt brenktl~roughoccurred during the first decade of Itenaissance wielded considerable power, setting u p training t h e 19th century when the pharmacist Friedrich Serturner exrequirements. examinations. and restrictiol~sO H the number tracted morpllule from crude upium 'rhe announcement of his and locations of shops Conflicts within guilds t h a t held pharmethod onened LID the era of alkaloidal chemistrl-. which remacists and near competitors uften led to gurernment intersulted in ;he isulaiion of several pure drugs from ;rude prepaventiol~and new laws that clarified t h e professiollal role of rations The French pharmacists Joseph Pellctier and Joseph pharmacy Eventually, however. interprofessional frictioll Caventou isolated several alkaloids, notably q u i l ~ i ~ in l e 1820 would lead to the separatiun of pharil~aeistsinto their own orNot only were these new. pure drugs rapidly adopted by ganizations, often under governnlelltal authority ( e g , t h e physicians because their potency was assured, but their existence allowed physiologists to administer drugs accurately French C'ollGge de W arnlacie in 1777 I during their research, which became the wellspring for mod'rhe cooperatloll between pharmaceutical g-uilds and goverllmental bodies also led to t h e stal~dardizatio~l of ~nedicines ern pharmacology through the pubiicatiol~ of books called p!rnl-~i~orop~rrrs UeMuch later. after 1850 or so, t h e scientific disciplines of cause of Freater pl~armaceutiealsophistication, the increased pharmacy began to become more professiollalized in colleges l ~ u i l ~ b of e r herbals and distillatioll books. and the availability and manufacturine concerns with a subsequent decline 111 drug shop S C I ~ I I ~ Warmacists P. interested in research left t h e shop of new chugs, pl~ysicianswanted assurance that their prescriptions would be prepared uniformly within their city or behind for the institutional lnboratoy Despite the impressive achievemel~tsof a few pharmacy state To this fnd, in 1499 the guild of phj-sicians and pharmacists of Florence sanctioned the Nuorladison. 11:l: Eo l-lkst Tirll tbs u ~ t t i lthr Yvrrr AT). 1.932 (Cambridge. England: Cambridge Cnir~ersityPress, 1951).Much has bcen translated or American lnstitute vf the IIistory of Warmacy. 19871 describes in detail 89 key works t h a t document American pl~armacyfrom written about Arabic nlateria rnediea and drug therapy. to which t h e principal key is Sami K IIamarneh's RihIirgl-nph,y o ~ r 1720 to 1940 (microform or photoduplicated copies of 85 of the 89 works are available from Lniversity Micrufilms international of M ~ d i r i n rorld Phnl-lllnr>~i ~ r:Ad~diprwlIsla~il t Stuttgart: WisAIIII Arbor. k11.1For the scientific aspects of pllarmaey see the senschaftlichc Verlagsgesellschaft. 1964). a part of the lnternaISIS Cu~~lulrrtir~r~ Rihli(gl-oplr~(Lundon. ~ l a n s e l l 1971) . and its tio~laleGesellschaft fur Geschichte dcr Warmazie series, r l m o ~ ~ g IIamarneh's other publications, see especially Q~-igin,.s.o f Pho I.continuations, which includes pharmacy. Useful World Wide Web resources include IIlSTLlNE from the National Librarv of n 7 o t ~n ~ r dT t ~ ~ l a l > , v tl~cb~Vral-Enst (Tokyo. Yaito Foundation. Medicine (]flw/igrn.nlmsil~g~~d) and the ~ a r m a z i e i l i s - 1973). also of much eeneral interest is '"Tl~eHise of Professional torisehen Uiblvgraghie or PIlU (http://~v~vw.ubka.uni-karlsruhe. Warmacg in Islam" r!1f1brlHist1962; 6: 59). For a detailed view into 10th-century Spain (with a useful bibliography). see SK de/Dharnl/Dhb.html).Some general information about the hisI I a m a n ~ e hand G Sonnedecker. A Plrnl-nlorrbr~ticolV i t w o f A b r ~ 1 tory of pl~armacycan be obtained from the website of the rimerican institute of the IIistoV of Pharmacy thttp.// www, aihp. c n s k ol-Zol~lnr~:i in ~Mr~c>l-ish .Spain (Leiden. LJ Brill. 19631, lmportant works by Max 3leyerhof include several on nlateria medug), On Antiquity: 1' 1c most definitive paper of general scope on iea. such as his monograph T l ~Ahl-idg~d r V r ~ s i nofATtrr ~t Rr>okof' Sirllpltb Tlrr~gs"of Ahlllnd ibn Mr~,lr.orll~llnd al-C;li~ifiyi(PublieaE m p t is by Frans Jonekheere, I,(, 'Prc;po~n tru rclr Rrrllkdes'dans tion no 4. Cairo. The Egyptian University Faculty of I'ol-go rg iso tiorr d r Irr p/iu ~ . l ~ n r ~i (g>, v p f i ~ n tnVeroffelltliehung r Nr 29: Berlin: Ueutsehe Akademie der Wissenschaften zu Berlin. kledicine/Guvern~nel~t Press. 1932), on al-Ueruni in Sfrtdi~rlzrI,li vul 3 lnstitut f u r Orientforschung. 1955: S o ~ ~ d e r d r u caus k " r l e ~ p t o l - G ~ s t . / i i r h t rd r s N n f u r r r ~ i s s r ~ ~ ~ s r hrr cnd~ fdt ~r r~ ~Mebrlizin, ogische Studien . . . " ) . CU Leake. Thp Old Eg>~ptian2Vl~dirolPo(Uerlu~.1943. pp 159-208): and his four articles in the Ciba Sym11jri (Lawrence: Lniversity of Kansas Press. 1952) gives an posia (vol6. Nos 5 and 6. 1944).See likewise the writings ofklartin Levey. s i ~ c has Tlrv ~h'(dicalFol-rilr~lo~y, or Agwhadlrin rlf o l oven~iewof the documents. for a first-hand i ~ n p r e s s i oof~the ~ paKir~di(Madison: University of Wiscu~lsu~ Press. 1966). pyrus most important pharmaceutically, see Uendix Ebbell's translation. T l i . Prrl>,vl-us ~ Ehcbl-s: Thr, Glra trst Bgyp tio n h'edirol On Medieval Europe: A volume still not superseded Docurilr~rt(Copenhagen: Levin & Munksgaard; London: II. Mil(althougl~outdated in details) is George F Fort. ~ l ~ ~ c 1 iEr oc ol ~ t s York. 1883; reprinted New ford. Oxford Lniversitg Press. 1937).IIenry Sigerist. A H i s t o ~ y orllj Dr1,ring tt~cbMidrllr A g ~ (Yew nf !k'e~dicin~r.Vol I : Prinlifir~c~ a n d Alrtlrrir M ~ d i r i ~(New r ~ York: York. AM Kelley. 1970); see also David Iliesman. Ttrt. S t i ~ l i: ~ f Mrrllcinw in t h Mirldlr ~ A g ~ s(New York: PU IIoeber. 19351, 11 Oxford University Press. 1951-1961) is t h e best general survey. See also J . 1Vorth Lstes. Thp 11rl~diralSkills n f A n w i ~ r r tB g ~ ~ p t valuable yuide and c o m m e n t a v is IIenry L Sigerist's. '"Il~e (Canton. MA, Science IIistury/USA, 19891, a n d Lise Manniche. Latin Medical Literature ofthe Early Middle rlges" ( J Hist ~Mvd A I TAnwiwt F:g>~pfin~~. Hrl-ha1 ( A u s t u ~University . of Texas Press. 1958. 13: 127). Four papcrs colltailled in t h e A 5 ~ ~ ~ ~ l p o s i r 1 ~ ~ ~ l 0 7 7 R.yzorrtirrr fiI(bdicirtr (Washingtun, UC: Uumbarton Oaks 1989). On Mesopotamia, a n excellent book of breadth. relevant to pharmacy. is Martin Levey's. Chrb~ilist11sa n d rhrbril irol T ~ r l l - ICesearch Library and Collection, 1985). edited by John Scarriolngp i ~ rAlrrir~rtTVf~snpntrrlllio(Amsterdam. New York. Elseborough. relate to the history of pl~armaey.Works ofmore specifically pl~armaceuticalinterest must illelude the definitive study vier. 1959). on rlssgria, see monogragl~sby Ilegi~laldC 'l'l~omgon the renowned pharnlaconledical edicts in t h e Kingdon1 of the son. The best sociohistorical review in English is IIenry L Sigerist. A History of !lI(bdicin,rb, Vnl TI: Bnl-I>)Grvrh, Hi~rrIuon,(/ Two Sicilies by Wolfgang-IIa~enIIein and Kurt Sappert. Die

CHAPTER 2: EVOLUTION OF PHARMACY

Medizinalordnung Friedrichs IX. Eine pharmaziehistorische Studie (Eutin: Internationale GesellschaR fiir Geschichte der Pharmazie, 1957). In the periodical literature, note particularly the writings of Alfons Lutz, such as "Der verschollene friihsalernitanische Antidotarius magnus . . ."and its rich bibliography (new series, vol 16; Stuttgart: Veroffentlichungen der Internationalen Gesellschaft fiir Geschichte der Pharmazie, 1960,pp 97-133); also see the works of Rudolf Schmitz, such as ". . . Apothekerstandes im Hoch und Spat-Mittelalter" (vol13; Stuttgart: Veroffentlichungen der lnternationalen Gesellschaft fiir Geschichte der Pharmaie, 1958, pp 157-165) and "Ueber deutsche mittelalterliche Quellen zur Geschichte von Pharrnazie und Medizin" (Deut Apotheker-Xtg 1960; 100: 980). English language studies of unusual value and clarity include articles by GE Trease, such as m e Spicers and Apothecaries of the Royal Household in the Reigns of Henry IU, Edward 1and Edward U"Wottingham Mediaeval Studiesl959; 3: 19; abridged in Pharm J, 4 April 1949, pp 246248). A uniquely useful work is Sister Mary Francis Xavier [Welhoefer], "Statutes of the Guild of Physicians, Apothecaries and Merchants in Florence (1313-1316): A Brief Commentary, with an Introduction and Translation," (unpublished PhD dissertation, University of Wisconsin, 1935), even though it is dated as to many details. On medieval European materia medica, see Henry E Sigerist, "'Materia Medica in the Middle Ages" (Bull Hist Med 1939; 7: 417), and his "Studien und Texte zur friihmittelalterlichen Rezeptliteratur" (vol 13; Leipzig: Studien zur Geschichte der Medizin, 1923,pp 187ff).Probably the earliest pharmacist's textbook and manual has been translated into German by Leo Zimmermann, Saladini de Asculo . . . Compendium aromatariorum (Leipzig, 1919); for a Hebrew translation, see Suessmann Muntner, editor, Sefer ha-rokhim (Tel-Aviv: np, 1953). On Modern Europe: For a reliable and concise medical overview, see Erwin Ackerknecht, A Short History o f Medicine (NewYork: Ronald Press, 1955);for detailed references, supplement it with FieMingH Garrison,An introduction to the History of Medicine, 4th ed (Philadelphia; London: WE Saunders, 1929; republished 1960),noting especially the bibliographic essays of AppendixILI. Some international survey volumes on pharmacy, with particular reference to the modern period, are listed in Sonnedecker and Berman's Some Bibliographic Aids for Historica! Writers i n Pharmacy (Madison, WI:American Institute of the History of Pharmacy, 1958). A gap has been closed, meanwhile, by Leslie G Matthews, History o f Pharmacy i n Britain (Edinburgh and London: E & S Livingstone, 1962) and Cecil Wall, HC Cameron, and EA Underwood, A History of the Worshipful Society ofApothecariesofLondon, Vol1: 1617-1815 (London: Oxford University Press, 1963). For those contemplating research in British archives, see L Richmond, J Stevenson & A Turton, eds., The Pharmaceutical Industry: A Guide to Historicar! Records (Burlingkon,VT: A s h ~ t e2003). , There is not yet a comprehensive, upto-date history that deals with European pharmacy; bibliographies, such as those cited in the earlier section on general literature guides, will yield books and monographs from particular topical and national viewpoints. For an example of a specialized topic, see Richard Palmer, "Pharmacy in the Republic of Venice," in The Medical Renaissance of the Sixteenth Century, A Wear, editor (New York: Cambridge Wniverity Press, 1985);see also R P~tzsch,editor, The Pharmacy: Windows on History (Roche, 1996).A specialized book of note is M.S. Conroy, In Hea/th and Sickness: Pharmacy, Pharmacists, and the Pharmaceutical Industry i n Late Imperial, Early Soviet Russia (New York, Columbia University Press, 1994). Especially rich in European history are the publications, 1927 to the present, of the International Society for the History of Pharmacy; a partial key has been published by Herbert Hugel, Die "Veroffentlichungen der Internationalen Gesellschaft fur Geschichte der Pharmazie 1953-1965 :Eine Bibliographie" (new series Bd 29; Stutgart: Veriiffentlichungen der lnternationalen Gesellschaft fiir Ge schichte der Pharmazie, 1967). On the US: The standard volume in English, Krerners and Urdang's History of Pharmacy, revised by Glenn Sonnedecker

17

(Philadelphia: Lippincott, 1976), devotes approximately twothirds of the main text to the United States, and its bibliopaphie s open up a wide range of other American literature. Noteworthy are the anniversary issues of Druggists Circular (vol51, January 1907) and Pharmaceutical Era (vol 16, no 27, 31 December 1896). See also Glenn Sonnedecker, "Structure and Stress of AmericanPharmacyV(Pharm J , 14April1956,pp 3-8). A series of 18 historical articles on American pharmacy were published in S A P h A during 2000,2001, and 2002. Four papers covering a wide variety of American topics are contained in G J Higby & EC Stroud, eds., Apothecaries and the Drug Trade (Madison:AmericanInstitute ofthe HistoryofPharmacy, 2001). The story of American pharmacy's umbrella organization is told by George Griffenhagen, 150 Years of Caring: A Pictorial History of the American Pharmaceutical Association (Washington, DC: APIA, 2002). Pharmaceutical education is explored in depth by Robert A. Buerki, "In Search of Excellence: The First Century of the American Association of Colleges of Pharmaq," Am J P h a r m Ed63 (Fall Supplement 1999):1-210. Ausefullook at certain aspects of colonial American pharmaq can be found in Renate Wilson, Pious Traders in Medicine: a German Pharmaceutical Network i n Eighteenth- Century North America (University Park, PA: Pennsylvania State University Press, 2000). Several different aspects of 19th-centurypractice are considered by Gregory Higby, In Service to American Pharmacy: The Professional Life o f William Procter, Jr(Tusca1oosa: University of Alabama Press, 1992). A solid biography of a 20th-century American pharmacist is James Madison, Eli Liyly: A Life, 1885-1977 (Indianapolis: Indiana Elistorical Society, 1989). Other valuable biographies include Michael A Flannery, John Uri Llgvd: The Great American Eclectic (Carbondale: Southern Illinois University Press, 1998) and Sabine Knoll-Schiitze, Friedrich Hoffmann (1832-1904) and the Fharmaceutische Rundschau' (New York: Peter Lang, 2003). Changes in the use and production of drugs are explored by John Harley Warner, The Therapeutic Perspective: Medical Practice, Knowledge, and Identiw i n America, 1820-18#5(Cambridge: Harvard University Press, 1986) and John P Swann, Academic Scientists and the Pharmaceutical Industry: Cooperative Research i n Twentieth-Centuly America (Baltimore:Johns Hopkins University Press, 1988).See also John Parascandola, The Development o f American Pharmacology: John J. AbeI and the Shaping of a Discipline (Baltimore: Johns Hopkins University Press, 1992) and Marry M Marks, The Progress o f Experiment: Science and Therapeutic Reform i n the United States, 1900-1990 (Cambridge, UK; New York: Cambridge University Press, 1997). Short histories of individual drugs are provided by Walter Sneader, Drug Prototypes and Their Exploitation (New York: John Wiley, 1996). For a contemporary use of historical arguments in policy analysis, see a series of articles written by RW Holland & CM Nimmo on "Transitions in Pharmacy Practiceg'' that appear in the Amer J Health-System Pharm 56 (1999): 1758-64,1981-7,22344 1,2458-62,57 (2000):64-72. A useful bibliography that is still in print is by George Griffenhagen, Bibliography o f Papers Published by the American Pharmaceutical Association that were presented before the Association's Section on Historical Pharmacy, 1904-1 967 (Madison, WI: American Institute of the History of Pharmacy, nd), which includes subject and author index s; although it emphasizes American history, it is by no means restricted to it. The "Pharmacy" section of the annual bibliography in the Bulletin of the History of Medicine at one time offered an important key to the literature, which was cumulated in Bibliography of the History of Medicine of the United States and Canada, 1939-1960, Genevieve Miller, editor (Baltimore: Johns Hopkins University Press, 1964). See also other bibliographies listed earlier in the section on *nerd literature guides. Also noteworthy is the "Bookshelf' section of Pharmacy i n History, a quarterly of the American Institute of the History of Pharmacy (Madison, WI); and the sections on "14istory and Ethics," "Sociology and Economics," and "Literature" in the ongoing International Pharmaceutical Abstracts (Washington,DC: American Society of Hospital Pharmacists).

18

PART I: ORIENTATION

* aRON

OLOG

p6ii'P-",mMA

a'STS

The dating of events often invulves uncertainties, approsimations. and questions of meaning-that are not apparent in a coneise table such as t h a t below. Particularly. dates before the 18th centun; often are unverifiable or estimated.

1776

1777 1 783

UCE

2040:) 1500

Eat-liest fotmulary known in hislormy(Sumerian). EIbers Papyrus, Eggplian rnanuscripl pertaining lo pharmacy and lherapy.

1785

460

Hippocratcs. famous Greek p h y ~ i c i ~ is ~ nborn. .

350 372

Diocles %:rilesa n i r n p ~ r t a n lrealise t or1 maleria mrdica. 'Cheophrnstus ( 372-285 ,. l h e "Father of bolany," is born.

1787 1790 1 793

AD

50 130 303 857 925 1035 1178 1 180 1225 1297 1345 1348 1480 1499 1529 1546 1589 1604 16 17 1618 1620 1628 1646 1665 1680 1703 1715 17 18 1736 1752 . .

.

1762 1765 1773

1774

Declaration of Independence is written, and the position of Apothecary General is created for the Continental b y CMtopher Marmhd, famwa American pharmackt, makes medicine4 for wounded soldiem. Collhge de Pharmacie is estabhhed in P h . P i U h de R d e r , a pharmacbt, makw f i s t human flight in a balloon accompanied by the Marquia d'llrlanda. WilliamWithe~publiaheshistreatiseon~fi. Thoma Fowler intmduces F o w l e h Solution (potasaium arsenite dution). Ergot introduced in ohtetrica by P a u l l i h ~ . First US patent law w.Eliaha Perkins taka out k t medical patent in 1796. Yellow fever epidemic strike8 Philadelphia. Trommsd&a Journal derphmmaeie is founded, the k t pmfesional-scientsc j d devoted to pharmacy. Edward Jenner pubbhes his work on vaccination. German pharmackt Friedrich Sertiirner reports kolation of morphine. Journal &pkarmacie et & c h i d e founded;first publiahed aa Bulktin de phmmade. Bernard Conrtois, a French phamac~st,discovers iodine. French pharmacist-chemista Joseph Caventou and Pieme Pelletier isolate strychnine. Pelletie~andCaventonLolakqninine. First edition of United Stafes Pharmacopoeia is published. Philadelphia College of Pharmacy ia Gunded as the first local association and school of pharmacy in the United States. Maaaachekh College of Pharmacy founded. Fir& American profemiond journal of pharmacy published,the Anserdcan J o u m l of Pharmacy. AntoiueEalard, French pharmacist, discovers bromine. Hennel syntheaizea ethyl alcohol. Friedrich Wiihler aynthesizas urea, thw bridging gulf between organic and inorganic c h h t r y . New York College of Pharmacy i~ founded. Chloroform i s prepared independently by Justus von Liebig and by Eugene Soubeiraa Pierre Robiquet:, French pharmacist, iaolates codeine. Friedlieb Ferdinand Range, German pharmackt, prepares carbolic acid and aniline. Crawford Long performs the frat operation wing ether anestheda. OliverWendellHoh~pointsoutthatpuerperalfever

Diosco~ideswrilrs an irliport;knl buok on rlialeria 1798 medica. 1806 Galen. a Ronian physician wlio rsperirnrnlerl wilh compounded dr'ugs, is born. 1809 C:osmas and Damian. palron sxirits of' pharmac?. 3lld medicine. ;ire mar'lyr'ed. 1 8 11 Johann Mesue Senior 1777-857 ). Arabian physician. dies. 1 8 18 Hhazes (86.59251, Persian pliysicia~~. dies. Avicenna!9HO-1035~,physiciar~andphilosopher,dies. 1820 Pharmacists are mentioned in b e n c h records. Guild of Pepperers is alreadj active in London. Apothecaiy shop is eslab1isht.d a t Cologne. 182 1 Guild of Pharmacists is org;~nized i11 Bruges !Flanders ). Apothecary shops have been established iri Lundori. 1 823 The Black Death (bubonic plague> slrikes Europe. 1825 Poison law is eriactrd by &~niesI of Scotland. Guild phaimacopoeia is publishrrl in Flo1,erice. 1lal.v. 1826 Paracelsus 11493-1541) publishes his first treatise. Th e Nuremberg Pharmacopoeia 1 Dispensalorj of' 1828 Valer'ius Curdus) is permhaps ~ h tGrst . lo become ,'oiI'icial." C;alileo Galilei clt.~no~lslrales the Paw of Llling bodies. 1829 Louis Hkbert becunles lir'sl pharmacist lo seltle in 1831 Korlll America. Society of Apothecaries in Lolldon is orgariizrd. 1832 First Idondonphatmacopoeia is p~lblislied. 1834 Pilgrims sellre a l Plymoulll, Massachusells. William Harvey p~tblishrshis book on the circulation 1842 of the blood. W i l l i a m D a v i s o p r r a t r s a n a p o ~ l ~ e c a r ~ y s l ~ o p . p o s s i b l y1843 o ~ l eo l l h e first in America (Boslo11). i~ cmtagiws. Sir Isaac Newton describes h e law of gravilalio~~. 1848 Fir& American mde of pharmaoenticd ekhic~PIEAntonie van Leeuwenhoek discovers yeast plants. pared by Philadelphia College of Pharmacy. English apothecaries are authorized to prescribe First drug import law enacted by Congreas to curb as well as dispe~ise. adulteratiom. Bartt-am's Botanical Gardens eslablished a t 1852 American Pharnm08utid hmciationis founded a s Philadelphia. the k t national organization. EI-Fr Geoffi-oy, French pliarmacisl. esiablishes the f'irsl Charla Darwin publshea h i Origin of Specks. tabulatio~~ofr~ela~ions~ii~~sbe~ween~emicals~~bs~;~nces. 1865 F~~tinternatiodpharmaoenticalconf~nceia First law related t o pharmacy iri America is enactrd held in Brunawick, Germany. ~ I Vir'ginia. I 1868 M v e r ~ i t gof Michigan opem pharmacy catme that will have far-reaching infiuence in modernizing AmeriFirst hospital pharmacy in America is t.sl;lblished >kt Penns~)lvania Hospilal i11 Philadelphia; J o n a l h a n can pharmaceuticaleducation. Robt.r'ls is l h r a p l h e c z y . 1883 Fir& National Retail Drug&tshmdation founded. Antoinc Baumb publislies llis & l ~ n ~ ede r ~phnrmrrcic s iri First National Formulary issued by American Phar1888 France. maceutical hamiation. John Morgan, Arrierican medicaI educalio11 piunerr, ad1890 Emil vrm Eehring and s h i b a s a b ~ Kitasah introvocates presct-iption writing in US. duce actrum fierapy. Karl Wilhelm Scheelr: isolates oxygen aboul 1775: 1893 Felix H o f i m a n n and Arthmr Eiehengriiu discover mpirin. Joseph Priestley indept.ndenl1.i isolates oxygen by 1774. 1895 W i l h e h Roentgen discovem =-rays. Scheele discovers chlorine. 1898 Marie and Pierre Curie discover radium.

CHAPTER 2: EVOLUTION OF PHARMACY

1899 1900 laOB

1 1910 1912 1922 1928 1935 1937 1938

National &sociation of Retail Druggids is founded in the US. Walter Reed proves mosquitoes carry yellow fever. American h o d a t i o n of Colleges of Pharmacy a founded. F h t International Pharmacopeial Codemme held a t BmseL, Belgium. Firtat h e r i m PhD ~upervisedin pharmacy granted at University of Wisconsin. Federal Food and Drugs Act paased in the US. P a d Ehrlich and Sahachiro H a h introduce arsphenamine (also known as Salvardan or "606") in widespread clinical trial for the treatment of syphiL. Fir& Assembly of International Pharmaoeutical Federation 'The Hague, PJetherlan&). Sir Frederick Eanting and Charle~Best isolate insulin. Sir Alexander Fleming discwerrs penicillin, the first antibiotic. Gerhard Domagk introduces prontod, the frat aulfa drug. American Journal of Phannae@utiealErdueation k founded, the brat periodical devotd b pharmaceutical

education. League of Natiom C o d a s i o n on Intarnational Phannacopeial Stanholds confereneea. Imporbant revision of Federal Pure Food and Drugs Act

1952 1955 1989 1968 1969 1973

1975

1977 1979 1982 IS84

WS). 1940 1942 1944 194.5 1947 1948 1949

1951

Howard F l o w and Ernmt Chain hold the fimt clinical hiah of penicillin. American Society of Hospital Pharmacbtr is founded. Antibiotic activity of streptampin is announced Atomic energy released for use in warfare and medicine. Medical Sewice Corps created in US ArmJ , with pharmacy represented by special group of commia8ioned officers. Firat Pan-l@ericanC o g r e 5 5 of Pharmacy and Biochemistry. Cortirone and ACTH are introduced for rheumatic arthritis. Influence far changs initiated by analysis and ~uggeated reform fmm Pharmamntical Survey (US). Firmt International Pharmacopoeia of the World Health Organization.

1986 1989 1980 1995 1986 19W a003

19

Chlorpmmaeine is introduced into pqchiatry, thus opening the field of p ~ y c h o p ~ w l o g y . Salkpoliomyelitb vaccine is released for general use. Synthetic modificatiomi of natural penhillin introduced. Americm Swiety of Pharmacognory founded. Important amendment8 of the US Food, Drug, and Cometic h t . American SocieQ of Consultant Phammci~h(ASCP) wtablihed. US Supreme Court decision (No 72-1176)holds that states may require that licensed pharmaci~ts have

ownerahipcontrol of pharmacies. Gongma e n a d Health Mahtenance O r g h t i o n Act, W c i a l d w ~ t a n d ~ t i cprogram m i~ unified by US Pharmaoopeia absorbing National Formulary. Report by Study Commkmim on Pharmacy (AACP) givw impetw to trend hward drug information and counseling role of pharmacists. Clinical biala of adenine ambinwide against herpes rake prospect of cantrolling viral dimam@. American College of Clinical Pharmaay @ founded. Specialty ceditication begins in American pharmacy with the board certification af 63 pharmacbts in the field of nudear pharmacy. Drug Price Competition and Patent Term Re-atiun Act encourages growth of generim. Americnn&sociation of Pharmaceutical Scientists is founded. American Council on Pharmaceutical Education IACPE) announces intent to develop accreditation atandards for Doctor of Pharmacy programs only. Omnibus Budget ReconcilatimAct (OBRA) requires that pharmactts coun@elMedicaid patients (effective 1993). Pharmacy TechnicianCert5cation Board formed. National hsociation of Retail Druggists (f. 1898) changes name bNational Community Pharmacists Association. National hmciation of Eoarda of Pharmacy mABP) proposes reg-ular competency t e a h for pharmad-. After 160years, the APhA change1its name to the h e r ican Pharmachtm hmciation

Ethics and Professional Michael Momtagne, PhD Robert L ~ccarthy,PhD

The quest to construct systematically an ethical framework for Western civilization was begun over 2000 years ago by Socrates. He approached ethics as a science, as being "governed by principles of universal validity, so that what was g o d for one was *od for all, and what was my neighbor's duty was my duty also."' However, aweptance of the Socratic approach has proved burdensome. 2000 years of humankind universally adhere s to not even one ethical principle. No set of pfinc.ples, no matter how thought out or how well mnstructed, can provide the individual profes sional with guidance for each decision about clients, peers, or society. There are people who believe that because each situation is different, each decision requires separate analysis of possible o u h m e s hm different actions and the weighing of fight and wrong. Regardless of one's stance or approach, however, the health professional in today's society needs continual selfexamination of professional duties and ethical principles to prepared for the conflicts and dilemmas they will face.

BEING PROFESSIONAL In this discussion,professional ethics is used only to denote "the profession's interpretation of the will of society for the conduct of the members of that profession augmented by the special knowledge that only the members of the profession possess."2 In other mnhxts1 the term might be used to denote those ethical principles to which society believes any individual claimingprofessional status should subscribe. What is to be gained by development of a set of ethical principles, or a code of ethics (Fig 3l),by a profession to which it expects its members to abide? ~ i r s t a, code of ethics makes the decision-making prmess more efficient. In opposition to situational ethicists, Veatch claims:

"They may at least act as rules-of-thumb for handling easy cases. They may at least summarize ethical reasoning that has gone before by others who have found themselves in somewhat similar situations. They may at least serve as guidelines for formulatlng thinking about the problem at hand."4

Second, individual professionals occasionally may need guidelines for directing their professional behavior. Each decision made a professional requires upon a store of technological information as well as the individual's own sense of right and wrong. Almost assuredly, all professionals will be confronted with situations that they have never considered in great detail. Where one can find no apparent theological or personal ethical principles to One might turn to P~~~~~~~~~~ ethics for guidance. Finally, professional ethics establish a pattern of behavior that clients come to expect from members of the profession. Once a consistent pattern of behavior is discerned by clients, they expect that behavior to remain constant, and their expectations become part of the relationship they establish with the professional. To better understand the role of and necessity for ethics in professions, one must f i s t look at the characteristics of professions.

PROFESSIONAL CHARACl'ERISTICS

T h e first characteristic of a professional is possession of a specialized body of knowledge; using body of knowledge enables the practitioner to perform a highly useful-al function* ~ 1 lawful 1 ocEupations provide some positive bnefit to smiety and are based on specialized knowledge. The profes,ions generally are more useful than many other oc,pations, but social utility alone dms not make an occupation a profession. An applied body of knowledge may be composed of knowl"Yet if those who must resolve the ever-increasing ethical dilemedge of a manual skill or intellectual knowledge. The latter is of mas in medicin-includhg patients, family members, physie he ~ h a r cians, nurses, hospital administrators, and public policy-mak- p h a r 3 ' significance as a criterion for ~ r o fssions. m a ~ i sis t not considered a professional because of g''"d typing ers-treat every case as something entirely fresh, entirely novel, they will have lost perhapsthe best way ofreaching ~ 0 1 ~ - skills- Rather, he or she possesses the relevant professional knowledge about drugs and ~ a t i e n t that s ~ e r m i t the s ~ h m a tiom: to understand the general principles of and face cist to advise patients and prescribers concerning drug therapy, each new situation from a systematic ethical ~ t a n c e . " ~ detect drug interactions, select appropriate product sources, Clinical practice predisposes pharmacists to a situationalist a p and exercise professional judgment. proach to ethics through its emphasis on individual differences The exercise of proper judgment is a key element in this in response to therapeutic regimens. Some guidelines, however, first professional characteristic. Professional services tradiexist for adjusting drug therapy in patients with compromised tionally are rendered to an individual rather than to a group. renal or hepatic function, electrolyte or hormonal imbalance, Using the specialized body of knowledge of the profession and and other pathological abnormalities. Therapeutic guidelines the intellectual abilities of the professional, the practitioner give us a place to begin solving a clinical problem. Rules of makes a judgment as to the best course of treatment for each morality serve the same purpose: individual. 20

WAPTER 3: ETHICS AND PROFESSIONALISM

21

Code of Ethics Amerlcan Phamacists Association Preamble

Pharmacists are health professionals who assist individuals in making the best use of medications. This Code, prepared and phmim> is intended to state publicly the principles that form the fundamentalbasis of the roles and responsibilities of pharmacists. These principles, based on moral obligations and virtues, are established to guide pharmacists in relationships with patients, health professionals, and society. 1. A pharmacist r e s p e d the covemtal relationship between the patient and pharmacist. Consideringthe patient-phmmcist relationship as a covenant means that a pharmacist has moral obligations in response to the g8t of trust received from miety. In return for this @t, a pharmacist promises to help individuals achieve optimum benefit from their medications, to be mmmittedtotheirwelfare, and to maintain their trust.

11. A pharmacist Promotes the good of eveW patient in a caring, compassionate, and coddential manner. A pharmacist places concern for the well-being of the patient at the center of professional practice. In doing so, a pharmacigt considers

needs stated by the patientas well a~ those defined by health science. A pharmacist is to protectingthe it^ Of the patient. With a caFing attitude and a cornp=sionate spirit, a pharmacist focuses on serving the patient in a private and confidential manner.

m w

of 111. A p u C i s t respects the autonomy and each patient. A pharrnscht promotes the right ofself-detemhtionand recognizes individual self-worth by meouraglng patients to participate in decisions abut their health. A phannadst communleates with patlents In terms that are understandable. In all cases, a pharmacist respects personal and cultural Merences among patients.

IY. A pharmacist acts with honesty and integrity in professional relationships. A p h a d t has a. ddYto tell the truth and to act with comiction of ,,~ence, A~~~~~~ (1. - . torypractices, bebvior or work concfiiom that imp& pprfewional judgment, and d o n s that compromise dedicationto the best interrsts of patients.

V. A pharmacist maintains professional competence. A ~harmaciahas a d a y to maintain howledge and abiities as new medications, devices, and technologies become available and as health

information advances.

VI. A pharmacist respects the values and abilities of coll e w e s a d OW health profession&. When appropriate, a pharmacist asks for the cohsultation of colleagues or other health professionals or refers the patient. A p h m a cist achowiedges that colleagues and other health pmfe8sionsls may differ in the beliefs and values they apply to the care of the patient.

VII. A phannacht serves etal needs-

and soci-

The primaryobligation of a pharmacist is to indiddual patients. However, heobligations d a pharmacist may at times e*nd hyond the Mlvidual ta the community and society. In these situations, the pharrnacistrecognizes the responsibilitiesthat accompanythese obligations and acts accordingly.

VIII. A pharmacist seeksjustice in the distributionof health

resources. When health resources are alIocated, a pharmacist is fair and equitable, balaneingthe needs of patients and society.

Figun 3-1. Code of ethic (Originally published in "Code of Ethics for Pharmacists." Am I Health-5ysl Pham 1995; 52: 2 13 1 . 0 1995, American Society of Health-System Pharmacists, Inc. All rights re2rved. Reprinted wiith permission.)

The second characteristic of a professional is a ~ eoft spec& attitudes that influence professional behavior. The basic cornponent of this set of attitudes is altruism, an unseEsh concern for the welfare of others: T h e professional man, it has been said, does not work in order to be paid: he is paid in order that he may work. Every decision he makes in the course of his career is based on his aenx of what is right, not on his estimate of what is p r ~ f i t a b l e . ~

Professionals are concerned with matters that are vital to the health or well-bing of their clients. The practitioner employs highly specialized khnical knowledge, which the patient or client d w not ~ possess. Both the client'a lack of knowledge and the vital nature of professional services provide the professional with an opportunity to exploit the client. The consequences of such exploitation are Bevere. The smooth functioning of the professions requires that the practitioner must consider the needs of the patient as paramount, relegating his or her own material needs to an inferior position. Mal sanction, the third characteristic of a professional, is a resultant effect of the two characteristics already discussed. Whether an mcupation is considered to be a profession depen&, to a large degree, on whether k e t y views it as such.

One measure of ~ o c i a sanction l is the granting of exclwive rights of practice through the licensing power of the state. Li~ensingnot only attempts to protect the public from incompetent pr actitioners, but also frequently creates a relationship of trust btween smiety and the professionals, bcause thin the sphem ofprofeBsion~ ~e professional exercises power over patients. by Gmenwd,

*

"rrlhe professional dictates what is good or evil for the client, who has no choice but to accede to professional judgment Here the premise is that, because he [or she] lacks the requisite theoretical background, the client cannot diagnose his [or her] own needs or discriminate amcmg the range of possibilities for meeting them.'%

The extent of the public's trust is a measure of the degree of social sanction, and thia is evident in s m i e t y ' ~permitting the exercise of sovereign power over professional matters. Given the legal monopoly inherent in professional licensing, the failure of society to impose W e r controls on the profession is sanctioning, by implication, the profession's performance and self-regulation. Thus, professionshave evolved as m p a t i o n s connected with high status. The functional relationship of professions to

22

PART 1: OR1ENTATION

Oath of a Pharmacist American Association of Colleges of Pharmacy At this time, 1vow to devote my professional life to the sewice of all humailkind through the professioil of pharmacy 1 will consider the welfare of humanity and relief of humail suffering my primary concerns. 1 will apply my knowledge, experience, and skills to t h e best of my ability to assure optimal drug therapy outcomes for the patients 1sen7e. 1will do my best to keep abreast of developmeilts and maintain professioilal competency in my profession of pharmacy. 1 will maintain t h e highest principles of moral, ethical, and legal conduct. 1will embrace and advocate change in t h e professioil of pllarmacy t h a t improves patient care. 1 take these vows voluntarily with the full realizatioil of the responsibility with which 1 am entrusted by t h e public. org/slte/ terFigure 3-2. Oath of a pharmac~st(From http,/lhmvw tlary asp7TRAC KID 5 &VlD 5 2 & CID 5 686 & DID 5 3339 Accessed May 14, 2004 )

society reinforces their status position, and t h e status itself acts as a motivating factor in t h e drive of any occupatiol~to gain recopition as a profession. Several studies have attempted to identifi which occupations qualif?: as professions. ' r l e most prominent study was done by Can-Saunders and Wilson in 1933.' Primarily because of t h e commercial elemellts illherellt in moderll ~ I l a r m a c ypraci o ~to~ phartice, t h e study reached no definitive c o ~ ~ c l u s as macj2s professional status. More recent studies have produced similar results. k~onta~~e,"mith,"mith and ~ n a ~ ~ and , ' ' ) U e n z i ~and ~ Metdin' col~sistel~tly found pi~armacyto fall short of full professional status. The key issues illelude a lack of autonomy (eg, pharmacists follow orders, fill prescriptions, decided by others, the prescriber) and potential or real conflicts regarding professional compensation based more so on products than on sen~ices(eg, pharmacists counsel patients on nonprescriptiol~products without charging a fee, but compel~satiol~ comes through t h e sale of that product). A 1 professions, however, can be found to fall short of being a complete professiol~in at least a few respects. Pharmacy h a s a legitimate claim to a theoretical body of knowledge, to a growinp degree of socially sanctioned decision-making- authority, and to a commitmel~tof sen~icefiu~ctionsas articulated by a code of ethics and an oath (Fig 3-21 that is sworn by individuals entering the profession.

ETHlCAL DECISIONMAKING fiamapy ethics has a deal of recellt attention, but tile study of etllics, ethical questions, a n d codes of ethics has beell a n integral r-omponent of p~llamaeyalld prac. tice for cellturies, ,rhe first code ofetllics for medicille was cred. ited to IIippocrates 111 t h e 4th century nc. In many ways, the IIippocratic code is timeless. For example, his direction that no physician should "give a deadly drug to anybody if asked for it, nor . . . make a suggestiol~to this effect""! provides one moral perspective on the contemporary issue of assisted suicide. Over t h e past decade or so, t h e attention given to pharmacy ethics in t h e professiollal and scientific literature, and in schools and colleges of pharmacy, has changed a great deal,

Only 2 of the 52 schools t h a t responded to a 1980 sun7ey required a formal, separate course in ethics; 32 schools offered no course, required or elective, of which ethics was a n explicit part.',i Today, however, most pharmacy schools require some instruction in ethics, h 1991 sun7ey of ethics instruction at pharmacy schools found that, "while the quantity of ethics instructiol~h a s not increased, there are encouraging signs that the quality and depth of ethics educatiol~is irnproring.""' Several factors appear responsible for the heightened attention given to the study of ethics in pl~armacy,including the explosiol~of biotechnologg: and the rapidly rising cost of health care in the LS, of which drugs are an important component.

Macro Ethical Issues versus Micro Ethical Situations Ethical situations in pharmacy can be divided into two broad categories: macro and micro. filacro cthicol issr~~cs are issues t h a t are not specific to a given pharmacist, but rather are those t h a t must be addressed by all pharmacists and by society in general. These include abortion, assisted suicide, genetic engineering, rationing- of and access to health ceae, organ transplantation, and in rniilJ S w l n l Sc,~rrtc,rn r ~ d:Vlrcilc.lrtr i A m s t ~ r r i ; i m , N ~ t l 1 ~ r l ; i n r i sElspvipr : Sr:i~nt:~)

Finally, tllose who teach pharmacy have rlnwr~e'nm.Ior~rrt(~l of Phnrnrnnc~prrt~c~c~l ISdrtc~c~t~or~ I!\l~x:indriii, V h : !\/\(:Pi J{)rLrnnl( ) f P / l , o r r n o c ,Tr,nc,hl ~ NY: P]l;lrnl;lt:plltie:;ll Prori11r:ts P r ~ s s )

These jourllals are only a few ofthe thousands of scientific journals published worldwide. Finding articles on one particular l ~ gissues of area of interest requires more effort than s c a l ~ l ~ ithe a few journal titles regularly. Not long ago, someone researching a topic would be urged to begin with a standard bibliography, and to follow this by using printed indexes and abstracts t h a t could be collsulted only in a library, Advances in computer technology have made most printed finding tools obsolete. Printed sources are outdated t h e day they are published and, in the opiniol~of most, to use t h a n online tools. Most o n l u ~ e are much less collvel~iel~t indexes can be accessed from desktop computers using the lnternet. Many indexes link to t h e full t e s t articles tl~emselves, thus obriating many steps (both logically and geographically).

CHAPTER 8: INFORMATION RESOURCES IN PHARMACY AND THE PHARMACEUTICAL SCIENCES

Researchers may also subscribe to table-of-contents alerting services, whereby the tables of content of selected journals are e-mailed to the researcher a t the time of the publication of the issue. Some are services that must be purchased, such as those through companies like Ingenta. Or, publishers may offer the servioe as part of an individual or institutional subscription. Finally, there are "packaged" medical collections that allow users to search across collections of textbooks, databases, and other materials. Collections such as Stat!Ref, MDConsult, and UpToDate are discussed under "textbks."

Databases Online databases, because of their convenienoe and ubiquity, are now the first choice to consult for locating pharmaceutical literature. For clinical literature, the databases of choice are MEDLINE, EMBASE, evidence-based medicine databases, the Iowa Drug Information Service (IDIS), and International Pharmaceutical Abstracts. For drug development, Chemical Abstracts and BIOSIS Previews are the most comprehensive. Each of these is available in print, through the World Wide Web ('"the web"), on magnetic tape to be loaded on a lmal mainhime, or through commercial vendors such as Dialog or Ovid. Educational institutions and corporations oRen ~rovideaccess for their researchers to one or more of these databases. An individual also can purchase access through a subscription or per-search arrangement with database providers or vendors. Searching online databases appears to be easy4eceptively *but doing a successful search can require a great deal of skill and prior experience. Novice searchers are often too impatient to learn proper searching techniques and may either miss many relevant items or retrieve a large n u m h r of irrelevant ones. Attending a class, consulting a manual, or working with a librarian can much improve a researcher's ability to do a comprehensive and highly relevant search.

MEDLINE MEDLINE is prduced by the US National Library of Medicine (Bethesda, MD). Its coverage of 4600 highly regarded clinical journals makes it the preeminent biomedical database. I t is subsidized by the US government, with one search engine, PubMed, available at no cost all over the world. The resulting low or no cost to its users means that it is often the first and only choice of those seeking medical information. Its coverage is strongest in clinical and therapeutic topics. The National Library of Medicine produces MED LINE and makes it available directly to the public, but a n u m h r of other vendors make the database available as well. Each of these vendors has its own set of searching ~ r o t m l susuallv . called search engines; each is a little differeicfrom the' others: and each has a somewhat different way of indexing the files. The same search done with different MEDLINE search engines may yield different results. PubMed the MEDLINE search engine provided free to the world over the Internet by the National Library of Medicine, is a very easy to use and powerful search engine. Included as part of its website are excellent tutorials. Those who learn to use PubMed well get excellent results, but it is very easy to do a bad search in PubMed. The commercial vendor Ovid provides a search engine that forces its users to do better searches, so many institutions and corporations purchase a m s s to it. Finally, there are several other free Internetaccessible versions of MEDLINE. Their search engines are considered to be less powerful than PubMed or Ovid and they should not h used. PubMed also provides links to the articles it cites that are available in fulltext on the Internet. However, the articles must

(w,

65

be free or part of their library's subscription in order for users to access them. Another feature of PubMed, Loansome Doc, lets unaj5liated searchers set up accounts with a medical library and order articles directlv &om them (at a cost). Institutions with subscriptions to 0 v i i may also choose to subscribe to electronic journals so that their users can connect directly to the articles they find in MEDLINE.

EMBASE Another highly regarded medical database is EMBASE, produced and provided by Elsevier, a commercial publisher based in Amsterdam, Netherlands. Although its coverage of 4000 journals is comparable to MEDLINE, there is surprisingly little overlap between the two. In one 2000 study1, a search for controlled clinical trials for 3 medical conditions, done in b t h MEDLINE and EMBASE, yielded a total of 4111citations, but only 30%of these citations appeared in both databases. EMBASE covers European literature in much more depth than does MEDLINE. I t also is considered to be somewhat stronger in drug information and in areas of biological science related to human medicine. Because of its European f m s and its high cost as compared to MEDLINE, EMBASE is searched less oRen in the US than perhaps it should be. EMEASE is available through online vendors such as Dialog and Ovid, and through the web. A recent product, EMBASE.com, includes not only EMBASE, but also unique MEDLINE records so that b t h databases are searched simultaneouslv. EMBASE.com also includes links to articles from some major medical journals. Subsets on specific topics such as drug information or cardiology are available separately.

Evidence-Based Medicine (EBM) Databases Increasingly health professionals are asked to base their decisions on evidence as demonstrated in randomized controlled trials (RCT's). In b t h PubMed and Ovid, MEDLINE searches can be limited to RCT's. However, strong proponents of EBM feel that only RCT's that meet vigorous standards of methodology should be used. They prefer "systematic reviews": reviews in which all RCT's on a particular topic are collected and analyzed, a meta-analysis is performed (if possible), and that evidence is then used to come to a clinical decision. PubMed allows the searcher to limit his or her results to systematic reviews. There are also several efforts to collect and make available systematic reviews. The Cochrane Library, the hst-known such collection,is a volunteer effort begun in Great Britain. International teams donate their time to iden* all published and nonpublished RCT's on a particular topic and then to prepare a systematicreview with implications for practioe. Abstracts of the systematic reviews are available free on the Internet. The reviews themselves may be purchased from the Cochrane Library organization or searched through subscription to Ovid, Dialog, and other vendors. A major drawback to the Cochrane Library is the amount of time it takes for volunteers to com~letetheir ~roiects.Similar commercial products finish their reviews somewhat faster. These include Clinical Evidence (BMJ ), PIER (American Coll e g of Physicians), and Infopoems (Infopoems).Also, the American College of Physicians, through its ACP Journal Club, monitors major internal medicine journals and selects for review those articles with the most significance for therapeutic practice. 1

0

IOWA DRUG INFORMATION SYSTEM Iowa Drug Information System (IDIS) is prduoed by the College of Pharmacy of the University of Iowa. IDIS is a handy selfcontained product that allows the user to search for drug therapy articles selected from 200 clinical journals and to access the fulltext of the articles. Access is provided on the web,

PART 1: ORIENTATION

by CU-ItOkI, or on microfiche. This product is especially useful for drug information centers and IIkIO's t h a t may not otherwise be able to access a large collectio~~ of electronic journals.

ways it can be searched are by keywurds, broad subject areas, and codes representing taxonomic groups. Vendors illelude UlOSlS, Ovid. Uialog, and STY. Ovid provides links to fulltext articles.

INTERNATIONAL PHARMACEUTICALABSTRACTS The scope of t h e I n t ~ ~ r n a t r o n aPhornlac~~utrcal l Abstracts ( I P A ) is different from either MBDI,I:YE or BfiIRASB IPA is produced by t h e rimerican Society of IIealth-System Pharmacists (riSIIP) and covers 850 pharmacy periodicals I t is a small database, but it covers publicatiol~snot indexed elsewhere, including pharmacy trade magazines, state pharmacy journals, and the meeting- abstracts of pl~armacy-relatedassociations Some drug therapy journals t h a t are indexed in ;l.IBDI,IXB also are indexed by IPA IIowever, because IPA's indexing rules are somewhat different from :VIEDT,TXB's, a researcher may sometimes turn up materials in IPA t h a t were missed in MEDI,I.VE searches Llany pharmacy and pharmaceutical sciellce topics are much better searched in IPA than in any other database This is the best database to use to find large numbers of articles on pharmacy administration. drug laws and legislation, and pharmacy ethics Pharmaceutical manufacturing is covered as well Ovid, Uialog, and the rimerican Society of IIealth-System W a r macists make IPA available tl~roughthe web and on CU-ItOLI Links from IPA to t h e indexedfulltext articles are not available as of this writing

CHEMICAL ABSTRACTS C h ~ nicol l Abstracts (sometimes called CApIr1,s or C A Sca reh) covers areas of interest to pharmaceutical scientists. Perhaps the world's largest scientific database, Chcnlicol Abstracts is produced by t h e rimerican Chemical Society's Chemical ribstracts Service ( C h S ) in Columbus, Ohio. It c u l ~ t a i l ~17s million abstracts from journals, patents, technical reports, buoks, cunference proceedings, and dissertatiol~s.It is the most important database for those interested in drug development. AH important adjunct to Chrnlicol Abstracts is t h e CriS Reg-istry System t h a t assigns code numbers to chemical substances, providing- a unique identifier for each substance no matter how many names the chemical may have worldwide. This ChS registry number is so valuable that other databases use it to make sure t h a t searchers can find all literature relating to a particular chemical. The CriS Itegistry System may be searched separately in some database systems. 11special type of searching t h a t can be done in Chclu icaIAbstracts is structure searching. It allows the user to draw the chemical structure of a substance and to search from t h a t . There are links from a Chcnlicol A b s t m c t s search to full-text articles available on the web, but to access them the searcher or the searcher's institutiol~must subscribe to the journal that contains t h e article. l include Ovid, Uialog, and Vendors of C h r ~ ~ l i c aAbstracts STY. Some subsets of the database are available on CU-ItOkI, Some institutions and corporations subscribe to SciFinder (or its academic equivalent, SciFinder Scholar), a user-friendly web interface t h a t allows unlimited searching. Othenvise. Chcbnl icol Abstracts is very expensive to search and should be accessed only by those trained to do so. Classes are offered around t h e country by C h S , ricademic chemistry or science librarians can often direct a researcher to an experienced freelance literature researcher.

Other Databases In addition to t h e major online databases described above, there are many specialized databases t h a t might be of use in t h e study of pharmacy Some of these are available on standalone CU-ItOLls, but most are accessible only tl~ruughone of t h e two major database vendors, Uialog and Ovid

from t h p p11 t>lir,:itions Irr,p helrrncl. Kuc~c~t~orts, :inri Phc~rrnc~c~c)r,c~c)~ 1 , 0 ~ I? (7' S .

11ei1s I ' l ~ r t ~ c ,'I'r~ols c~l ~ l . ; i n g I ~ r > rPA: n ~ , Adis ~ n t ~ r n : i t i r > n : iEv:iI11:it~s IL "kpy p:iywrs"from 1600 in t~rn:itir>n:il r:linir:;iI jo11r11;ils. r l c i ~ sK A I l Irtslght ~ l . : i n g I ~ r > rPA: n ~ , Ariis rnt~rn:itir>n;il).Rpports 1111 d r u g s u n r i ~ rd ~ v ~ l r > p n w inntr, , l ~ ~ d i nr,linu:;il g :inri m : i r k ~ t i n gunfrjrm:itir>n. ISSPI('om P h o r r ~ ~ o c ~ u rclrtci ~ t ~ c:l.lr,ci~c~c~l ~d Iluf!~c,e, :Vc,lr!s ~ ( : h i r , h ~ s t ITK: ~r, ESPr(:OM R ~ ~ s i n p Ts sn t ~ l l i g ~ n rF, ~~ ~~l.l t p of x t :irtir,I~sfronl PhelrmclI'ornpcl rr,? Irts~ght:ind :l.lr,cilc.cllIrtcirlstn. 1Vemrk. 12:l.11511:rZll~c,cic1 r r d I'ornplurnurttc~n.:l.iuci~c~~rtu Ilotrl helsu ~l.r>ndr>n: Rritish I.it>r:iry). rndpx to ,596 j r > ~ ~ r n : i lmostly s, Ellrr>pp:in, r t s r,ovPr:igP of r:r>mplpn~pnt;iry m ~ r i i r 1:s~thp ~ ~m~o s t 11spf111: i s p ~ r , for t pl~;irnm:ir,ists. D r > r : ~ ~ m pdplivpi-y nt s y s t ~ n :iviiiI:it>l~. l Ilurfr!urtt Ilrrlg F ~ l u11,onrion: D P ~ \ - PtI Irnfr>rnrn;itir>n k ( : r > v ~ r 1s 150 p11;irm:ir,~~~tir::il j r > ~ ~ r n : ion l s rirug d ~ v ~ l o p r n :ind ~ n t nl:in~~f:ir:t~ M11r:h ~r~. morp l ~ i g l ~ fi>r,~lspd ly on d r u g s tl1:in 1s I'hrrn~c~c~l r2hstrclc.t~. Ilurfc!urtt Ilrrlg Kr,g~stn.F ~ l v~l.r>nrir>n: D ~ n \ - ~ rnfr>rnrn:itir>n): nt Rptripvps groups of rirugs wit11 r:r>mmr>ns t r ~ ~ r , t ~ ~f ~r ;: i tl l l r ~ s . IlI0l:IS:VISS FllrZ K l ~ rMD: g, D ~ ~ ~ P I ~ P s ) : Npws s t o r i ~ :ind s ~ ~ n p ~ ~ h l i[ isrh> ~ r , r~ i~ m prp1:itung nts to I!S r~g111:ition. Ilrrlg Ilcltel Kr,pc)rt I Rirr,~lon;i:Pro11s S r , i ~ i ~ r(, ~ : ~k I ~ ~ ~ I I I11pr1:it~d I ~ I I s Iin~ fr>rnm;it~r>n on nIr>rpt11:in 6;1,00fl t>lo:ir,tlv~r,onlpol~nds. F-I)-(' K l ~ t ~~ x of t FD-(: R ~ p o r t s indllstry ' n ~ n - s l ~ t t inr,l~~riing ~rs Prc,st~r~pt~or' Phorrnclc~vrtt~c~c~ls & K~otuc~hrtolog~ [ P Irtk Shrtmt) ;ind :2:orr,~)rc~se~r1pt1or~ Phelrrnc~c~rrlt~c~ols clrtci : V r l t r ~ t ~ o r r~'I'c~rr. ~ ~ l s S/rx,vt). I:l.lASIVorlci11~>11don: rkIS (ilot>:il S ~ n - i r , ~ (:oll~r,tio11 sk ofd:it:ih:is~st11:it p r o f lp pl~:irnm:ir~l~tir,:il r:omp:inips, thp pl~:irnmiir:~l~tir,:il in[illsti-y t>y r:r>lIntry, :ind npw d r u g 1:11111r,I1~s. :VIlrZ P~pc,l~rtr: :Vv;ilor dis:ipprr>v:il t>ythp FD!\. Phorrnc~c~vrlt~e~c~l clrtci H < , o l t h ~ ~ c ~ Irtcirlstn. rt' :Vr,fr!sI Rir,hmr>nd,Sllrrpy, Engl;ind: P,JR P11h lit::itir>nsk (:r>rnplptp tpxt of P.JR's indl~sti-y n ~ w s l ~ t t ~SI'KIP: rs: 1Vorlci P h c ~ r r n c ~ c ~ r r ~:2:rwc!s; t ~ c ~ u iI'l~rt~c.cl: 1Vorlci :l.lud~c,cllIlrf!lc,uc1 rtci Il~c~grtc)st~c, :Vlost P&T committees are composed of members of the institution's medical staff and illelude one or more representatives from t h e pl~armacy.Chapter 127 discusses P&r committees and their roles. ln the Gllited States+the Food iidministration (FDA) has the responsibility to determine t h a t marketed drugs are safe and effective. The FDA produces Approrfirrnc6' [Ill, mollly referred to as the P D R , Otller titles okell 111 macies alld pllarmacy libraries in the L'nited States are AHFS Drrg I n f i ~ m tion ~ a [ 121 (sometimes called t h e A n ~ t ~ r i c aHospin tal FOrnI ry S6brr'ictb); Drrl,g Facts COnIparistln,s [ 131; fiIosbvJs D rrlg COn,srl,/t[ 14 1; a [,TSp DT, VO/rl,nII, Drrl,g Tnfilr. tiOn filr the' Heba/thCo rtb PrO,&ss~(ln,a/ [ 15 1 , Each of these with its own criteria for works is arranged slightly differently inclusion, but all illelude mollographs for drugs witll details o n tlleir tllerapeutic use, The PDR lists only those drugs sold under a trade name, and t h e monographs it publishes are tile FDIl.approved labelillgfor those drugs, N1 of the other compelldia contain illformatioll from the labelillg as well a s additiollal data from other sources, such as journal articles and textbooks. They also illelude descriptiolls of so-called off-labt'lr~,scs,therapeutic uses 3. r~ppre)t!!,ci ~ l r r l gPrc)cirLc,tsf , ! ~ t'I'hrrt~prrlt~c~ h I S ~ f!oIrrtc,r ~LI ISt!cl!rlcltlorts. Rnck\lllr: MD: Fnnd and Drug Administrntinn, 1JS Drpnrtnlrnt of of a d r u g t h a t do not appear on the FDA-approved labeling. ExIIrnlth nnd IIumnn Services [ \ w w . f r l n . ~ n vnnnunl. ~: cept for t h e PDR, these compendia are written or edited by ;. I S I r o ! r ~ Ir I f !L r i e t sl i 1 1 1 r 1 pharmacists or otl]er health.eare professiollals, 'rle criteria for mrrtts. Englc\rnnd, CO: Thnmsnn hIICROhIEDEX [htt~:lht.ww.n~i- illclusioll h1 tllese compelldia vary from title to for examcrnmcdrx.cnm I: nnnunl. ple, Drrq Facts and Conlpa risons illeludes some nonprescription products, All of these titles, including t h e PDR, are issued annually and most are updated by supplemel~tsthrougho~utt h e Nomenclature year, h notable exception is Drr~,gFacts a n d Con~parisons, Every drug has at least two names, its full chemical name and which is published both as a loose-leaf sewice updated montl~ly its generic drug name, h drug may also have other names inand as an annual volume. eluding variant chemical names, proprietary trade names, and Uy virtue of its electronic format, the DRUGDEX S.vsk>n~ variant generic names, rldditionally, drug names sometimes [ 1 6 ]c o l ~ t a u much ~s more il~formatiol~ t h a l ~call fit illto any oneTable 8 - 1 lists some ofthe names used differ between coul~tries. volume prillted compendium. DRT,TGDF:X's drug mollographs for t h e drug acetaminophen. For more informatiol~on drug are longer and more detailed thall t l ~ o s efound iH t h e above names, see Chapter 2 7 . compendia, and each monograph iilcludes extensive references The LTSP Dictiona r.v o f U S A N and Tntcrnational D r r q to the medical literature, l n addition to monog-raphs about inXawtbs 171 is the authoritative list ofthe L'nited States adopted dividual drug products, DRT"GDEX illeludes Drug Consults, names (LShYs) for drugs, As t h e title indicates, this work is published by the publisher of the LTSP, t h e United States W a r macopeial Convention, as part of its standards-setting responTable &I. Selected Names of a Drug sibilities. The World IIealth Organization establishes internstional nonproprietary names (1NYs) and publishes them in TYPEOFNAME NAME Tntt'matiOna/ A!On,prO]>ri6'tar.~ X o ~ l r S(TNNj fir Pha ~ I U C ~ Y J ~ C U / United States Approved Name Acetam Inophen Sr~,bstonccs[ a ] . (USAN) 'ltvo other important sources for verifying drug names, esUnlted States Pharmacopela Acetam lnophen pecially those used outside of t h e Lnited States, are Indtbx (UsP) N O HiIn r ~ m[ 9 ] and the Il1crc.k Tndcx [ 101. Recommended lnternatlonal Nonpropr~etaryName Paracetamol Tndcx .Von~inr~m~ is edited by the Swiss Warmaceutical Soci(Rec-INN) ety and illeludes drug names from around t h e world. Most InEuropean Pharmaco~oiea Paracetamol d m .Vonlinr~,nlmonographs illelude chemical names and strucChemical names N-(4-Hydroxypheny1)acetamlde tures, generic names, proprietary names, therapeutic uses, and mal~ufacturers. 4'-Hydroxyacetan~l~de p-Acetam~nophenol Thtb Mcrch Tndtbx h a s over 10,000 monographs on drugs, Asomal (Turkey) Prop"etary names (country) commol~organic chemicals, and a variety of other substances Becetamol (Sw~tzerland) used in t h e pl~armaceuticaland chemical industries. Each Drlstanclto (Argentina) fi1crc.h Tndcx monograph illeludes t h e substance's various Progeslc (Indonesia; names (including chemical, generic, and proprietary), physical Hong Kong) constants, chemical formula and structure, patent information, Tylenol (United States therapeutic category, and literature citatiolls. and others) 7. I,XP !llc.tlc)rtc~ry of I,:.';2:2:or11i Irtturrtot~ortc~! Ilrrlg :2Tr1mrs.Rnckvillc,

rb

o a t a from MA;smith, A; ~ ~ ~p ~cds. , k ~~~~k ~ ~ l ~~ ~ Encyclopedia o f Chemicals. Drugs, and Biologicals. 13th ed. Whitehouse 8. ! l t t ~ r r t ~ellto! t l :vOrtprOprl u t c l y :vcl rnrs (!:v:v) for P h o r m o c ~ r r l t ~ c ~ r ~ !station, N]: Me(&, 2001 , and swiss pharmaceutical society, cd. Index Srrhstclrtc,vs. Cunlulntivr List Nn. 10. Grnrvn: WIIO lhttn://\r\r~t.. hlorninum- lntcrnational Drug Directory, 18th cd. Stuttgart, Germany: whn.int/rn~:2002. Avnilnhlc ns CD-ROM nnlj;. Mcdpharm. 2004.

MD: 1JS Phnrn~ncnpcinlCnnvrntinn 1 h t t n : / / \ t ~ t . w . u s ~ . nnnnunl. r~~:

d ~

,~

CHAPTER 8: INFORMATION RESOURCES IN PHARMACY AND THE PHARMACEUTICAL SCIENCES

which answer questions a b u t specific drugs and drug therapies. In addition to prescription drugs, the Drug Consults cover such topics as investigational drugs, herbal medications, and drugs of abuse. DRUGDEX monographs are written by drug information specialists. The DRUGDEX database is updated quarterly, but the individual monographs in it are not updated as frequently. Each monograph includes the date of its latest revision and its author's name. 11. Physicians* Desk Reference. Montvale, NJ: Thomson PDR (httaYhw.wdr.net), annual. 12.AHFS Drug Information. Eethesda, MD: ASHP I W w w w mg), annual.

13. Drug Facts and Comparisons. St Louis, MO: Facts and Comparisons ~~w~ 1, lme-leaf updated monthly or annual bound volume. 14.Mosby's Drug Consult. S t Louis, MO: Mosby (http:llwww.us. ,1annual. 15. USP DI, Volume I, Drug Information for the Health Care Pmfessional. Englewwd, CO: Thomson MICROMEDEX Ihttp:llwww. miF1.omedex.OOm1, annual. 16.DRUGDEX System. E n g l e w d , CO: MICROMEDEX Ihttp:/lww.

69

US Drug Compendia: Catalogs The major catalog of products commonly found in US drugstores and pharmacies is the Drug Topics Red Book [ 2 2 ] .This catalog lists average wholesale prices and manufacturers for both prescription and nonprescription prducts, including a variety of health and beauty aids. I t includes generic drug information that is often difficult to find elsewhere. The Red Book also includes other information of use to a practicing pharmacist, such as lists of the top-selling prescription drugs, and directories of poison control centers and state b a r d s of pharmacy. 22.Drug Topics Red Book. Montvale, NJ: Thomson PDR (httpYhww. @.net), annual.

'

micmrnedex.cmn), quarterly.

US Drug Compendia: Nonprescription Products The number of nonpre scription drugs and the market for them continues to grow. There are several drug compendia dedicated to these prducts and their proper use. The Handbook of Nonprescription Drugs [ 1 7 ]is organized by symptom or disorder. Each chapter includes a description of the svm~tomldisorderand available treatments. The b k includes Lblls of available drugs and their ingredients, and extensive decision trees to aid health professionals in consulting with patients about nonprescription therapies. Chapters include literature references. Nonprescription Drug Therapy [ l a ] is also arranged by symptomldisorder. While it covers the same topics as the Handbook of Nonprescription Drugs, it is much more concise. It is available as a loose-leaf service updated quarterly or as an annual bound volume. The Physicians' Desk Reference for Nonprescription Drugs and Dietary Supplements [ 1 9 ] includes participating manufacturer s' label information for nonprescription prducts.

US Drug Compendia: Physical ldentification Several of the drug compendia described a b v e include color photographs of tablets, capsules, and other dosage forms to aid in their identification. However, the most useful souroes for the physical identzcation of drugs are ones that include an index of the i d e s imprinted on the dosage forms. Both Ident-A-Drug Reference for Drug Tablet and Capsule Identification [ 2 3 ] and the IDENTIDEX System [ 2 4 ]include such an index The IDENTIDEX System also indexes the physical description (color and shape) of the dosage form and includes street drugs. In addition, the IDENTIDEX System includes monographs on the toxicology of the substances indexed. 23.Ident-A-Drug Refei-ence for Drug Tablet and Capsule Identification. Stmkton, CA:Therapeutic Research Center (http:llwww.therapeutip.eseach.oom), annual.

24.IDELWIDEX System. E n g l e w d , CO: MICROMEDEX ( & & l w w . miF1.omedex.oOm), quarterly.

US Drug Compendia: Consumer Drug Information

Drug information for consumers can be found in a variety of publications including books, newspapers, magazines, and pamphlets as well as at many websites on the Internet. This section will consider only two types of b k s : guides sold to consumers by trade publishers, and compendia sold to pharmacists and other health-care professionals by organizations better known for their professional publications. 17.&ad, RR, ed. Handbook of Nonpi-escription Drugs: An Intemctive Appmach to Self-care, 14th ed. Washington, DC: APhA Among the most popular of the consumer guides are: Grif(httpdhw.aphanet.org), 2004. fith's Complete Guide to Prescription and Nonprescription 18.Covington, TR, ed. Nonpi-escription Drug Therapy: Guiding Patient Drugs [ 2 5 ] ;Rybacki's Essential Guide to Prescription Drugs Self-caw. St. Louis: F a d s and Comparisons IhttaYhww.fadsand[ 2 6 ] ;and The Pill Book [ 2 7 ] .All of these books include basic inoomaarisons.oom),loose-leaf service updated quarterly or annual formation about drugs including the conditions they are used to volume. treat, their safe use and their possible adverse effects. 19.Physicians* Desk Reference for Nonpmscription Drugs and Dietary Patient Drug Facts [ 2 8 ] and USP DI, Volume II, Aduice for Supplements. Montvale, NJ: Thomson PDR ( ~ : / l w w w . ~ . n e t ) , the Patient [ 2 9 ] are b t h marketed to pharmacists and other annual. health-care professionals to assist them in their patient counseling activities. Patient Drug Facts includes both a quarterly loose-leaf update service and computer software. The loose-leaf US Drug Compendia: Parenterals is for use by the pharmacist in patient counseling, and the software provides customized printouts for patients. USP DI, VolParenteral drugs are those that are injected directly into the ume II, Aduice for the Patient is published annually with supM y and not absorbed through the gastrointestinal system. plements issued during the year. Pharmacists are given hissel's Handbook on Injectable Drugs [ 2 0 ] has dosage, stapermission to make copies of individual monographs for pability, and compatibility information. The Handbook also intients when filling prescriptions for the drugs. USP DI, Volume cludes monographs for some investigational drugs and for some II, Advice for the Patient is also sold directly to consumers by foreign drugs. The King Guide to Parenteral Admixtures [211 is a Consumer Reports under the title Consumer Drug Reference. comprehensivereference on the compatibilityof parenterals. This Its monographs are available free on the Internet at various work is in tabular format and includes information on the comsites including the National Library of Medicine's consumer patibility of both drug-drug and drug-infusionfluid mixtures. health site, MedlinePlus thttpJ/~~~~.medlineplus.~tov>. 20.Trissel LA. Handbook on Injectable Drugs, 12th ed. Bethesda, MD: ASHP (http:llwww .ashp.org), 2003. 25.G r i c t h HW. Complete Guide to Prescription & Nonpi-escription annual. Drugs. New York: Perigee (htta:llwnrminwu~am.oom), 21.Catania PA, ed. King Guide to Pai-enteml Admixtwes. St Louis, MO: 26.Rybacki JJ. The Essential Guide to Prescription Drugs. New York: King Guide Publications , 1- ( loose-leaf updated quarterly or annual bound volume. HqerColIins annual.

(v,

PART 1: ORIENTATION

27. Silvcrmnn: IIM: rd. T/rx, PI!! Kook. N e w Ynrk: Bnntnm h t t ~ : l h r \ t w . rnndonlhnusc.com I: l i r n n i n l . ZX.P~~cialiclacl~~s FarIt is updated quarterly. n ~ a c t ~ r ~ ~ t[i3c2a]s(Mexico), rot^ I , i s t ~[ 3 3 ] (Germany), and Vidal Il1~:vlcr'sS i d ~Efficts o f Drugs: a n Ent:vclo~>~~dia o f Ad rLTsr of Hcrbs and Rclattd Rtw~tbditbs[ 3 8 ] is written for the layperson. Each monograph iilcludes a review of the literature and recommendations from t h e author.

:I&).I I n n s t r n PD: IInrn ,JR. Ilrrlg Irrtc,rr~c~t~orts: ~ l r r c ~ l orrd ~ s ~ :Vlortclgrs rnrrtt. S t . Lnuis: Fncts nnd Cnnlpnrisnns 1 httn://\t~vw.hctsnndcnn~pnrisnns.com I. loose-lcnf u p d n t r d qunrtcrly. 40. Ilrrlg Irttrrt~c~t~c)rt F(1c.t~.S t Lnuis, MO: F n c t s nnd C n m p n r i s n n s [ httn://\r\r\r.fnctsnndcnn~~nrisnns.cnm I: l n n s r - l r n f u p d n t r d q u n r t c r l y nr nnnunl l n u n d vnlunlr. 41. ISf!ulrtt~tltlortsof Ilrrlg Irttrmc.tlc)rts. S t Lnuis, hIO: F i r s t DntnBnnk [httn://\t~vw.firstdntnhnnk.cnnl I: lnnsr-lcnf u p d n t r d (j tinlcs p r r ycnr. 42. Ilrrtg Irttrroc~t~ort F(1c.t~: Hiotir,i s 7.5 m g f i r :i r,hild. How m11t:11 of :i fl:iv r l r ~ ds l l s p p n s i r ~ nr:ont:iining 12.5 m g :intihir>tirl.i m l . m11st t > ~ g i v ~ nt o ~ I I Pr,hilri ppr r i o s ~ ? Hrm- n3;iny m g of ;i d r u g iirP t h ~ Inr ~iic:h ~ t ~ i i s p o o n f i ~ofl ii s y r l ~ p t11:it t:ont:iins 0..5',; of tllp dr11g7

REDUCING AND ENLARGING FORMULAS Uetermine the total weight or volume of ingredients and convert, if necessary, to t h e system of t h e quantities desired. The quantities in the original and new formulas will have the same ratio.

Examples 1. TIIP frn-nrn111:i for ;i s y r u p i s Drug M 1/10 g SII~,~-OSP ,130 g I flflfl m l . P ~ ~ r i fW i ~: di t ~ [IS r ;I. F i n d ~ I I P rl11:intiti~sr ~ r l u i r ~ frlr d 1flfl ml..

140 g x 100 mL 1000 mL 450 g Sucrose: x 100 mL 1000 mL

Drug >I:

-

14.0 g

-

45.0 g

Purified Water: to make 100 mL h. W11;it rl11:in t i t i ~ ;s i r ~r ~ r l ~ ~t oi rr,omprn~nd ~d 6 0 m l , of ~ I I P s y r u p ?

Urug >I:

140 g x 60 mL 1000 mL

-

8.40 g

Sucrose:

450 g 1000 mL

-

27.0 g

X

60 mL

several ingredients, are a type of formula enlargement. The expnxsion usually used i s D m , which means let such doses be given. Occasionally the p r m i b e r will not me this expression, but inspection of amounts of the ingredients indicatea that thk is what is d ~ i r e dFor . example, @ SolidH 50mg Solid K 150 mg GquidN 0.2d M ft capules, D.T.D. NO24. The pharmacist checked the individual dosea of the ingredients and found them to be slightly M o w the average adult dose, confirming that the prescriber wanted the quantities listed to be multiplied by 24.

60 mg Solid H:-X 24 ~apSule8= 1200 mg or 1.2 g capsule

Solid K: mg x 24 caps* capsule

=

Liquid N:OV2mL x 24 caps& capsule

3600 mg or 3.6 g = 4.8 mL

Problems 1. The formula for a liquid preparation b Liquid C 36 mZ, Solid B 9g Liquid R 2.6 mL Liquid P 20 mL M i e d Water, sufficient to make 100 mZ, Calculate the quantith of the ingredients to make 2.6 L. 2. The formula for an ointment is g SolidG 1 Liquid D 30 Solid M 3 Ointment b, sufficient to make 100 Calculate quantith of the ingredients for 2 lb (apoth). 3. How much of each of the three solids and how much @lied water are needed to properly compound the following pmripiion order? SolidN 0.1 mg Solid Q 2.5 mg 160.0 mg Solid R Purified Water,qs 6 mZ, M ft solution, D.T.D. No 48. 4. How much of each h g d i e n t k required to compound S4 mZ, of the following pduct? Solid S 7.5 g Solid T 25 g Oil C 350 mZ, Alcohol 250 mL M i e d Water, qs 1OOO mL

Purified Water: to make 60 mL 2. ( : i i ~ r : l ~ ~~i iI tI~P: i n ~ o l l n t sIIPPTIPTI f i r 1 0 0 g of ; i n t i s ~ p t i r ,p o n - r i ~ r:is follo\\-s: I: S O I!I~ ~ 2 g Solid R 1g Solid (: 7g Solid I) 25 g Solid E 11.5~ 1.in g

Factor

100 g 150 g

- --

0.667

Solid A : 2 g x 0.667 - 1.33 g Solid U:1 g x 0.667 - 0.667 g Solid C : 7 g x 0.667 - 4.67 g Solid U: 25 g x 0.667 - 16.7 g Solid E:115 g x 0.667 - 76.7 g 3. Prpsc:riptions, \ \ - I I P ~ P tllp instr11t:tion to ~ I I P pI~:irnl;ir,ist r:iilIs f i r m:iking ;I r:~rt;iinn l l m h ~ rof dosps of :in ingrpdipnt o r m i x t l ~ of r~

PERCENTAGE Percent, written as 5 , means per hundred. Fifteen percent is written 15qi and means 15/100. 0.15, or 15 parts in a total of 100 parts. Percent is a type of ratio and h a s units of parts per 100 parts. Thus, 10?t of 1500 tablets is 10/100 x 1500 tablets 150 tablets. To change percent to a fraction, t h e percent number becomes t h e numerator and 100 is the denominator. To change a fraction to percent, put t h e fractiol~in a form having 100 as its denominator; multiply by 100 so that the numerator becomes the percent. -- -

1 2

50 50 x 100 100'100

1 8

12.5 12.5 x 100 100' 100

-- -

-

509

-

12.5~;

Calculations involving percentages are encountered continually by pharmacists. ' r h e ~must be familiar not ollly with the arithmetical principles, but also wit11 certain compendia1 inter-

CHAPTER11:METROLOGYANDPHARMACEUTICALCALCULATIONS

pretations of the different type percentages involving solutions and mixture&. The USP states Percentage concentrations of solutions are expressed as follows:

119

Weight-in-Volume Percentages This is the type of percent problem most oRen encountered on prescriptions. The volume ompied by the solute and the volume of the solvent are not known bcause s f i c i e n t solvent is added to make a given or known hnal volume.

Pemenf weight in weight-rw /wl exprwaea the number of g of a constituentin 100 g of product.

Pemenf weight in volume--rw l v) exprwaea the number of g of a constituent in 100 mL of product, and is wed r e g a d w s of whether water m another liquid is the solvent. Percenf vohme in vo~wne-4v/v)expresses the number of rnL of a constituent in 100 mL of product.

The term percent used without qualxcation means, for mixture8 of solids, pement weight in weight; for solutions or su8pensions of solids in liquids, pement weight in volume; for solutions of liquids in liquids, pement volume in volume; and for solutions of gases in liquids, percent weight in volume. For example, a one percent solution is prepared by dissolving one g of a solid or one mL of a liquid in sufEcient of the solvent to make 100 mL of the solution.

EXAMPLES 1. Prepare 1 f 3 of a 10%solution. Since thia is a solution of a solid in a liquid, this is a w / v mlution.

logdrug x29.6xlffg22.96gdrug 100mLsoh 18 2.96 g i~ dissolved in sufficient @led water to make 29.6 mL of solution. 2. How much of a drug is required to compound 4 ff, of a 3%solution in alcohol?

3gdrug x-x4fg= 100mLsoln 18

3.5bgdrug

3. How much 0.9%mlution of sodium chloride can In?made h m X 3

of NaCl?

loo m~ s o h X- 31'1

Ratio Strength Ratio strength is another manner of e x p m i n g concentration. Such phrases as "1 in la" are understood to mean that one part of a substance is to be diluted with a diluent to make 10 parts of the h i s h e d prcduct. For example, a 1:10 solution means 1 mL of a liquid or one g of a solid dissolved in sufficient solvent to make 10 mL of solution. Ratio strength can b converted to percent by

10 mL solution

x 100 m~ solution = 10 g substance

10 g substance = 10% 100 mL solution The expression "part& per thousand" (eg, 1:5000) always means parts weight in volume when dealing with solutions of solids in liquids and is similar to the a b v e expression. A 1 : 5 0 solution means 1g of solute in sufEcient solvent to make 5000 mL of solution. This can be converted to percent by 1g substance 5000 mL solution

x 100 mL solution = 0.02 g substance

0.02 g substance = 0.02% 100 mL solution The expression "tritur ation" has two different meanings in pharmacy. One refers to the p m s s of particle-size reduction, commonly by grinding or rubbing in a mortar with the aid of a pestle. The other meaning refers to a dilution of a potent powdered drug with a suitable powdered diluent in a definite proportion by weight. It is the seoond meaning that is used in this chapter. When pharmacists refer to a "1 in 10 triturationn they mean a mixture of solids composed of 1g of drug plus s f i c i e n t diluent (another solid) to make 10 g of mixture or dilution. In this case the "1 in 10triturationn is actually a solid dilution of a drug with an inert solid. The strength of a trituration may also b stated as percent w lw. Thus, the term hitnation has come to mean a solid dilution of a potent drug with a chemically and physiologically inert solid. The meanings implied by the USP statements in the section on percentage are illustrated blow with a few examples of the the types of percentages.

x 0.5 3 = 1730 mL soln

0.9 g NaCl

13 4. How many grams of a drug are required to make 120 mL of a 26% solution?

25 drug x 120 mL = 30 g drug 100 mL soln 6. How would you prepare 480 mZ, of a 1 in 760 solution of an antimptic? Remember: percent w / v is indicated. 1 in 750 means 1 g of the antiseptic &solved in sufficient solvent to make 750 mL solution.

750 mL soln

x48OmL=0.64gdmg

Diesolve 0.64 g of antiseptic in sufficient solvent to make 480 mL solution. 6. How much of a substance is needed to prepare 1 L of a 1:10,000 solution? The ratio 1:10,000 means 1 g of a substance in 10,000 mL of solution.

1g substance

1000 mL

10,000 mL s o h

1L

x 1L = 0.1 g substance

7. How would you prepare 120 mL of 0.25%mlution of neomyein sulfate? The M U Mof ~ neomycin sulfate is a solution which cantains 1 g n e o m ~ i nsulfaWl0 mL,

10 mL stmk soln

xx 1g b g

100 mL s o h

1 2 0 m ~ s o l n= = 3 mL stock s o h

Add sufficient purified water to 3 mL of st& 120 mL.

solution to make

Problems How would you maHe of a 12.6W 2. How many liters of a 4%solution can be made bom 43 of a solid? 3. How many liters of an 8%solution can be made h m 600 g of a solid? 4. How manygrams ofadrugareneededtomab4Lofa 1 in600 solution?

120

PART 2 PHARMACEUTICS

Weight-in-Weight Percentages Density m u s t be considered in some of these problems If a weight-in-weight solution is requested on a prescription, both t h e solute and solvent m u s t be weighed, or the solute a n d t h e solvent may be measured if their densities are taken into consideration in determining the volumes Since t h e solutiol~sa r e made to a given weight, a given volume is not always obtainable

EXAMPLES 1. What weighta of mlute and mlvent are required to make 2 3 of a 3% w / w solution of a drug in alcohol?

3 gsolute 31.1 g s o h 1 0 0 g ~ h 13soln

X

2 3 soln = 1.87 g solute

31.1 g soln x 2 3 s o h = 62.2 g s o h 13 soln 62.2 g s o h

-

1.87 g solute = 60.3 g solvent

2. The solubility of h r i c acid is 1g in 18 mL of water at 26°C. What is the percent- strength,w / w , of a saturated mlution? 1g of h r i c acid + 18 mL of water make a saturated mlution, 18 dof water weighs 18g; hence, the weight of solution is 19g. The amount of h r i c acid p-t k 1g in 19 g of mlution; therefore, the following relationship can k set up:

'

drug x 100 g aoln = 5.26 g drug 19 g s o h

6.26 g drug 100 g soln

=

5.26%

3. How many grams of a chemical are needed to prepare 200 g of a 10% w / w solution? 10% W / Wmeans 10 g of solute in 100 g total mlution. The following; relationship may be set up:

10 g solute x 200 g soln = 20 g solute 100 g soln 4. How would one make a 2% w / w mlution of a drug in 240 mL of alcohol? The density of alcohol is 0.816 g/mL. a. First, convert 240 mL to weight. Rememkr: alcohol k the solvent and it has a density different h m that of water.

OV8l6 x 240 mL dmhol = 195.8 g (196 g) alcohol 1mL a h h o l b. 2% w / w means 2 g solute in 100g solution. In this problem the final weight of mlution is not known; 240 mL (196 g)of alcohol repreaents the mlvent only. The solvent is 98% w l w of the total mlution, m the following relatiomhip may h eet up:

''lute

98 g dmhol

x 196 g aloohol= 4.00 g solute

c. Dismlve 4.00 g of the drug in 240 mL alcohol. The d t i n g mlution will be 2% w / w and have a volume slightly larger than 240 mL h a m e of the volume displacement of the drug. .iHow . much of a 6% w l w solution can k made h m 28.4 g of a chemical?

100 "ln X 28.4 g chemical = 668 g soh 5 g chemical 6. How many d of a 70% w / w mlution having a density of 1.2 ghnL will k needed to prepare 600 mL of a 10% w / v solution?

a. Drug needed

'Ogbg

100 mL s o h (10%)

xMX)mLsoh(1040)=60gbg

b. Weight of 70%mlution needed

loogBoln(70%)x 60 g drug = 85.7 g s o h (70%)

70 g b g

c. Volume of 70%solution needed.

mL (7m)x 85.7 g s o h ( 7 h ) = 71.4 mL soln (70%) 1.2 g soln (70%)

Compounding problems involving solid preparations (such as mixtures of powder) and semisolid preparations (such as 0% ments, creams, and suppositories) are also percent w / w . The following is an example of this. 1. How much drug is required to make 2 3 of a 10% ointment? 10 g drug 100goht

31.1 g oint x 2 3 oint = 6.22 g drug 130int

The same @ure could be med for such mixture8 as powders and suppository masms. Instead of using units in the various measuring systems, quantitim can k indicated 'by parts." The term ws" then can mean any unit in any meas* system, BB long as the unit&are kept oomtant. 2. How many grams of each of the following three ingredients are required to malre 30 g of tbe prduct? @ SolidA 0.6 part Powder B 3.0 p& Powder C, qs 30.0 p& Sinoe the product k a mixture of powders, percent w / w is indicated. In the a h v e prmiption order tbe total p d u c t k 30 parts k a m e Powder C is umd to 'qs" or k a k e up to" 30 parts. Therefore, 0.6 g of Powder A and 3.0 g of Powder B are needed.

30 g total

-

0.5 g powder A

-

3.0 g powder B = 26.5 g powder C

3. How much of each of the following ingredients is needed to make 60 g of the ointment? @ SolidD 3.0 @ Solid E 6.0 parts Ointment Barn Q 30.0 parts 39.0 parts total

3'0gs01idD x 60goint 39.0 g oint

= 4.62

gmlidD

6'0gsolidE x 60goint 39.0 g oint

= 9.23

gmlidE

30'0gbsaeQ x 6Ogoint 39.0 g oint

= 46.2gbsaeQ

4. What is the percent strength of a salt solution obtained by diluting 100 g of a 6% solution to 200 g? ABsign the 6% mlution as mln 1 h i g n the final mlution as soln 2

6gsa1t 100gsolnl x100gsoln2=2.6salt 100 g soln 1 x 200 g soh2 2.5ggsoln 2 100

= 2.5% wb

Problems 1. How much of the drug and mlolvent are needed to compound the following presaiption? @ CompoundA 6% w/w Solvent, qs 43 2. How many grams of solute are needed to prepare 240 g of a 12% w /w eolution? 3. H o w m a n y k g o f a 2 ~ w / w s o l u t i o n c a n h m a d e ~ o1 mkgofthe solute? 4. How would you prepare, mhg 120 mL of glycerin ( h i t y , 1.25 ghnL), a solution that is 3% w / w with respct to a drug?

CHAPTER 11: METROLOGY AND PHARMACEUTICALCALCULATIONS

5. How much of each substance is needed to prepare a total of 24 g

of the following suppository mass? Compound K 0.3 g Solid H 0.15 g Suppository base, qs 2.0 g 6. How would one prepare 600 mL of a 15% w / w aqueous solution? 7. How much of each of the ingredients is required to make 1 kg of tbe following mixture? Powder P 1 part Powder Q 8 parts PowderR 12p& Powder S 16 parts Total 36 parts 8. How much of each *dent is required to prepare the followhg ointment? @ Coal Tar Solution 10% Hydrophilic Ointment, qs 30 g

Volume-in-Volume Percentages A direct calculation of percentage from the total volume is made. Volumes, unlike weights, may not be additive. However, this does not p w e n t a problem bcause the h a 1 solution is made up to the desired volume with the diluent.

1. How many minims of a liquid are needed to make 6 a of a hand lotion containing 0.6% v / v of the liquid?

0.5 mL liq 29.6 mL lotion 100 mL lotion 1ff lotion x 6 8 lotion = 14.4 TT31 liq

Add sufficient lotion to 14.4 m of the liquid to make 6 a of the pduct. 2. How much S W c alcohol is required to compound 600 mL of a 10% alcohol mixture?

100 mL (90%) 90 mL alcohol

In the case of potent substanm, a properly prepared stmk solution permits the phmmacist to obtain accurately a quantity of solid that might otherwise be diiEcult to weigh. In the case of frequently prescribd salt solutions, a st& solution readily amount of salt without the necessity of provides the weighing and dissolving it every time. Stmk solutions may Iw of various cancentrations depending on the requirements for use. The stmk solutions should be 1ab l e d properly and fractional p a r k needed to make various strengths also may be listed as a further convenience. There is a type of compounding and dispensing problem that involves the cancept of stock solutions. This involves the pa-

~~

tient diluting a dose from the prescription order to a given volume to obtain a solution of desired cancentration. For example, how many grams of a salt are required to make 90 mL of a stock solution, 5 mL of which makes a 1:3000 solution when diluted to 500 mL? Assign the stmk solution as Soln 1 Assign the k a l dilution as Soln 2 I g salt 3000 mL soln 2

500mLs0h2 x 9 0 m l s o l n l = 3.0gsalt 5 mL soln 1

Problems

Examples

16.2 W liq 1mL liq

121

10 mL &oh01 100 mL (10%)

500 ml ( 1 ~ )

Problems 1. How many minims of a liquid are needed to make 4 a of a 12.6% v / v solution? 2. What volume of 60% v / v alcohol could be prepared kom 1 L of 96% v / v alcobol? 3. What is the percent- streng;th, weight in weight, of a liquid made by dholving 16 g of a salt in 30 mL of water? 4. How much drug will h required to prepare 1 a of a 2.6% solution? 5. What is the percentage, weight in weight, of sugar in a syrup made by dissolving 6 kg of sugar in 8 kg of water? 6. How many grams of a drug are required to prepare 120 mL of a 12.6% aqueous solution? 7. How much drug is needed to compound a liter of a 1:2600 aqueous solution? 8. A mlution contains 37% of active ingredient. How much of this solution is needed to prepare 480 mL of an aqueous mlution oontknhg 2.6% of the active ingredient? 9. How much of a drug is required to make 2 qt of a 1:1200 solution?

STOCK SOLUTIONS To facilitate the dispensing of certain soluble substances, the pharmacist frequently p r e p a w or purchases solutions of high cancentration. Portions of these concentrated solutions are diluted to give required solutions of lesser strength. These cancentrated solutions are known as stock solutions. This p r w dure is satisfactory if the substanoes are stable in solution or if the solutions are to be used bfore they deoompose.

1. How much of a drug is needed to compound 120 mL of a pnxmiption order such that when 1 teaapmnful of the solution is diluted to 1 qt, a 1:760 solution results? 2. How many grams of a drug are needed to make 240 mL of a solution ofsuchshngth that when 5 mL is diluted to 2 qt, a 12500 solution mulh? 3. An ampule of mlution of an anti-inflammatory drug contains 4 mg of d&mL. What volume of tbe mlution is needed to prepare a liter of solution that contains 2 I L of~ the drughnL?

PARTS PER MILLION An e x p w i o n that is masionally used in campounding prescriptions is parts per million (ppm). This is another way of expressing cancentration, particularly cancentr ations of very dilute preparations. A 1% solution may be expressed as 1 psrU100; a 0.1% solution is 0.1 p a r t d l 0 or 1parU1000. A one ppm solution contains 1 part of solutdl million parts of solution; 6 ppm is 5 part&soluten million part&solution, and so on. Remembr that the two p m b must have the same units, except in the metric system where one g = one mL of water. Sodium fluoride is a drug that may b prescrikl by a dentist as a preventative for tooth decay in children. It is used only in very dilute solutions due to the drug's toxicity and h a u s e only minute quantities are needed. For example, how much sodium fluoride would be needed to prepare the following pr+ scription? B S d Fluoride, qs P u a d water, qs 60 mL Make soln such that when 1B is diluted to 1 glassful of water a 2 ppm soln results. Sig: 1f3 in a glassful of water a day. The mathematics to solve this campounding problem are easy once the steps for calculating the answer are outlined. This problem should be worked "backward." a. The amount of NaF needed is not known. b. One ghsful of water has a volume of 240 mL. The concentration of N& in 240 mL is 2 ppm. c. The NaF mlution poured into the g k came bom a teasp~onful d m (1 f3 1, which is equal to 6 mL. d. The 6-mL dose came h m the preaaiption order h t t l e containing a NaF solution.

2 g NaF 1 , 0 , 0 0 0 mL dilution

X

240 mL dilution 5 m ~X 6 0~* Q

CHAPTER 11 : METROLOGY AND PHARMACEUTICAL CALCULATIONS

123

There is a total of 14.0 g of active i n w e n t in 190 g of total mixture.

In a total of 66 parts, 20 parts of 96% alcohol + 46 parts of 30% alcohol are needed. Since the total is proportional to 500 d, the following can h calculated.

l4.Ogbg x 100gmixture = 7.37 g h g 190 g mixture 7.37 g h g 100 g mixture = 7.37%

20 parts (mL) 95% x 500 (mL) 60% = 164 mL 95% 65 parts (mL) 50%

Problems

Since w l u m e ~are not additive, s d c i e n t water may h needed to

1. What percent of a drug i~ contained in a mixture of powder consisting; of 0.6 kg, containing;0.038% of a drug, and 10 kg, contain-

ing 0.043% of a drug? 2. What is the streng;th of a mixture p d u d by combining;the following;lots of alcohol2 L of 96%, 2 L of SO%,and 7 L of 60%? 3. What is the p m n t of drug content in the followingmixture: 2 kg of 3%, 300 g of 2.6%, and 600 g of 4.2% =in?

make 500 mL. 3. How many grams of an ointment containing; 0.18% of active in-

@kt

must ke mixed with 60 grams of an ointment w n t w

0.14% of active ingredient to make a p d u c t containing 0.15% of

active hgdient?

ALLlGATlON ALTERNATE Alligation is a rapid m e t h d of calculation that is useful to the pharmacist. The name is derived from the Latin alligatio, meaning the act of attaching, and it refers to lines drawn during calculation to bind quantities together. This methcd is used to find the proportions in which substances of different strengths or cancentrations must be mixed to yield a mixture of desired strength or concentration. When the proportion is found, a calculation may be performed to find the exact amounts of the substances required.

0.14%

/ \ 0.03 p&

of0.14% 0.04 parts of 0.15%

(g) x 50 g 0.14% = 16.6 g 0.18% 0.03 parts (g) 0.14%

OVo1

4. Occasionally, it is neoessary for a pharmacist to inmase the sixength of a p d u c t . For example, a preaaiption mlh for 60 g of a 10% ointment. The pharmacist only has a 6% ointment and the

pure ingredient available. How much of tbe 6% ointment and the pure ingredient are needed to compound the premripiion?

Rules 1. Line up the concentrations of all the startkg materials in a ver-

tical column in order of concentration, traditionally from high to low. Pure drugs are defined as king 100%; mlvents or vehiclea are designated as 0%. 2. Place tbe conoentration of the desired prduct in a ~econd column such that it is bracketed by concentrationsof starting; materials. d d u c t simply falls hWith two stadkg materials, the d ~ i r e p tween the two. 3. Cross subtract the two columns to give a parts formula that can be dto calculate spciflc amounts of each starting material.

5%

/

\90p*of5% 95 parts of 10%

p*(g)lm x 5 0 g 10% = 2.63 g 100% 95 % parts (g)10%

Examples and Procedure 1. In what proportion must a preparation containkg 10% of drug h mixed with one containkg 15% of drug to @uoe a mixture of 12% drug strength?

Applying the a h v e rulm gives:

15%\

10%

/

f 2parta0f15% \3partaofl(Wo 6 parts of 12%

The conoentrations of the s t a d k g material are lined up in the rust column in decreasing or increasing order and the d & d percent or conoentration is placed in the center column. The third column i~ obtained by cross-subtracting as indicated by the arrows and g i v a~parts formula for mixing the two s t d i n g mater i a l ~Thus, . mixing 2 parts of 16% drug preparation with 3 parts of 10% drug preparation will pmduce 5 parts of a drug mixture of tbe h i r e d 12% strength. 2. In what proportion mmt 30% alcohol and 95% alcohol h mixed to make 500 mL of 60% ahhol? Set up the problem in the following manner:

30%

/

\ 4 6 p66 && parts o f 3of 0% 60%

Problems 1. How much ointment containing 12% drug and bow much ointment containing 16% drug must h used to make 1kg of a prduct containing; 12.6% drug? 2. In what proportion should 50% alcohol and pufied water be mixed to make a 35% alcohol solution? (The purified water is 0%

alcohol.) Nobe: This problem may k solved by a methd other than *ation as was shown ahve. 3. How many grams of 28% w / w ammonia water should h added to 500 g of 6% w /w ammonia water to p d u o e a 10% w / w ammonia conoentxation? 4. How many mL of 20% d e x h e in water and how many mL of 50% dextrosein water are needed to make 1L of 35% dextrosein water?

PROOF SPIRIT For tax purposes, the US government calculates the strength of pure or absolute alcohol (herein r e f e d to as C A O H ) by means ofproof degrees. This means that 100p m f spirit contains 50%(by volume) or 42.49% (by weight) of C a O H , and its s-c gravity is 0.93426 at 60°F. Thus,2 proof degrea equals 1% (by volume) of C a O H . One p m f gallon is one gal of 50% (by volume) of C a O H at 15.56"C (60°F). In other words, a p m f gallon is a gallon that oontains l/2 gal of C a O H . A proof gallon is 100proof. The tern 10 degrees under proof (10" up) signifies that 1100 volumes of the spirit contains 90 volumes of proof spirit plus 10

124

PART 2: PHARMACEUTICS

volumes of water, and 30 drgrrrs or'cr proof (30' op) indicates t h a t 100 volumes diluted with waterjlelds 130 volumes of proof spirit. To prepare proof spirit, 50 volumes of C2115011are mixed with 53.71volumes ofwater to allow for the contraction t h a t occurs to yield 100 volumes of product. The terms p r o o f s trcngth, proof gullon, and proof spirit are used so t h a t t h e tax is levied only on t h e actual quantity of C2115011contained in any mixture. 'r~erefore,it is sometimes necessary for the pl~armacistto colnvert alcohol purchased to proof strength to compute tax ref~unds or colnvert proof strengths to percent for compounding purposes. h quantity of solutioln that colntailns 1/2 gal of C2115011is

because the solid will take u p a certain volume. Only 120 mL would be dispensed. What is the hr>II!SP i s 9sr.; t! / I!; thprpfi>rp,

proof gal

gal x 5 strength 504;

- -

+ 16 g drug = 136 g solution

136 legdrug g solution x 100gmlution

1/8 gal x 9 5 5 50':; -

1. What is the solubility of a chemical if a saturated aqueous mlution is 0.6%w /w? 2. How many grams are needed to make 500 mL of a saturated mlution if 1 g of the solute is soluble in 14 mL of mlvent?

'rlequalltities of

admillistered topatiellts are usually expressed by tile term n l i ~ l i t ~ q l l , i r ~ u( ~m6~~ nq t),sr,l e reasoll t h a t weight ~ulnits(mg, g) are not used is because t h e electrical activity of the ions, which in this ilnstallce is important, may be best expressed as mEq. (See Chapter 17 for additiolnal discussioln on electrolytic equilibria.) 11mEq is 1/1000 of a n 6>yr~,irw/6>nt (Eq),11n Eq is the weight of a substalnce that combines with or replaces one gram-atomic weight (g-at w t ) ofhydrogen. 1n pharmacy the terms equivalent and equivalent weight ((Eqwt) have been used interchangeably. For problem solving it is colnvelnielnt to identify t h e molar weight iin terms of mg per mmol and the number of mEq per mmol as follows:

0.2375 proof gal

g mole

gal x 5 strength 500; 0.5 proof gal x 50?t 49!t - 0.510 gal

Proof gal gal -

mE q mol

--

thprpfi>rp,

-

Problems 1 . H o w n ~ ; i n yproof g:illr>ns:irp thprp in 1 q t of

;i

p r ~ p i i r i i t i o nthiit i s

1 ; i h ~ l ~7Sr,i d I! / I ! ;i1~:01101:~

2. Hen- n ~ ; i n yproof' g;illr>ns:irp thprp in

;i

pint of ;in ~ l l x i rtl1:it c:on-

t:iins 1 ,lr,i :il~:o1101:~ 3. H o w n111t:h Di111t~d!\lr:r>hr>l1!SP r:;in tw m:idp from 1 g:il of' 190 proof' ;ilt:ol1ol:~

SATURATED SOLUTIONS Occasionally, it is necessary for a pharmacist to make saturated solutions. Solubility 111 t h e L'SP/NF is expressed as the number of milliliters of a solvent t h a t will dissolve one g of a solid; for example, one g dissolves in 0.5 mL of water. I n other words, if one g of a solid is dissolved in 0.5 mL of water, a saturated solution results, AH example will illustrate this. IIow much of a drug is needed to make 120 mL of a saturated solutioln if one g of the drug dissolr~esin 7.5 mL of water'? Calculate t h e amount of drug t h a t can be dissolved in 120 mL water. 1g drug x 120 mL water 7.5 mL water

-

-

16 g drug

When 16 g of the drug are dissolved in 120 mL of water, a saturated solution results t h a t h a s a volume greater than 120 mL

-

mg mmol

- -- - -

2. Horn- n111~:11l3il11t~d!\l~:ol~ol1!SP L::~II t > n~~ ; i df r~o n ~1 q t of':il~:ol~ol I! / I ! ;

11.8ghg

11.8ghg 11.8%w/w 100 g solution -

Molecular weight I:it>pIpd 1/2 proof g:illon? D i l u t ~ d!\lhr>l1!SP i s ,19',;

=

MILLIEQUIVALENTS

The second equatioln is t h e same a s t h e first because proof strength is always twice t h e ':t r < / r < strength. With these equations, given any two variables the third can be calculated.

1 pt

120 g (mL) water

valelnce

For example, KC1 has a molecular weight of 74.5; t h e above parameters would be 74.5 mg-/mmol and one mEq/mmol. Water of hydrati011 colntributes to t h e molecular weight (mol w t ) of a compound but not to the valence, and t h e total mol wt is used to calculate mEq.

Examples 1. Calcium (CaZf)hBB a gram-atomic weight of 40.08. Determine the number of mEs/mmol. As tbe valence of the calcium ion is 2, there are 2 mEs/mmol. 2. Amlution(100mL) that oontah 409.6 mgof NaCV100mLhas how many mEq of Naf and Cl? The molecular weight of NaCl is 68.5.

1 mEq C11 mEq Na+ There is mmol NaC1 and mmol NaCl 1 mEq C11 mmol NaCl 409.5 mg Nac1 mL mm01 NaC1 68.6 mg NaC1 100 x 100 mL= 7.0 mEq C1-

Since NaCl is a 1:l electrolyte, the solution oontains 7.0 mEq of C1- and 7.0 mEq of Naf. 3. A prescription order calls for a 500 mL solution of p o h i u m chloride to h made rn that it will oontain 400 mEq of Kf. How many

grams of KC1 h o l wt: 74.6) are needed?

1 mEq

1gKC1 1 0 mg KC1

74.5 mg and mmol mmol 74.6mgKC1x1mmolKC1

' mmol KC1

mEq K+ x 400 mEq K+ = 29.8 g KC1

CHAPTER 11 : METROLOGY AND PHARMACEUTICAL CALCULATIONS

4. How many mEq of Kf are in a 260-mg tablet of potassium phenoxymethyl penicillin 61-101 wt: 388.6; valence: I)?

1mEq Kf mmol Pen

1mEq Kf 388.5 mg Pen mmol Pen and m m o l ~ e n 1mmol Pen 250 mg Pen 388.5 mg Pen Tab X 1Tab = 0 . 6 4 mEq Kf

6. How many mEq of Mg are there in 1 0 mL of a 50% M a g n ~ ~ i u m Sulfate ~qjection?The mol wt of M ~ S O . 7~H P is 246.

2 mEq MgW 2 mEq M$+ mmol drug

246 mg drug mmol drug and mmol drug 1mmol drug 1000 mg drug 50 g drug 100 mL 246 mg drug g drug X 10 mL = 40.7 mEq M$+

TEMPERATURE Rules The relationship of Centigrade (C) and Fahrenheit (I degrees ?)is: 9 ("C) = 5 PF) - 160 Where "C is the number of degrees Centigrade, and "F is the number of d e g r e s Fahrenheit.

Examples 1. Convert 7 7 " ~ into "C.

9 (OC) = 5 (77) - 160

oc = 385 9 160 = 25°C -

2. Convert 10°C into "F.

6. A vial of W u m Chloride Injection contains 3 mEq/mL. What is the percentage strength of this solution? The mol wt of NaCl is 58.5.

9 (10) = 5 (TI - 160 0

1mEq and 58.5 mg 1g

58.5 mg

1OOOmg X~

mmol 1mmol x-x1mEq

-17'6g

100 mL

-

mmol 3mEq mL

F = 90+160= 5 0 " ~ 5

Problems X

100 mL = 17.6 g

17.6%

Problems

coned a. b. c. d.

30°C into "F 100°C into T 37°C into "F 120°F into "C

REFERENCES

1. What is the mEq wt of ferrous ion ( ~ e ' + ) which has a atomic weight of 55.86 g? 2. What is the mEq wt of s d u m phosphate (Na2HP04. 7H20)? 3. How many mEq of Naf a r e in 60 mZ, of a 6% solution of sodium saocharin (mol wt: 241 g; valence: 1P 4. How many mEq of CaZf a r e there in a W 0 - q calcium lactate pentahydrate h o l wt: 308.30 g) tablet? 5. How many mEq of s d u m are there in a 6 gr sodium bicarhnate tablet? The mol wt of NaHC03 is 84 and t h e valence is 1. 6. How many mEq of Na are there in 600 mZ, of l/Z n o m d d h e m lution? Normal saline solution contabu 9 g NaCVL, mol wt NaCl is 58.5. 7. How much KC1 is needed t o make a pint of syrup that contains 1 0 mEq of K+ in each tabhpoonful? The mol wt of KC1 is 74.5.

1. Speciftmtwns, Tolerances, and Other Technical Requf ensents fir W&hing and Measutsng Devices. NBS H a n d b k 44. Washington DC:US Department of Commerce, NBS, USGPO, 1989. 2. Goldstein SW, M a h k s AM. Profesmond Equilibkurn and Compounding Accuracy (pamphlet ). W a s h i q h n DC:AHA, 1967. 3. USP XXW, 2003. 4. Morrell CA, Ordway EM. Drug Std 1954; 22216. 6. Madlon-Ihy DF, Mosch FS. J h d y h c d 2000,4%8):741. 6. Shirkey HC. Dosage (pomlogy). In Shirkey HC, ed. Pediatk Therrapy, 6 t h ed. S t Louis:Mosby, 1975, p 19. 7. Benitz WE, Tatro DS. The Pediat#c Drug H a n d b d , 3rd ed. S t Lo&. Mosby, 1996. 8. Nebon JD. Pocketbook of Pediatk Antimicrobid Therapy, 4th ed. Dallas. J@dane, 1981.

ANSWERS TO PROBLEMS DENSITY

DNtStON 1. 769 caps& 2. 160 dosea 3. 13% caps&

ADDITION 1. 2480 g o r 2.48 kg 2. 1160 g or 1.16 kg

125

+ 15 mg remainder + 300 mg remainder

CONVERSIONS 1.

SUBTRACTION

a. b. c. d. e. f.

422 mg 19.4 mg 109g 7780mg 99.4 g 464g

a. b. c. d. e.

1lb, 3 oz, 173 gr 6.94 gr l k , 5 3,6 3 , 2 6 gr 0.00164 gr 2.2 1b

2.

MULTIPUCATION 3.

a. 0.648 mg b. 0.203 mg

126

PART 2: PHARMACEUTICS

r:. 10.8 mg d. 0.325 or 0.324 g P . 1.299 or 1.296 g 4. ;I.

12.3 n11,

7. Powder P 27.8 g Powder Q 222 g Powder R 333 g Powder S 416 g 8. 3 g of d tar solution;27 g of hydrophilic ointment

t>. 1 1 . 1 ml. r,. 237 n11, d. ,173 n11, P . 0.309 ml. f 0.00l.i4 g r g. 0.0772 g r :I.

,180 g r h. 8 3 r:. ,137 lP2 g r d. 2880 g r P . '13, l o p ;I.

PERCENT ( v / v , w / v , and w / w ) 1.240 TT31 2.1mJnL 3. 34.8%w /w 4. 0.740 gr 5. 38.6%w / w 6. 16 g 7. 0.4 g 8. 32.4 mLof a 37%solution 9. 1.68 g

DOSAGE CALCULATION STOCK SOLUTtONS

PARTS PER MILLION PROBLEM-SOLVING METHODOLOGY 1 . D.T.D. No. 1.1 m ~ ; i n d s i s p ~ n 1.1 s ~s11~,11d r l s ~ s!\ss~lming . t h dosps ~ 11:iv~t w ~ n< : I l ~ r , k ~t dh, ~ iirP y f i r < : h ~ n ~ i ~ :.J,i l lK, s ;ind 1. I 1 0 mg, .50

mg, a n d 300 mg, r ~ s p ~ r : t i v ~ l y ) . 2. D r u g Q: 0.5 g Drug R: 0.3 g 3. 0.469 ml.Mos~;1.88 ml./ri;iy ,I. 50 dosps 5. 0.0,1,1,1 m g

DILUTION AND CONCENTRATION 1. 9 g of 10%meam and 21 g of diluent (base) 2. 0.01 g 3. 40g

MfXING PRODUCTS OF DIFFERENT STRENGTHS

REDUCING AND ENLARGING 1 . 1,iqllid (: 875 n11,

Solid R 225 g 1,iqllid R 62.5 n11, 1,iqllid P 300 n11, 2. Solid ( i 7-46 g I.irl111d D 22.1 g Soliri M 22.4 g R ~ S ,192 P g 3. Solid N ,1.8 nIg Solid Q 120 m g Solid R 7.2 g !\rid s ~ ~ t f i r : ipllrifi~ri ~nt w:itpr to m : i k ~8/10 m l , s o l ~ ~ t i o n ,I. Solid S 0.67,; g Soliri T 2.2.5 g Oil (: ?I.,; n11, !\lt:ol1ol 22.,i n11,

ALLIGATION ALTERNATE 1. 2. 3. 4.

875 g of 12%ointment and 125 g of 16%ointment 35 parts of 5O?k alcohol and 16 of purified water 139 g of 28%ammonia water 500 mL each of tbe 20%and 60% solutions are needed

PROOF SPIRIT 1. 0.376 p f gal 2. 0.036 p f gal 3. 1.94 gal

SATURATED SOLUTIONS 1. 1 gin 199mL 2. 35.7 gof m l u t d p e n s e 500mL

PERCENTAGE fl!

I f!

~so~fltfoll,s

1 . Dissolvp 1 1 . 1 g in suffi S:

where

camparing two means. The F distribution is used to campare two variances, F being defined by the ratio of the variances, with nl - 1 DF in the numerator and nz - 1 DF in the denominator of the ratio Fgi,-,,mm-l = s'f/sf Similar to the chi-square distribution, the F distribution consists of only positive values and is a skewed distribution. The ratio of two variances is compared to values in the F table (Table 12- 15") with the appropriate DF in the numerator and denominator to test for statistical significance. If the calculated the value in the table at a given level, the variratio level of significanoe. ~h~ following two exantes differ at the amples describe the use of the test for comparing variances for independent and dependent samples. Example 17 shows a test to compare the variances of two independent samples using the F test. Example 18 shows the test for comparing variances in related or paired samples, which

143

s3

- 2 xyj - (2x l z ~ =/ larger ~~l vanance

'-

St

?al-1

- Z ~x - (Z .~,,jVn~ = smaller variance w2- 1

To test for signilkance, the F ratio is referred to the F table (see Table 12-15) with f l = n l - 1 and fi = n z - 1 DF. The null hypothesis that the two variances are the same is rejected at the 2P level of significance. Example 17-Two treatments showed the results in Table 12-16. Entering Table 12-15 with fi = 6 and f 2 = 5 DF, we find that the tabulated values of F are 4.95 and 6.98 for P = 2 (0.05) = 0.10 and P = 2 (0.025) = 0.05, respectively. Thus, the probabilityof getting a value of F larger than the calculated vaIue 5.75 is between P = 0.05 and P = 0.10. Since P i s not equal to or less than 0.05, we conclude that there is insufficient evidence to indicate that the two varianoes are different. If it is desired to compare the variances fmm p a i d data, the F test described above would be inappropriate. Instead, proceed as exemplified below.

Table 12-15. The F Table lo%, 5%, 2.5%, and I% PointF for the Distribution of F fl

Tz

5

10

15

20

25

30

40

60

120

=

DEGREES OF FREEWM (FOR GREATER MEAN SQUARE)

P

1

2

3

4

5

6

7

8

9

10

20

M

40

60

120

r

0.10 0.05 0.025 0.01 0.10 0.05 0.025 0.01 0.10 0.05 0.025 0.01 0.10 0.05 0.025 0.01 0.10 0.05 0.025 0.01 0.10 0.05 0.025 0.01 0.10 0.05 0.025 0.01 0.10 0.05 0.025 0.01 0.10 0.05 0.025 0.01 0.10 0.05 0.025 0.01

4.06 6.61 10.01 16.26 3.28 4.96 6.94 10.04 3.07 4.54 6.20 8.68 2.97 4.35 5.87 8.10 2.92 4.24 5.69 7.77 2.88 4.17 5.57 7.56 2.84 4.08 5.42 7.31 2.79 4.00 5.29 7.08 2.75 3.92 5.15 6.85 2.71 3.84 5.02 6.64

3.78 5.79 8.43 13.27 2.92 4.10 5.46 7.56 2.70 3.68 4.76 6.36 2.59 3.49 4.46 5.85 2.53 3.39 4.29 5.57 2.49 3.32 4.18 5.39 2.44 3.23 4.05 5.18 2.39 3.15 3.93 4.98 2.35 3.07 3.80 4.79 2.30 3.00 3.69 4.60

3.62 5.41 7.76 12.06 2.73 3.71 4.83 6.55 2.49 3.29 4.15 5.42 2.38 3.10 3.86 4.94 2.32 2.99 3.69 4.68 2.28 2.92 3.59 4.51 2.23 2.84 3.46 4.31 2.18 2.76 3.34 4.13 2.13 2.68 3.23 3.95 2.08 2.60 3.12 3.78

3.52 5.19 7.39 11.39 2.61 3.4-8 4.47 5.99 2.36 3.06 3.80 4.89 2.25 2.87 3.51 4.43 2.18 2.76 3.35 4.18 2.14 2.69 3.25 4.02 2.09 2.61 3.13 3.83 2.04 2.53 3.01 3.65 1.99 2.45 2.89 3.48 1.94 2.37 2.79 3.32

3.45 5.05 7.15 10.97 2.52 3.33 4.24 5.64 2.27 2.90 3.58 4.56 2.16 2.71 3.29 4.10 2.09 2.60 3.13 3.86 2.05 2.53 3.03 3.70 2.00 2.45 2.90 3.51 1.95 2.37 2.79 3.34 1.90 2.29 2.67 3.17 1.85 2.21 2.57 3.02

3.40 4.95 6.98 10.67 2.46 3.22 4.07 5.39 2.21 2.79 3.41 4.32 2.09 2.60 3.13 3.87 2.02 2.49 2.97 3.63 1.98 2.42 2.87 3.47 1.93 2.34 2.74 3.29 1.87 2.25 2.63 3.12 1.82 2.18 2.52 2.96 1.77 2.10 2.41 2.80

3.37 4.88 6.85 10.45 2.41 3.14 3.95 5.21 2.16 2.71 3.29 4.14 2.04 2.51 3.01 3.71 1.97 2.40 2.85 3.46 1.93 2.33 2.75 3.30 1.87 2.25 2.62 3.12 1.82 2.17 2.51 2.95 1.77 2.09 2.39 2.79 1.72 2.01 2.29 2.64

3.34 4.82 6.76 10.27 2.38 3.07 3.85 5.06 2.12 2.64 3.20 4.00 2.00 2.45 2.91 3.56 1.93 2.34 2.75 3.32 1.88 2.27 2.65 3.17 1.83 2.18 2.53 2.99 1.77 2.10 2.41 2.82 1.72 2.02 2.30 2.66 1.67 1.94 2.19 2.51

3.32 4.77 6.68 10.15 2.35 3.02 3.78 4.95 2.09 2.59 3.12 3.89 1.96 2.39 2.84 3.45 1.89 2.28 2.68 3.21 1.85 2.21 2.57 3.06 1.79 2.12 2.45 2.88 1.74 2.04 2.33 2.72 1.68 1.96 2.22 2.56 1.63 1.88 2.11 2.41

3.30 4.74 6.62 10.05 2.32 2.98 3.72 4.85 2.06 2.54 3.06 3.80 1.94 2.35 2.77 3.37 1.87 2.24 2.61 3.13 1.82 2.16 2.51 2.98 1.76 2.08 2.39 2.80 1.71 1.99 2.27 2.63 1.65 1.91 2.16 2.47 1.60 1.83 2.05 2.32

3.21 4.56 6.33 9.55 2.20 2.77 3.42 4.41 1.92 2.33 2.76 3.36 1.79 2.12 2.46 2.94 1.72 2.01 2.30 2.70 1.67 1.93 2.20 2.55 1.61 1.84 2.07 2.37 1.54 1.75 1.94 2.20 1.48 1.66 1.82 2.03 1.42 1.57 1.71 1.87

3.17 4.50 6.23 9.38 2.16 2.70 3.31 4.25 1.87 2.25 2.64 3.20 1.74 2.04 2.35 2.77 1.66 1.92 2.18 2.54 1.61 1.84 2.07 2.38 1.54 1.74 1.94 2.20 1.48 1.65 1.82 2.03 1.41 1.55 1.69 1.86 1.34 1.46 1.57 1.69

3.16 4.46 6.18 9.29 2.13 2.66 3.26 4.17 1.85 2.20 2.58 3.12 1.71 1.99 2.29 2.69 1.63 1.87 2.12 2.45 1.57 1.79 2.01 2.29 1.51 1.69 1.88 2.11 1.44 1.59 1.74 1.93 1.37 1.50 1.61 1.76 1.30 1.39 1.48 1.59

3.14 4.43 6.12 9.20 2.11 2.62 3.20 4.08 1.82 2.16 2.52 3.05 1.68 1.95 2.22 2.61 1.59 1.82 2.05 2.36 1.54 1.74 1.94 2.21 1.47 1.64 1.80 2.02 1.40 1.53 1.67 1.84 1.32 1.43 1.53 1.66 1.24 1.32 1.39 1.47

3.12 4.40 6.07 9.11 2.08 2.58 3.14 4.00 1.79 2.11 2.46 2.96 1.64 1.90 2.16 2.52 1.56 1.77 1.98 2.27 1.50 1.68 1.87 2.11 1.42 1.58 1.72 1.92 1.35 1.47 1.58 1.73 1.26 1.35 1.43 1.53 1.17 1.22 1.27 1.32

3.10 4.36 6.02 9.02 2.06 2.54 3.08 3.91 1.76 2.07 2.40 2.87 1.61 1.84 2.09 2.42 1.52 1.71 1.91 2.17 1.46 1.62 1.79 2.01 1.38 1.51 1.64 1.81 1.29 1.39 1.48 1.60 1.19 1.25 1.31 1.38 1.00 1.00 1.00 1.00

Adapted from Snedecor W, Cochran WG. Statistical Methods, 7th ed. Ames: Iowa State University Press, 19M.

145

CHA!TER 12: STATISTICS

treatments are different. Some or all of the treatments may Iw different. Various multiple-oompan prc~wlureshave k e n proposed to solve this problem. It is not always apparent when a particular pmedure is best, given the variety of prooedum available. Several of these tests are d e m i k l here, with discussion of their application. The general p m d u r e is to list the ranked means from lowest to highest and underline the means that are not statistically si@cantly different h m each other. Sometimes brackets or parentheses are used instead of an underline. The pwedure is carried out by calculating a 5% allowance, which is d e h e d as the critical difference between means which allows one to reject the null hypothesis ( w = pj) and accept the alternativehypothesis Iki # kj) for any two sample means Ti and Tj at P = 0.05. TOcalculate the 5% allowthe data is reqa.

Table 12-18. ANOVA for Example 19 ANALYSIS OF VARIANCE M U RCE OF VARIATDN

DEGREES OF FREEDOM

Between regimens Within regimens Total

t-1=9

160.54

Z (n1- 1)" = 20

17.81

8.22

9 = 2.17

43.33

N-1=29

* x(ni - l ) = hr

,,,,

SU MSOFMEAN SQUARES SQUARES

203.87

- t.

The ratio BMS~WMShas an F distribution under the null hypothesis, with (t - 1)DF in the numerator and (N- t) DF in the denominator. If the ratio exceeds the appropriate F value found in the table, then at least two of the treatments tested are significantly different. The computations consist of simple arithmetic, summing individual values and their s q u m . The following numerical example illustrates the computations and should clmify these ~ l t h it~always ~ ~ is h usefulto practice some calculations, computer programs are available that should IE used for most practical situations. fiawle 19-&ups of three subjects each were given one of 10fwd

2 = poled

from heanalysis DF = d m of beedom for the pooled variance bom the anal+ of variance. nl,nj = the n u m k of obmrvationsh m which the means Fl and ?jwere determined, mgectivel~. t = a critical value at P = 0.06 which depends upon the DF and the de-

~ ~ ~ ~ , " ~ ~ ~ ~ ~ , eb~x e m ~ l i f i e d

Least S@nificantDifference Procedure-For this p

regimens and showed the weight gains Ub)in Table 12-19. T h ~are e unpaired data, and this type of study ia referred to as a oompletely randomized experiment. There are only two souroes of variation; the variation ktween regimens and the variation within regimens, as indicated in Table 12-18. The s u m s - o f - s q m are obtained as Total SS = Z'.2

-

5% allowance = t

(VZ+ -(312 +...+---

=-

3

ad2

G21oY2

N

"n,

n1

(16)'

(148)2

3

30

3

"s

- 160.54 = 43.33

and t = 2.086 from Table 12-10 for 20 DF and P = 0.05 (two tails).

The mean qm are obtained by dividing the sums-of-sqm by their oorreaponding DF. The mean square within regimens, 2,is the p~oledvariance for the 10 samplm. Since this is the only variance that -hidentifiedasrandomaamplingerror(hem-sq-ktwregimens haa in addition a component due to the variability among regh e m ) , it b m a the denominator in the F ratio, so that

F=

2.17

%, 3 = 3,3 DF = 20

= 160.54

W~thinreaimens SS = 203.87

+ I/%)

where t is the value oft h m Table 12-10 (two tails). This is the least conservative p d m , and a s s u m that the probability that any one camparison is judged to be significant by c h a m alone is 5%. However, the probability of one or more comparimns b i n g judged significant would be greater than 5%. A p plied to the results of Example 19,

(Z X ) ~ I N= 934 - (148)930 = 203.81

G xlIZ G x2I2 Between regimens SS = -+ -+

/n,

d

6%allowance=tJsz(l/~+ll~)=2.086d2.17(1/3+1/3)=2.51

Thus, any two means differing by 2.51 or more are judged to be different.

mean square ktween regimens 1 7.81 - 2.17 - 8.22 mean square within regimens

Banked Means B

Toteatfor~cance,theFratioisreferredtotheFtable(eeTable 12-16)with f~= t - 1= 9 and fa = Zhr - 1)= 20 DF. We find that the calculated value 8.22 is larger than the tabulated value 3.46 for P = 0.01. Therefore, as the probability of these 10 sampla k i n g drawn from the -epopulation is 1-8 than 0.06 (actually, it is 1-8 than 0.01),it is eoncluded that they are not all the same (ie, not all the means are equal), MULTIPLE COMPARISONSIN ANOVA-If the F test is significant and more than two treatments are included in the experiment (t > 21, it may not b obvious immediately which

1.0

A, C

J 15.3

I

2.3

6.0

F,G 5.7

D,H 6.3

or, (MC)(IJFGDH)(E).

Any two means underscoml by the same line (or included in the same parentheses) do not differ statistically at P = 0.05. Any two means not underscored by the same line (or not included in the same parentheses) are st a t i s t i d y sign%cantly different a t P 5 0.05.

Table 12-19. Weight Gains in Ten had Regimens K U D REGIMEN

B

A

2 3 2

z XI z X! n1 n, - 1

b

1 2 0

C

D

F

E

H

G

1

I

(t = 10 REGIMENS)

2 4 1

4 8 7

9 8 11

3 8 6

6 5 6

7 6 6

4 4 7

4 6 6

7 21 3 2 2.3

19 129 3 2 6.3

28 266 3 2 9.3

17 109 3 2 5.7

17 97 3 2 5.7

19 121 3 2 6.3

15 81 3 2 5.0

16 88 3 2 5.3

Sums

7 17 3 2 2.3

3 5 3 2 1 .O

H x = 148 ZX= = 934 N=30 z (n,- 1) = 20

~

147

CHAPTER 12: STATISTICS

Table 12-22. Critical Values using Duncan's Test for Example 19 Tk

k

2 3 4 5 6

2.95 3.10 3.18 3.25 3.30

4 2.51 2.64 2.70 2.76 2.81

from J . Here, t~ = 3.07 from Table 12-23 fork = 9 treatments, 20 DF, and P = 0.05 (two-tails).

k

Tk

4

7 8 9 10

3.34 3.36 3.38 3.40

2-34 2m86 2.87 2.89

+ I /nil= 3.07 $2.1 7(1/3 + 1/3)

5% allowance = tn Jsz(l/n,

= 3.68

Thus, any regimen mean that differs from the mean for Regimen J by 3.68 or more is judged to be different from J. Ranked M e a m A, c 2.3

B 1 .O

where t~ is Dunnet's t~ value for k treatments (excluding the standard or control) obtained from Table 12-23. Like the Studentized Range procedure, this is One of the most conservative prmdures, and it ensures that the probability of one or more comparisons between treatments and a standard or control being judged significant by chance alone is 5%. The one-tail values (listed in tables for P = 0.10) are used when the objective of the study is to select only those treatments that have higher (or lower) means than the standard or control. The two-tail values (listed in the table for P = 0.05) are used when the objective of the study is to select those treatments that are either higher or lower than the standard or control. Of course, the decision to carry out a onetailed or a two-tailed test must be made hefore the study begins. In Example 19, suppose J i s a standard regimen, and it is desired to determine which regimens show different weight gains

I

J

F,G

D ,H

5.0

5.3

5.7

6.3

E 9.3

It would be concluded that B showed a statistically significant smaller weight gain than J, showed a statistically cantly larger weight gain than J , and there was insuj5cient evidenoe to indicate that the other regimens were different from J. In the same example, if Regimen A is a control group and we knew beforehand that all of the other regimens had to be at least as pd as the control or better, it may be desired to select those regimens that are statistically significantly better. We proceed as follows: 10

= 2.60 from Table 12.23 for k = 9 treatments, 20 DF, u~d

P

= 0.10 (this corresponds to a one-tail P = 0.05)

5%allowa~~ce = I,, &(l ln, + 1 In,)= 2.60 $2- 17( 1/:3

+ 1/3)

= 3.12

Thus, any regimen mean that is larger than the mean for Regimen A by 3.12 or more is judged to he better than A.

Table 12-23. The t,, Table Valueso f t D for Dunnett's Procedure for Comparing Several Treatments With a Control at t4e 5% Level of Significance (Use P Values for a One-Tailed Test and P = 0.05 Values for a Two-Tailed Test)

= 0.10

x(NUMBER OF TREATMENTS, M C W DING THE CONTROL] DF

10 11 12 13 14 15 16 17 18 19 20 24 30 40 60 120 m

P

2

3

4

5

6

7

8

9

0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05 0.10 0.05

2.1 5 2.57 2.1 3 2.53 2.1 1 2.50 2.09 2 A8 2.08 2 A6 2.07 2 A4 2.06 2.42 2.05 2A1 2.04 2 A0 2.03 2.39 2.03 2.38 2.01 2.35 19 9 2.32 1.97 229 1.95 227 1.93 224 1.92 221

2.34 2.76 2.31 2.72 2.29 2.68 2.27 2.65 2.25 2.63 224 2.61 2.23 2.59 222 2.58 2.21 2.56 220 2.55 2.19 2.54 2.17 2.51 2.1 5 2 A7 2.1 3 2.44 2.10 2.41 2.08 2.38 2.06 2.35

2.47 2.89 2.44 2.84 2A1 2.81 2.39 2.78 2.37 2.75 2.36 2.73 2.34 2.71 2.33 2.69 2.32 2.68 2.31 2.66 2.30 2.65 228 2.61 225 2.58 2.23 2.54 2.21 2.51 2.18 2 A7 2.1 6 2.44

2.56 2.99 2.53 2.94 2.50 2.90 2 A8 2.87 2 A6 2.84 2 A4 2.82 2.43 2.80 2.42 2.78 2.41 2.76 2 A0 2.75 2.39 2.73 2.36 2.70 2.33 2.66 2.31 2.62 2.28 2.58 2.26 2.55 2.23 2.51

2.64 3.07 2.60 3.02 2.58 2.98 2.55 2.94 2.53 2.9 1 2.51 2.89 2.50 2.87 2.49 2.85 2.48 2.83 2.47 2.8 1 2.46 2.80 2.43 2.76 2.40 2.72 2.37 2.68 2.35 2.64 2.32 2.60 2.29 2.57

2.70 3.14 2.67 3.08 2.64 3.04 2.61 3.00 2.59 2.97 2.57 2.95 2.56 2.92 2.54 2.90 2.53 2.89 2.52 2.87 2.51 2.86 2.48 2.8 1 2.45 2.77 2.42 2.73 2.39 2.69 2.37 2.65 2.34 2.61

2.76 3.19 2.72 3.14 2.69 3.09 2.66 3.06 2.64 3.02 2.62 3.00 2.61 2.97 2.59 2.95 2.58 2.94 2.57 2.92 2.56 2.90 2.53 2.86 2.50 2.82 2.47 2.77 2.44 2.73 2.4 1 2.69 2.38 2.65

2.8 1 3.24 2.77 3.19 2.74 3.14 2.71 3.10 2.69 3.07 2.67 3.04 2.65 3.02 2.64 3.00 2.62 2.98 2.61 2.96 2.60 2.95 2.57 2.90 2.54 2.86 2.51 2.8 1 2.48 2.77 2.45 2.73 2.42 2.69

Adapted from Dunnett CW.Am Stat Aaocl 1955; 50: 1096.

148

PART 2: PHARMACEUTICS

Ranked Means

B 1 .O

A. C 2.3

I 5.0

J 5.3

Total SS = Z .i$ -! (C :c,)IIn,where (Z F, C 5.7

D, H

E

6.3

9.3

It can be concluded that F, G, D, H, and E showed a statistically significantly h t t e r weight gain than A, and that there is insufficient evidence to indicate that B, C,I, and J were any better than A. OTHER ANOVA DESIGNS COMMON TO PHARMACEUTICAL PROBLEMSA somewhat more complex design is the two-way ANOVA. This design is analogous to the paired t test, but consists of more than two treatments; ie, more than one treatment is applied to the same experimental unit (eg, patient) or related units (eg, litter mates, males between 50 and 60 yr, etc). This design has the same advantages and disadvantages as the paired t test d e s c r i w earlier in this chapter. The ANOVA table is similar to the one-waytable, but includes some new terms. me betweenmtreatments term has the same interpretation as that in the one-way analysis, representing differences between treatments. A new term, between rows, represents the variability of the units to which the treatments have been applied (eg, ~atients).Finally, the table contains an error term, sometimes referred to as row x treatment interaction (patient x drug in a clinical trial). The treatment mean 'quare is divided the error mean 'quare (EMS) to form an ratio, for PUToses Of performing a statistical test. Some complications can exist in the interpretstion of this table and the F ratios. The examples here consider treatments as including all treatments of interest, and rows as a random Of units taken O' m a large population of such units. For to compare a plaoebo>a generic drug, and a drug (three atments) use a random Of patients as the experimental units, with each patient to take each Of the three treatment 'is the comparison Of five analytical methds (five treatments) where 10 analysts, selected at random, each perform assays with each method. Example 2+Three variations of an acne preparation and a controI are to be tested for sn., initation. The four pduds, A, B , C, and the control, each are applied to sites on the backs of eight patients. The a s signrnent of the four p i d u c t s to the four sites on the patient is random; ie, a random assignment of treatments to the four sites on each patient is done for each patient, using a random-number table. The pmduds are applied, and aRer 24 hr, the degree of irritation is determined by assessing irritation subjectiveIy on a scale of 1 to 10. A value of 1 means no irritation and a value of 10 means extreme irritation. The results are shown in Table 12-24. The computations are similar to those for the one-way ANOVA. The sum+f-squ are5 for treatments is obtained as before. The sum-ofsquares for patients is determined exactly as for treatments except the operation is across mws. This is the same as rotating the table 90" and treating the rows as mIumns in the table matrix. The EMS (expected sum of squares) is obtain4 by subtracting the mw and column sum-ofsquares from the total sum+f-squares. The student may wish to follow the computations for this example, in general, however, the use of a statisticalmmputerpmgramisencouraged,asitismuchquickerandeliminates potential arithmetical errors.

Table 12-24. Skin Irritation Test

=

992

Between treatments SS = 149' =

- 17W/32 =

88.875

502 + 3g2 + 3 Z 2 ] / 8 - 1 7 0 7 3 2

27.625

Between rabbits SS = 12 1" =

=

= CT

14'

+ . . . 20'"/4

-

CT 3705/1

-

CT

23.125

Error = Total SS - Between treatments SS -

Between rabbits SS = 88.8'15 - 27.625

- 2:1.125

= 98.125

Table 12-25 shows the ANOVA. Since the F ratio for treatments (5.07) ex&$ the tabled Fvaluewith 3 and 21 DF at the 5% level, it can be concluded that at least two of the treatments differ. Although one may apply one of the a posteriori tests discussed under one-way ANOVA, inspedion of the resuIts suggests that results for Treatments A and B are similar and both are greater in magnitude than Treatments

,d

the mntrol.

CROSSOVER DESIGN-A design that is popular in experimental research is the crossover design. This is in the class of paired-sample or two-way designs in that all treatments are applied to each experimental unit. For example, in practically all human bioequivalence studies, each subject takes all of the treatments. That is, if a control marketed drug is to be cornpared to two new formulations, each subject takes all three prduds. The difference between the crossover and the two-way design (also known as a blmk design) is that b the two-way design, the order or plaoement of treatments are assigned randomly to each patient. In the crossover design, an additional constraint, order or balance, is imposed on the experiment. For example, in a bioequivalenoe study of three prducts, these are taken during thee perids. In the crossover design, each p r d u c t appears an equal number of times in each perid. Table 12-26 shows how three prducts, A, B, and C, may be assigned to nine subjects in a bioavailability study. Note that Treatments A, B, and appear three times in each perid and that each subject takes all three products- The balancing of order of administration compensates for perid effects. If any extraneous variables affect the outcome differently in one period compared to another, all treatments may be affected equally. This would result in a fair comparison of the different heatments. ln a purely random assignment of treatments, it would he unlikely that treatments would be assigned in such a balanoed Order- In an unbalanced design, differencesdue to periods would not affect treatments in a potential bias and a larger experimental error-the experimental error would include the usual causes of variability plus variability due to period effects. Thus, the crossover design can be considered an improvement over the two-way design in that the has kenreduced and the experiment made more efficient. Many such designs are available, but care should be exercised to apply the correct design to each experimental situation. The crossover design is related to the Latin square design. Several very g d referenoes are available on principles of experimental design. In particular, the bcmk by Cox6is recommended

,,,

TREATMENT RABBIT

A

B

C

CONTROL

Ex

Ex2

1

7 4 8 8 7 6 5 4 49

5 3 9 6 7 7 6 7 50

5 5 7 4 4 5 4 5 39

4 2 6 5 2 4 5 4 32

21 14 30 23 20 22 20 20 170

It5 54 230

2 3 4 5 6 7 8 Totals

Table 12-25. AHOVA for Data of Table 12-24 ANALYSIS OF VARlANCE

i:

SOURCF OF VARWTnN

DF

SUMMF-SQUARES

MEAN SQUARE

F RATIO

126 102 106 992

Between treatments Between rabbits Error Total

3 7 21 3t

27.625 23.125 38.125 88.875

9.208 3.304 1.815

5.07

CHA!TER 12: STATISTICS

Table 12-26. Example of Crossover Design PEMOD I

SUBJECT

1 2 3 4 5 6 7 8 9

PERIOD 2

B A B C A C B C A

Table 12-28. ANOVA for Bioavailability Study PERDD 3

A B C A C B C A B

C C A B B A A B C

b u s e it is not overly technical and can IR understood without resorting to t m much mathematics.

Example 21-Three drug formulations were administered to nine subjects in a bioavailability study actording to tbe m m v e r design illustrated in Table 12-26.The area under the b l d level curve8 were computed for each d-, and the r d k are shwn in Table 12-27. The ANOVA (Table 12-28)separates the total variance into four parts: subjects, perid (order of administration), treatments, and error.

2 $ = 384,720

Z xi = 2992 Total SS = S xf

-

(Zqyln= 33,182.1

- (Z xd2/n = 29,834.1 Treatment SS = Z (beat. sum3/9 - (2 xd2/n= 11 16.6 Subjwt SS = Z C d ) / 3

Order SS = {Zl a+ Z U a+ S IU2]/9 - Q X Error SS

= Total SS

~ ) ~ /=X264.3

- Subject SS - Treatment SS - Order

SS = 1947.2

Neither treatments nor order are sign&ant (see Table 12-15). For 2 and 14 DF, an F value of 3.70 is needed for signifmnce. Treatment has a higher resultl but fails to reach kgfieam in this In the w r l ~ Of bi~uivdenoe ing, bicequivalenoestudies were designed to have a power of 0.8 to detect a difference of 20% btween treatments. This means that a s e c i e n t number of subjects should IE included in the study so that if a true difference of 20% or more exists btween two treatments, there wfl be a t least m 80% chmm of k d i n g a s i w c a n t difference. This m e t h d of evaluating equivalence has been rep1aced by a more cofidenceinte~d ap

roach.^

If the

designbwmes unManoed' due to dropouts' Or Other oonditiom, a oomputer can used Another experimental design common in clinicaltrials is the ORen a s ~ z i t - ~ zdesign' ot For two treatments m w m ~ d m&g ob8emations in two m u p s Of patiem Over time. Although an equal number of patients in each group is desirab.ble, it is not neoessary for the data analysis. The observations are made at

Table 12-27. Results of BioavailabilityStudy SUBJECT

PERDD I

1 2 3 4 5 6 7 8 9 Period sum Treatment sum Treatment average

B = 107 A=100 B = 98 C = 71 A=92 C=113 B=169 C=88 A=122 1: 960 A: 945 105

PEMOD

C=102 C=106 A = 90 B=54 B=111 A = 115 A=187 B=95 C=168 11: 1028 B: 969 107.7

A =99 B=89 C = 128 A=63 C=107 B=91 C=195 A=77 B=155 111: 1004 C: 1078 119.8

149

SUM

308 295 316 188 310

:::

260 445 2992

ANALYSIS OF VARIANCE M U RCE OF VARIATION

DF

SUMSOF-SQUARES

Between subjects Between treatments Order Error Totat

8 2 2 14 26

29,834.1 1,116.5 264.3 1,947.2 33,162.1

MEAN SQUARE

3729.3 558.3 132.1 177.0

F RATK)

3.15 0.75

the same time perids in b t h groups. The example shows the basic design and ANOVA table. The details of the calculations are not shown. Usually, a sofiware program is used to analyze d, summsrize the data. The details of the analysis me given in Boltons and Winer.lB Example 2 2 - 4 pilot study to compare the effects of an antihyperbs;ve drug versus *laoeh was dMigned with four on drug and four on plaoeh. Blmd bgM hm belinewere measured for 6 we& at biweekly intervals. Tbe m u l t e are shown in Table 12P9,

The ANOVA is shown in Table 12-30.The terms of i n t e r ~ are t Treatments and Treatment x Times. The former term measdifferences of the overall average mults of the two treatments. The error term for Treatmenk is the mean q u a r e for Patienh. The Weatment x Time8 term compare8 the time trends for the two treatments. The error term for the Treatment x Time8 effect is Patient x Time8 (treatments). If the trends are parallel, this term will not k significant. Significance for this term indicah a lack of parallelism, sugge&ing that differenktween treatments depend on the time of o h v a t i o n . As with most experimental data, a graphic display is rewmmended. Figure 12-9is a plot of the average d t s versus time. The significant difference ktween treatments dP < 0.06) is apparent h m the plot and the ANOVA. The time trends of h t h treatments are similar, and can k exphhed by the experimental variability (Treatment x Time8 is not significant).

NONPARAIYIETRIC TESTS O F SIGNIFICANCF-The validity of the ht for two means depends to some extent (especiay for small samples) on the assumptions that the two pOpu]atiOns distributed approximatply normally and have mentially varianoes. A pdure for bsting the equality of vsrianoes has hn discussed pre~ously.

Statistical prooedures that do not depend on the mumption of nonparametric tests. Three commonly UBed prooedures are the Rank Sum bt for unpaired data, and the Signed-RankSum and Sign tests for p-d data. Rank Sum Test of S+nificance-The rank sum of signormality a=

nificance is the nonparametric analog of the two-independent sample t h t . The nl and nz observations are taken h m two independent groups. the n and ns observations sre arranged inorder of size, the oombined values are ranked hm for the lowest, to (n, + n,) for the highest, and the sumof the T of the nl observations in the sampleis oomput&. Valuea that are t i 4 are given average ranks. Aho ,,al+ n2 + 1)- T, and enter Table 12-31 16 with elllateTr = n,, n ~and , T or T' , whichever is smaller. If the calculated T (or T') is equal to or less than the tabled value, the null hypothesis is rejected at the signXcance level P. Example 23-Data were available on the duration of loss of the rightingreflex bin)for 10mice given a standard barbiturate and for 11 mice given a tBBt barbiturate (Table 12-32).Entering Table 12-31with

Table 12-29. Reduction in Diastolic Bload Pressure from Baseline DRUG WEEK

PLACEBO WEEK

PATIENT

2

4

6

PATIENT

2

4

6

1 3 4 7 Average

10 8 12 10 10.0

8 6 14 10 9.5

12 14 8 14 12.0

2 5 6 8

10 6 4 0 5.0

8 2 0 4 3.5

12 10 2 10 8.5

150

PART 2: PHARMACEUTICS

Table 12-30. ANOVA for E x a m p l e 22

b

SOURCE

DF

SS

MS

F

Patients Treatments Times Treatment x times Patient x times (treatments) Total

6 1 2 2 12

109 140.2 60.3 6.3 104

18.2 140.2 30.2 3.2 8.7

7.7 3.5 0.4

23

419.8

=

number o l positive differences = I1

c = number of negative diirerences = 4 Xk ( b

- c - 1 ) -- 1 b

-

+c

4

-

11+4

1 ) = -36 = 15

2.40

Table 12-12 shows that for 1 DF the probability of getting a value larger than the calculated value 2.40 is between P = 0.10 and P = 0.20.Since P is not qua1 to or less than 0.06,it is concluded that there is insufficient evidenoe to indicate that the morning and afternmn values are different. This conclusion is not in agreement with that of the t test and the signed-rank test. The reason for this is that the statistical sign test considers only the sign of the differenoe and not the magnitude, and thus is a lesssensitive test in borderline sib,tions such this one. of

X2

nl = 10,na = 11,and T' = 69.6,we find that the calculatd T' value 69.6 is less than the tabulatd value 73 for P = 0.01.Therefore, because the probability of the standard drug and test drug values being the same is REJECTION OF ABERRANT OBSERVATIONF+It is Iess than 0.06(actually, it is Iess than 0.01),it is concluded that they are practice among ,-hemists and others working in the different. This test compares the mdians of the twepopulations samOr physical sciences to make observations in The rn4jan ofan o r d e d set ofob$ervations is defind as the pled. This is done for the purpose lmth of obtaining a dlemost value for an d d number of observations, and as the average of mom accurate result and also detecting mistakes in dilution, the two middlemost values for an even number of observations. Thus, weighing, and so on- I t is quite a common ~ractioeto reject the the mdian for the standard drug is ( 130 + 148)/2= 139 and the median for the test drug is 103. most extreme of the three results if it appears to disagree with Signed-Rank Sum Test of Significance-The signed-rank sum test of the others. significanoe is the nonparametric analog of the paired t test. The differY o ~ d e n , ' ~a. chemist '~ as well as a statistician, made a study enoes between the n p a i r 4 values are r a n k 4 in order of absolute size the problem of rejxtion of observations in an attempt to anfrom 1, for the lowest, to n, for the highest, ignoring zem differen-. swer three questions: Tied values are assign4 an average rank. After the differenoes are ranked, the signs of the differen- are attached to the ranks, and the 1. If the extreme observation of triplicates is always reject4 sum of the positive ranks and of the negative ranks are obtained. Enter when only normal variation is present, how accurate is the result? Table 12-33with n = the number of non-zero differenoes and the sum T 2. Is the average of the two closest observations as g d an estimate of positive or negative ranks, whichever is smaller. When the calculated as the average of aII three? T is equal to or less than the tabled T, the null hyp~thesisis r e j d at 3. By how much should the outlying observation of triplicates the significancelevel P. differ from the other two in order to be reasonably assured Example 24-The pmedure is illustrated for data given in Example that this difference is due to a blunder rather than normal 12 (Table 12-34).Entering Table 12-33 with n = 16 and T = 22.6,we van ation? find that the calculated T value 22.6 is less than the tabulated value 26 He found that rejection of the outlying observation resulted not for P = 0.06.Therefore, because the pmbability of the morning and afternoon~aluesbeingthesameislessthan0.06,itisconc~udedthatthey odyinthevafiationbeinggreatlyunderestimatedbutthe are different. mean was biased.

,

Sign T e s t T h e sign test also is used for paired data, but it is not as powerful as the signed-rank test; it is more d a c u l t to find significant differenoes when they exist with the sign test. Count the numher of positive differenoes (b) and the n u m k r of negative differenoes (c),ignoring zero differences, and calculate (lb - c l - lj-> b+c

X"

where I b - c I is the absolute (ie, positive) differenoe b - c. This is referred to the chi-square table (see Table 12-12) with DF = 1, the test k i n g essentially the same as the chisquare test illustrated in Example 16. Example 25-The p d u r e is illustratd for the data given in Examples 12 and 24.

If one wished to follow a simple rule of reje~tion'~.'~ of observations in samples of three so as to reject not more than 5% of the extreme observations arising from normal variation, a rejehOn ratio of D/d greater than 2 0 would k required.

D/d = 20 where D = difference between the most extreme observation and its closest d

=

neighbor differenoe between two closest observations

the USP there is an exoellent chapter on the design and analysis of biological assays in which are included some tests for rejection of outlying observations. These and other tests can applied to chemical, as well as, biological assays.'g Two criteria are presented here, one for rejecting single suspect observations in one group and the other for rejecting a whole group of observations. To use the first criterion, arrange the observations in the group in order of their magnitude and n u m b r them fiom 1 to n heginning with the supposedly erratic or outlying observation, thus Yl,Yz, Ys,

. . .,Yn

where yl is the suspect o k a t i o n If there are 3 to 7 observations in the group, calculate

Mz GI=urn

'

Drug o Plocebo

TI P

I

K

2

I

.I

4

6

-

Y1

- Ul

If there are 8 to 10 observations in the group, and the smalle8t vdue seems suspect, again arrange them in order from lowest to highest and calculate

Wk .

Figure 12-9. Plot of average results for Example 22.

Go=

A-Y1 Yn-1 - yl

Table 12-31. The Rank Sum Table ValuesofT or T', Whichever IsSmaller, Significant at the lo%, 5%, and I% Levels N, (SMALLER SAMPLE) M

8 9

10 11 12 13 14 15 16 17 18 19 20

P

4

0.10 0.05 0.01 0.10 0.05 0.01

15 14 11 16 14 11

23 21 17 24 22 18

31 29 25 33 31 26

41 38 34 43 40 35

51 49 43 54 51 45

0.10 0.05 0.01 0.10 0.05 0.01 0.10 0.05 0.01 0.10 0.05 0.01 0.10 0.05 0.01 0.10 0.05 0.01 0.10 0.05 0.01 0.10 0.05 0.01 0.10 0.05 0.01 0.10 0.05 0.01 0.10 0.05 0.01

17 15 12 18 16 12 19 17 13 20 18 14 21 19 14 22 20 15 24 21 15 25 21 16 26 22 16 27 23 17 28 24 18

26 23 19 27 24 20 28 26 21 30 27 22 31 28 22 33 29 23 34 30 24 35 32 25 37 33 26 38 34 27 40 35 28

35 32 27 37 34 28 38 35 30 40 37 31 42 38 32 44 40 33 46 42 34 47 43 36 49 45 37 51 46 38 53

45 42 37 47 44 38 49 46 40 52 48 41 54 50 43 56 52 44 58 54 46 61 56 47 63 58 49 65 60 50 67 62 52

56 53 47 59 55 49 62 58 51 64 60 53 67 62 54 69 65 56 72 67 58 75 70 60 77 72 62 80 74 64 83 77 66

5

6

7

48 39

8

9

1

0

11

12

13

14

15

17

16

18

19

20

313 303 283 320 309 289

348 337 315

when nl > 20 and n2 > 20, significance values are given to a good approximation by

nl(n1 + n~ + 1Y2 - z b'nln~(n1+ nz + 1Y12

66 62 56 69 65 58 72 68 61 75 71 63 78 73 65 81 76 67 84 79 69

87 82 72 90 84 74 93

87 76 96 90 78 99 93 81

where z is 1.64 for the 10% level, 1.96 for the 5%, and 2.58 for the 1%. The probability figures given are for a twatailed test. For a one-tailed test, P is halved.

82 78 71 86 81 73 89 84 76 92 88 79 96 91 81 99 94 84 103 97 86 106 100 89 110 103 92 113 107 M 117 110 97

100 96 87 104 99 90 108 103 93 112 106 96 116 110 99 120 113 102 123 117 105 127 121 108 131 124 111 135 128 114

120 115 105 125 119 109 129 123 112 133 127 115 138 131 119 142 135 122 146 139 125 1M 143 129 155 147 132

142 136 125 147 141 129 152 145 133 156 1M 136 161 154 140 166 158 144 171 163 147 175 167 151

166 160 147 171 164 151 176 169 155 182 174 159 187 179 163 192 182 168 197 188 172

192 184 171 197 190 175 203 195 180 208 200 184 214 205 189 220 210 193

219 211 196 225 217 201 231 222 206 237 228 210 243 234 215

249 240 223 255 246 228 262 252 234 268 258 239

280 270 252 287 277 258 294 283 263

Adapted from Tate MW, Clelland RC. Nonparametric and Sttortcut Statistics. Danville IL: Interstate Print, 1957.

Table 12-32. Data for Example 23 SIANDARD DRUG

TEST DRUG

RANK

96 109 126 130 130 148 153 158 169 Died

4.5 8 13 15 15 17 18 19 20 21

T = 150.5 = 10 T'= ndnl + n l + 1) - T = lO(10

nl

Table 12-33. The Signed-Rank Sum Table Values o f T for Signed-Rank Test, Significant at the TO%, 5%, and I % Lewls

RANK

0 91 92 96 99 103 117 118 119 120 130

n2 =

+ 11 + 1) - 1 M . 5 =

1 2 3 4.5 6 7 9 10 11 12 15 11

69.5

P n

5 6 7 8 9 10 11 12 13 14 15 16 17

0.10

0 2 3 5 8 10 14 17 21 25 30 35 41

OX15

0 2 3 5 8 10 13 17 21 25 29 34

P 0.01

0 1 3 5 7 9 12 16 19 23

n

0.10

OD5

Om

18 19 20 21 22 23 24 25 26 27 28 29 30

47 53 60 67 75 83 91 100 110 120 130 141 152

40 46 52 58 65 73 81 89 97 106 116 126 136

27 32 37 43 49 55 61 68 75 83 91 100 109

152

PART 2: PHARMACEUTICS

truly d m not blong to the group and the obsemation is re-

Table 12-34. Signed Ranks from Example 24 DIFFERENCES

2

2

-3 4

-3 6

8

15

-4

-6

6

jetted. The values of G for a probability P = 0.01, that an outlier oould c~xurat either end are shown in Table 12-35. This

SKNEDRANKS

same criterion oould be used for testing whether the largest or smallest average in a group of averages differs significantly h m the remainder of the averaes (Table 12-35). Exwnple Z6-Suppse among the gains in weight of six rate after a feeding experiment, one weight was found to he much Iws than the other five. Can that observation be diwded? The six gains in weight

12.5

-1

-1 - 12.5

-6 5 4

10 6

4

6 ignore

0 5 7 4

are 36,40,38,42,20, and 39. yl,

Rearrange these in order from smallest to largest and label . . .,ys,where n = 6. 20

10 14 10 Sum of positive ranks = 97.5 Sum of negative ranks = 22.5 n = 15

=

T I,,

If there are 11 to 13 obsen~ations,follow the same procedure. but use the statistic

v.i - y l GI - -

.v,)-I - . V I

If there are 14-25 obsen7ations,follow the same procedure, but use the statistic G,I

-

Y.i - Y I -YI

.V,)--L

If the largest value is open to suspiciol~as possibly being aberrant, arrange t h e obsen~ationsin order from highest to lowest and number them, always labeling the suspect obsen~ationy If t h e calculated value of GI, G?, G, o f ~ o r r t ~ s p o n cstates l i ~ it might be expected t h a t additivity would hold better at the boiling point. l n the homologous series ofl~ol~bral~ched primary derivatives, the accuracy of a calculatio~~ of molar volume is relatively good, 'l'he deviations illcrease gradually with poly-substituted derivatives, 1,l-bis-derir~atives,ortho derivatives, and branched isomers; nevertlleless, the additivity scheme can sen7e as a first approximation. COEFF'C'ENTS AND THE I' 'ONSTANT-In the early theory of ~ ~ a r c o s ilipid s , solubility was regarded as the most important factor for the u ~ h i b i t i oof l ~cell activity ~ lt ht e begillllillg of the 20'" celltury Meyer and Overton proposed that narcotic efficiel~cyparallels the coefficient for the partiti011 of a drug between oil and water, rlltl~oughthis theory cannot explain t h e mechanism of narcotic action, it does explail~the role of transport to nen7etissues. It is more logical to use partiti011 coefficiel~tsthan solubility in a single solvent for structure-activity correlatiolls since. in a biological system, one is dealing with a l~eterogel~eous system rather than a simple solution. Partition coefficiel~tshave been used in t h e study of drug absorption, distribution, metabolism, toxicity, and structure-activity correlatiol~. It has been showl~t h a t the partiti011 coefficiel~tsfor a given compoul~din two different solvent systems (eg. ether/\vater, oetanol/water) are related a s follows: log P ,

-

a log P,

All of the above Complementarity is involved Shape, group symmetry as well as size are important

Stereospeclf I C In general

+b

where a and b are constants. 'l'l~issuggests t h a t one can use the results from one set of solvents to predict results in a second set,

IIansch's group1["[) systematically has extended the use of partitioll measured from oetanol/~vater,to s e n ~ e a s a measure of t h e ease of passage of orgallie molecules t~lroug \various ~l lipoproteill barriers and/or a s a measure of t h e hydrophobic binding with proteill (such as boville serum albumin). From t h e partition coefficients of a variety of derivatives of t h e type X-CIiII,IOCII,COOII. X-CIiII5, alld C f i ~ ~ 5 ( C ~ ~ 2the ) , ,substituellt -~, collstallts ( T I ) for the and tile aliphatic function (X) have beell determined. 'l'he TI collstallt is defined as TI -

log Px

-

log PH

where P , is tile partitioll coefficiellt of a derivative, alld pH t h a t of t h e parent compound, Although TI varies col~til~uously for a gir,en fullctioll depelldlllg on its electronic the variatioll generally is small; therefore, it is called adclitir.v(a measure of t h e degree of total molecular randomness) also increases as materials go from solid to liquid to gas. I t is the balance of enthalpy, entropy, and temperature that determines if changes proceed spontaneously. Obviously, if systems tend to settle to states of lowest energy, it means t l ~ a ent thalpy and entropy collsideratiol~smay counteract each other. Much of thermodyl~amicsis col~cerl~ed with explaining and quantitating t h e changes t h a t systems undergo. Latent heat is heat absorbed when a change of state takes place without a temperature change, as when ice turns to water at 0' . This example is one in which the heat required to produce the change of state is designated the hcat cf fr~,sion,.The counterpart, t h e heat of rwporization, is used when a change of state from liquid to gas is involved. As molecules of a liquid in a closed, evacuated container continually leave t h e surface and go into the free space above it, some molecules return to the surface, depending on their concentratiol~in the vapor. Lltimately, a conditiol~of c q r ~ ~ i l i b r i r ~ ~ n ~ is established, and t h e rate of escape equals t h e rate of return. The vapor then is saturated and the pressure is known a s the r'al>orprcssr~~rt~. Vapor pressure depends on the temperature, but not on the amounts of liquid and vapor, so long as equilibrium is established and both liquid and vapor are present. IIeat is absorbed in the vaporizatiol~process, and therefore t h e vapor pressure illcreases with temperature, 11s the temperature is raised further, the density of the vapor increases, and that of the liquid decreases. Cltimately, the densities equal each other and liquid and vapor cannot be distinguished. The temperature at which this happens is called the critical trn~pcratr~u-c, and above it there can be no liquid phase. h very important process t h a t il~volvesa change of state from liquid to vapor and back to liquid is t h a t of distillation^. Solids also have vapor pressures t h a t depend on temperature. When a solid is collverted directly into gas, it is said to sr~,blin~rb. Sublimatiol~pressures of solids are much lower than those of liquids a t any given temperature. When a solid is transformed directly into a liquid, two types of melting may be distinguished. In the first type, c ~ s t a l l i n n~tblting, t~ a rigid solid becomes a liquid, during which procedure two phases are present-the bulk of the solid or its inner parts are not really changing. The second type is an~orphousn~rblting.This il~volves an intermediate plastic-like conditiol~t h a t envelops the whole mass, the viscosity decreases and a state of liquidity follows. Crystalline melting involves more definite melting poults and latent heats t h a n does amorphous melting.

Sublimation A 1 solids have some tendelley to pass directly into the vapor state, 11ta given temperature each solid has a definite, t110ugh generally small, vapor pressure; the latter increases with a rise in temperature. Sr~,blin~ation is the term applied to the process a solid to vapor without intermediate passage of tral~sformil~g through the liquid state. 1n pl~armaceuticalmanufacturing the

CHAPTER 13: MOLECULAR STRUCTCIRE, PROPERTIES, AND STATES OF MATTER

A

SOLID UI

E

2 8 C

C TEMPERATURE

179

tain physical changes will not take place or certain state8 of b ing will not exist. At these points, some properties are constant and are referred to as the critical temperature, p m u r e , or volume. At the usual critical point, the properties of liquid and gas are identical and the phase diagram curve of P versus T ends. (Phase diagrams will be discussed later.) When a liquid changes to a vapor, increased disorder or randomness--and therefore increased entropy-results. At the critical temperature, the entropy of vaporization is zero, a~ is the enthalpy of vaporization, as the gas and liquid are indistinguishable. Although the gas-liquid critical point is the one most discussed, others do m.Each critical point mads the disappearam of a state. Note that most liquids behave similarly not only at their critical temperat-, but also at equal fractions of their For example, the normal biling points of critical temperat-. many liquids are approximately equal fractions ( a b u t 60%)of (in absolute temperature de-1. their critical temperat-

Figure 1 1 9 . Phase diagram to illustrate the principle of sublimation

Supercritical Fluid P r o w commonly includes also the mndensation of the vapor back to the solid state. A solid sublimes only when the pressure of its vapor is below that of the triple point for that substance. The triple point is the point, having a definite pressure and temperature, at which the solid, liquid, and vapor phases of a chemical entity are able to mexist i n d e k i t e l ~ If . the P m m of vapor over the solid is a b v e that of the triple point, the liquid phase will b produmd bfore transformation to vapor can p&. Figure 13-9 depicts a phase diagram flu8trating the principle involved. The line OA indicates the melting point of the solid form of a substance at .~&OUB pressures; only along this line can b t h solid and liquid forms exist together in equilibrium. To the left only the solid form is stable; to the right only the liquid form remains permanently. The line 03 shows the vapor pressure of B e liquid form of B e substance at various temperatures. It is called the vapor-pressure curue of the liquid and repwents the conditions of temperature and vapor pressure for coexistence of liquid and vapor phases. Abve this line only the liquid phase exists permanently; blow it only vapor m s . The line OC represents the vapor pwsure of the solid at various temperatures. It is designated as the sublimation cume of the solid and represents the conditions of temperature and vapor pressure for the coexistence of solid and vapor phases. To the left of this line only solid can exist; to the right only the vapor form is stable. The intersection of the three lines, is the triple point. It is apparent h m the diagram that point 0, at pressof vapor below that of the triple point it is possible to pass directly h m the vapor to the solid state, and vice versa, simply by changing the temperature. At pressures a b v e the triple point the liquid phase must intervene in transformations between solid and vapor phases, in a closed system. Because the melting point of a solid commonly is taken at 1atm (atmosphere)of pressure, it is evident that if the triple-point pressure is less than 1 atm, fusion of the solid form will m r on heating in a closed vessel. If, on the other hand, the triple-point pressure is greater than 1 atm, the solid form cannot b melted by heating at atmospheric pwsure. In a current of air, however, the conditions are somewhat different; some solids that melt when heated in a closed system now sublime appreciably even at ordinary temperat-, b cause the vapor pressure of the solid d m not attain the triplepoint pressure. Thus, camphor, naphthalene, p-dichlorobnzene, and idine, all of which have a triple-point pressure blow 1atm, will vaporize in a current of air but melt when heated in a closed system.

Over the last decade, supercritical fluid chromatograph (SFC) and related unzed chromatography techniques continue to w w , especially in food and natural p d u c b errtractions and analysis.~,m When the temperature and pressure of a liquid go byond the critical points, a supercritical fluid may form. Under these s m s e d conditions, polar and nonpolar compounds are completely miscible. For example, dense fluid solvents, like supercritical COa(Tc = 31.1°, PC= 73.8 bar) and ethane (Tc = 32.3", PC= 48.8 bar) have b n shown to offer advantages for the solubilization of amino acids. Other applications of supercritical fluids include chromatography of polar drugs and elimination oftofie wmteBT7um

viSUalimtionOf changesof state This section is to serve as an intrcduction to the following one on eutectics. When a pure substance mls and is transformed from a liquid to a solid, a graph (Fig 13-10)of decreasing temperature versus time is continuous. At the temperature at which solid crystallizes (ie, the melting poin t), the oooling m e h o m e s horizontal. The same is true at the boiling point-the temperature of a liquid at which the continuing application of heat no longer rdses the temperature, but rather converts the liquid into vapor. It is the point where the vapor pressure of the liquid (or the sum of its components) equals that of the atmosphere above the liquid.

Y

LT

Z dn YI

E C

"

Critical Point The critical point is expressed as a certain value of temperature or pressure (or molar volume) a b v e which or blow which wr-

TIME

Figure 13-10. A single change of state as shown by a slowing of the cooling rate.

CHAPTER 13: MOLECULAR STRUCWRE, PROPERTIES, AND STATES OF MATTER

ing-rate changes are plotted against each particular composition studied. Note that Figure 13-12 is idealized in that no solid-solid solution of A and B is formed. If the two components are somewhat soluble in each other, the &asam would differ by having two thin solution areas along the lefi and right axes; such partly in evidence in Figure 13-13. Two pharmaceutical examples of e u W c formation are 1. A mixture of two common antipyretic-andgeaic compounds: aspirin and acetaminophen. There always has h e n some *magic*

as-a~ e u ~ formation; c indeed, as a binary position dm melt at a lower temperature thm other combha-

dm have weaker ,,,,lldiw

tiom, the eutectiC

if

any, h d , being very fme grained, it d&olW more rapidly, It is known that many drug oompounds form eutectics and the asp~-acetaminophen(APm) eutectic (37s APAP by' weight) dm dissolve more quickly than a &rngle of hetwo of the same composition, Because a formed eutectic is created under equilibrium conditions of intimate mixing as noted the contact of two oompounds closer hatachievble by &imply mthe dry powders, The in dismlution rate ob&ed by -ing hee u h t i c may in a greater speed of phyeiological absorption. 2. This example i8 in Figure 13-13. It was found that urea and formed a eutectic containing amroximately 46% urea and 64% acetaminophen (by weight) which melted in the 110" to 116" range.

-

*

160

-

150

-

140

-

110

-

110

u ru

5 +

% APAP

INHALERSInhalers are classified as b i n g one of two types, surface or solution. Surface-TypeInhale-The volatile material maid= on the surface of the d&et (cotton or other cellulosicmaterial, usuall~). This r e p m a t 8 a conventional adsorption situation; it i~ easy to app&te the fact that the more surface area the the the surfam area of the material exposed to the airflow and the greater the opportunity for volaidization. Hence, a larger or more lm& packed pledget will cause a larger d m to emanate from an inhaler than will a smaller Or tightlypacked pl&et' It i8 convenient to make this type of inhaler if the volatile material itself is a liquid. The dose8 p d u c e d stay relatively high h a u s e the to a zero-order This fledstcharge is i8 reasonable k a m e the volatile material has formed a multimolecuhedm a m o n o m o l d ) layer on the fled& surlar (as f a c ~Thm, . even though molecul= are stripped off,the surface areaand hence the dose--remain essentially unchanged. However, as some of the pledst are dauded, the total W& surfam area of the volatile material d m and m d m the dose during s u m i v e w. Solution-TypeInhaler-The volatile material k dismlved in a suitable nonvolatile mlvent, and this mlution is p l a d on the pledget. The situation may In? taken as an example of the operation of Raoulf's and Henry's laws; that r,the vapor mm Of tki?oom~ond are proportional in mme way to their oonoentrati011~.To keep the v a p o r - ~ u r e contribution d t h e solvent low in order to enhance the vapca v u r e of the mlute, a mlvent of very low vapor i8 u d 88 the vehicle. In thh inhaler type the exgosed surface area of the material d m not change as the inhaler is used, what d m change is the concentration of the volatile material in the mlvent. Thus,the d m gradually d m = according to a fust-order d e m e as the drug concentration decremx. Of courm, the nature of the pledget and the M e r M y exert some effect here a h , k a m e if the airflow through the inhaler and the pledget d m not permit volatilization of the material, insigniflcant, low dose8 w i l l result.

aooorw

If the drug is a volatile solid, the solution-type inhaler should IE made because solids do not lend themselves to easy pledgetcharging p m d u r e s even if a volatile solvent such as ether is used to deliver the material to the pledget during manufactur-

0

20

40

60

B1

100

100

BO

80

40

20

o

IWlWl 'LUAER IW:WI

181

Figure 13-13. Phase diagram of the urea:acetarninophen (APAP) (46%: 54%) eutectic melting in the 1 1 0 to 1 1 5" range. (From Goldberg AH, et at. I Pharm Sci 1966; 55:482.)

Gases AEBOSOLS-Gases are used directly in dosage forms in the field of aerosols. Although this subject, including the use of the so-called liquefied propellants, is covered elsewhere, note that pressure packs often use nitrogen, nitrous oxide, or carbon dioxide to expel the contents h m their containers. The latter two gases are much more soluble in water, so some aeration (which may IE desired) of the material discharged will take plaoe. C a r b n dioxide is a b u t six times as soluble in water as nitrogen, and nitrous oxide a b u t four times as soluble as nitrogen. Thus, if it is desired to have some of the gas dissolved in the p d u c t , either nitrous oxide or carban dioxide can h used. In organic solvents and in fatty materials, such as found in emulsions, nitrous oxide is somewhat more soluble than c a r b n dioxide. There is not a great deal of differencein solubility prop erties; however, the possibility exists that the pH-lowering effeet of carbon dioxide as it forms carbonic acid may be just as undesirable, as it may cause precipitation of a carbnate in an alkaline product.

ing. Further amplification and clar5cation of the surface- and solution-type classscation of inhalers might be achieved by considering the existing analogy to chromatographic systems. The surfaoetype inhaler oorresponds to adsorption chromatography, with the material being adsorbed initially on a carrier and then desorbed by a passing stream of liquid or gas. The solution-type inhaler corresponds to partition chromatography, in which material in a solvent is supported by some medium, is partitioned btween its original solvent and a passing stream of gas or liquid, and thus is removed. Another point of sign%cance concerns the relationship of the volatile activeingredient to the solvent. An inmase indose should result when the active is dissolved insolvents that came it to deviate more pesitively h m Raoult's law. Thus, the less the solute-solvent interaction and the greater the solu&solute interaction, the more pronounced will IN the tendency toward volatilization of the solute. Using relative solubility a~ a gauge of such interaction, one would expect delivery of larger doses of a volatile solid from dibutyl phthalate (if the solute was less soluble in it) than h m benzyl salicylate (if it was more soluble in it) at the same concentrations. Although it might seem that the vapor pressure of the drug and additives would assume a position of p r i m m importance, this dws not appear to IE the case. Vapor-pmsure values r e p w e n t an equilibrium situation, whereas what is involved in the inhaler situation is a p r o w controlled by factors affecting rates of volatilization. Although it is true that volatile materials usually have a p pwiable vapor pressures, it generally is not true that a oompound with a vapor pressure value of twice that of another cornpound will volatilize twice as fast. Besides this fact, inhaler recovery times may bessentially zero and no equilibration time may be needed. Also, no decrease in dosage would be noted with the surface-type inhaler and no regular (ie, linear with oonoentration) decreases in dose would be noted with the solution-type inhaler ifthe vapor pressure was the controllingfactor.

182

PART 2: PHARMACEUTICS

L'nfortunately (from the standpoint of not having a more straightfonvard system to analyze), equilibrium and rate eoncepts are inextricably mixed in the present situation. This easily can lead to the basically incorrect tendency to try to predict kinetic data from tl~ermodynamicvalues. IIowever, because vaporizatiol~relatively is unencumbered with entropy and orientation factors, rates of volatilizatiol~often are qualitatively proportional to t h e equilibrium properties of t h e materials involved. Equimolar quantities ofthe followil~gcompounds, allowed to evaporate a t room temperature underthe same conditions, will complete the evaporatiol~process in this order: ether, acetone.

strong cohesive forces of solids nor the weak ones of gases. They are also intermediate in t h a t they have neither the orderliness of a c y s t a l nor the ral~doml~ess of a gas. One then might consider a liquid a highly compressed gas or slightly released solid. Uue to the concept of molecular motion, there must be some free space in liquids, Also, if the motiol~is completely random, some spaces may be larger than others a t a particular point in time. ' r ~ u s liquids , may have holes, and this concept h a s exp l a u ~ e dphenomena such as the expallsiol~of volume t h a t materials undergo up011 fusion (holes are created), diffusion in liquids, viscosity (movement of holes in t h e opposite direction of the riscous flow), and density decreases as temperature rises

chloroform, carbon tet.rachloride, ethyl acetat.e, andwater. ' h i s

(the solubi1it.y of holes increases). It might be said that liquids

order corresponds both to the vapor pressures of t h e materials and their boiling points. To further cloud the cause-and-effect relationship, the very in mole fracmagnitude of t h e numbers (the col~cel~tratiol~s tions) is such t h a t t h e partial vapor pressure of a volatile solid may increase proportiol~atelywith the mole fraction. IIence, alt110ugh vapor-pressure concepts should not be neglected in inhaler development. it is the rates of volatilizatiol~t h a t must be col~trolledor modified. For more infurmation and experimental data on inhalers see Kennon and Gulesich:'[' Various drug-delivery systems for use with metered-dose inhalers (MUls) are commercially available. They are intended for delivering oral aerosolized medication from MUls to the lungs. RELATrVE HUMIDITY-In the productiol~of effervescent products, one ofthe most vital factors to be considered is the use of controlled-humidity conditions. I t is well-known that the effective control of humidity is related closely to the success or failure of attempts to produce effervescent products. It is useful to bring to light some of the facets of this area of technology Two factors predomillate when one views the situation: the effective col~cel~tratiol~ of water in the air and the temperature. 1n chemical reactions, particularly the kind involved here, t h e effect of temperature on an equilibrium condition is not very significant when compared to t h e influence manifested by concentration. Certainly, water of hydration, crystallization, or simple adsorptiol~(which is tellaciously held at room temperature) does not disappear at temperatures under 100' F.What is effective and influential, however, in keeping and increasing such additiollal moisture on solids, is the concentration of water in t h e air. The concept proposed here is t h a t considerations based purely on relative humidity probably will be unfruitful. For purposes of illustration. Table 13-10 shows the arnoullts of water t h a t are found under conditions ellcoul~teredduringthe development of effervescent products. The followil~gpoults may be drawn from this information, 111 0 5 relative humidity (ItII) at 36' F is equivalentto 25';; ItII at room temperature. Either of these conditions represents a fairly dry day, but certainly not a g air surely lowers very d y day. 'rherefore, although h e a t u ~ the the ItII, it probably does not lower the ability ofthe water in the air to cause trouble. Regardless of the temperature of the processing rooms, experiellce h a s showl~t h a t for water concentrations present at 72"F, the range of 10 to 1 5 5 ItII should not be exceeded if minimum difficulties are desired.

are solutiolls of holes in material, whereas gases are solutiolls of matter in free space. With respect to fluid mechanics, a fluid can be considered a material that cal~notsustain shear forces when in static equilibrium. This is the factor d i s t u ~ p ~ i s h i solids ng from fluids, the latter of which may be gases or liquids. This movement under the slightest stress sometimes is referred to as "no sideways frictiol~."I t can be seen in operatio11 in the case where a sailor standingwatch near t h e gangplank of a docked ship can step on a mooring rope and cause t h e ship to move toward t h e dock. Liquids, just like gases, take t h e shape oftheir container, but only the lower part of it, as the liquid occupies a definite volume; gases, on t h e otherhand, expand to fill their entire container. lntermolecular spaces are greater 111 a gas t h a n in a liquid, thus they can be compressed. Itelative to gases, both liquids and solids are quite incompressible. They can be considered already compressed due to the stronger il~termolecularforces. After a fluid is set in motion, it comes to rest because ofthe internal friction caused by t h e molecules sliding over each other; this resistance to flow is called r~isrosity,and it can be quantified. To effect good quantification with viscometers, a normal, smooth (laminar or layer) flow is needed. With excessive stirring, at a so-called critical r~~~locity, t h e fluid becomes turbulent, and i l ~ s t r u m e l ~ tmeasuremel~ts al are difficult to effect, 11s the temperature offluids increases, viscosity decreases. l n general, also, a s pressure increases, viscosity illcreases. Because fluids have some structure. they may change up011 standing so that, when one is considering riscous behavior, the recent past history of t h e sample may have great effects. Thixotrol>.vis the term usedfor liquids t h a t flow freely ifrecently stirred, b u t gel when left undisturbed. Solids also flow, but more slowly, even under minor stresses including those produced by their own weight,The wavy, bumpy surface oftarred roads, particularly seen on hills, is a result of a flow p h e l ~ o m e l ~ o l ~ . Of interest also is the clr~,stcrtheoryof liquids, t h e maul concept being t h a t localized order exists but does not extend to a great distance. One property explained by this visualizatiol~is that, as t h e temperature rises, the clusters disintegrate and viscosity decreases, r h ~ o t h e ris t h a t transmitting momentum t11rough a liquid is due not only to molecular movement, but also to the transmissions of elastic waves through the groups of semistationary clusters. It is possible that the clustertheory affords another way of looking at pl~armaceuticalcomplexes in solution.

Liquids

Complexes

The liquid may be collsidered an illtermediate in t h e trallsitiolls from solid to gas, Liquids have lleither tile

In addition t o structure in solvents, it also is possible for solutes

Table 13-10. Moisture Content (dm3) Existing a t the Conditions Noted RELATIVEHUMIDITY (401 TEMPERATURE

10

15

25

40

RT (22°C or 72°F) Hot (36°C or 97°F)

1.9 4.1

2.9 6.2

4.8 10.3

7.7 16.5

to create a structure of a Sort within the solvent. ' ~ I U Sit, has been showl~t h a t benzocau~e111 water solutiol~with caffeine exhibits a much-reduced rate of hydrolysis. In a somewhat simil a r vein, it also has been noted t h a t different salts of t h e same compoul~d(eg, hydrochloride versus nitrate) may exhibit differe n t stability characteristics. Similarly, it has been shown that saccharill in certain chlorpromazil~ehydrochloride solutiolls enhances the light-stability of t h e drug. It appears that such changes are because t h e ionic e l ~ v i r o l ~ m emay l ~ t form a protective molecular overcoat or loose ionic atmosphere complex around the drug.

CHAPTER 13: MOLECULAR STRUCWRE, PROPERTIES, AND STATES OF MATTER

Liquid Crystals Lipids, when heated, usually do not pass directly from a cry5 talline to an isotropic structure, but rather assume intermediate liquid crystal phases. Of most interest pharmaceutically and physiologically is the canept that these structum are undoubtedly involved intimately in the structure, and hence in the function, of membranes and ells. All biological systems are basically aqueous, and it is particularly in such systems that lyotropic mesomorphism (the formation of liquid-crystal phases in the p m e n e of water) takes place; that is, the lipid phases undergo transformations involving crystal, liquid-crystal, and liquid forms. It is these changes that me mediators of the various physiological absorption, transport, storage, and excretory functions of ells. Many in vitro studies of biologically significant lipids have h e n performed in an attempt to elucidate the mechanisms of their interaction and behavioral properties in aqueous systems. Liquid-crystalsdiffer h m solids and gases in that they have some freedom to move and to take on many different shapes while maintaining a high degree of order through quite long d i s b m , relatively spe&ng. ~nthe labratory, liquid-crystals can be prepared h m one wmponent by heat treatment (thermotropic systems) or from one or more camponents by adding cantrolled amounts of water or other polar solvents (lyotropic mesomorphism). Note that the only molecules of signifkame here are asymmetric and have a d e k i t e long direction, so their tridimensional orientation is essential. This should be remembred throughout the discussion. For present purposes, three of l i q u i d q t a 1 phases will be descrikl briefly so that a t least some appmiation for this ~ a r k u l m state of matter may be gained. The phases generally are characterized as being nematic, smectic, or cholesteric.

183

6P

Figure 1 3-1 5. The srnectic liquidxrystal pha*. (Adapted from Fergmon

J1Brown G H . J m Oil Chem Sot 1968; 45:120.)

The smectic arrangement U similar to the nematic in that there is still =entially only one axis of rotation, except in this case there is no

overlap. The logs go through the pipe as a member of a g r o u p i t would h mea of hag ram in no one and all are tied. V i,,e group, bowever, dm not followthe Bame as the o h s ; within any one group there may, or may not, be equal spacings sideways htweenthelo~ax~.Note~thatthethich~softhelayersisahut the same as the length of tbe molenrl~~. Cholesteric Phme-The cholesteric arrangement (Fig; 13-16)is to Nematic Phase-Nematic molecules P i g 13-14 ) are set in parallel arrangements and have d r i c t e d rotation a h u t at least one axis. The mme extent a cambinationof the nematic and smectic; the layers are nematic, but in addition certain layeriw formations that rmmble the molecules are parallel or nearly so. One might picture this as a long h x smectic phase are incorporated. In es=ce, the result is a helical, t h t filled with pen& with the latter k i n g able to roll. Overall, the system might k considered to k thread- or cable-like. Another picture would h g repetition of the nematic phase that, corkmew-lib, slowly changm head direction (eg, the lead end of the pencil) as one pro& to examk that of a group of logs going through a pipe. There is overlap of the ine underlying layers of molecules. The cholmteric arrangement is, in pen& or logs mmewhat, aa there is with cars in an auto race. Smectic Phase-The smectic or "two-dimensional" crystal (Fig 13toto, much W e r than a smectic layer. AU three structures are involved in building cells,and each type can 15)has i k moleculm arranged in layers with their long axe8 ~ ~ m n t i a l l y (when viewed totally) form curved surfaces, m e m b r m , or any other normal tie, at right angles) to the plane of t h layers. Their centers of gravity are then mobile in two directions in their plane, and the required micelle-lih shapes. Some r m c h e r s have canstructed d molecul~can rotate a h & one axis. Overall, one could consider the armdels using these struhrea and have shown how the m d a n h of many cellular functions can h visualized using the b w n properties of rangement layer-like, with the degree of order just demrild in each layer. liquid crystals.

Figure 13-14. The I I e m a t ~phase of a liquid crystal. (Adapted from Fergason JL, Brown GH. J Am Oil Chem Soc 1968; 45:120.)

Figure 13-16. A 180" turn of the molecules in the cholesteter~liquic!+rystal phaw. (Adapted fmm Fergmon JL, Brown GH. J Am Oil Chern Soc 1968; 45: 120.)

184

PART 2: PHARMACEUTICS

The Glassy State Although glass usually is thought of as a specific, nonconducting, transparent solid, it actually is a type of solid matter. I t can be considered neither a typical solid nor liquid. The atoms of most solid states generally are strictly ordered structurally, whereas glassy materials are highly disordered- Glasses may, however, have some short-range order, just as do ~ o l ~ m e rAnsother characteristic of glasses is that they do not have melting points, but rather slowly and gradually become liquids when they are heated. Sometimes glasses are considered supermled liquids, but this is not strictly accurate. A graph of volume versus temperature for most substanoes shows that the volume of a liquid decreases as the crystallization temperature is approached. If solidification is accomplished by crystallization, the volume decreases sharply at the freezing point, after which it continues to decrease gradually depending on its mfficient of thermal expansion. This type of bhavior is not exhibited when solidification is followed by glass formation. The uniqueness of the glassy state is evident in its cooling curve. As indicated in Figure 13-17, as a glass-former is cooled, it dws not suddenly undergo a large drop in volume (or density, or index of refraction) at any particular temperature or as it passes through the melting point, nor dws its volume decrease as rapidly as that of a supermled liquid, although it follows the curve of the latter initially during mling. With supermled liquids, the m l i n g curve is a simple continuation of the liquid curve itself, with no melting or transition points. Atomically, the structure of the glassy state is marked by a random selection of polyhedral molecules considered to be linked together at their corners. Certain materials are easy to cast into a glassy state, others can he made glassy with great difficulty, and some seemingly not a t all. At present there seems to he no specific theory to help predict this bhavior. Materials that do form glasses appear, however, to have a very high viscosity at their melting point; this inhibits the formation of an ordered structure. In addition, non-glass-formers tend to exhibit large energy differences between the ordered form of the solid and the disordered liquid. Thus, the low-energy, ordered form of the solid tends to be developed. Obviously, the energetic tendencies here are balanced by entropy factors, which tend to favor states of minimum order. Although the most well-known glass-formers are the metal oxides, many other materials can exist in the glassy state; even steel can be so cast if it is m l e d very, very quickly. This technique produces glasses as the materials become solid before they have a c h a m to develop a crystalline structure. With regard to crystal formation, note that, in a crystallization p r e s s ,

-c E Y1

k

0

a

L

a

+

TRAMSITION-

a

g

! =.

9

/ ' / ,-MELTING

Y

,-5,0

$ ? ,'/

G

L * . ;#.

~

~

I

~

+t

'4

~QO"

TEMPERATURE

Figure 13-17. Composite cooling C U N P of liquids forming g l m , supercooled liquid and solid-crystal states.

when concentrated solutions of the material to b crystallized are m l e d slowly, larger and more perfect crystals form. Incomplete or imperfect crystallization, whether due to technique or to the nature of the material itself (eg, natural and synthetic high polymer s), often causes the formation of lites, glasses, or liquid crystals. Crystallites have no recognizable regular crystal pattern; rather, they are, in a sense, incipient crystals. Many shapes and arrangements are possible such as globular, rows or clouds of globules, threads, cylinders, or rds-

Sol ids The most significant physical property of the solid state is the high degree of order in which substances such as metals and minerals exist. The structure may be crystalline and lattice-like or noncrystalline, such as in plastic, glass, or gels, which are not lattice-like or only partly so. These latter materials do have much more order than liquids and gases. These materials also have, in varying degrees, some plastic and elastic properties, wherein some resistance to applied stresses exists, but when the stress reaches a certain intensity either flow or fracture ensues. Although different class5cations exist, four major different types of hands hold solids together; the strong hands impart higher melting points to substances. In order of decreasing strength, the hand types are metallic, ionic (salts), valence (diamond), and molecular (many organic compounds). Thus, in some solids, the atoms or molecules or ions may he arranged in a regularly repeating pattern (crystalline state), whereas other solids are considered noncrystalline or amorphous if they do not have this characteristic of regularity. There is some blurring of the division, but in general, metals, minerals, rocks, and alloys are examples of the former class; glass, w d , ceramics, and plastics are examples of the latter. Alloys are an example of a mixed solid having characteristics of regularity but being intermediate between the strictly crystalline and amorphous states. They are metal substanoes consisting of two or more elements, not counting the tram amounts of materials which make any element less than 100% pure. Alloys are solid solutions of one of two types. In the interstitial type, the smaller solute atoms o m p y the interstices between the solvent atoms; the overall structure is quite like the parent or solvent metal. In the other type, substitutional, all atoms OCCUPY(ie, contribute to building) a common lattice. In general, alloys are stronger and harder than pure metals. This is probably because hath dislmations in the crystalline lattice and the perfectly regular crystal structure of pure metals permit the planes of the crystals to slip over each other. These prmsses are inhibited in alloys bcause the resident or solute atoms interact with the dislmations and with the regular EXtions, so any lattice distortions prduced make slipping more difficult. A process that also depends on the internal structure, and possibilities for partial shifting of it, is annealing. This is based on the concept that a ductile metal becomes harder and less workable as cold work is done on it. Finally, a point is reached where cracking is imminent. To restore the original ductility, the metal is heated and slowly m l e d . The temperatures used just permit the relaxation of the overstrained areas. A visualization might consider this a type of partial recrystallization or atomic rearrangement.

Polymorphism Polyrnorp hisrn, the existenoe of one or more crystalline and/or amorphous forms, is a characteristic of most solid substances. As applied to crystals, it refers to the different crystal structures the same chemical compound may have. The various forms also usually have different x-ray difiaction patterns, melting points, infrared spectra, and, most importantly from a pharmaoeutical standpoint, different solubilities.

CHAPTER 13: MOLECULAR STRUCWRE, PROPERTIES, AND STATES OF MATTER

Particularly, in many cases in which dissolution in the gastrointestinal tract is the rate-limiting factor in abmrption, differing solubilities may have a great effect, either g o d or bad. Different polymorphic forms are produced, depending on such factors as stor age temperature, recrystallization solvent, and the rate of m l i n g (and, hence, the rate of crystallization) of the solvent. It appears that all organic materials exist in several polymorphic forms with the n u m b r of forms found depending on the effort spent searching. In drugs, polymorphs of such diverse molecules h m oortisone and prdnisolone to aspirin have b n found. As an example of the latter case, two different aspirin polymorphs form, de-

pending on whether the material is crystallizedfrom 95%aloohol or n-hexane. The two forms have different melting points, but, most importantly, the form p d u o e d h m the hexane dissolves in water much more quickly. Toscani et als2 have reported the stability hierarchy of three polymorphic forms of sulfanilamide.

REFERENCES Feynman RP. Science 1974; 183:601. SchcrenbornBF'. ChemEngNews31, Jan24,1977. Htzer KS. J Am Chem Soc 1948; 70:2140. Fieaer LF, Fieser M. Inffoducfon to Organic Chmistsbry Boston: DC Heath, 1957, inside back cover. 5. F'auling LC. The Nabure of the Chemical Bond, 3rd ed. Ithaca, NY: Cornell University Pre~s,1960,pp 225-226. 6. Wuling LC. The Nabure of the Chemical Bond, 3rd ed. Ithaca, NY: Cornell Univereity Press, 1960, p 93. 7. Wuling LC. The Nabure of the Chemical Bond, 3rd ed. Ithaca, NY: Cornell University F're~s,1960,Chap 3. 8. Faans K. Physical Methods of Organic Chemism, 2nd ed. Vol 1, Part II. New York Wiley Interscienoe, 1949, p 1162. 9. Cammarata A. J Med Chem 1967; 10:525. 10. Lien EJ, et al.J P h w m Sci 1982; 71M1. 1. 2. 3. 4.

185

11. Lien EJ, et al. J P h w m Sci 1984; 73:553. 12. Lien EJ, et al. Prog Drug Re8 1997;489. 13. Olah GA, et al. J Am Chem Soc 1967;89:711. 14. 8joholm I, 8 d i n T. Biochem P h w m d 1972;21:3041. 15. Martin AN, et al. Physical Pharmacy, 3rd ed. Philadelphia: Lea & Febiger, 1983,5841. 16. Hansch C, Andereon 8M. J Org Chem 1967;32:2583. 17. Hansch C, Andereon SM. J Med Chem 1967; 10:745. 18. Hansch C, et al. J Med Chem 1973; 16:1207. 19. Hansch C, et al.J Med Chem 1977;20304. 20. Hansch C. F w m m Sci 1968; 23:293. 21. Fujita T, et al.J Am Chem Soc 1964; 86:5175. 22. Iwam J, et al.JMed Chem 1965;8:150. 23. Gao H, et al. Phwma Res 1995; 12:1279. 24. Lien EJ, et al. Prog Drug Res 1997; 489. 25. C k t e r TL,et al. And Chem 2002; 742801. 26. Yang C, et al.J Agr Food C h m 2002; 50:W. 27. Lemert RM, et al.J Phys Chem 1% 94:6021. 28. Crowther JB,Henion JD. And Chem 1985;57:2711. 29. G o l d h g AH, et al. J Pharm Sci 1966; 55:482. 30. Kennon L, Gdeaich JJ. J Pharm Sci 1962;51:278. 31. Fergmn JL, Brown GH. J Am Oil Chem Soc 1968; 45320. 32. T d 8. P h m Res 1996: 13351.

EJ, et al. Stereochemistry and Biological Activity of Drugs. Boston: Blackwell, 1983. Eliel EL. Stereochemisbry of Cwbon Compounds. New York: McGrawW, 1962. Hansch C, Leo k Exploring QSAR. Fundamentals and Applicatwns in Chemis@y and Biology. Wmashington DC, AC8 l + o f e ~ a i o dReference h k , 1995. Hansch C, et al. Exploring WAR. Hydrophobic, Elechwnic and 8teric Constants, ibid, 1995. Leo JA. Chem Rev 1993;93: 1281. Lien EJ. SAR Side Effectsand Drug De&n. New York: Dekker, 1987. Ari-

x Formation

The word complex has many meanings in chemistry, so it is necessary at the outset to describe the types of systems that are ineluded in this chapter. A complex is a species formed by the ass,,,-iation of two or more interacting molecules or ions. T~ sharpen this concept the following dehitions are provided: A substmte, S, is the interactant whose physical or =hemica]prop erties are observed experimentally. A L, is the second interactant whose conoentration may be varid independently in an experimental study. A complex is a species of definite substratetdigand stoichiome try that can be form4 in an equilibrium p m s s in solution, and also may exist in the solid state.

.

I t is obvious that the complex must possess some properties that are different &om those of its constituents; otherwise, there would he no evidence for its existence. Among the properties that may he altered upon complex formation are solubility, energy absorption, conductanoe, partitioning behavior, and chemical reactivity. I t is by studying such properties of the substrate, as a function of concentration, that complex formation may he recognized and described quantitatively- The terms complex formation, complexation, binding, and association are synonymous in the context of this chapter. Because complex formation is an equilibrium prmss, the methds of themdynamics can be applied to describe it in the state of equilibrium. Moreover, the methods of chemical kinetics can be used to study the rate of approach to equilibrium. Finally, there may b~?interest in establishing the structure and properties of the complex These dehitions are expressed suminctl~in the following chemical equation for the formation of a complex S,L,. mS

+ nL s S,L,

This shows that the distinction hetween substrate and ligand is arbitrary and is made solely for experimental convenience. The definition omits any consideration of the forces acting btween substrate and ligand in the complex; thus, it is very general. Therefore, the phenomena of intere st may be restricted further by s p e c i ~ n g that complexes are not formed with classic covalent bonds. TYPES OF COMPLEXESThe definition of a complex leads to a classification into two groups based on type of chemical handing. Coordination ComplexeeThese complexes are form4 by cwrdinate bonds in which a pair of electrons is, in some degree, transferred from one interactant to the other. The most import ant examples are the metal-ion mrdination complexes between metal ions and bases. Such mmplexes can be viewd as pducts ofLewis acidphase reactions. ton acids then constitute a s m a l case of this type. ~ 0 1 Compl-eThese % ~ s m e s are form4 by noncovahnt interactions between the substrate and ligand. The noncovalent foms

arise fmm el-static, induction and dispersion interactions, and they include, or give rise to, hydrogen-bonding, chargetransfer, and hydmphobic effects. Among the kinds of mmplex s&es that are includd in this class are small molde-small molecule complexes, small molecule-macromolde s m e s reg, drug-protein and en zpie-substrate complexes),ion-pairs, dimers, and other s e l f - a s s ~ a t dspxies, inclusion COmplexes, intramolecular interactions (such as bas+base interactions in the DNA helix),and clathrate complexes,in which the crystal structure of one interactant encloses m o l d e s of the second interactant. The following sections amplify these brief descriptions of cwrdination and molecular

METAL-ION COORDINATION COMPLEXES DESCRIPTIVE COORDINATION CHEMISTRY--Coordination complexesconsist of a central metal ion (the substrate) handed to an electron-pair donor (a base, the ligand). The ligd , may be conventional~~~~~~d base such as ammonia, an ion such as &loride ion, or even m aromatic compound. The complex may be neutral or charged. Coordination complexes also are called mrdination compounds. The number of hands &om the metal ion to the ligand (or ligands) is called the coordinationnumber of the complex, and the mrdination number is evidently the largest possible number of such bnds. ~h~ maximum mrdination number is determined by the structure ofthe metal ion; numbrs 4 and 6 are most common, but other mrdination numbers are possible. In solutions of Cu(I1) in the pre sence of amrnOnia, these complexes can form: Cu(NHs)'+, Cu(NJ&)$+,Cu(N&).;+, Cu(NHs)2+.The maximum mrdination number of Cu(IT) is 4. A ligand, like ammonia, that has a single basic group capable of bnding to the metal ion is a unidentate ligand. A figand having mom than one amssible basic binding site is multidentate;for example, ethylenediamine, H2NCH2CH2NH2, is a bidentate Kgand. If a metal ion binds to two or more sites on a multidentate ligand, a cyclic complex is formed necessarily; this cyclic complex is a chelate. Thus, ethylenediamineforms a chelate with Cu(I1):

.

~ / $i2W 2 1

l4-' shows several common multidentate ligands> and Table 14-2 lists abbreviations for some ligands. Thus, the complex shown in Structure 1may be written Cu(en)g+.Of course, this complex ion must be assmiated with an appropriate number of anions.

CHAPTER 14: COMPLEX FORMATION

Table 14-1. Some Important Multidentate Ligands4 HzNCHzCHzNHz

Ethylenediamine

w &3

P

8Hydroxyquinoline (oxine)

4

Ethylenediaminetetraacetic acid

(HO~CCHZ)~NCH~CH~N(CH~COZH)Z upon the disxrdation of the proton.

The nomenclature of mrdination complexes is fairly mmplicated, and only the simplest features are reviewed here.' If the complex is an ion, the is listed then the anion. 2. ~ i barn-): ~ neutral ~ ligands h are named as the molecule, ex~ p fort H& (aqua) and N H (ammine). ~ Positive l i ~ d end s in ium (eg, hydrazinium, H m H s + )and negative &and8 in -0 (eg, atetato).Some excepiions are chloro, fluoro, cyano, 0x0, and hydroxo (OH-). 3. Ligands (order):the order is anionic, neutral,and cationic. There are subrulea within them categories; for example, simple ions generally prde p o ~ t o m iions, c and organic ions appear last, 4. Complex (ending8):anionic mmplexm a d in -ate or -ic (if named as the acid). Cationic or neutral oomplexm do not have characteristic endings. 6. Central atom or ion (oxidation state):g;ven by a Roman numeral in ~arenthws; no sign is med for witive oxidation s t a b , but a negative sign indicate8 a negative oxidation state.

LPt(a)NWs

NO*CllSO4 W[Cr(SCN)r

mHa)d [Co(m)aldSOda &Fe(CN) J K[CrOFd

kl

S+ L S L k-1

* Proton acid groups in these ligandsare converted to basic groups

Examples:

Clearly, the classification of labile versus inert is arbitrary, but it has experimental utility because inert complexes can be investigated by conventional chemical techniques, as they may persist long enough to h studied as isolated species; however, labile complexes tend to dissociate upon perturbation of the chemical system. At a more fundamental level, the lability or inertness of a complex can be related to its electronic c o d g u r a t i ~ n . ~ It is important to note that the labile or inert classification is a kinetic one and generally is distinct &om a consideration of complex stability, which is a thermdynamic concept (to k treated subsequently). To express this distinction more concretely, consider the example of complex formation

Dimethylglyoxime

W =NOH

CHqC=NOH

187

where k1 is the rate constant for association and k-l is the dissociation rate constant. Then, approximately, if (kIIL]+ k- is greater than the rate of mixing, the complex is labile. The stability of the complex, however, is described by the equilibrium constant for its formation, which is equal to the ratio kllk- 1. Although labile complexes form and dissociate rapidly, even inert complexes can undergo re actions in which one or more ligands are replaced, thus forming a new complex. Such reactions are called substitution reactions, and because ligands are bases, these are nucleophilic substitutions. A nucleophile, or nucleus-lover, is an electron-rich species that reacts with an electrophilic site; nucleophilicity refers to re activity, ie, kinetics. Basicity refers to equilibrium behavior. The following equation is a typical nucleophilic substitution reaction (a hydrolysis reaction) in which water is the nucleophile. C O ( N J ~ ~ )+~Hz0 C ~ ~+J +C O ( N J ~ ~ ) ~ ~ (+HC1~O)~+

ISOMERISM AND STEREOCHEMISTRY-From organic chemistry it is known that the geometry of handing about the saturated carbon atom is that of a regular tetrahedron (the coordination number of c a r b n k i n g 4). As a consequence, there is only one substanoe with the formula CA2B2,where C is carbon and A or B represent atoms or groups bonded to the carbn.For example, there is only one cornpound (methylene ride) with the formula CHzClz. It is otherwise with metal-ion coordination complexes having coordination number 4, for which it has h e n found that CMoronitr*ineetwen*-* there may be two compounds of structure MAzBz,where M repplatinum(IV) sulfate resents the metal ion. These two compounds are geometrical hmoni- tetrathio-at-in* isomers, and their existence means that they have a square plachromate an) nar structure. For example, the two dichlorodiammineplat~ ( e ~ y l e n e d i a m i n e ~ o bsulfate a l ~ ~ ) inum(U) isomers have these structure s: Potassium hexacyamferrate(I1) Potassium oxotetrduomhromateCv)

Not all mrdination oomplexes Can IE formed simply by mixing the reactants in solution. It has l m n found convenient to classify mrdination complexes as either labile or inert complexe8: A labile complex is one whose rates of formation and dissociation are faater than, m comparable ta,the typical time of mixing ofthe reactant solutions. inertcomplex is one whose formation and dissociation rates are slower than the typical time of mixing of the reactant solutions. able 142. common ~bbreviations of Some Ligands LIGAND

ABBREVIATION

Pyridine Thiourea Ethylenediamine Glycine Oxalate 2,4-Pentanedione (acetylacetone) I,10-Phenanthroline 2,2'-Bipyridine Ethylenediaminetetraacetate

PY

tu

en

S~Y ox acac phen bipy EDTA, Y

F'

NH3

I I

CI-Pt--CI

a-Pt-NH3

I

NH3

NH3

cis

trans

In the cis isomer, two like ligands are adjacent; in the trans isomer, they are opposite each other. The metal and the four ligand groups all lie in the same plane. Figure 14-1 shows alternative representations of the square planar complex structure. The demonstration of geometrical isomerism by chemical methdswas based on the isolation of hath isomers, which is possible if the complexes are inert. There exists also the possibility of cis and trans isomerism in square planar complexes of the structure M(A&, where AB is an unsymmetrical bidentate ligand, such as glycinate.

?\

A-M-B

\A

cis

7\

A-M-A

trans

188

PART 2: PHARMACEUTICS

A

I I A

W+B

.A

0-M-0

4

A

i

.r;

F-,

......ji

;

h,I

/

n

\k4/,

pair). Each enantiomer is a nonsuperirnposable mirror imageof the other as reflected in the central w r t ~ aplane. l

\P

t: I

Figure 14-3. Optical isomers of M(AA13 (top pair) and [~t(en),]~+ (bottom

Figure 14-1. Equ~vdlentrepresentdtlons of the squdre pldndr complex trans-lv1A:B:

Most complexes of coordu~ationnumber 4 have the square planar structure, but some are tetrahedral. Yearly all complexes with coordination number 6 are octahedral; ie, the coordinate bonds lie alollg the x, y, and z axes of a Cartesian coordil~ate system with the metal ion at the origin. This structure is consistent with the experimental observatiolls t h a t only two isomers can be isolated of each of t h e structures ~ ~ I L H and ? kl11,~H,~. The cis and trans isomers of the octahedral dichlorotetraamminecobalt(lll) chloride have these structures: r

CI

Nh

1

-'

I

,

A-Pt

Figure 14-2 shows equivalent ways to draw a n octahedral complex. It should be noted t h a t chloride in the above cobalt compounds plays two different roles; two chlorides are ligands, being coordillately bound to the cobalt, whereas the other chloride sen7esa s a coul~teriol~ to the complex cation. Octahedral complexes can exhibit optical isomerism when two structures are related as l~ollsuperimposablemirror images. Such isomers are called (>nun t i o n ~ r ~The s . optical isomers of k l ( ~ l r i ) ,where ~. rlri is a symmetrical bidentate ligand, are shown in Figure 14-3, which also shows t h e specific example [ Pt(~bn),~]" '. A B

I

*,

*

B A

B 0

,

?+

A-1-

:&,,

A /-k,.b

IL b!

A-

>>I

\:i/

,

\

-F. /

r,il €3

e

Figure 14-2. Equ~valentrepresentsltlons of the octdhedrdl complex cislvlAiBi

1 , .x 1%

A

trans

cis

A+B

The existellee of geometrical and optical isomers of coordi.,tion has prorided valuable insigllt illto possible complex structures, as lloted above; but, in addition, tllese iso. whell subjected to substitutioll reactions, have led to im. portant inferences concerning the mechal~ismsof these reactions, yor example, llucleop~ilicsubstitution reactiolls of Square plallar complexes are kllowll to be bimoleeular displacement processes, on the basis (in part) of complete retelltioll of configuration; cis reactants yield cis products, and tmn,s reactants yield tru ns products.,iThis rules out a dissociatiol~( Su 1) mechal~ism.The reaction is believed to take place ria a trigonal bipyramidal structure in which t h e metal-ion coordillatiol~ number is increased a s showl~below.

6 ck

B

A

A

A

-x -

B Cis

A

--

-K

I A rr;ir L$

A-PI-?

B-~I-Y

I

A ir~7m

T H E O R I E S O F COORDINATE BONDING-11 great range in complexing behavior is observed in the interactions of different metal ions with different ligands, 11successful theory of coordinate bonding should be able to describe and predict the chemistry of coordillatiol~complexes given the identities of the metal ion and the ligand. Uevelopments in this field have been col~cerl~ed particularly with t h e t r a n s i t i o l ~elements, which may be defined as those elements having partly filled d or f shells in any of their commol~oxidation states''; with this definition, slightly more than half ofthe elements are transitiol~elements. In addition, of course, some main group elements may form complexes. 11theory of coordil~atecomplexing should be able to accoullt for the coordinatiol~numbers of ions and t h e stereochemistry of their complexes. It should explain commonly observed regularities in complex stability, such as the chcluk~tbffict: the greater the number of sites of bonding of each ligand to the metal ion, the greater the complex stability, Another pattern is t h a t of the complexes of certain divalent metal ions, whose stabilities v a y in the order kin ,:: Fe :c Co :c Ni ,:: Cu ,:; Zn.The electronic absorptiol~spectra (ie. t h e allowed electronic transitions) of complexes are a readily obsen~edproperty t h a t a theory should describe. Many metal coordu~ationcomplexes absorb strongly in t h e visible region. Metal ions and their complexes also may have magnetic properties t h a t can be accounted for theoretically. Substances having no unpaired electrolls are diamagnetic, whereas those with unpaired electrons are paramagnetic,

CHAPTER 14: COMPLEX FORMATION

and these properties easily are distinguished experimentally.

2 e, orbils

Thus,a theory should be able to predict the number of unpaired

I

electrons in the mrdination complex. Many theories have been developed, and they are essentially all different in concept. It is not possible here to treat any of them in detail, but their basic approaches will IE outlined. The electrostatic theory is completely classical (ie, nonquantum mechanical)? Ions are treated as spherical charges and molecules are treated as dipoles; the energy of a complex is cal-

culatedasasumofch~~g&arge,charg~ipole,andcharg~ induced dipole terms and repulsive fomes. Experimental values of dipole moments and intermolecular distances are employed in the calculations, which yield mults for b n d energies in remarkably g o d agreement with experimental values for many complexes. However, the theory necessarily is approximate, because it dces not include quantum mechanical effects and it oversimplXe8 the structural differences among metal ions and ligands. The valence bond theory of Pa&g6 is a quantum mechanical theory. A mrdinate b n d is formed when a pair of electrons on a ligand is donated to a vacant orbital on the metal ion. The ooordination number is determined by the numbr of available orbitals, and the geometry of the complex is determined by the directional properties of the hybrid orbitals formed by combination of the atomic orbitals (the tetrahedral arrangement of hybrid spSorbitals of carbon). This theory has l m n quite suooessful in amunting for complex s t e r d e m i s t r y . It also can incorporate observations on magnetic type, as illustrated by the electroniccofigurations in Table 14-3.' From the vacant atomic orbitals of Fez+ or FeS+ there can be formed six equivalent hybrid orbitals of composition 3da4s4ps; thus, octahedral complexes are anticipated. Each ligand oontributes two electrons to a hybrid orbital, resulting, in the case of Fe(CN)t-, in a complex having no unpaired electrons and, therefore, diamagnetic; FdCNIg-, on the other hand, possesses one unpaired electron, in agreement with experimental conclusions. The valence b n d theory is useful mainly in this qualitative pictorial way. In principle, b n d energies can be calculated; in practice, this is extremely diEcult. As the coordinate b n d has l m n treated thus far, it consists entirely of a pair of electrons donated by the ligand to a vacant metal orbital Another type of donation is sometimes possible (as in the case of the two hexacyanato complexes shown in Table 14-31. If the ligand pessesses vacant orbitals, the metal may contribute electrons h m its d orbitals to vacant p or d orbitals on the ligand, thus prcducing a b n d with double-bnd character. This phenomenon is called back-bonding. The valence shell electron-pair repulsion theory is a very simple approach to the prediction of complex geometry. This is based on the principle that the valence shell electrons of the metal are directed in space so as to minimize their total repulsive energy. Thus, if there were two electron pairs, they will distribute themselves on opposite sides of the central ion, and a linear complex will be formed. This theory is not able to cdculate b n d energies. The crystal field theory has k e n very fruitfulin the study of mrdination oomplexes. (The word "crystaln in this context is a historical aocident; the theory is applicable to complexes in soTable 14-3. Electronic Configurations of Some Iron Species According to Valence Bond Theory8 SPEQES

rn

FeO

1 1 1 1 1 1 1- 1 - 1 -1 1 1 1 1

Fez+ Fe3+

4s

1 1 -1 1 1 -

4p

-

-

-

-

-

fi 3 3 11 fi 11 11 fi Fe(~~)s3-fi 11 1 3 fi fi 3 11 fi Fe(cnd- fi

-

-

-

'Electrons in dosed shells are not shown; thus the electron configuration of F

~ is O

182p6383d648.

189

I

I

1'

/ 1

I i i

6

Dq

// 1

3d50rbitals

A

= IOD,

// '\\\

'\

40, \\

\,

1

3 ta orbitals Figure 14-4. Energy-level diagram showing crystal-field splitting of the 5-fold degeneracy of metal-ion 3d orbitals in an octahedral complex.

lution as well as in the solid state.) The basis of the theory is seen readily with the example of an wtahedral complex of a metal ion, such as iron. The five 3d orbitals are of equal energy (they are said to be 5-fold degenerate). According to crystal field theory, arranging the ligands colinear with d orbitals require8 more energy ( h a u s e of electron-electron repulsion) than d m the apgro,*ch of liganda between d orbitals. Two d orbitals (d, and d, have l o b s along the three Csrtesian coordinates that d e k e the geometry of the cctahedral complex; thus, the electrical field of the ligands destabilizes (raises the energy of) these two orbitals. The other three orbitals (d,,, d,, d,) are di&ed between the axes, so they are stabilized by the field of the ligands. Thus,the 5-fold degeneracy is split to produce two doubly degenerate orbitals (labled eg) and three triply degenerate orbitals (labeled t-1, with no net energy change. This crystal-field splitting is shown in Figure 14-4. The total-energy difference A is conventionally labled 10%. It, therefore, follows that the e, orbitals are destabilized by 6 4 , and the tZgorbitals are stabilized by 4Dq.8 Now, the f i s t orbitals to b filled upon formation of the complex will tend to IE the lower energy t2, orbitals, unless the stabilization is slight, in which case normal Hund's rule bhavior will be observed, the electrons tending to remain unpaired. Thus, large splitting will lead to the formation of paired electrons (low-spin complexes), whereas small splitting will lead to more u n p W electrons (high-spin complex+es). A further subtlety can mur in which a distortion of the regular cctahedral geometry takes place to lower the total energy of the system. This is known a~ the Jahn-Teller effect,with the w u l t that for many cctahedral complexes four of the ligands are coplanar with, and equidistant h m , the metal ions; the other two ligands lie at a greater distance from the metal ion. The crystal field theory has k e n developed in great detail, and many explanations and predictions have h e n achieved suooessfully. It especially is useful for explaining complex absorption spectra, and spectral measurements can be used to obtain values of the crystal field splitting, A. The molecular orbital theory (which also is called the ligand field theory) is a quantum mechanical description in which molecular orbitals are constructed mathematically by the linear combination of atomic orbitals (MO-LCAO). The number of molecular orbitals (MOs) formed is equal to the n u m b r of atomic orbitals (AOs) taken, but the MOs are formed in pairs; one member of each pair is a symmetric, lower energy, bonding MO, and the other is an antisymmetric, higher energy, antibnding MO. The complex electronic codguration and energy are established by assigning electrons to the bnding MOs. This concept is illustrated in Figure 14-5, shows a schematic MO diagram for OctdLedral complex in which the figand forms only single coordinate bonds (no back-bonding)? The

-,

190

PART 2: PHARMACEUTICS

combines with the species. Pearson has related hardness to the MO theory and developed the quantitative aspects of HSAB theory.'' At the start of this chapter it was specified that complexes are not formed with covalent bonds, but in the case of mrdination complexes it is seen that a coordinate b n d may have extensive covalent character, even though b t h electrons are donated by one of the reactants. One of the goals of theory is to IE able to calculate the fractions of ionic and covalent character of the coordinate bond. Very roughly, it may be expected that when the b n d is between atoms that differ greatly in their electronegativities (propensities for attracting negative charge), the bond will be largely ionic, whereas if the atoms have similar electronegativities, the b n d will be largely covalent.

q0

4s 3d

MOLECULAR COMPLEXES

Metal Atomic orbitals

Complex Molecular orbitals

Ligand A m i c orbitals

Figure 14-5. Schematic molecular orbital diagram for an octahedral complex. The vertical distance represents energy. Each circle denotes an orbital.

combination of AOs must take place according to mrtain quantum mechanical rules. For example, the metal s orbital combines with a ligand n orbital to generate a handing n orbital and an antibonding n* orbital. The nine metal AOs combine with six ligand to prduce l 5 MOs- The octahedral is formed by using the six handing MOs (lowest energy MOs). The M0 theory is the most of the theories of bnding> although quantitative calculations may extremely difficult to make. Basolo and Pearsonlo have presented a comparison of the several theories. Another view that has h e n found useful for its explanatory and predictive power is the hard and soft acid-base (HSAB)conmpt. A hard acid is defined as one in which the electron-pair acmptor atom is small in size, with high positive-charge density and low polarizability. A soft acid is large and polarizable. A hard base has high electronegativity and low polarizability, whereas a soft base is easily polarizable. Examples of these classes are listed inTable 14-4.Polarizability is a measureof the ease with which the electron cloud can he deformed under the influenm of a field. Hardness and softness are related inversely. The HSAB principle states that hard acids prefer to cmrdinate to hard bases and soft acids to soft bases. This empirical generalization can account qualitatively for much mrdinatecomplex chemistry. The HSAB conmpt has h e n extended by the intrduction of a quantitative definition of hardness" as 1

=

dV dr

where is the distance ktween the interacting sFies. I t is conventional to express the intermolecular forms in terms of the corresponding energies. The most important noncovalent energy functions, as established by theoretical arguments, are listed in Table 14-5.

Table 1 4 5 . Potential-Eneyy Functions for Noncovalent Interactions' n p E o F INTERAC~KIN

POTENTIAL-ENERGY FUNCTION

Electrostatic

Charge Klz > Kls,. . ., > K1,. This is a result of a statistical effect.The origin of the statistical effect can be demonstrated readily for the case n = 2. The formation of the 1:1complex is favored over the formation of the 1:2 complex by a factor of 2, because there are two available sites for binding in reactant S, where as there is only one available site in reactant SL. Moreover, dissociation of SLz is favored over dissociation of SL by a factor of 2 because SLz has twice as many ligands to surrender. The combination of these statistical factors leads to the result Kll = 4Klz, solely as a consequence of the statistical effect. This argument was generalized by J ~ n e s . ' ~ Considering the stability of metal-ion coordination complexes, when successive complexes form, two additional factors may operate in addition to the statistical effect. One of these is the steric efict, which is a result of the bulky nature of the ligand (relative to the HzO that it replaces). As successive ligands are added to the metal ion, crowding inhibits the addition of the next ligand, resulting in a decrease in the value of the binding constants. A second factor is the electrostatic effect, which plays a role when the central cation complexes with an anionic ligand. Then, as successive ligands approach the central ion they experience differentfields, because the net charg on the central ion changes with the addition of each ligand.'" The chelate effect was mentioned earlier in this chapter. The formation of a cyclic complex upon binding of a metal ion to a multidentate ligand leads to greater complex stability than when the same metal ion complexes with an analogous unidentate ligand. Complex stability is favored especially by the formation of 5- and 6-membered rings. A multidentate ligand that is also a macrqcle (such as a crown ether) can form particularly strong complexes; this is called the macrocyclic efict+z8 A useful approach in understanding complex stability is to seek correlations of stability with other properties of the interactants. For example, the Irving- Williams order of stability of of with a common band, MnZ+< Fez+< CoZ+< NiZ+< CuZ+< ZnZ+ can be correlated with the ionization potentials (corresponding to the last electron lost) of the ions. Similarly, for complexes of a common metal ion, with a series of structurally related ligands of measurable Br~nstedbasicity, the complex stabilities (expressed as the logarithms of the binding constants) often are correlatedlinearlywiththepK,valuesofthebases.z9Basesof different structural classes (eg, aliphatic primary amines or substituted pyridines) usually give rise to different lines, showing that basicity is not the only controlling feature. The hard-soft acid-base concept descrihd earlier provides additional insight into the effects that properties such as polarizability, electronegativity, ionization potential, electron affinity, and basicity can have in affecting complex stability. In molecular complexes, it is useful to start with Equation 2, in which AG,,, corresponds to AGyl in Equation 6. The value of AG,,, is determined by the three terms AGMM,AGnas, and AGssIf one of these terms greatly predominates over the others, then fairly simple correlations between AGY1 and a molecular property related to the dominant term might be expected. If, however, two or three terms contribute sign5cantly to AG,,,, they may combine in complicated ways, perhaps even opposing each other, so clear relationships may not be observed. Often the

198

PART 2: PHARMACEUTICS

most fruitful experiments are those in which one interactant is held as a col~stalltfeature, and changes in the structure of the other interactant are made. Table 14-5 provides some tl~eoreticalguidance. If solute-solute interactions of the dipole or induced-dipole type are important, one might aal~ticipatecorrelations with interactant dipole moment or polarizability, l n charge-transfer complexing, substituent effects that increase electron density in t h e donor or decrease it in the acceptor (Structures 5, 6, and 7 are examples of t h e latter type) may be expected to illcrease complex stability. Such effects have been ~ b s e r r ~ e d : ' ~ ) ~ ~ ~ ' If t h e hydropl~obicinteractiol~makes an important contri-

bution to complex stability, the il~corporatiol~ of organic solvents will reduce t h e stability, According to the cavity theory of t h e hydrophobic effect, complex stability is related to t h e change in surface area up011 complex formation, so it may be anticipated that, for such systems, complex stability is related to t h e size of t h e interactants. Such a dependellee h a s been seen, but it is complicated by t h e presence of additional effects:" Another prediction of t h e cavity model is that, for a given complex, stability should be determined primarily by the solvent surface tension, and there is some experimel~talsupport for this predictiol~. "" I,,','

COMPLEXES IN PHARMACY A P P L I C A T I O N T O D R U G DELIVERY-Some of t h e properties of a drug are so pertillellt to dosage forms alld drug delivery that it is reasonable to identify them as pharmaceutical or biopharmaceutical properties. Complex formation may affect these properties, sometimes to advantage and sometimes adversely. klany of these properties, wit11 correspondi~gexamples of drug complexes, are given in Table 14-9:"' dosage form migllt be prepared either with t h e separate compol~el~ts S (the substrate or drug) and I, (the ligand or complexing agent), or with the preformed solid complex. ln a solutioll dosage form the metllod of preparatioll makes HO difference, because t h e complexatio~~ equilibrium immediately establishes t h e equilibrium composition. I t must be remembered that the fractiol~of drug in t h e complexed form is give11by Equatioll 11, so tllat the free-liga~dcon cent ratio^ is a critical variable, and excess ligand may have to be added in ord e r t o ''drive t h e equilibrium" in favor of the boulld (complexed) form. In a solid dosage form it may be preferable to incorporate the solid complex rather t h a n a pl~ysicalmixture of the drug and complexil~gagent. For many systems it h a s been showl~t h a t the complex prorides faster dissolutiol~and greater bioavailability t h a n does the pl~ysicalmixture. The processing characteristics (physical state, stability, flowability, etc) of t h e complex also may be better t11an those of the free drug. .Uot all complexatio~~ is u~tel~tiollal or desirable, and some may be t h e result of unwanted dosage-form incon~patibilitit~s c o m p l e x a t i o ~reactions. ~ For example, some widely used polyethers (Tweens, Carbowaxes, or PEGS) can form precipitates with II-bond donors such as phenols and carboxylic acids, 11substallce used widely in liquid dosage forms a s a complexer of metal ions is EU'l'rI (etl~ylenediaminetetraaeeticacid), The purpose of this applicatiol~of complexation is to improve drug stability by illhibiting reactions (usually oxidatiolls) t h a t are catalyzed by metal ions, t h e complexed form of the metal ion being catalytically inactive. Citric acid (in the form of the citrate anion) also is used for this ' r l e cyclodextrins have been shown to have effects on all of the properties listed in Table 14-9, and many pharmaceutical applicatiolls have been proposed. ' " ~ g O ~ ~ " i i i i i COMPLEXES I N PHARMACEUTICAL ANALYSISThe formati011 ofmetal-ion coordu~atiol~ complexes provides the basis of many analytical metl~odsfor the d e t e r m u ~ a t i o of l ~metals. Titration of divalent and trivalent metal ions with a solution of EU'I'II is a standard procedure called complexometric or

Table 14-9. Pharmaceutical Properties Aff eeted by Comrrlexation PROPERTY

EX4MPLEhb

Physical state Volatility Solid-state stability Chemical stability Solubility Dissolution rate Partition coefficient Permeability Absorption rate Bioavailability Biological activity

Nitroglycerin-cyclodextrin Iodine-PVP Vitamin A-cyclodextrin Benzocaine-caffeine Aspirin-caffeine Phenobarbital-cyclodextrin Benzoic acid-caffeine Prednisone-dialkylamides Salicylamide-caffeine Digoxiniyclodextrin lndomethaciniyclodextrin

" Listed in order of drug-complexingagent Citations of the original literature will be found in Ref 34.

c~elatometrictitration,.'"rlle tlleoretical titratioll is cal. ,,lated readily, alld it can be showll that t h e large end. poi,t [hbreakxis tile result ofthe 1:1stoichiometry betweell the metal ion and t h e multidentate E U T h tetraanion. The endpoint can be detected visually with metallochromic indicators or, potentiometrically, with ion-selective membrane electrodes. Very low concentrations of metal ions can be determined with a ligand t h a t produces spectrometrically by complexatio~~ a spectral change. If t h e complex absorbs in the visible region of t h e spectrum, this is called colorimetric analysis. 'rlousands of such methods have been d e ~ e l o ~ e d . ~ ~ " l examples tvo are the determillatiol~of Fe(ll1) by complexatio~~ with 1,lO-phenanthroline (see Table 14-1), and of IIg(l1) by complexatio~~ with dithizone ( d i p ~ ~ e ~ ~ y l t ~ ~ i o c a rSb a zC( o .UIINIIC[;II:i)g. ~~e), Gravimetric analysis of metal ions can be accomplished ria their precipitatiol~as insoluble coordination complexes. For example, Ni(l1) forms an illsoluble square planar bis(dimethy1glyoxime) complex, and many metal ions yield illsoluble complexes with 8hydroxyquil~olil~e (see Table 14-1 for t h e structures of these ligands). In some illstallces the analytical situation call be reversed to make the metal ion sen7ea s t h e analytical reagent and t h e organic ligand as the sample. ' r l e firric h.vclroxan~att~ method for t h e detection and determination of carboxylic acid derivatives is a good example, in which a carboxylic acid derivative such as an ester, amide, or anhydride is reacted wit11 hydroxylamine to form the corresponding hydroxamic acid. 0 H-C-X I ~ excess I

II

0

+

NH70H

li

-+

R-C-NtiOH

+

IiX

of Fe(ll1) is added, and this forms a red-violet coordillatiol~complex with t h e hydroxamic acid; the col~cel~tratiol~ of t h e complex is determined spectrometrically. Colorimetric analyses also can be based on molecular complex formation. Itecall t h a t charge-transfer complexatio~~ often is accompanied by t h e development of an intense chargetransfer absorptiol~band, and this can be put to analytical use. For example, tertiary amines can be determined spectrometrically by complexatio~~ wit11 tetracyanoethylene (Structure 5). Many complex formati011 reactions are used in col~junction with, or a s the basis for, a separation, either by liquid-liquid extractiol~or chromatograpl~y,11classical method for amines, t h e acid-dye>n ~ r t h o dis, based up011 complex formati011 between an amine and a dye molecule. ' r l e complex is extractedfrom the aqueous phase in which it is formed into an organic solvent, where t h e dye collcel~tratiol~ is measured spectrometrically. The success ofthe method is based on the col~ditiol~ t h a t only t h e complexed form of the dye is extractable, so each molecule of amine results in the complexatiol~of one molecule of dye, and this is extracted into t h e organic phase, where its concentration is an indirect measure of t h e amount of amine, ln order to ensure the nonestractability of the excess (uncomplexed) dye, a

CHAPTER 14: COMPLEX FORMATION

dye is used that is a neutral weak acid, and the aqueous pH is controlled a t a level a b v e the pK, of the dye, thus converting it to its anionic form.w The principle can be reversed to determine acidic compounds with basic dyes.41In a similar way metal ions may be extracted into organic solvents upon complexation with hydrophobic ligands. Chromatographic separations can make use of the same principle, most notably in a technique called ion-pair chromatography. In an application of great pharmaceutical importance, an amine sample in its cation form is complexed with a hydrophobic anion (eg, an alkyl sulfonate, RS0,-), and reversephase liquid chromatography is performed. The mobile phase is

polar (often aqueous), and the stationary phase is nonpolar (eg, a C-18-handed packing). Although the protonated amine has little affinity for the nonpolar stationary phase, its complex (called an ion-pair)with the hydrophobic counterion masks its polar nature, and the ion-pair can partition between the two chromatographic phases. Several other forms of chromatography take advantage of complex formation between a sample solute and a molecular entity in the stationary phase to generate selective chromatographic retention behavior. In hydrophobic chromatography the hydrophobic interaction provides the driving force for assmiation. Affinity chromatography is based on fairly specific interactions hetween the migrating solute and a ligand that is chemi"Y' bonded to the phase- For an can k by ~ n i t y On a prepared with an 'Ihibitor of the formation of the inhibitor complex on the column removes the enzyme &om the mixture- In a the 'pecific anti@nantihdy interaction can be applied to isolate antihdies. type of based On formation is chiral chromatography, used to separate optical isomers based On interactions between the isomers and a phase that possesses chiral binding sites. For example, stationary phases have been prepared with covalently bound cycldextrins, which are capable of effecting chiral separations. PROTEIN-BINDING O F DRUGS-Systemically delivdrugs are made to the tissues and Organs of the by means of the b l d , which is a complicated mixture of substances, some of which are of forming oom~lexes with drugs. ~ e c a u s eit is widely ampted that the harma amlogical response to a drug is determined by the concentration of the '%ee" (ie, unbound, uncomplexed) drug rather than the total drug concentration, drug-binding by constituents of the b l d has important practical implications. Of all the constituents of b l d that might take part in complex formation, the most important and most studied is the prokin albumin (HSA for human Serum albumin, BSA for the closely related bovine Serum albumin)- The normal HSA concentration in the b l d is remarkably high, being 3.5 to 4.5 g/100 mL, and the concentration can vary with age, exercise, stress, and disease.42It is a very soluble, very stable protein and consists of 585 amino acid residues, having a calculated molecular weight of 66,439 and a net charge of-15 units at PH 7. The amino acid sequence is known.4" Serum albumin is a strikingly indiscriminate wm~lefing agent, having a significant d h i t y for very many compounds, including drugs- The molecule appears to be appreciably flefible and able to adapt its shape to fit the ~ o ~ ~ c ushape l a r of the ligand binding to it. There are multiple binding sites, but the number that are a m ssible appears to depend upon the particular ligand; moreover, not all the sites are equivalent.42The principal driving force for wm~lefingis the hydrophobic interaction, and hydrophobic compounds, such as long-chain fatty acids (actually as their anions at physiological pH) are bound avidly to HSA. Typical site-binding constants are l o 4 to 10' i t - ' - Gxtain metal ions also can bind to HSA, and the complex with Cu(ll) is particularly stable. Since the binding sites of HSA are evidently not all identical, the simple binding model exemplzed by Equation 13 is not

199

applicable precisely, but this equation often forms the basis for discussions of the binding equilibria. Provided that this oversimplification is recognized, some useful insights can he gained. The symblism is recast as follows: let P = protein, P, = total protein concentration, D = drug (ligand), D, = total drug ooncentration, and [Dl = &ee (unbound) drug concentration. Then i = (Dt - [D])/P,, is the average number of drug molecules b u n d per molecule of protein at h e - d r u g concentration [Dl. Equation 13 now is written =

2 :

nklD1 i

+ kID1

(26)

In the context of drug-protein binding, ~ o r k e roften s make use of the concepts fraction of drug bound ( f b ) and fraction of drug unbound (fd. Obviousl~,fb + f~ = 1-One can write the definitions fu = [DyDt and fu = (D, - [D])/Dt-Algebraic combination of these expressions leads to

PI

=

) . '

1

+ k [ D ] + nkP,

and f = U

1 +kpj ~+~IIJ]+&P,

(28)

Equations 27 and 28 show that fb and f, depend upon the concentrations of b t h the protein and the drug. Clearly, however, when k[D] .v are iron, lead, copper, cobalt, nickel, mercury, and zinc The standard chelating agents for this purpose are the monocalcium disodium salt of EU'rri, dimercaprol (HAL, Structure 101, and rlpel~icillamil~e (Structure 11)

iron poisoning is treated with t h e chelator, deferoxamine,

Structure 12.

REFERENCES 1. Bnsnln F: Prnrsnn RG. :Vluc~hort~srns of Irtorgc~rtlc.Kroc.tlc)rrs:2nd cd. Nrw Ynrk: Wilcy. lY(i7: Chnp 1. 2. Bnsnln F: Pcnrsnn RG. :Vlre~hort~srns of Irtorgc~rtlc~ Krc~c~tlorrs: 2nd rd. Nrw Ynrk: Wilcy, lY(i7: p 141. :i. Bnsnln F: Prnrsnn RG. :Vlpc~horr~srns of Irtorgortlc. Kroc~t~orr~s. 2nd cd. New Ynrk: Wilry, lY(i7: p :i75. 4. Cnttnn F11: Wilkinsnn G. rldl!clrre,r,d Irrorgc~rtlc~I'hprnlstn, 4th cd. New Ynrk: Wilcy-Intcrscicncc, 1980. p (jlY. 5. Bnsnln F: Pcnrsnn RG. :Vlrc~horr~srns o f Irtorgc~rt~c, Kuc~c~tlorrs: 2nd rd. New Ynrk: Wilry: lY(i7: p (in. G . Pnulinfi L. Thr :Vcltrrn, of thr I'hvm~c~ul Korrii: :3rd rd. Ithncn. NY: Cnrncll IJnivcrsit~rPrrss. lY(i0: Chnp 5.

7. .Jnnrs MM. ISlprnurtton I'oortilrtot~orr.I'hurn 1 s t ~ Enfilcwnnd . ClitYs: N.J: Prrnticc-IInll, lY(i4. p 1:I:i. 8. .Jnnrs MM. ISlr,rnrrrtcly I'c)c)rc~~rtot~orr. I'hrrn 1 s t ~ Englrwnnd . ClitYs: N.J: Prrnticr-IInll, lY(i4. p 144. 11. IInnzlik RP. Irr,orgcl 11,1(, Aspt,(,ts of H10log1e~c1lc~rtci0rgc111,1c, I3/r,r,rn1 s t ~ . New Ynrk: Acndcnlic Press: l97(j, p $17. 10. Bnsnln: Prnrsnn, :Vlre~~r~~r*,rtsrns of Irtorgclrtlc. Krnc~tlorrs,p 104. 11. Prnrsnn RG. .I I'lrrm IS(irre. 1987; (i4: 5Gl. 12. Isrnclnchvili ,IN. Irrtr~rmoluc~rrlor clrtd Srrrfoc,r Forc,rs. Nrw Ynrk: Acndrnlic Prcss: 19%: Chnp 2. 13. Isrnclnchvili .IN. Irrtt,ro~c)luc,rllorclrtci Srlrfoc,r Fore,rs. Nrw Ynrk: Acndcmic Press: 19%: p 98. 14. Mullikcn RS: Prrsnn WE. :Vlolpc~rrlnrI'ornplrrrus. New I'nrk: WilryIntrrscirncr: 1969: Chnp 1. 15. Tnnfnrd C. Thu H?drophohlc. ISff(vc,t:2nd cd. New Ynrk: Wilr~r-Intrrscirncc: 1980. l(j. .Jcncks WP. I'otc~lys~s I rt I'hrrn 1 s t nrtd ~ ISrtzyrnology. New Ynrk: hlcGrnw-IIill. 1969: p 417. 17. Cnnnnrs k1, Mulski M.J: Pnulsnn 11. .I Org I'hurn 19112; 57: 17114. 18. Wntsnn ,ID. :Viol(,c,rrlnrK~ologyof thp ( : ( U ~ P : 2nd cd. New Ynrk: iV11 Bcnjnn~in:1970: p 1:IZ. 19. Szcjtli .J. I:~c~lodnr,pntr:itir>n.

Q-lf the differential heat of solutiol~of two polymorphic forms of a drug were measured in water a t standard temperature and pressure ( S T P )and form 11had a larger heat t h a n form U, which is more stable a t STP'? A-More energy is required to dissolve form 11; therefore, it must be the more stable polymorph a t STP.

IS -

(32)

j R q.,..IT

-

.,..

lT

(33)

With the il~troductiol~ of entropy, the second law may be stated as follows: For any spolltalleous process in an isolated system, there is an u~creasein the value of entropy. Alternatively, the first and second laws may be combined with the classic tl~ermodynamic stqtement, "the enernthe ulliverse is the elltrOPY lS ulcreasing," C A R N O T CYCLE-Uefore giving specific examples for t h e calculation of t h e entropy, it is instructive to provide t h e background leading to t h e above definition. T h e concePts of "Id work "Id thus be the Origill the elltrOPY permitting t h e flow ofheat into a system, work may be done by t h e system. T h e hypothetical instrument t h a t is capable heat to work is referred to a s a t'nl?in" (Fig 15-1).The second law dictates t h a t not all of t h e heat may cha'lges in a be cO'lverted into work, eve'1 if reversible manner. In fact. t h e maximum work, W,,,:,,, t h a t may be obtained is specified by the heat flow illto t h e system the temperature differellee Over which the heat ellgille is operating; t h a t is,

m1t,,,, - ~ I ( T - IT

(34)

~ T I

where T~ T g ' ln 1824 Carnot established this equation, which perhaps may be understood best by il~troducil~g t h e Cornwt c:vcle. Consider the system, as shown in Fig 15-1, c o l ~ t a i l ~ uan~ gideal "'

I Tcat Keservoir at 'I':

ENTROPY AND THE SECOND LAW Although the first law provides the framework for calculatu~g t h e change in energy associated with chemical reactions or physical changes in state, there is insufficient informatiol~to allow prediction of the likelil~oodof whether the change will occur. Consider a system composed of two parts that are a t different temperatures, TI and T g , separated by an impermeable, adiabatic partition. When t h e partition is removed, heat will flow from t h e part at a higher temperature to the part at a lower temperature, According to the first law, the energy of the whole system, t h e sum of parts one and two, has not changed. intuitively it is knowl~t h a t the above change will occur regardless of the fact t h a t the first law does not provide a method of predicting t h e occurrence. Such changes are described a s spontaneous, for t h e obvious reason that they occur without additional stimulation. I t should be noted t h a t this spontaneous change involved an increase in the disorder or, if

hq,,,/T

where the subscript rcr Sqi,/T

(53)

Thus, all real processes may be written as d S 2 6q/T

(54)

This concept may be extended to determine the condition of spontaneity. Consider a system that is transformed irreversibly from state 1to state 2 and then reversibly &om state 2 back to state 1. The overall change is given by

I

.?rn.w 2

r2 r2

Scnce 1

Scuce 1

.5cece 1

SqirrlT +

+ SqwoIT< 0

(55)

I

(56)

.?rnre 2

Scnce

dS < O 1

which may be rearranged, with changing the limits of integration, to yield -9cn.w 2

S~,IT<

-5cnce 1

ds .5cere 1

(57)

or, equivalently, for idnitesimal changes SqirrIT < d S

(58)

This is known as the Cla usius inequality. For isolated systems, where bundaries do not permit the passage of energy or matter, Sqi, = 0, the result is given dS > 0

(59)

That is, for every spontaneous change in an isolated system there is an increase in the entropy. The second law may he generalized in another way. The total entropy for any process is given by the sum of the entropy of the system and the surroundings; that is, dS,t = dSxys + dssurr

(60)

For reversible processes, the entropy change in a system is the negative of the entropy change prduced in the surroundings. The total entropy, therefore, is zero. For irreversible processes the total entropy, system plus surroundings, increases. The mathematical statement of this relationship is

z z

AS,, = 0 reversible process

(61)

ASt, > 0 irreversible process

(62)

THE THIRD LAW The third law of thermodynamics simply defines the zero point of the entropy scale. The entropy of a pure, perfectly crystalline substanoe is zero at absolute zero. Intuitively, at the lowest possible temperature a system that has perfect three-dimensional order should have no entropy. The d e h i n g of a zero for the

as = s,,, - SO as = I ( c p i ~ )-d 0~

(63)

as = s,,,

(65)

(64)

01

(52)

The discussion, thus far, has been limited to reversible processes that are strictly impossible to achieve in the laboratory (even though such a process may be approximated very closely). The question is, what is the entropy chang for an irreversible change? Here the entropy change is given by

SqirrIT +

entropy is unlike the other state functions intrduoed previously.Thus,thevalueoftheentropy,S,ofasysteminany state, in principle, may be calculated. What would he the entropy of a crystalline solid at 150 K, Slm?This may be calculated as

If the heat capacity over the range of 0 to 150 K is known, the value of the entropy may be calculated.

Free Energy The concept of free energy is probably the most useful aspect of thermodynamics. The criteria for determining the spontaneity of a chemical reaction or phase change were presented akmve; however, it involved carrying out the change in an isolated system. One can imagine how inconvenient and often impossible i t would be to apply such a mnstraint to the labratory setting. F~~this sake, additional functions have been defined to allow prediction of the spontaneity of a change in state. The rationale for the development of other functions was to allow maximum flexibility in their application. The two functions introduced are Helmholtz free energy, A, and Gibbs free energy, G. The functions for predicting spontaneity are 1. 2. 3. 4.

Isolatd system: dS > 0 Isothermal and imhoric system: dA < 0 lsothermal and isobaric: dG < 0 Constant volume and entropy: d E < 0

Helmholtz h e energy is defined as A E - T S (66) Helmholtz h e energy is the energy available to do pressure-volume work for reversible isothermal processes; a decrease in the Helmholtz h e energy is equal to the capacity of the system to do work. An alternative view is that, for systems a t constant volume and temperature, a change in state is spontaneous if, and only if, there is a decrease in the Helmholtz h e energy. Thus, with the intrduction of aA, the spontaneity of changes m r r i n g at constant volume and temperature may be predicted. As most reactions carried out in the labratory are under conditions of constant Pressure and temperature, Gibbs energy is the most useful function and is defined as GE+PV-TS (67) which can he converted into a more usable form by an analogous method used with the Helmholtz function- Taking the differential and applying the constraints of constant Pressure and temperature yields dG=dE+PdT-TdS but dE = Sq

-

(68)

6W = TdS - SW; thus, upon substitution, -dG = 6W

-

PdV

(69)

A decrease in Gibbs &ee energy is equal to the non-PV work done by the system or, equivalently, dG = -SW{,,pv,

(70)

which also provides the conditions of a spontaneous change under the constraints of constant temperature and pressure. A direct application of the relationship between Gibbs h e energy and non-PV work is used in potentiometry.

CHAPTER 15: THERMODYNAMICS

These relationships for predicting spontaneity often are expressed in a differential form, which presents the state functions in a concise manner as well as facilitating their use to specific problems. The four differential equations are

207

S i m p l i m g yields Dividing through by the number of mols gives

dE = TdS - Pdv dH = TdS + VdP

dA

=

-SdT

dG = -SdT

PdV

Molar free energy, G/n, is encountered so frequently it is given a special symbol, p, and Equation 82 is written as

+ VdP

(83)

-

p = p0 + R T l n P

These expressions represent the four fundamental equations

of thermodynamics, which in reality are four ways of looking a t one fundamental equation describing the conditions of spontaneity. +One mol of liquid water is vaporized reversibly at 100" and 1 atm pressure. The molar heat of vaporization is 9.725 kcallmol; what are qp, AH, AE, aA,AG, and AS? A-The value of qp actually is given in the question, as the heat required to vaporize 1mol of liquid is the definition of the molar he at of vaporization; thus, qp = 9-725 kcal. Recognizing that the pressure is constant, AH = qp = 9.725 kcal. To calculate AE,the work first must be determined. The work is given by

However, the volume of the gas, V, is much larger than the volume of the liquid, V1,which implies that the work is given by Assuming the gas is ideal, the work is

W = nRT

= (1mo1)(1.987 callmol K)(373 K) =

741 cal

From the above, AE may be calculated from The change in entropy is a straightforward calculation, once the enthalpy is known:

The molar free energy also is referred to as the chemical potential. NONIDEALITY-Equation 83 describes the molar free e n e r a of an ideal gas, but for real gases the molar free energy is not related directly to the pressure. Thus, a function, the fugacity, f , has been introduced, which provides the same functional form of equation for a real gas: p = p0 + RTlnf

(84)

The fugacity is related to the pressure by the following equation, which is provided without derivation:

where Vid represents the volume of an ideal gas. This equation may be justified by consideringthe assumptions of an ideal gas, which are that the molecules are point particles without volume, and no intermolecular attractive or repulsive forms. Both of these effects have a direct impact on the measured volume; thus, the fugacity may be considered as a function that corrects for inaccuracies of these assumptions. Clearly, the fugacity approaches the pressure as the real volume approaches the ideal volume. A similar approach is applied when dealing with mixtures. Consider the molar free energy of a mixture of gases. From Raoult's law, the partial pressure, Pi, of a gas is given by where xi is the mol fraction of the ith component and P is the total pressure. Molar free energy is

Helmholtz free energy is given by AA = AE

-

For the purposes of evaluating mixtures, it generally is more convenient to define a new standard state, pO(T,P), which consists simply of the pure gas a t 1atm, thereby yielding

TAS = 8984 - (373)(26.0)= -741 cal

which also may have h e n obtained by recognizing that

Pi = poi(pure) (T, P) + RT lnxI Finally, the change in Gibbs free energy is determined from AG = AE

+ PAV - TAS = 8984 + 741 - (373X26.0) = 0 cal

which, too, may have been obtained by recognizing the absence of non-PV work. STANDARD MOLAR GTBBS FREE ENERGY-The fundamental equation for Gibbs free energy has been given as dG = -SdT

+ VdP

(78)

Consider the change in free energy with pressure at constant temperature. One may begin by defining a standard free energy, GO(T),which corresponds to the free energy of the ideal gas under a pressure of 1atm. Because the temperature is constant, the change in free energy is given by

between the limits of 1 atm and the pressure, P. For an ideal gas, the volume is a strong function of pressure; thus, with substitution, and after integration, the result is

In fact, this equation is applicable not only to the gas state but any ideal state of aggregation. This becomes more apparent by letting the mole fraction go to unity (that is, a pure substance), whenm the logarithmic term goes to zero and the molar free e n e r a is equal to the standard-state molar free energy. For solutions, there is a corresponding term that describes the departure for an ideal mixture, the activity, a. Equation 88 is applicable only for ideal mixtures. However, with the introduction of the activity, a, the above expression may be written as follows, which is general for all mixtures: For solutions, poi (T, P ) is the molar free energy of the liquid in the pure state.

Equilibria Equilibrium is related intimately to spontaneity, thus the functions a b v e used to predict the spontaneity also may be used for establishing conditions of equilibrium. In essence, if no spontaneous change is predicted, the system is at equilibrium.

208

PART 2: PHARMACEUTICS

Consider the followil~gchemical reactiol~for an ideal gas:

be showl~t h a t Gibbs free energ?: is related to the following state ful~ctiolls:

IG'- AH'

For this reaction, t h e equilibrium constant is written a s Let the mular free energy of each component for the cundition of equilibrium be defined as G., and GI A(.wlution> For the overall dissolution, the equilibrium existing htween solute molecules in the solid and solute molecules in solution may h treated as an equilibrium. Thus, for Solute A in equilibrium with its solution,

*

A(solid> A(mlution> Using the Law of Mass Action, an equilibrium constant for this system can he defined, just as any equilibrium constant may he written, as

~

~

CHAPTER 16: SOLUTIONS AND PHASE EQUILIBRIA

where a denotes the activity of the solute in each phase. Because the activity of a solid is defined as unity, Because the activity of a compound in dilute solution is approximated by its concentration, and h a u s e this concentration is the saturation solubility,Ks,the van't Hoff equation (for a more complete treatment, see Martin et all) may be used, which defines the relationship between an equilibrium constant (here,

solubility) and absolute temperature.

where d log KddT is the change of log Ks with a unit change of absolute temperature, T; AT3 is a constant that, in this situation, is the heat of solution for the overall p m s s (solid & liquid & solution); and R is the gas constant, 1.99 cal/mol/deg. Equation 3, a differential, may be solved to give

where J is a constant. A more w f u l form of this equation is

where &,TI, is the saturation solubility at absolute temperature TI, and K s , is~ the solubility at temperature Tz. Through the use of Equation 5, if AT3 and the solubility at one temperature are known, the solubility at any other temperature can Iw calculated. EFFECT OF TEMPEBATURE-As is evident h m Equation 4, the solubility of a solid in a liquid depends on the temperature. In the p r e s s of solution, if heat is absorkd (as eviden& by a reduction in temperature), AH is by convention positive and the solubility of the solute will increase with increasing temperature. Such is the case for most salts, as is shown in Figure 16-2 in which the solubility of the solute is plotted as the ordinate and the temperature as the abscissa, and the line joining the experimentalpoints repwents the solubility curve for that solute.

Figure 16-2. Effect of heat on solubility.

213

If a solute gives offheat during the p w m s of solution (as evidenced by an increase in temperature), by convention AH is negative and solubility decreases with an increase in temperature. This is the case with calcium hydroxide and, at higher temperature&,with calcium sulfate. (Because of the slight solubility of these substanoes, their solubility curves are not included.) When heat is neither absorM nor given off,the solubility is not affected by variation of temperature as is nearly the case with scdium chloride. Solubility curves usually are continuous as long as the chemical composition of the solid phase in contact with the solution remains unchanged, but if there is a transition of the d i d phase from one form to another, a break will be found in the curve. Such is the case with NaaS04 10H30, which dissolves with absorption of heat up to a temperature of 32.4", at which point there is a transition of the solid phase to anhydrous sodium sulfate, NaaS04, which dissolves with evolution of heat. This change is evidenced by increased solubility of the hydrated salt up to 32.4", but above this temperature the solubility decreases. These temperature effectsare what would be predicted h m Equation 4. When the heat of solution is negative, signifying that energy is released during dissolution, the relation btween log KS and lfY is typxed in Figure 16-3 (CurveA), where as lfY increases, log Ks increases. It can be seen that with increasing temperature (Titself actually i n c r e w p m e d i n g left in Fig 16-3A), there is a decrease in solubility. On the other hand, when the heat of solution is p o s i t i v e h a t is, when heat is absorbed in the solution prcwless--the relation between log & and 1PT is typified in Figure 1633. Hence, as temperature increases (lfYdecreases), the solubility increases. EFFECT OF SALTELThe solubility of a nonelectrolyte in water either is d e c r e d or increased generally by the addition of an electrolyte; it is only rarely that the solubility is not altered. When the solubility of a nonelectrolyte is decreased, the effect is referred to as salting-out; if it is increased, it is described as salting-in. Inorganic electrolytes commonly decrease solubility, though there are some exoeptions to the generalization. Salting-out m s because the ions of the added elwholyte interact with water molecules, and thus, in a sense,d u r n the amount of water available for dissolution of the nonelectrolyte. (Refer to the section on Thermodynamicsof the Solution Process for another view.) The greater the degree of hydration of the ions, the more the solubility of the nonelectrolyte is decreased. If, for example, one compares the effect of equivalent amounts of lithium chloride, s d u m chloride, potassium chloride, rubidium chloride, and w i u m chloride (all of which blong to the family of alkali metals and are of the same valence type),

-

Figure 16-3. Typified relationship between the logarithm of the saturation solubility and the reciprocal of the absolute temperature.

214

PART 2 PHARMACEUTICS

lithium chloride decreases the solubility of a nonelectrolyte tu the greatest extent and the salting-out effect decreases in the order given This is also t h e order of t h e degree of hydrati011 of t h e cations, lithium ion-being t h e smallest ion and, therefore, having t h e greatest density of positive charge per unit of surface area (see Chapter 13 under Ele~ctroneghrotri~~t~~ Value~s&is the most extensively hydrated of t h e cations, whereas cesium ion is hydrated the least Salting-out is encountered frequently in pharmaceutical operations Salting-in commul~lyoccurs when either the salts of various organic acids or organic-substituted ammol~iumsalts are added

to aqueous solutions of no~~eleetrolytesIn the first ease, the solubilizing effect is associated with the anion, in t h e second, it is associatedwith t h e cation In both cases t h e solubility increases as t h e col~cel~tratiol~ of added salt is increased The solubility increase may be relatively great, sometimes amounting to severa1 times t h e solubility of t h e nonelectrolyte in water SO1,UBILITY O F SOLUTES CONTAINING TWO OR M O R E SPECIES-ln cases where t h e solute phase col~sistsof twu or more species (as 111 an ionizable inorganic salt),when the solute goes into solution, the solutiol~phase often c o l ~ t a i l ~each s of these species as discrete entities For some such substance, AR, t h e following relatiol~shipfor the solution process may be written

,

AR,,,,I,,I,) Al,,,~,,,,,,,,, + R,,,,I,,,,,,,,,

,,

(14

-

.

)l,lll< I 1

'

03,%) I t 1

.

1 1 1 ~, A ~ > I

1

(6)

and a ,.,,~ , ~ are l , t h e activities ofA where a ,,,, 1,,,,,,,,, air .,,I\,, and R in solutiol~and of AR in the solid phase Itecall from the earlier discussiol~t h a t the activity of a solid is defined as unity, and that in a very dilute solutiol~(eg, for a slightly suluble salt) col~cel~tratiol~s may be substituted for activities Equatiol~6 the11 becomes K,

,,

-

CzCir

where C z and CIr are t h e concentrations ofA and R in solutiol~ 1n this situatiol~K,,,has a special name, t h e solubrlrtyproduct, K,?,, TI] LIs . K s l , - CzCIr

[dissolved AgCl] - [ h g + ]- [ e l - ] -

I -

the solubility ofrlgC1 is equal to G 156 x lo-''), which is 125 x 10 - i mol/liter .\.lultiplying this by the molecular weigllt silver chloride (1431, we obtaill a solubility of approximately 1 8 mg-/liter For a salt ofthe type WCII the solubility product expression takes the form [ W"

for

(7)

This equation will huld true theoretically only for slightly soluble salts As an example of this type of solution, consider the solubility of silver chloride, K s l , - [rig+] [ e l - ] where the brackets [ ] designate molar concentrations At 25' the solubility product has a value of 156 x 10- I", the cuncentration of silver and chloride ions being expressed in molAiter The same numerical value applies also to solutions of silver chloride c o l ~ t a i l ~ uan ~ gexcess of either silver or chloride ions lf the silver-ion concentration is increased by the addition of a soluble silver salt, t h e chloride-ion col~cel~tratiol~ must decrease until the product ofthe two concentrations again is equal numerically to t h e solubility product To effect t h e decrease in chloride-ion concentration, silver chloride is precipitated, and hence its solubility is decreased 1n a similar manner, an increase in chloride-ion concentration by the addition of a soluble chloride effects a decrease in the silver-ion concentration until the l~umericalvalue of the solubility product is attained rig-ain, this decrease in silver-iun concentration is brought about by the precipitation of silver chloride 'rhis phel~omenonof decrease in solubility due to the presence of one of the ions in solutiol~is knowl~as t h e con~n~on-ron ebffict.

I[ C1- 1'

-

K,Yl,

' it"ou1d

be [AS'+ ]'[S1 - 1 '

-

Ksl.

because from the Law of .\.lass hctioll WCl',.,,I,,l, = W'+,.,,I,,,,,,,,,+ 2v1- .,,I,,,,,,,,, and I

11s there is a n equilibrium between t h e solute and saturated sulution phases. the Law of .\.lass rlction defines an equilibrium constant, K, Kt,

The solubility of silver chloride in a saturated aqueous solution of t h e salt may be calculated by assuming that the coneentration of silver ion is t h e same as the cuncentration of chluride ion, both expressed 111 mol/liter, and t h a t t h e concentration of dissolved silver chloride is l~umericallythe same as each silver chloride molecule gives rise to one silver ion and one chloride ion, because

I

)

2hs I + , .,,I,,,,,,,, , + ~ S ' - , - , , I , , ,, ,,,ti

For further details of methods of using solubility-product calculations, see textbooks on qualitative or quantitative analyses or pl~ysicalchemistry Itecall that t h e solubility-product principle is valid for aqueous solutiolls of slightly soluble salts, provided t h a t t h e coneentration of added salt is not too great Where the concentrations are high, deviatiol~sfrom t h e t h e o q occur and these have been explained by assuming- t h a t in such solutiolls the nature of the solvent has been changed Frequently, deviations also may occur as the result of the formati011 of complexes between the two salts AH example of increased solubility, by virtue of complexion formation, is seen in t h e effect of solutiol~sof soluble iodides on mercuric iodide According to t h e solubility-product principle. it might be expected that soluble iodides would decrease the solubility uf mercuric iodide, but because ufthe formation of the ,,l,ble ,,it ~ ~ 1I, which 1 ~ 1dissociates as K ' I I ~ ~ , ), 2 ~ +' ( I I ~ ~- ~ ) ' the iodide ion no longer functions as a commol~ion It is possible to formulate some general rules regarding the effect of the additioll of soluble salts to s.iglltly soluble salts where t h e added salt does not have a n ion common to t h e sligrltly soluble salt lf the ions of the added soluble salt are not highly hydrated (see the previous section, Effict of Salts), the solubility product of the slightly soluble salt will increase because the ions ofthe added salt tend to decrease the interionic attraction between the ions of the slightly soluble salt OH the other hand, if the ions of the added soluble salt are hydrated, water molecules become less available and t h e u~teriunicattraction between t h e ions of the slightly soluble salt increases with a resultal~tdecrease in solubility product rlnother way of considering- this effect is discussed later (see The~rn~o&no~urcs of the>Solutron Procebss) 1n general, t h e effect of temperature is what would be expected increasingthe temperature of the solutiol~results in an increase ofthe solubility product SOLUEILITY FOLLOWING A CHEMICAL REACTION-Thus far the discussiol~has been concerned with solubility t h a t comes about because of interplay of entirely pl~ysical forces The dissolutiol~of some substance resulted from overcoming the physical il~teractiollsbetween solute molecules and solvent molecules by t h e energ-?: produced when a solute molecule interacted physically with a solvent molecule The solution process, however. can be facilitated also by a chemical re-

CHAPTER 16: SOLUTIONS AND PHASE EQUILIBRIA

action. Almost always the chemical enhancement of solubility in aqueous systems is due to the formation of a salt following an acid-base re action. An alkaloidal base, or any other nitrogenous base of relatively high molecular weight, generally is slightly soluble in water, but if the pH of the medium is reduced by addition of acid, the solubility of the base is considerably increased as the pH continues to he reduced. The reason for this increase in solubility is that the base is converted to a salt, which is relatively soluble in water. Conversely, the solubility of a salt of an alkaloid or other nitrogenous base is reduced as pH is increased by addition of alkali.

The solubility of slightly soluble acid subst anms is, on the other hand, increased as the pH is increased by addition of alkali, the reason again being that a salt, relatively soluble in water, is formed. Examples of acid substances whose solubility is thus increased are aspirin, theophylline and the penicillins, cephalosporins, and barbiturates. Conversely, the solubility of salts of the same substances is decreased as the pH decreases. Among some inorganic compounds a somewhat similar hehavior is observed. Tribasic calcium phosphate, C E ~ ? ( P Ofor ~)~, example, is almost insoluble in water, but if an acid is added its solubility increases rapidly with a decrease in p ~ hi^ . is because hydrogen ions have such a strong al3nity for phosphate ions forming nonionized phosphoric acid that the calcium phosphate is dissolved in order to release phosphate ions. Or, stated in another way, the solubilizationis an example of a reaction in which a strong acid (the source of the hydrogen ions) displaces a weak acid. In all of these examples solubilizationoccurs as the result of an interaction of the solute with an acid or a base, and thus the species in solution is not the same as the undissolved Compounds that do not react with either acids or bases are slightly, or not at all, iduenced in their aqueous solubility by variations of pH. Such effects if observed are generally due to ionic salt effects. I t is possible to analyze quantitatively the solubility following an acid-base reaction by considering it as a two-step process. The first example is an organic acid, designated as HA, that is relatively insoluble in water. Its two-step dissolution can be represented as mwlid)

W(w1ution)

followed by HArwlution) 5 H+(wlution)+ A-(wlution> The equilibrium constant for the first step is the solubility of HA(Ks = [HAl,luti,), just as was developed earlier when no chemical reaction h k place, and the equilibrium constant for the second step is the dissociation constant of the acid is IH+][A-

lHAl

Since the total amount of compound in solution is the sum of nonionized and ionized forms of the acid, the total solubility may be designated as S,(HA), or = [HA] + [ A - ) =

Equation 9 demonstrates quantitatively how the total solubility of the acid increases as the hydrogen-ion concentration decreases (ie, as the pH increases). I t is possible to develop an equation similar to Equation 9 for the solubility of a basic drug B, such as a relatively insoluble nitrogenous base (eg, an alkaloid), at various hydrogen-ion concentrations. The solubility of the base in water may be represented in two steps as B(wlid>2 B(wlution> B(wlution>$ BH+(solution)+ OH-(wlution,

Again, if Ks is the solubility of the kee base in water and Kh is its dissociation constant,

[BH*][OH-] K,, =

[BI

the total solubility ofthe base in water

is given by

S~(B) = [B] + [BH+]= [B] + It is convenient to rewrite Equation 10 in terms of hydrogen-ion concentration by making use of the dissociation constant for water Kw = [H+][OH-] = 1 x 10-l4 Equation 10 then becomes (11)

Equation 11quantitatively shows how the total solubilityof the base increases as the hydrogen-ion concentration of the solvent it is possible the increases- If K~ and Kb are total solubility of a basic drug at various hydrogen-ion concentrations using this equation. Equations 9 and 11have assumed that the salt formed following a chemical reaction is idnitely soluble. This, of course, i"Ot an as suggested and demonRather, for an acidic Or basic strated by Kramer and drug there should be a pH at which maximum solubility occurs where this solubility remains the sum of the solution concentrations of the &ee and salt forms of the drug at that pH. Using a basic drug B as the example, this would mean that a solution of B, at pH values greater than the pH of maximum solubility, would be saturated with &ee-base form but not with the salt form, and the use of Equation 11would be valid for the prediction of solubility. On the other hand, at pH values less than the pH of maximum solubility, the solution would be saturated with salt form and Equation 11 is no longer re ally valid. Because in this situation the total solubility of the base, st(^), is

S~(B) = [Bl + [BH+lB

I

KO = -

, , ,S

215

[HA]

IHA] + K c , -

IH'I

(8)

and because Ks = [HA], Equation 8 becomes

Equation 9 is very useful hecause it equates the total solubility of an acid drug with the hydrogen-ion concentration of the solvent. If the water solubility, Ks, and the d i s k a t i o n constant, KO,are known, the total solubility of the acid can he calculated a t various hydrogen-ion concentrations.

where the subscript s designates a solution saturated with salt, the correct equation to use a t PH values less than the PH m a i m would ~ he

[OH-l s,,,=IBH+I,(l+y)=[BH+l,(l+&)

(12)

A relationship similar to Equation 12 likewise can be developed for an acidic drug at a pH greater than its pH of maximum solubility. EFFECTING SOLUTION OF SOLIDS IN THE PRESCRIPTION LABORATORY-The m e t h d usually employed by the pharmacist when soluble compounds are to be dissolved in water in compounding a prescription requires the use of the mortar and pestle. The ordinary practice is to crush the substance into &agments in the mortar with the pestle and pour the solvent on it, meanwhile stirring with the pestle until solution is effected. If definite quantities are used and the whole of

216

PART 2: PHARMACEUTICS

the solvent is required to dissolve the given weight of the salt, only a portion of the solvent should be added first, and, when this is saturated, the solution is poured off and a fresh portion of solvent added. This operation is repeated until the solid is dissolved entirely and all the portions combined. Other methd s of affecting solution are to shake the solid with the liquid in a b t t l e or flask or to apply heat to the substams in a suitable vessel. Substances vary greatly in the rate at which they dissolve; some are capable of producing a saturated solution quickly, 0thers require several hours to attain saturation. With hygrosoopic substams like pepsin, silver corn-

pounds, and some others, the best m e t h d of effecting solution in water is to place the substance directly upon the surface of the water and then stir vigorously with a glass rod. If the ordinary p r d u r e , such as using a mortar and pestle, is employed with these substances, gummy lumps form that are exceedingly difficult to dissolve. me solubility ofchemicals and the ofliquids are important physical factors for the pharmacist to know, as they ohn have a bearing on intelligently and properly filling prescriptions. For the information of the pharmacist, the USP provides tabular data indicating the degree of solubility or miscibility of many official substances. DETERMINATION OF SOLUBILITY-F~~ the pharmacist and chemist, the question of solubility is of impofiance. ~~t only is it necessary to know solubilities when preparing and dispensing medicines, but such information is also necessary to effect separation of s u b s t a m s in qualitative and quantitative analysis. ~ ~ ~the t rate determination of the solubility of a substanoe is one of the b s t methds for determining its purity. The details of the determination of the solubility are affected markedly by the physical and chemical characteristics of the solute and solvent and also by the temperature at which the solubility is to h determined. Accordingly, it is not possible to describe a universally applicable method, but in general the following rules must b observed in solubility determinations. 1. The purity of both the d i ~ o l v e dsubstanoe and the solvent is e s sential, because impurities in either affwt the solubility. 2. A constancy of temperature must be maintained accurately during the course of the determination. 3. Complete saturation must be a t h i n d . 4. Accurate analysis of the saturatd solution and m m t expres sion of the results are imperative.

Consideration should he given also to the varying rates of dissolution of different compounds and to the marked effect of the degrees of fineness of the particles on the time required for the saturation of the solution. THE PHASE RULE AND PHASE-SOLUBILITY ANALY SIS-Phase-solubility analysis is a useful and accurate m e t h d for the determination of the purity of a substanoe. I t involves the application of precise solubility methds to the principle that constancy of solubility, in the same manner as const ancy of melting point, indicates that a material is pure or &ee fiom foreign admixture. It is important to recognize that the technique can he used to obtain the exact solubility of the pure substanoe without the necessity of the experimental material itself b i n g pure. The m e t h d is based on the themdynamic principles of heterogeneous equilibria that are among the soundest of theoretical concepts of chemistry. Thus, it does not depend on any assumptions regarding kinetics or structure of matter, but is applicable to all species of molecules, and is sufficiently sensitive to distinguish between optical isomers. The requirements for an analysis are simple, as the equipment needed is basic to most laboratories and the quantities of substanoes required are small. The standard solubility m e t h d consists of five steps: 1. Mixing, in separate systems, increasing amounts of a substance with measured amounts of a solvent.

2. Establishment of equilibrium for each system at identical constant temperature and pressure. 3. Separation of the solid phase from the solutions. 4. Determination of the concentration of the material dissolved in the various solutions. 6. Plotting the concentration of the dissolved material of interest per unit of solvent ( y-axis, or solution concentration) against the mass of total material per unit of solvent (x-axis or system concentration).

The solubility method has b n established on the sound theeretical principles of the Gibbs phase rule: F = C - P + 2, which relates C, the number of components; F, the degrees of freedom (presswe, temperature, and concentration); and P, the n u m h r phases for a heterogeneous Solubility analyses are carried out at constant temperature and Pressure, So a Pwe solid in solution would show only one degree of freedom, because only one phase is present at COmxntrations below saturation. This is represented by section AB in Figure 16-4.For a pure solid in a saturated solution at equilibrium (Fig 16-4, BC), two phases are resent, solid and solution; there is no variation in concentration, and thus, at constant and pressure, no degrees of freedomThe curve ABC of Figure 16-4represents the type of solubility diagram obtained for: (1)a pure material, (2) equal amounts of two or more materials having identical solubilities, or (3) a mixture of two or more materials present in the unique ratio of their solubilities. These latter two cases are rare and often may k detected by a change in systemLine segment BC of Figure 16-4indicates purity because it does hhasno ~ slope.~ If, however, ~ ~this section ~ , exhibit a slope, its numerical value indicates the fraction of impurity present. Line segment BC, extrapolated to the y-axis at D,is the actual solubility of the pure substanceA representative type of solubility curve, which is obtained when a s u b s t a m contains one impurity, is illustrated in Figw e 16-5. Here, at B the solution b m e s saturated with one From to there are two phases present: a tion saturated with Component I (usually the major WmPnent) containing also some Component I1 (usually the minor component), and a solid phase of Component 1. The one degree of h e d o m revealed by the slope of the line segment BC is the ,centration of component IT, which is the impurity (usually the minor component). A mixture of d and 1 isomers could have

B

3 2

A SYSTEM CONCENTRATION. mq /mL

Figure 164. Phme-solubility diagram for a pure substance.

C

CHA!TER 16: SOLUTIONS AND PHASE EQUILIBRIA

E

o

E

System Concentration Figure 1 6 5 . Type of solu biliiy curve obtained when a substance contains one impurity.

such a curve, as would any simple mixtures in which the solubilities are independent of each other. with ~h~ section CD indicates that the solventis b t h components of the two-component mixture. Here, three with b t h components phases sl.e pmnt: a solution is pasand the two solid ph88es. N~ Of siblei hence, degree of worn is possible (indicated by the lack of slope of section CD). The distance AE on the ordinah repments the solubility of the major component, and the dist a m EF represents the solubility of the minor component. ~h~ equilibration pms is time consuming, requiring as long as 3 weeks in certain cases, but this is offiet by the fact that all of the sample can be recovered &r a determination. hi^ adds to the usernof the methd, lmly in cases where the s u b s t a m is expensive Or =cult to obtain. A use for the methd other than the determination of purity or of solubility is to obtain especially pure samples by m v e r i n g the solid midues at system conentration, 00BC in figure 1 6 5 . ~ h the ~ spending to points On not only as a quantitative analytical tool, but m e t h d is also for p d c a t i o n .

Solutions of Liquids in Liquids BINMY S Y S T E M S m e following types of liquid-pairs may b recognized as binary systems. 1. Those that are soluble wmpletely in each other in all proportions.

homogeneous mixtures of substances showing mutualsolubility behavior. At m m temperature (here assumed to be 25'1, by drawing a line psrallel to the abscissa at 2 5", we k d that we actually can prepare two sets of homogeneous solutions, one containing from 0% to about 7.5% phenol and the other containing phenol h m 72% to a b u t 95% (its limit of solubility). At compositions between 7.5% and 72% phenol a t 25" two liquid layers or phase8 will separate. In sample tubes containing a concentration of phenol in this two-layer region at 25" one layer always will be phenol-rich and always contain 72% phenol while the other layer will Iw water-rich and always contain 7.5% phenol These values are obtained by interpolation of the two points of intersection of the line drawn at 25" with the experimental curve. As it may be deduoed, at other temperatures, the composition of the two layers in the two-layer region is determined by the points of intersection of the curve with a line (called the tie line) drawn parallel to the abscissa at that temperature. The relative amounts of the two layers or p h w s , phenol-rich and water-rich in this example, will depend on the concentration of phenol added. As expected, the proportion of phenol-rich layer relative to the water-rich layer increases as the concentration of phenol added increases. For example, at 20% ~ h e n oin l water at 25", there would b more of the water-rich layer than of the phenol-rich layer, whereas at 50% phenol in water there would lw more of the phenol-rich layer. The relative portion of each layer may b calculated h m such tie lines at any temperature and compositions as well as the amount of phenol present in each of the two phases. To determine how these calculations are made and for further discussion of this topic the student should Martin et A simple and practical advantage in the use of phase diagrams is pointed Martin et aL1 Based on diagrams such as Figure 16-& they point Out that the most conenhated s w tion of phenol that should perhaps be used by ~ h m a c i s t is s One Containing 76% whu phenol in water (equivalent to 80% w h 1-At m m temperatm this mixture is a homogeneous solution ~ and , will remain homogeneous to around 3.5", at which temperature *zing 0-8. I t should be noted that ~ i ~ u e f i e d Phenol USP contains 90% w/w phenol and freezes at 17". This means that if the storage area in the pharmacy falls to a b u t 63"F, the preparation will M z e , resulting in a stmk solution no longer convenient to use. In the case of phenol and water, the mutual solubility increases with an i n c r e w in temperature and the critical solu-

Examples: alwhol and water, glycerin and water, alcohol and glycerin. 2. Those that are soluble in each other in definite gropokiona. Examples: phenol and water, ether and water, nicotine and water. 3. Those that are impermptibly soluble in each other in any proportion. Examples: castor oil and water, liquid petrolatum and water.

The mutual solubility of liquid pairs of Type 2 has l m n studied extensively and found to show interesting regularities. If a series of t u b s containing varying, but known, percentages of phenol and water are heated (or cooled, ifneoessary) just to the point of formation of a homogeneous solution, and the tempera t m s at such points is noted, upon plotting the results a curve is obtained similar to that in Figure 16-6. On this graph the area inside the m e represents the region where mixture8 of phenol and water will separate into two layers, while in the region outside of the curve homogeneous solutions will be obtained. The maximum temperature on this curve is called the critical solution temperature, that is, the temperature above which a homogeneous solution m s regardless of the composition of the mixture. For phenol and water the critical solution temperature m r s a t a composition of 34.5% phenol in water. Temperature versus composition curves, as depicted in Figure 16-6, provide much usefulinformation in the preparation of

217

HOMOGENEOUS

TWO LAYER

o

20

40

x

60

BCI

100

PHENN~LRY W T

Figure 166. Phenol-water mlubility. (Fmm Campbell AN, Campbell MR. J Am Chem Soc 1 937; 59: 2481.)

218

PART 2 PHARMACEUTICS

tion temperature occurs at a relatively high point 1n a certain number of cases, however, the mutual solubility increases with decrease in temperature and the critical solution temperature occurs at a relatively low value Llost of the substallces t h a t show lower critical solution temperatures are amines as, for example, triethylamine with water In addition to pairs ofliquids t h a t show tbrthtbr upper or lower critical solutiol~temperatures, there are other pairs t h a t show both upper and lower critical solutiol~temperatures and the mutual solubility cun7eis of the closed type rlH example of this type of liquid pair is found in t h e case of nicotine and water (Fig 16-7) Llixtures of nicotine and water represented by points

100% alcohol

within the eun7e will separate into two layers, but mixtures represented by poults outside of the curve are perfectly miscible with each other In a discussion of solutiol~sof liquids in liquids it is evident t h a t the distinction between the terms solute and solvent loses its significance For example, in a solutiol~of water and glycerin, which shall be collsidered to be the soluble and which the solvent'?r i g a u ~when , two liquids are only partially soluble in each other, the distinction between solute and solvent might be reversed easily In such cases the term solvent usually is given to t h e collstituel~tpresent in larger quantity TERNARY SYSTEMS-The addition of a third liquid to a binary liquid system to produce a ternary or three-component system can result in several possible combil~atiol~s If the t h - d liquid is soluble in ollly olle of the two original liquids or if its solubility in t h e two original liquids is markedly different, the mutual solubility of the original pair will be decreased AII upper critical solutiol~temperature will be elevated and a lower critical solutiol~temperature lowered On the other hand, t h e addition of a liquid haring rougl~lythe same solubilof the original pair will result in a n inity in both compol~el~ts crease in their mutual solubility I ~ upper I critical solutiol~ temperature the11 will be lowered and a lower critical solutiol~ temperature elevated AH equilateral-trial~glegraph may be used to represent terllary systems In tllis TYPE of grapl], each side of the triallgle represellts O(A of olle of t h e ComPollellts alld the apex opposite t h a t side represents 100!t ofthat component This is illustrated usillg a ~ a r t i c u l a r l yCommoll ternary system ulvolving two solvents t h a t are completely miscible and a third that is miscible with only one of t h e two IH Figure 16-8, water and alcohol are the miscible solvents and castor oil is the third solvent t h a t is soluble in alcohol but not in water Such diagrams could be ap-

Ild

-

'As&lsd

-

I#.

*b-

wi $

'46+

v v y v v v V " \ 100% oil

water

Figure 16-8. Phase didgrdm dt constdnt temperdture for d terndry y s tern two llqulds completely mlsclble In one dnother with d third llquld solubleIn only one of the two (ndtdfrom Lordn ~ I R ~, ~~p tJ AhP ~ 5 ' A 1 ~d 1 q 5 1 , 4 0 4 6 5 )

plied, for example, t o surfactant/oil/water systems, flavor/ water/alcohol systems, drug/progellant mixture systems, ~r,g~,vater~propy~elle glycol systems or any otller such system you might think of t h a t would fit into this category The data in Figure 16-8 were obtained by determining the amount of water needed to just cloud solutiolls of oil in alcohol a t different concentrations and at room temperature The percentage of each solvellt just cloudillg tile system was tllen cal. culated and plotted as s h o w l ~in t h e figure For example, a cloudy solutioll developed at a mixture of about 6 7 ( ~alcohol, 2 7 5 oil, alld 6 ~ i y o t e tllat tile percelltages of t h e tllree compo,e,ts must always equal 1005 l H the regioll labeled nlrst.rblt~, ally combillatioll of tile tllree compollellts will result in a solution The pl~armacistcan pick any combillatiol~in this region for reasons of taste, safety, stability, or cost Figure 16-8 is collstructed for room temperature, any other temperature as a would have its own phase diagram ll~cludil~gtemperature variable would create a three-dimensional relationship with ternary diagrams such as Figure 16-8 stacked in t h e x-.v plane as a fullctiol~of temperature on t h e z-axis Other possibilities exist in ternary liquid systems-for example, those in which two compol~el~ts are completely miscible and the third is partially miscible with each, and t h a t in which all combil~atiol~s of two of the three compol~el~ts are only partially miscible

M-

E

X

p

06-

Solutions of Gases in Liquids

11-.

d. M@

-

Id.

H-

eI O a O w m w = R m 9 0 hICOTICIE PER CENT

Figure 16-7. Nicotine-water solubility.

Nearly all gases are more or less soluble in liquids. One has but to recall the solubility of carbn dioxide, hydrogen suEde, or air in water as common examples. The amount of gas dissolved in a liquid in general follows Henry's law,which states that the weight of gas dissolved by a given amount of a liquid at a given temperature is proportional to its pressure. Thus, if the pressure is doubled, twioe as much gas will dissolve as at the initial pwsure. The extent to which a gas is dissolved in a liquid, at a given temperature, may be expressed in terms of the solubility mfficient, which is the volume of gas measured under the oonditions of the experiment

CHA!TER 16: SOLUTIONS AND PHASE EQUILIBRIA

that is absorbed by one volume of the liquid. The degree of solubility also is expwsed sometimes in terms of the absorption coefficient,which is the volume of gas, reduced to standard conditions, dissolved by one volume of liquid under a p m u r e of one atmosphere. Although Henry's law expresses fairly accurately the solubility of slightly soluble gases, it deviates considerably in the case of very soluble gases such as hydrogen chloride and ammania. Such deviations most frequently are due to chemical interaction of solute and solvent. The solubility of gases in liquids decreases with a rise in temperature and, in general, also when salts are added to the solvent, the latter effect being referred to as the salting-out of the gas. Solutions of gases potentially are dangerous when exposed to warm temperatures because of the liberation and expansion of the dissolved gas, which may cause the container to burst. Bottles ~ n t a i n i n gsuch solutions (eggstrong ammonia 801~tion) should b m l e d bfore opening, i f ~ r a c t i c dand the S b P Per should b covered with a cloth before attempting its removal.

219

E

$

=g

+

A

Mole Fraetlon Figure 16-10. Phme diagram for a discontinuoussolid solution for Solid A and Solid 8: true solid solutbns and p are wparated by a eutectic phaw. (Adapted f tom Grant DM, Abougela IKA. Analyticat Pr~.&ings: Proc&ings of the Anawical Division of the Royal Society of Chemistry. Dec 1992.)

Solutions of Solids in Solids Various mixtures of one solid in another are being considered in the phamaeutical scienm p r i m d y as a m e w inwage bioavailability. For example, melts of solid miKtures of drugs with excipients and eutectic mixture8 are k i n g investigated (see Chapter 13). I t is possible to have a true solution of one solid in another to give rise to a continuum of one solid dispersed in another as depicted in 16-9. Such a system is referml to as a continuous dispersion; it is very rarely found. To achieve this would mean that two materials would have to b of similar size, structure, and interaction energy so that they might enter and mmpy a mutual crystaVine structure at the molecular level. Hence, such solid solutions may m m r only among racemic mixture8 of chid campounds. If it were ~ 0 8 8 ~ ble to form a solid solution of a drug in a water-soluble excipient, bioavailability could increase dramatically because the drug would transfer into water as individual molecules. There are three types of continuous dispersions depicted in Figure 16-9: [l] shows an ideal dispersion of constant melting point, while [2] and [3] (nonideal solutions) show dispersions having a maximum or minimum, wpectively. Each of the latter dispersions show an upper or liq uidus line and a lower or solidus line that might b viewed as representing the direction of melt(oo~lingor heating) used arrive at the temperaing or solidification in each mixture. The composition of the liquid and solid phases in the region between the two lines can be quantified in a way that is related to the tie-line treatment for phenol-water systems, although more complicated.

I

0 A

More common are the discontinuous solid dispersions illusin where two true solid solutions a ,p,aw by a eutectic phase. Such a systpm is found for urea/acetaminophen; which exists as solid solutions in very regjons at very high ma conenhation and very high ac-

,

etaminophen conoentration.

At this point it is worthwhile to briefly consider solid camThe interaction of a drug with an excipient b form a new phase through strong hydrogen-hnd formation can gjve a phase that is pmisely a solid solution, but nonetheless important in its on bioavailability-hth in a positive and negative sense. The phase diagram was obtained by fusing and caoling mixtures of in firn g ~ i m f ~(G) ] ~and i phenobmbitone ~ (P). When a complex is stable up b its melting point, the liquidus curve shows a peak to as a congruent point. Two congruently melting complexes, PG, and PsG (at x = 0.25 and 0.75 in Fig 16-11), are found for the griseofulvin-phenobarbital system.

the In this discussion of the thermodynamics of the solution pn)w s , the solute is assumed to Iw in the liquid state, hence, the

1

0.5 Mob Fmetlon. X(B)

1 B

Figure 16-9. Phme diagram for a continuous solution of a Solid A in a Solid B (orof B in A: [I ]is an ideal mlution, [2]and 131,nonideal solutions. (Data fmm Duddu 5. PhD thesis. University of Minnesota, 1 993.)

(GI Mole Fraction x(P) PI Figure 16-11. Ternperature-zoncentration relationship for fused mixtures of griseofulvin ( G ) and phenobarbital (P). (Adapted from Grant DJW, Abougela IKA. Analytical Proceedings: Proceedin~sof the Analytcal Division of the Royal Society of Chernisty. Dec 1 992.)

220

PART 2: PHARMACEUTICS

The magnitude of the various attractive forces involved between solute, solvent, and solute-solvent molecules may vary greatly and thus could lead to varying degrees of positive or negative enthalpy changes in the solutiol~process The reason for this is t h a t t h e molecular structure of t h e various solutes a n d solvents determining t h e interactiol~scan themselves vary greatly For a discussion of these effects, see Martin Considering only the process, Pf o l ' The solute-solute interactiol~t h a t must be overcome can v a y from the strong ion-ion interaction (as in a salt), to the and assuming that the solute is a liquid (or a super-cooled liqweaker dipole-dipole interaction ( a s in nearly all organic uid in the case of a solid) at a temperature close to room temmedicinals t h a t are not salts), to t h e weakest induced perature, where the energy needed for melting (heat of fusion) dipole-induced dipole interactiol~(as with naphthalene) is not being considered The attractive forces in the solvent t h a t must be overcome For a physical or chemical reaction to occur spol~tal~eously are, most frequently, t h e dipole-dipole interaction ( a s found in at a constant temperature and pressure, the net free-energy water or acetone) and t h e induced dipole-induced dipole interchange, AG, for the reaction should be negative (see Thtbrnloclyaction (as in liquid petrolatum) nanlrcs, Chapter 15) Furthermore, it is known that the free-enT h e energy-releasing solute-solvent interactions t h a t ergy change depends on heat-related enthalpy (AH') and ordermust be taken into accoullt may be one of four types In derelated entropy ( A S ) factors as seen in creasil~genergy of interactiol~these are ion-dipole interactions (eg, a sodium ion interacting with water), dipole-dipole interactions (eg, a n organic acid dissolved in water), where T is t h e temperature Itecall also that the relation bedipole-induced dipole interaction, to be discussed later (eg, an tween free energy and t h e equilibrium constant, K, for a reacorganic acid dissolved in carbon tetrachloride) and induced tion is given by dipole-induced dipole il~teractiolls(eg, naphthalene dissolved in benzene) Since t h e enerm-releasing solute-solvent interaction Equatiolls 13 and 14 certainly apply to t h e solution of a drug should approximate t h e energy needed to overcome the soBecause the solubility is, 111 reality, an equilibrium constant, lute-solute and solvent-solvent interactions, it should be apEquatiol~14 indicates t h a t t h e greater the negative value of parent why it is not possible to dissolve a salt like sodium AG, the greater the solubility The interplay of these two factors, AH' and A S in Equatiol~ chloride in benzene The interaction between the ions and benzene does not supply enough energy to overcome the in13, determines t h e free-energy change, and hence whether disteraction between the ions in the solute and therefore gives solutiol~of a drug will occur spontaneously Thus, if in the sorise to a positive heat of sulution On t h e other hand, the inlutiol~process AH' is negative and A S positive, dissolution is fateraction of sodium and chloride ions with water molecules vored because AC; will be neg-atir~e As the heat of solutiol~is quite significant in t h e dissolutiol~ does provide an amount of energy approximatu~gthe energy needed to separate the ions in t h e solute and t h e molecules UI process one must look a t its origin (For an excellent and mure the solvent complete discussiol~of the il~teractiollsand driving forces unConsideration must next be given to entropy effects in disderljlng the dissolution process, see IIiguchi ") The mechanism solutiol~processes Entropy is an indicator of the disorder or of solubility involves severing of the bonds that hold together the ions or molecules of a solute, the separation of molecules of ral~doml~ess of a system The more positive t h e entrupy change solventto create a space in t h e solr~entinto which t h e solute can ( A S ) is, the greater the degree of r a l ~ d o m l ~ eor s s disorder of the be fitted and the ultimate response of solute and solvent to reaction system and the more favorably disposed is the reacwhatever forces of interaction may exist between them 1n ortion Cnlike AH', the entropy change (an entropy of mixing) 111 der to sever the bonds between molecules or ions of solute in the an ideal solution, is not zero, but has some positive value as liquid state, energy must be supplied, as is the case also when there is an illcrease in t h e disorderliness or entropy of the sysmolecules of solvent are to be separated l f h e a t is the source of tem up011 dissolutiol~ 'rh~lus,in an ideal solutiol~with AH' zero energy it is apparent that both processes require the absorption and A S positive, AC; wuuld have a negative value and t h e proof heat cess would therefore be spontaneous Solute-solvent interaction, on t h e other hand, generally is 1n a nonideal solution, on the other hand, where I H ' is not accompanied by t h e evolutiol~of h e a t as the process occurs zero, A S can be equal to, greater than, or less t h a n the entropy spol~tal~eously In effecting solutiol~there is, accordingly, a of mixing found for the ideal solution h nonideal solutiol~with heat-absorbing effect and a heat-releasing effect to be considan entropy of mixing equal to t h a t ofthe ideal solution is called ered beyond those required to melt a solid If there is no, or a regular solufron. These solutiolls usually occur with nonpolar interactiol~ between solute and solvent, the only efvery little, or weakly polar solutes and solvents Such solutiolls are acfect will be t h a t of absorption uf heat to produce the necessary companied by a positive enthalpy change, implying t h a t the soseparations of solute and solvent molecules or ions If there is lute-sulvent molecular interaction is less than the solute-soa significant interaction between sulute and svlvent, t h e lute and solvent-solvent molecular interactions Itegular amount of heat in excess of t h a t required to overcome t h e sosolutiolls are amellable to rigorous physical chemical analysis, lute-solute and t h e solvent-solvent forces is liberated If the which will not be covered in this chapter but which can be found opposing heat effects are equal, there will be no change of in outline form in Martin et a1 ' temperature The possibility exists in a nonideal solutiol~t h a t t h e entropy When I H ' is zero, and there is no volume change. an rclcol change is greater t h a n for an ideal solutiol~Such a solution ocsolufron is said to exist because the solute-solute, solvent-solcurs when there is a n association among solute or sulvent vent, and solute-solvent interactions are the same For such an molecules In essence, t h e dissolutiol~process occurs when ideal solution, t h e solubility of a solid can be predicted from its starting at a relatively ordered (low entropy) state and proheat of fusion (the energy needed to melt the solid) at temperagressing to a disorderly (high entropy) state tures below its melting point The student is referred to Llartin et al' to see how this calculatiol~is made The overall entropy change is positive, greater than t h a t of When the heat of solution h a s a positive (energ?: absorbed) t h e ideal case, and favorable to dissolutiol~ As may be or negative (energy liberated) value, the solutiol~is said to be a expected, the enthalpy change in such a solution is positive nonrdcal solufron. h negative heat of solutiol~favors solubility because associatiun in a solute or solvent must be overcome The facilitated solubility of citric acid ( a n ul~symmetrical while a positive heat works against dissolutiol~ heat of solution (AH') is a term different from that in Equation 3 ( I H ) The heat of solutiol~for a solid solute going into solutiol~ as defined in Equatiol~3 is the net heat effect for the overall dissolution

CHAPTER 16: SOLUTIONS AND PHASE EQUILIBRIA

molecule), as compared to inositol (a symmetrical molecule), may be explained on the basis of such a favorable entropy change." The solubility of citric acid is greater than that of inositol, yet on the basis of their heats of solution, inositol should be more soluble. One may regard this phenomenon in another way. The reason for the higher solubility of citric acid is that, although " there is no hindrance in the transfer of a citric acid molecule as it goes from the solute to the solution phase, when the structurally unsymmetrical citric acid attempts to return to the solute phase from solution, it must assume an orientation that will allow ready interaction with polar groups already ori-

221

acter, and glycerin could he considered a polar or semipolar solvent even though it is capable of forming hydrogen hands.

Solvent Types WATER--Water is a unique solvent. Be sides being a highly associated liquid, giving rise to its high boiling point, it has another very important property, a high dielectric constant. The die1ectric constant ( E ) indicates the effect that a substance has, when it acts as a medium, on the ease with which two oppositely charged ions may be separated. The ease of solubilizing

ented. If it does not have the required orientation, it will not re-

salts in solvents like water and glycerin can be explained on the

turn readily to the solute, but rather will remain in solution, thus bringing a b u t a solubilitylarger than expected on the basis of heat of solution. On the other hand, the structurally symmetrical inositol, as it leaves the solution phase, can interact with the solute phase without requiring a definite orientation; all orientations are equivalent. Hence, inositol can enter the solute phase without hindrance, and therefore no facilitation of its solubility is observed. In general, unsymmetrical molecules tend to be more soluble than svmmetrical molecules. Another type of nonideal solution wcurs when there is an entropy change less than that expected of an ideal solution. Such nonideal hehavior can w m r with polar solutes and solvents. In a nonideal solution of this type there is significant interaction between solute and solvent. As may k expected, the enthalpy change ( A H ' ) in such a solution is negative and favors dissolution, but this effect is tempered by the unfavorable entropy change occurring at the same time. The reason for the lower-than-ideal entropy change can be visualized where the equilibrium system is more orderly and has a lower entropy than that expected for an ideal solution. The overall entropy change of solution thus would be less and not favorable to dissolution. One may rationalize the lower-than-expected solubility of lithium fluoride on the basis of this phenomenon. Compared with other alkali halides, it has a solubilitylower than would be expected based solely on enthalpy changes. Because of the small size of ions in this salt there may be considerable ordering of water molecules in the solution. This effect must, of course, lead to a lowered entropy and an unfavorable effect on solubility. The effect of soluble salts on the solubility of nonelectrolytes may be considered as a result of an unfavorable entropy effect (see Solubility of Solute Containing Two or More Species, ahve).

basis of their high dielectricconstant. Also, in general, the more polar the solvent, the greater its dielectric constant. An important concept has been introduced to pharmaceutical systems: pharmacists frequently are concerned with dissolving relatively nonpolar drugs in aqueous or mixed polar aqueous solvents." To understand what may be happening in such cases, factors concerned with the entropic effects arising from interactions originating with the nonpolar solutes must k considered. Previously it had been noted that the favorable entropic effect on dissolution was due to the disruption of a s k ations occurring among solute or solvent molecules. Now consider the effects on solubility due to solute interactions in the solution p h a s e k c a u s e the solutes under discussion are relatively nonpolar, the interactions are of the London Force type or a hydrophobic association. This hvdro~hobicassociation in aaueous solutions mav cause signkcah structuring of water wi'th a resultant orderei or low-entropy system that is unfavorable to solution. Therefore, the solution of an essentially nonpolar molecular in water is not a favorable prow ss. It should be stressed that this is due to not only an unfavorable enthalpy change but also an unfavorable entropy change generated by water structuring. Such an unfavorable entropy change, known as the hydrophobic effect, is quite significant in the solution process. As an example of this effect, the aqueous solubility of a series of alkylp-aminobenzoates shows a 10-million-folddecrease in solubility in going from the 1-carbonanalog to the 12-carbn analog. These findings demonstrate clearly the considerable effect that hydrophobic associations can have. A L C O H O L W t h a n o l , as a solvent, is next in importance to water. An advantage of ethanol is that growth of microorganisms does not mcur in solutions containing alcohol in a reasonable concentration. Resins, volatile oils, alkaloids, glycosides, etc are dissolved by alcohol, but many therapeutically inert principles, such as gums, albumin, and starch, are insoluble, which makes it more useful as a selective solvent. Mixtures of water and alcohol, in proportions varying to suit specilk cases, are used extensively. Thev are often referred to as hvdroalcoholic solvents. ~ l ~ c e risi nan excellent solvent, although its range is not as extensive as that of water or alcohol. In higher concentrations it has preservative action. It dissolves the fib alkalies, a large number of salts, vegetable acids, pepsin, tannin, and some active principles of plants, but it also dissolves gums, soluble carbhydrates, and starch. It also is of special value as a simple solvent (as in phenol glycerite), or where the major portion of the glycerin simply is added as a preservative and stabilizer of solutions that have been prepared with other solvents (see Glvcerines. C h a ~ t e411. r "~ropylene glGcol, which has been used widely as a substitute for glycerin, is miscible with water, acetone, or chloroform in all proportions. I t is soluble in ether and will dissolve many essential oils but is immiscible with fixed oils. It is claimed to be as effective as ethyl alcohol in its power of inhibiting mold growth and fermentation. Isopropyl alcohol possesses solvent properties similar to those of ethyl alcohol and is used instead of the latter in a number of pharmaceutical manufacturing operations. I t has the advantage in that the commonly available product contains not

PHARMACEUTICAL SOLVENTS The discussion will focus now on solvents available to pharmacists and on the properties of these solvents. Pharmacists must obtain an understanding of the possible differencesin solubility of a given solute in various solvents because they are often called on to select a solvent that will dissolve the solute. A knowledge of the properties of solvents will allow the intelligent selection of suitable solvents. On the basis of the forces of interaction occurring in solvents one may broadly c l a s s i ~solvents as one of three types: 1. Polar solvents-those made up of strong dipoIar molecules having hydmgen bonding (water or hydrogen peroxide). 2. Semipolar solvents-those also made up of strong dipolar molecules but that do not form hydmgen bonds (acetone or pentyl alcohol). 3. Nonpolar solvents-those made up of molecules having a small or no dipol ar character (benzene, vegetable oil, or mineral oil).

Naturally, there are many solvents that may fit into more than one of these broad classes; for example, chloroform is a weak dipolar compound but generally is considered nonpolar in char-

222

PART 2: PHARMACEUTICS

over 1%of water, whereas ethyl alcohol contains about 5% water, often a disadvantage, lsopropyl alcohol is employed in some liniment and loti011 formulations. It callllot be taken internally. Gcntbrul Prol~~~rtit~s-Low-molecule-~veigl~t and polyhydroxy alcohol forms associated structures through llydrogen bonds just as in water. When the carbon-atom colltellt of an alcohol rises above five, generally only monomers the11 are present in the pure solvent, riltl~oughalcohols have high dielectric eonstants compared to other types of solvents, they are small compared to water, 11s has been discussed, t h e solubility of salts in a solvent should be paralleled by its dielectric constant. That is.

as the dielect.ric constant of a series of solvents increases, the probability of dissolvu~ga salt in the solvent u~creases.This behaviOr is for the Table 16-2, IIiguchi," shows how the solubility of salts follows the dielectric col~stalltof the alcohols. As mentioned earlier, absolute alcohol rarely is used pharmaceutically. IIowever, hydroalcoholic mixtures such as elixirs and spirits frequelltly are encountered, h very useful generalization is t h a t the dielectric properties of a mixed solvent, such as water and alcohol, can be approximated as the weighted average ofthe properties of the pure components. 'rlus, a mixture of 60% alcohol (by weight) 111 water should have a dielectric constant approximated by t . : , t l , x ~,k,,~ 0L. 6 ( ~ l , , ~ L + , , ~0 ,. ,4, (~~, )l , ~,): l [ L F ~ , ~ ~ , ~, ~ , 0.6(25) ,,.,

+ 0.4(80) - 47

J r l e dielectric collstallt of60';t alcohol in water is foulld experimelltally to be 43, which is in close agreemellt with tllat just calculated. The dielectric constant of glycerin is 46, close to t h e 60% alcohol mixture. One would therefore expect a salt like sodium chloride to have about tile same solubility in glyeerill as in alcohol, Jrle solubility of sodium chloride in glycerill is 8 , 3 g/lOO of solvellt alld in 60CO + H 9 0 + (CH,),CO . . . H- 0 The maximum number of carhan atoms that may be present per molecule possessing a hydrogen-bndable group, while still retaining water solubility, is approximately the same as for the dcoh01~. Although nitrogen is less electronegative than oxygen, and thus tends to form weaker hydrogen hands, amines are at least as soluble as alcohols containing an equivalent chain length. The reason for this is that alcohols form two hydrogen hands with a net interaction of 12 kcallmol. Primary amines can form three hydrogen bonds; two amine protons are shared with the oxygens of two water molecules, and the nitrogen accepts one water proton. The net interaction for the primary amine is between 12 and 13 kcallmol; hence, it shows an equal or greater solubility compared with corresponding alcohols. The solvent action of nonpolar liquids involves a somewhat different mechanism. Because they are unable to form dipoles with which to overcome the attractions between ions of an ionic salt, or to break a covalent hand to prduce an ionic compound or form association complexes with a solute, nonpolar liquids

223

are incapable of dissolving polar compounds. They only can dissolve, in general, other nonpolar substances in which the hands between molecules are weak. The forces involved usually are of the induced dipole-induced dipole type. Such is the case when one hydrmarbon is dissolved in another, or an oil or a fat is dissolved in petroleum ether. Sometimes it is observed that a polar substance, such as aloehol, will dissolve in a nonpolar liquid, such as hnzene. This apparent emption the preceding generalization may be explained by the assumption that the alcohol molecule hdums a temporary dipole in the benzene molecule which forms an association complexwith the solvent molecules. A binding form of this

kind is referred to as a p e n a n e n t dipole-induced dipole force. SOME USEFUL GENERALIZATIONSThe preceding discussion indicates that enough is known a b u t the mechanism of solubility to be able to formulate some generalizations concerning this important physical property of substances. Because of the greater importance of organic substams in the field of medicinal chemistry, certain of the more useful generalizations about organic chemicals are presented here in summary form. However, it should be remembered that the phenomenon of solubility usually involves several variables, and there may be exceptions to general rules. One general maxim that holds true in most instances is, the greater the structural similarity ktween and solvent, the greater the solubility. As o&n stated to the student, like dissolves like. Thus, phenol is almost insoluble in petroleum ether but is very soluble in glycerin. Organic compounds containing polar groups capable of forming hydrogen hands with water are soluble in water, provided that the molecular weight of the compound is not too great. I t is demonstrated easily that the polar groups OH, CHO, COH, CHOH, CHzOH, COOH, NO,, CO, NHz, and S 0 . a tend t,increase the solubility of an organic compound in water. On the other hand, nonpolar or very weak polar groups, such as the various hydrocarhan radicals, reduce solubility; the greater the number ofcarbon atoms in the radical, the greater the decrease in solubility. lntrduction of halogen atoms into a molecule in general tends to decrease solubility because of an increased molecular weight without a proportionate increase in polarity. The greater the number of polar groups contained per molecule, the greater the solubility of a compound, provided that the size of the rest of the molecule is not altered; thus, pyrogallol is much more soluble in water than phenol. The relative positions of the groups in the molecule also iduence solubility; thus, in water, resorcinol (m-dihydroxybenzene)is more soluble than catpchol (o-dihydrov13enzen~),and the latter is more soluble than hydroquinone @-dihydroxybenzene). Polymers and compounds of high molecular weight can be poorly soluble. High melting points &equently are indicative of low solubility for organic compounds. One reason for high melting points Table 16-3. Demonstration of Solubility Rules CHEMKALCOM WUND

SOW BILTTY"

Aniline, C ~ H ~ N H Z Benzene, C6H6 Benzoic acid, CsH5COOH Benzyl alcohol C6H5CH20H I-Butanol, C4HpOH t-Butyl alcohol, (CH3)KOH Carbon tetrachloride, CCl4 Chloroform, CHC13 Fumaric acid (trans-butenedioic acid) Hydroquinone, &H4(OH)z Maleic acid, cis-butenedioic acid Phenol, CsH50H Pyrocatechol, CsHs(0H)z Pyrogallol, C6H3(0H)3 Resorcinol, CsHs(0H)z

28.6 1430.0 275.0 25.0 12.0 Mixible 2000.0 200.0 150.0 14.0 5.0 15.0 2.3 1.7 0.9

"The number of mL of water required to dissolve 1 g of solute.

224

PART 2: PHARMACEUTICS

is the associatiol~of molecules, and this cohesive force tends to prevent dispersiol~of the solute in the solvent The ers form of a11 isomer is more soluble t h a n the trans form (Table 16-31 Solrwfron, which is evidence of t h e existence of a strong attractive force between solute and solvent, ellhances the solubility of the solute, provided there is not a marked ordering of the solvent molecules in the solutiol~phase Acrcls, especially strong acids, usually produce water-soluble salts when reacted with 11itroge~-eontaiHe?:1i11g organic bases

COLLIGATIVE PROPERTIES OF SOLUTIONS C'p to this point our concern has been with dissolving a solute in a solvent Once the dissolution h a s been brought about, naturally the solutiol~has a number of properties t h a t are different from t h a t of the pure solvent Of very great importance are the colligative properties t h a t a solutiol~possesses The c o l l r g u f r r ~ ~ ~ p r o ~of~at ~solutiol~ r f r ~ ~ sare those t h a t depend on t h e number of solute particles in solution, irrespective of whether these are molecules or ions, large or small Ideally, the effect of a solute particle of one species is considered to be the same as t h a t of an entirely different kind of particle, at least in dilute solutiol~Practically, there may be differences that may become s u b s t a l ~ t i a la s t h e concentration of t h e solution is illcreased The colligative properties t h a t will be considered are

Of these four, all of which are related, osmotic pressure h a s the greatest direct importallce in the pl~armaceuticalsciellces It is the property t h a t largely determines t h e physiological acceptability of a variety of solutions used for therapeutic purposes

Osmotic-Pressure Elevation OSMOSIS-Tile phenomenon of osmosis is based on the fact t h a t substal~cestend to move or diffuse from regions of higher concentration to regions of lower concentration. When a solutiol~is separated from t h e solvent by means of a membrane t h a t is permeable to the solvent but not to t h e solute (such a abl~~ it is membrane is referred to a s a s c n ~ i p c m ~ r ~membrane), possible to demonstrate visibly t h e diffusiol~of solvent into the col~cel~trated solution, as volume changes will occur. In a simil a r manner, if two solutiolls of different col~cel~tratiol~ are separated by a membrane, t h e solvent will move from the solutiol~ of lower solute concentration to the solution of higher solute c o ~ ~ c e n t r a t iThis o ~ ~diffusiol~ . of solvent through a membral~eis called osn~osis. There is a difference between the activity or escaping tendency of the water molecules found in the solvent and salt solution separated by the semipermeable membrane. Because actir

b

ANIONS

b

H+ Li+

349.8 38.7 50.1 73.5 61.9

OH -

198.0 76.3 78.4 76.8 40.9 79.8

Na+ K+

NH

+

~af' wg2+

59.5 53.0

CIBrI-

AcO~ ~ 0 4 ' -

CHAPTER 17: IONIC SOLUTIONS AND ELECTROLYTE EQUILIBRIA

Table 17-3. Values of Some Salting-Out Constants for Various Barbituratesat 25" BARBITURATE

KCL

KBR

NACL

NABR

Amobarbital Aprobarbital Barbital Phenobarbital Vinbarbital

0.1 68 0.136 0.092 0.092 0.1 25

0.095 0.062 0.042 0.034 0.036

0.212 0.184 0.1 36 0.1 32 0.143

0.143 0*120 O+OB8 O+O7' 0.096

235

of accepting a proton. This complementary relationship may be expressed by A =Ht+ B base

acid

The pair of substances thus related through mutual ability to gain or lose a proton is called a conjugate acid-base pair. Specific examples of such pairs are Base

Acid

H C l = H + + C1-

in which Kgis a salting-outconstant chosen empiricallyfor each salt. This equation is valid for solutions with ionic strength up to approximately 1. SALTING-OUT EFFECT-The aqueous solubility of a slightly soluble organic substance generally is affected markedly by the addition of an electrolyte. This effect is particularly noticeable when the electrolyte concentration re aches 0.5 M or higher. If the aqueous solution of the organic substance has a dielectric constant lower than that of pure water, its solubility is decreased and the substance is salted-out. The use of high concentrations of electrolytes, such as ammonium sulfate or s d i u m sulfate, for the separation of proteins by differential precipitation is perhaps the most striking example of this efThe aqueous of a few substances such as cyanic acid, glycine, and cystine have a higher dielectric constant than that of pure water, and these substances are salted-in. These phenomena can be expressed empirically as log S = log So2 Ksrn

IJ.

= H + + COJ2H,PO,- = H + + HPOJZH,O = H+ + OHHC0,-

H,O+ Al(H,0),.3+

= H + + H,O

= H + + AI(H,0),0H2+

It is apparent that not only molecules, but also cations and anions, may function as acids or bases. The complementary nature of the acid-base pairs listed is reminiscent of the complementary relationship of pairs of oxidants and reductants where, however,the ability to gain or lose one or more electron-rather than proton-is the distinguishingcharacteristic. Oxidant

(13)

where IT, = K, for univalent salts, K's = KsB for unibivalent salts, and KL = K,/4 for bivalent salts. The salting-out constant depends On the temperature as as the nature of both the organic substance and the electrolyte. The effect of the elecand the organic substance can be seen in 17-3- In all instances, if the anion is constant, the d i u m cation has a greater salting-out effect than the potassium cation, probably due to the higher c h a r s density of the former. Although the reasoning is less clear, it appears that, for a constant cation, chloride anion has a greater effect than bromide anion upon the salting-out phenomenon.

ACIDS AND BASES h h e n i u s defined an acid as a substanoe that yields hydrogen ions in aqueous solution and a base as a substance that yields hydrovl ions in aqueous solution. Except for the fact that hydrogen ions neutralize hydroxyl ions to form water, no complementary relationship between acids and bases (eg, that between oxidants and reductants) is evident in Arrhenius' definitions for these substanoes; rather, their oppositeness of is emphasized. Moreover, no a m u n t is taken of the behavior of acids and bases in nonaqueous solvents. Also, although acidity is associated with so elementary a particle as the proton (hydrogen ion), basicity is attributed to so relatively complex an assmiation of atoms as the hydroxyl ion. I t would seem that a simpler concept of a base could be devised. PROTON CONCEPT-In pondering the objections to Arrhenius' definitions, Bransted and Bjerrum in Denmark and Lowry in England developed, and in 1923 announced, a more satisfactory, and more general, theory of acids and bases. According to this theory, an acid is a substanoe capable of yielding a proton (hydrogen ion), whereas a base is a substance capable

Reductant

= Fed+ NB+ + e- = N a

(12)

in which Sorepresents the solubility of the organic substance in pure water and S is the solubility in the electrolyte solution. The slope of the straight line obtained by plotting log S versus rn is positive for salting-in and negative for salting-out. In terms of ionic strength this equation becomes log S = log So2 KL

= H + + CH,,COONH,+ = H + + NH,

CHjCOOH

Fei++ eIKI,

+ e- e 1-

However, these examples of acid-base pairs and oxidantreductant pairs represent reactions that are possible in principleonly.Ordinarilyacidswillnotrelease&eeprotonsanymore than reductants will release free electrons. That is, protons and electrons, respectively, can be transferred only &om one substance (an ion, atom, or molecule)to another. n u s , it is a fundamental fact of chemistry that oxidation of one substanoe will if reduction of another substance -rs simultaneously. Stated in another way, electrons will be released &om the reductant (oxidation)only ifan capable ofacoepting electrons (reduction) is present. For this reason oxidationreduction reactions must involve two conjugate oxidant-reduct, pairs of substances:

-,

oxidantl + reductantz z reductantl

+ oxidantz

where Subscript 1represents one conjugate oxidant-reductant pair and Subscript 2 represents the other. Similarly, an acid will not release a proton unless a base capable of ampting it is present simultaneous1~This means that any actual manifestation of acid-base behavior must involve interaction between two sets of conjugate acid-base airs, represented as A, + B2 B1 + Az

=

acid,

basep

base,

acidp

In such a reaction, which is called protolysis or a protolytic reaction, AI and BI constitute one conjugate acid-base pair, and Az and Bz the other; the proton given up by AI (which thereby hecomes BI) is transferred to Bz (which becomes Az). When an acid, such as hydrochloric, is dissolved in water, a protolytic reaction occurs. HCI

acid,

+ H:O e base2

GIbase1

+ H.]O'

wide

The ionic species & 0 + , called hydroniurn or oxoniurn ion, always is formed when an acid is dissolved in water. Often, for purposes of convenience, this is written simply as H+ and is

236

PART 2: PHARMACEUTICS

called hydrogen ion, although t h e "bare'' ion practically is nonexistent in solutiol~. When a base (eg, ammonia) is dissolved in water, t h e reaction of protolysis is t i l l : - I l ! O e h I 1 ; - + OH aci&

hasp,

bawl

acid,

The protoll theory of acid-base function makes t h e cul~cept ofhydrolysis superfluous. When, for example, sodium acetate is dissulved in water, this acid-base interaction occurs

h ~ d r o n i u mion. so they are converted in water to t h e hydronium ion When the strong bases sodium hydride, sodium amide, or sodium ethuxide are dissolved in water, each reacts with water to form sodium hydroxide These reactions illustrate the leveling effect of water OH bases Uecause the hydroxide ion is the strongest base t h a t can exist in water, any base stronger than the hydroxide ion undergoes protolysis to hydroxide l l ~ t r i l ~ sdifferences ic in t h e acidity of acids become evident if they are dissolved in a relatively poor proton acceptor such as anhydrous acetic acid Perchloric acid (IIClO,,), a strong acid, undergoes practically complete reaction with acetic acid to pro-

duce t h e a w f o n r u m ion (acid?) 1~ an aqueous solution of ammonium chloride the reactiol~is SII,l

+ tl,U bwf,

acid,

= YII,

I 11;11basel acid,

Transfer of protons (protolysis) is not limited to dissimilar conjugate acid-base pairs In the preceding examples 1110 sometimes behaves as an acid and a t other times as a base Such an amphoteric substance is called, in Brmsted's terminology, an an~phrprotrcsu b s t a n c ~ ~ E L E C T R O N - P A I R CONCEPT-The proton concept of acids and bases provides a more general definitiol~for these substances, but it does not indicate the basic reason for protoll transfer. nor does it esnlain how such substallces as sulfur trioxide, boron trichloride, stannic chloride, or carbon dioxidenone of which is capable of donating a proton-can behave as acids Both deficiencies ofthe protoll theory are avoided in the more inclusir~edefinitiol~of acids and bases proposed by Lewis in 1923 1n 1916 he proposed t h a t sharing of a pair of electrolls by two atoms established a bond (covalent) between the atoms, therefore. an acid is a substance capable of sharing a pair of electrol~smade available by another substance called a base, ~ bond. The base is the thereby forming a c o o r d r n a t ~corwlcnt substance t h a t donates a share in its electron pair to the acid The followil~gequation illustrates how Lewis' definitions explain the transfer of a protun (hydrogen ion) to ammonia to form ammol~iumion

The reaction of boron trichloride, which according to the Lewis theury is an acid, with ammonia is similar, for t h e boron lacks an electroll pair if it is to attain a stable octet confip~ration, while ammonia has a pair of electrolls t h a t may be shared, thus, C1 (:l Il 1

C1

I1 C1 H .N.11 + (:I. 1% N 11 H (:I A

LEVELING E F F E C T O F A SOLVENT-When t h e strong acids such as IICIO,l,112S0,1IIC'1, or IIYO are dissolved 111 water, the solutions-ifthey are of identical normality and are not too concentrated-all have about t h e same hydrogen-ion concentration, indicating t h e acids to be uf abuut t h e same strength The reason for this is t h a t each one of the acids undergoes practically complete protolysis in water I 1 acid,

-

I habe,

I

t

II,O' acid.>

bxur,

This phenomenon. called t h e It~ryblrngcffict o f ruattbr, occurs whenever the added acid is stronger t h a n t h e hydrol~iumion Such a reaction manifests the tendellev of nroton-transfer reactions to proceed spontaneously in the direction of forming a weaker acid or weaker base Since the strungest acid t h a t can exist in a11 amphiprotic solvent is t h e conjugate acid form of t h e solvent, any stronger acid will undergo protolysis to t h e weaker solvent acid lICIO,l, I12S01,1IC1. or IIYO are all stronger acids t h a n the 0

IIC'IOI

+ CHO'l

4.,14 = log-

1. Calculate the pH corresponding to a hydronium-ion ooncentration of 1 x g-iod. Solution:

-- 1

1

IH:,OCI

- antilog of 4.44

=

28,000 (rounded om

[HP'I 1 [H,O+] = -= 0.000036 or 3.6 x lo-' 28,000

1 pH = log 1x 10-~

This calculation also may be made as

= log 10,000 or log (1 x lot4)

log (1 x

4.44

pH = -log (3.6 x 10-7

(44)

+ pOH = pK,

=

This problem also may be solved as follows:

from which it is evident that pH also may he d e h e d as the negative logarithm of the hydronium-ionconcentration. In general, this type of notation is used to indicate the negative logarithm of the term that is preceded by the p, which gives rise to the following

pH

+ lo+"

log (2.8 x lo*') = log 2.8

log -

S i n e the logarithm of 1 is zero, the equation also may he written

fla

3.6 x lo-"

= log 28,000 or log (2.8 x

1

=

1 ,

+4.44 = -log [&O+]

lot4)= + 4 or

pH = 4

-4.44 = +log [&O+] Table 17-5. Hydroniumlon and Hydroxyl-Ion Concentrations NORMAUTYIN TERMS PH

o Increasing acidity Neutral point

t 2 3 4 5 6 7 8

9

Increasing alkalinity

10 11 12 13

14

IN

OF HYDRONIUM ION

OF HYDROXYL ION

1 10-I

10-14 to-I3 10-l2 10-l1 10-lo 10-9 to-8

lo-z lo-3 lo-4 10-5

la-7 to-8 10-9

lo-lo lo-11

10-l2 to-l3 10-1~

lo-7

to-G 10-5 10-4

la-3 lo-z to-' I

In &ding the antilog of -4.44 it should be kept in mind that the mana*ssa (the number to the right of the decimal point) of a log to the base 10 (the common or Briggsian logarithm base) is alwayspositive but that the characteristic (the number to the left of the decimal point) may beposia*ve or negaf ve. AS the entire log -4.44 is negative, it is obvious that one cannot Iwk up the antilog of -0.44. However, the number -4.44 also may be written (-5.00 + 0.561, or as more often written, 5.56; the bar across the characteristic indicates that it alone is negative, while the rest of the number is positive. Lwking ur the antilog of 0.56 it is found to be 3.6; as the antilog of -5.00 is 10- , it follows that the hydronium-ionconwnkation must be 3.6 x molsk. 2. Calculate the hydronium-ion wnwntration corresponding to a PH of 10.17. Solution: 10.17 = -log[H30t]

-10.17 = ~ O ~ [ H ! , O + I -10.17 =

(-11.00

+ 0.831 = c . 8 3

The antileg of 0.83 = 6.8. The antileg of -11.00 = 10-l1 The hydronium-ion conoenkation is therefore 6.8 x

lo-''

moVL.

CHAPTER 17: IONIC SOLUTIONS AND ELECTROLYTE EQUILIBRIA

In the section Ionization of Water, it was shown that the hydronium-ion concentration of pure water, at 25", is 1 x lop7N, oorresponding to a pH of 7. This figure, therefore, is designated as the neutral point, and all values blow a pH of 7 repwent acidity--the smaller the number, the greater the acidity. Values above 7 repwent alkalinity-the larger the number, the greater the alkalinity. The pH scale usually runs h m 0 to 14, but mathematically there is no reason why negative numbers or numbers a b v e 14 should not IH used. In practice, however, such values are never encountered h a u s e solutions that might be expected to have such values are too oonoentrated to be ionized extensivelyor the

interionic attraction is

80

IHA-]

I*2- -

When a weak acid, H A is added to water, n + 1 species, ineluding the un-ionized acid, can exist. ARer equilibrium is established, the sum of the oonoentrations of all species must IE equal to Ca, the stoichiometric (added) oonoentration of acid. Thus,for a triprotic acid H d , l lB&-I+ + EMa-I + [&-I

Ca = ~

(46) In addition, the oonoentrations of all acidic and basic species in solution vary with pH, and can be represented solely in terms of equilibrium oonstants and the hydronium-ion concentration. These relationships may I x expressed as &A] = lBs0+lnCa/D lBn-jA-'l = lB30+l"-j~l,. . .,K,CJD

(47)

(48)

in which n repwents the total number of dissociable hydrogens in the parent acid,j is the number of protons dismiated, Ca is the stoichiometric oonoentration of acid, and K represents the acid dissociation constants. The term D is a power series in &O+l and K, stsrting with [KO+] raised to the nth power. The last term is the p d u c t of all the dissmiation constants. The intermediate terms can be generated h m the last term by substituting &0+] for Knto obtain the next-to-last term, then substituting &O+] for Kn-' to obtain the next term, and onward until the f i s t term is reached. The following examples show the denominator, D, to be used for various types of acids:

HsA: D = 13&O+lS+ K1lBs0'1' + KiKa&O+l+ KlK&s (49) H,A:D

=

IH,0+1"

+ K,IHn20+1t K,K,

HA: D = [H,O+] + K,

[H30+]"C, =

[H20+]"K,[H,O+] + K,Kx

KlK2',G, +1S,[H30+] + KIK2

[ylOr]"

(54)

lo-'

and K2 = 2.3 x Equations 5264 have the same denominator, D, which can he calculated a x

+ Kl&O+] + KIKa = 1.0x + 6.4 x lo-' x 1.0 x x lo-' x 2.3 x lo-" = 1.0 x lo-'' + 6.4 x lo-*' + 14.7 x

D = &0+la

+ 6.4 10-l1

x 10-l1

= 21.2

Therefore,

[HA1 =

[HA-]=

[AaO' 12Cn 1.0 x 10-12 x 1.0 x lo-:' = 4.7 x I O - ~ M 21.2 x 10-l1

4[HsO+1Co

lo-"

X

X

21.2 x

1.0X lo-:'

lo-"

= 3.0 x

~o-~M

[Ae-] = K,K2:LCrl D

-

14.7

X

lo-" 21.2 x

X

1.0 X

lo-"

=

6.9 x ~ o - ~ M

PROTON-BALANCE EQUATION In the Bmnsted-Lowry system, the total numbr of protons released by acidic species must equal the total number of protons oonsumed by basic species. This results in a very useful relationship known as theproton-balanceequation (PBE),in which the sum of the oonoentration terms for species that form by p m ton consumption is equated to the sum of the concentration terms for species that are formed by the release of protons. The PBE forms the basis of a unified approach to pH calculations, as it is an exact acmmting of all proton transfers m&g in solution. When HCl is added to water, for example, it dissmiates yielding one C1- for each proton released. Thus,C1- is a species formed by the release of a proton. In the same solution, and actually in all aqueous solutions 2Hz0 e &O+

+ OH-

where &o+ * formed by proton consumption and OH- is formed by proton release. ~ hthe PBE ~ is , &O+I = [OH-]

+ [Cl-I

(55)

(50)

In general, the PBE can be formed in the following manner:

(51)

1. Start with the speeiw added to water. 2. Place all species that can form when protons are released on the right side of the equation 3. Place all egeciw that can form when grotona are consumed on the left side of the equation. 4, the of each speciM by the nUmh of phw tons gained or lost to form that species. 5. Add [&Of I the left side of the equation and [OH7 to the right side of the equation. T h e rwult from the interadion of two r n o l d of ~ water ~ as shown above.

The numerator in all instances is Ca multiplied by the term from the denominator that has [&O+]raised to the n - j power. Thus, for diprotic acids such as carbonic, suocinic, tartaric, and so on,

IHdl

(53)

Example4alculate the wnoenkatiorm of all suet acid specks in M solution of suet acid at pH 6. kasume that 4 = 6.4

- 6.4

SPECIES CONCENTRATION

4[H~o+lG IH,0+I2 + IT,IH,0+1 + KlKz

a 1.0 x

great as tO materially d u o e ionic

activity. The pH of the purest water obtainable, so-called 'oonductivity water', is 7 when the measurement is made carefully under oonditions to exclude c a r b n dioxide and prevent errors inherent in the measuring technique (such as acidity or alkalinity of the indicator). Upon agitating this water in the pwenoe of carban dioxide in the atmosphere (equilibrium water), the value drops rapidly to 5.7. This is the pH of nearly all distilled water that has k e n exposed to the atmosphere for even a short time and oRen is called 'equilibrium' water. It should IE emphasized strongly that the generalizations stated concerning neutrality, acidity, and alkalinity hold exactly only when (1)the solvent is water, (2) the temperature is 25", and (3) there are no other factors to c a w deviation from the simply formulated equilibria underlying the dehition of pH given in the preceding discussion.

=

241

242

PART 2: PHARMACEUTICS

ISxclrnplu-When II,jPO.ris nddcd to wntrr: the sprcirs I12P0., fnrnls with the rrlrnsc nf nnc prntnn; IIPO,' fnrms with the rrlcnsr nf twn prntnns; nnd PO.," fnrnls with the rclcnsr nfthrcr prntnns, which gives the fnllnwing PEE:

[II, [OH-], the quadratic equation simplifies to

[OH-] =

log (5.34

3' Na+ + HAHA- + H,O e A2- + H,Ot HA- + H,O = H,A + OH2H20+ H30+ + OH-

which is a quadratic with the following solution: [OH-] =

-

Natm-

(67)

( 1

=

Substanoes such as NaHCOs and NaH2P04 are termed ampholytes and are capable of functioning bath as acids and bases. When an ampholyte of the type NaHA is dissolved in water, the following series of reactions can m:

If [OH-] lB90+l, as is true generally, then [OH-]'

10-10 x 5.0 x 10-2

Ampholytes

Substituting @3H+l as a function of hydronium-ion ooncentration and simplifying, in the same manner as shown for a weak acid, gives IlOH-1

X

lo-"

pH = 14.00

ficiently a m a t e .

(cb

= 45.71

Both assumptions are valid:

5.41

than &Of] and &Of] is much greater than [OH-], the wumptions are valid and the value calculated for pH is suf-

[OH-] = Kb

x 10-lo

= 6.34 x

10-BM

10-l4

1.76 x 10-5

OH- =

As C, is much greater

B

,

= 5.71

J5.75 x 10-10x 2.6 x

=

K,, 1.00 x

--=

243

l&O+l

+

+ KlK2

(73)

K&&a lBsO+la + Kl&O+l+ KlKa

This gives a fourth-order equation in l&O+l, which can be simplified using certain judicious assumptions to [H,O+I =

J,c K,K,CS

(74)

In most instanoes, C,>> Kl,and the equation further simplifies to I H ! ~ O=~ fi I

(75)

and [KO+] beoomes independent of the cancentration of the salt. A special property of ampholytes is that the ooncentration of the species HA- is maximum at the pH corresponding to Equation 75. When the simplest amino acid salt, glycine hydrochloride, is dissolved in water, it acts as a diprotic acid and ionizes as

+NHsCHzCOUH + Ha0 & +N&CHsCOO-

+ &O+

+N&CH,COO- + Hz0 & NHZCH~COO-+ &O+ The form, +NHsCHaCOO-, is an ampholyte h u s e it also can act as a weak base:

+N&CHzCOO- + H z 0 & +N&CHzCOOH + OHThis type of substance, which carries b t h a charged acidic and a charged basic moiety on the same molecule is termed a m i t terion. Because the two charges balance each other, the molecule acts essentially as a neutral molecule. The pH at which the zwitterion COIl03ntratioIl is maximum is known a8 the isoelectric point, which can be calculated h m Equation 75. On the acid side of the iscelectric point, amino acids and pmteins are cationic and inoompatible with anionic materials such as the naturally o a r r i n g gums used as suspending andlor

CHAPTER 17: IONIC SOLUTIONS AND ELECTROLYTE EQUILIBRIA

or, expressed in terms of pH, as pH

=

pK,

+ log Cl, -

(83)

c,,

This equation generally is ,..led the Henderson-Hasselbalck equation. It applies to all buffer systems formed &om a single conjugate acid-base pair, regar& ss of the nature of the salts. For example, it applies equally well to the following buffer systems: ammonia-ammonium chloride, monosodium phosphate4isdium phosphate, and phenobarbital-sodium phenobarbital. In the ammonia-ammonium chloride system, ammoniaisobviouslythe base andthe ammoniumionisthe acid ccfi 'qua' the of the In the phosphate 'ysmonosodium phosphate is the acid and disodium phosphate is the base. For the phenobarbital buffer system, phenobarbital is the acid and the phenobarbital anion is the base (Cb equal to the concentration of sodium phenobarbital). As an of the of this equation, the pH of a buffer solution containing acetic acid and sodium acetate, each in 0.1 Mconcentration, may he calculated. The K, of acetic acid, as defined ahve, is 1.8 x lo-" at 25". Solution: First, the pK, of acetic acid is calculated:

pK, = -log K, = -log 1.8 =

x lo-"

-log 1.8 - log lo-"

= -0.26

-

(-5) = +4.74

0.1 pH = log - + 4.74 = +4.74 0.1

The Henderson-Hasselbalch equation predicts that any Solutions containing the same molar concentration of acetic acid as of sodium acetate will have the same pH. Thus, a solution of 0.01 M concentration of each will have the same pH, 4.74, as one of 0.1 M concentration of each component. Actually, there will be some difference in the pH of the solutions, for the actiuity coefficient of the components varies with concentration. For most practical purposes, however, the approximate values of pH calculated by the equation are satisfactory. I t should be pointed out that the buffer of higher concentration of each component will have a much greater capacity for neutralizing added acid or base and this point will be discussed further in the discussion of buffer capacity. The Henderson-Hasselbalch equation is useful also for calculating the ratio of molar concentrations of a buffer system required to produce a solution of specific pH. As an example, suppose that an acetic acid-sdum acetate buffer of pH 4.5 must be prepared. What ratio of the buffer components should be used? Solution: Rearranghg Equation 83, which is used to EalcuIate the pH of weak acid-salt type buffers, gives

[MI

log 7 = pH [ac~d]

-

pK,#

= 4.5

-

:I.T6 = -0.24 = (9.76 - 10)

-Ihasel - mtilog of ( 9 7 6 [acid1

tion of acid in a weak-acidloonjugate-basebuffer determines the capacity to 'heutralize" added base, while the concentration of salt of the weak acid determines the capacity to neutralize added acid. Similarly, in a weak-baselconjugate-acidbuffer the concentration of the weak base stabfishes the buffer toward added acid, while the concentration of the conjugate acid of the weak base determines the toward added base. When the buffer is equimolar in the concentrations of weak acid and conjugate base, or of weak base and conjugate acid, it has equal buffer capacity toward added strong acid or strong base. Van Slyke, the biochemist, intrduced a quantitative ex-

pression for evaluating buffer capacity. This may be defined as the amount, in gram-equivalents (g-eq)per liter, of strongacid or strongbase required to be added to a solution to change its pH by l unit; a solution has a buffer capacity of l when l L requires g-eq of strong base or acid to change the pH unit. (In practice, considerably smaller increments are measured, expressed as the ratio of acid or base added to the ,.hange of pH prduced.) From this definition it is apparent that the smaller the pH change in a solution caused by the addition of a specified quantity of acid or alkali, the greater the buffer capacity of the solution. The following examples illustrate certain basic principles and calculations concerning buffer action and buffer capacity. Example 1-What is the change of pH on adding 0.01rnol of NaOH to 1 L of 0.10M aoetic acid? (a) Calculate the pH of a 0.10molar solution of aoetic acid: IH,O+I =

Substituting this vdue into Equation 83:

"m

= !i1.75 x 10-I x 1.0 x l o - ' = 4.18 x lo-''

pH =

-

log 4.18 x lo-:' = 2.38

(b) On adding 0.01 rnol of NaOH to a liter of this solution, 0.01 rnol of acetic acid is converted to 0.01rnol of s d u m acetate, thereby decreasing Ca to 0.09M, Cb = 1.0 x 10-2M. Using the Henderson-Hasselbach equation gives pH = 4.76

0.01

+ log-0.09 = 4.76 - 0.95 = 3.81

~ h p~ , is, themfore, 1.43unit, ~h~ buffer Eapadty as d e h e d is , d d a t e d to be n~olsof NaOH added = 0.01 1 change in pH

Example 2-What is the change of pH on addingo. 1 rnol of NaOH to 1 L of buffer solution 0.1M in aoetic acid and 0.1M in d i u m acetate? (a) The pH of the buffer so~utionbefom adding NaOH is

I

10) = 0.576

The of this result is that the proportion of d i u m acetate to acetic acid should be 0.57 5 rnol of the former to 1 rnol of the latter to produce a pH of 4.5. A solution containing 0.0575 mol of s d i u m acetate and 0.1 mol of acetic acid per liter would meet this requirement, as would also one containing 0.00575 rnol of sodium acetate and 0.01 rnol of acetic acid per liter. me actual concentration would depend chieflyon the desired buffer capacity. BUFFER CAPACITY-The ability of a buffer to resist c h a n ~in s PH upon addition of acid or alkali may be meas u e d in terms of buffer capacity. In the preceding discussion of buffers, it has h n seen that, in a general way, the concentra-

1

pH = log ,--+ pK,, [ac~d 1

0.1 = log- + 4.76 = 4.76 0.1

Ib) On adding 0.01 mol of NaOH per Liter to this buffer solution,0.01 rnol of acetic acid is converted to 0.01 mol of s d i u m acetate, thereby demasing the concentration of acid to 0.09M and inmasing the mnoenkation of base to 0.11M. The pH is calculated as 0.1 1

pH = log-

245

0.09

= 0.087

+ 4.76

+ 4.78 = 4.85

The of pH in this case is only 0.09unit, a b u t 1/10the hepreoeding example, The capad@ is caldated as mols of NaOH added change of pH

in

- 0.01 - 0.11 0.09

Thus, the buffer capacity of the acetic acid-sdum aoetate buffer solution is apprordmateIy 10 limes that of the acetic acid solution. As is in part evident &om these examples, and may be further evidenced by calculations of pH changes in other systems, the degree of buffer a d o n and, tkrefore, the buffer capacity, depend on the kind and wncentration of the buffer components, the pH region invoIved and the kind of acid or alkali added.

PART 2: PHARMACEUTICS

STRONG ACIDS AND BASES AS "BUFFERSw-ln the foregoing discussion, buffer action was attributed to systems of (1)weak acids and their conjugate bases, (2) weak bases and their conjugate acids, and (3) certail~acid-base pairs t h a t can function in the mallner either of system 1 or 2 The ability to resist change in pII on adding acid or alkali is possessed also by relatively col~cel~trated solutiol~sof strong acids and strong bases If to 1 L of pure water having- a pII of 7 is added 1mL of 0 01 ll1 hydrochloric acid, t h e pII is reduced to about 5 If t h e same volume of the acid is added to 1 L of 0 001 M hydrochloric acid, which has a pII of about 3, t h e hydroniumion col~cel~tratiol~ is increased only about 15 and the pII is re-

l~g two suitable electrodes dipping into a solution c o l ~ t a i l ~ ihydronium ions depends on the col~cel~tratiol~ (or activity) of the latter The development of a potential difference is not a specific property of hydronium ions h solution of any ion will develop a potential proportiollal to the col~cel~tratiol~ of t h a t ion if a suitable pair of electrodes is placed in t h e solutiol~ The relationship between the potential difference and concentratiol~of an ion in eauilibrium with t h e electrodes mav be derived as follows When a metal is immersed into a solutiol~of one of its salts, there is a tendency for the metal to go into solutiol~in the form of ions This tendency is known as the solutron prtbssurebof t h e metal and is comparable to t h e tendelley of

duced hardly a t all ' h e nature ofthis buffer action is quite dif-

sugar molecules (eg, to dissolve in water) The metallic ions in

ferent from t h a t of the true buffer solutiolls The very simple l ~mL of 0 01 !11 IIC1, which represents explanation is t l ~ a t w h e 1 0 00001 g-eq of hydronium ions, is added to the 0 0000001 g-eq of hydronium ions in 1L of pure water, t h e hydronium-ion concentration is increased 100-fold (equivalent to two pII units), but when the same amount is added to the 0 001 g-eq of hydronium ions in 1L of 0 001 M IIC1, the increase is only 1/100 the concentration already present Similarly, if 1 mL of 0 01 ll1 NaOII is added to 1 L of pure water, the pII is illcreased to 9, while if the same volume is added to 1L of 0 001 molar NaOII. the pII is increased almost immeasurably In general, solutiolls of strong acids of pII 3 or less, and solutions of strong bases of pII 11 or more, exhibit this kind of buffer action by virtue of the relatively high concentration of hydronium or hydroxyl ions presellt The LSP illeludes among its Standard Buffer Solutions a series of hydrochloric acid buffers, covering t h e pII range 1 2 to 2 2, which also con tail^ potassium chloride The salt does not participate in the buffering mechanism, as is t h e case with salts of weak acids, instead, required to main tau^ the it serves as a nonreactive col~stituel~t proper electrolyte ellvirol~mel~t of the solutiolls

solution tend, OH t h e other hand, to become discharged by forming atoms, this effect being proportional to t h e osn~otrcprrssurtb of the ions For an atom of a metal to go into solutiol~a s a positive ion, electrons, equal in number to the charge on the ion, must be left behind on t h e metal electrode with t h e result t h a t t h e latterbecomes negatively charged The positively charged ions in solution, however. may become discharged as atoms by taking up electrolls from t h e metal electrode Uepel~dingon which effect predominates, the electrical charge on the electrode will be eit h e r positive or negative and may be expressed quantitatively by t h e followil~gequation proposed by Nernst in 1889

DETERMINATION OF pH Colorimetry A relatively simple and inexpensive method for determining the approximate pII of a solutiol~depends on t h e fact t h a t some conjugate acid-base pairs (indicators) possess one color in the acid form and another color in the base form Assume t h a t the acid form of a particular indicator is red, and t h e base form is yellow The color of a solutiol~of this illdieator will range from red when it is sufficiently acid, to yellow when it is sufficiently alkaline In the intermediate pII range (the transitiol~i n t e n d ) the color will be a blend of red and yellow depending up011 the ratio of t h e base to t h e acid form In general, altl~oughthere are slight differellees between indicators, color changes apparent to the eye cannot be discerned when t h e ratio of base to acid form, or acid to base form exceeds 10 1 The use of Equation 83 indicates t h a t t h e transitiol~range of most indicators is equal to the pK,, of the indicator z 1 pII unit, or a useful range of approximately two pII units Standard indicator solutiol~scan be made ~ of t h e indicaat k n o w l ~pII values within the t r a l ~ s i t i o lrange tor, and t h e pII of an unknown solutiol~can be determined by adding- t h e indicator to it and comparing the resulting color with t h e standard solutiolls Another method for using these indicators is to apply them to thin strips of filter paper h drop of the u l ~ k l ~ o w solutiol~ l~ is placed on a piece of the indicator paper and the resulting color is compared to a color chart supplied with t h e indicator paper These papers are available in a wide variety of pII ranges

Potentiometry Electrometric methods for the determination of pII are based on the fact t h a t the difference of electrical potential between

where E is t h e potential difference or electromotive force, R is t h e gas constant ( 8 316 joules), T is the absolute temperature, n is the valence ofthe ion, F is the Faraday of electricity (96,500 coulombs),p is the osmotic pressure ofthe ions, and P is the solutiol~pressure of t h e metal lnasmuch as it is impossible to measure the potential difference between one electrode and a solution with any degree of certaintv. it is customam to use two electrodes and to measure t h e potential difference between them If two electrodes, both of t h e same metal, are immersed in separate solutiolls c o l ~ t a i l ~ i l ~ g ions of t h a t metal-at osmotic pressure p , and p l , respecby means of a tube containing a nontively-and are col~l~ected reacting salt solutiol~( a so-called salt brrdgc), the potential developed across the two electrodes will be equal to the difference between the potential differences of the individual electrodes, thus,

As both electrodes are ofthe same metal. P I - P? and the equation may be simplified to

l n place of osmotic pressures it is permissible, for dilute solutions. to substitute the concentrations e l and el t h a t were found (see Chapter 161, to be proportiollal to p l and pl The equation the11 becomes

If either e l or c? is known, it is obvious t h a t the value of the other may be found if the potential difference, E , of this cell can be measured. For the deterrninatiol~of hvdronium-ion c o l ~ c e l ~ t r a t i oorl ~ pII, an electrode a t which an equilibrium between hydrogen gas and hydronium ion can be established must be used in place of metallic electrodes Such an electrode may be made by electrolytically coating a strip of platinum, or other noble metal. with platinum black and saturating t h e latter with pure hydrugel] gas This device f u l ~ c t i o l ~ass a hycl rogcn clcctrodc. 'ltvo such electrodes may be assembled a s showl~in Figure 17-3

CHAPTER 17: IONIC SOLUTIONS AND ELECTROLYTE EQUILIBRIA

247

prcduces potential difference of 0.2488 V. Amrdingly, before using Equation 86 for the calculation of pH h m the voltage of a cell made up of a calomel and a hydrogen e l w t d e d i p ping into the solution to be tested, 0.2488 V must be subtracted from the observed potential difference. Expressed mathematically, Equation 92 is used for calculating pH h m the potential difference of such a cell pH

E =

-

0.2488

(92)

0.0581

In measuring the potential difference between the elecbe drawn h m the cell, for with current flowing the voltage changes, owing to polarization effects at the electrcde. Because of this it is not possible to make aocurate measurements with a voltmeter that q u i r e s appwiable current to operate it. In its place a potentiometer is used that d m not draw a current from the cell b ing m e a s d . There are many limitations to the use of the hydrogen trcdes, it is imperative that very little current

Figure 17-3. Hydrogen-ion concentration chain.

In this diagram one elwtrde dips into Solution A, oontaining a known hydronium-ion concentration, and the other elecM e dips into Solution B, containing an unknown hydroniumion concentration. The two electrdes and solutions, sometimes called half-cells, then are connected by a bridge of neutral salt solution, which has no significant effect on the solutions it connects. The potential difference across the two electrodes is meas u r d by means of a potentiometer, P. If the concentration, c,, of hydronium ion in Solution A is 1 N, Equation 87 simpEes to RT l ~ = - - h nIi c2

(88)

or in terms of Briggsian logarithms RT nF

E = 2.303 -log,,

1 -

s

(89)

Iffor log, l / c , there is substituted its equivalent pH, the equation h o m e s RT E = 2.303 -pH

(90)

nF

electrode: It cannot he wed in mlukions wntaining strong oxidants such as ferric iron, dichromatw,nitric acid, peroxide, or chlorine or reductants such as sulfurow acid and hydrogen sulfide. It is affected by the presence of organic compoun& that are reduced fairly easily. It cannot h wed suooessfully in solutions containing cations that fall Mow hydrogen in the eledmxhemical mies. Erratic d t a are obtained in the measurement of unbuffered solutions dem s p e d precautions are taken. It is bwublwome to prepare and maintain.

As other e l m t d e s more convenient to use now are available, the hydrogen electrcde W a y is used rarely. Nevertheless, it is the ultimate standard for pH measurements. To avoid some of the diEculties with the hydrogen electrode, the quinhydmne electrode waa introduced and was popular for a long time, particularly for measurements of acid solutions. is that it consists of a me unusual featm of this piece of gold or platinum wire or foil dipping into the solution to b tested, in which has been dissolved a small quantity of quinhydrone. A calomel e l w t d e may IE used for reference,just as in determinations with the hydrogen elwt.de.

and k a l l y by substituting numerical values for R, n, T, and F, and assuming the temperature to be 20°, the following simple relationship is derived: E

E

=

0.0581pH or pH = 0.0581

(91)

The hydrogen e l e c t d e dipping into a solution of known hydronium-ion concentration, called the reference electrode, may be replaced by a calomel e l w e , one type of which is shown in Figure 17-4. The elements of a calomel electr@de are mercury and dome1 in an aqueous solution of potassium chloride. The potential of this e l e c t d e is constant, regardless of the hydronium-ion ooncentration of the solution into which it dips. The potential depends on the equilibrium that is set up btween mercury and mercurous ions h m the calomel, but the ooncentration of the latter is governed, according to the solubility-prcduct principle, by the concentration of chloride ions, which are derived mainly h m the potassium chloride in the solution. Therefore, the potential of this eleci.de varies with the concentration of potassium chloride in the electrolyte. Because the calomel electrcde always indicates voltaes that are higher, by a oonstant value, than those obtained when the normal hydrogen e1ect.de chain shown in Figure 17-3 is used, it is necessary to subtract the potential due to the calomel electr@de itself h m the obsemed voltage. As the magnitude of this voltage depends on the concentration of potassium chloride in the calomel-electrode electrolyte, it is necessary to know the concentration of the former. For most purpeses a saturated potassium chloride solution is used that

[Ill

H---W-ll

wv I1

PURE M E M

Figure 17-4. Calomel electrode.

248

PART 2: PHARMACEUTICS

Quinhydrone consists of an equimolecular mixture of quinone and hydrquinone; the relationship hetween these subst awes and hydrogen-ion concentration is

which precipitation will wcw. This equation can he rearranged to give

Quinone + 2 Hydrogen ions + 2 Electrons e Hydrquinone

In a solution containing hydrogen ions the potential of the quinhydrone electrcde is related logarithmically to hydroniumion concentration if the ratio of the hydroquinone concentration to that of quinone is constant and practically equal to 1.This ratio is maintained in an acid solution containing an excess of quinhydrone, and measurements may made quickly and accuratel~;however, quinhydrone cannot be used in more alkaline than pH 8. An electrde that, h a u s e of its simplicity of operation and o ' m oontamination Or change of the being tested, has r e p l a d b t h the hydrogen and quinhydrone elect r d e s is the glass electrode. It functions because when a thin membrane of a special composition of glass separates two solutions of different pH, a potential differenoe develops across the membrane that depends on the pH of b t h solutions. If the pH of one of the solutions is known, the other may be calculated from the potential differenoe. In practiix, the glass electrode usually consists of a bulb of the special glass fused to the end of a tube of ordinary glass. Inside the bulb is placed a solution of known pH, in contact with an internal silver-silver chloride or other electrode. This glass electrode and another reference electrde are immersed in the solution to he tested and the potential difference is measured. A potentiometer providing electronic amplification of the small current prduced is employed. The modern instruments available permit reading the pH directly and provide also for oompensation of variations due to temperature in the range of 0" to 50" and to the small but variable asymmetry potential inherent in the glass electrde.

In the broad realm of howledge concerning the preparation and action of drugs few, if any, variables are so important as pH. For the purpose of this presentation, four principal types of pH-dependence of drug systems will h discussed: solubility, stability, activity, and absorption.

' 2 Na+ + AA- + H,O = HA + OHMa+ A-

If the PH of the solution is lowered, more of the A- would h converted to the unionized acid, HA, in xcmdance with Le Chatelier's principle- Eventually, a PH will he obtained, below which the amount of HA formed e x d s its aqueous solubility, So, and the acid will precipitate o ' m solution; this pH can h designated as pH,- At this point, at which the amount of HA formed just equals So, a mass balance on the total amount of drug in solution yields (93)

Replacing [A-] as a function of hydronium-ion concentration gives

L: = S o +

K,C, [H:,Ot 1, + KO

TaEng logarithms gives p% = p&

c, - so + log sn

(96)

Thus, the blow which precipitation is a function of the amount of salt added initially, the pK, and the solubility of the fiee acid formed from the salt. The analogous equation for salts of weak bases and strong acids (such as pilmarpine hydrmHoride, hydrocHoride, or deine phosphate) would be

so

pHp = PK~ + log

(97)

in which pK, refers to the protonated form of the weak base. Example-Below what pH will free phenobarbital begin to precipitate b m a solution initially mntaining 1.3 g of s&um phenobarbitall100 mL at 25'? The molar solubility of phenobarbital is 0.0050 and its pK. is 7.41. The molecular weight of s d u m phenobarbital is 254. The molar concentration of salt initially added is

c

g/L

--=--

"-molwt

13 254-O.O5lM

pH,,= 7.1 1 + log = 7.41

0.061

- 0.005

0.005

+ 0.96 = 8.37

flii=&,

-

p% = 8.41

0.0056 + log 0.0291 - 0.0056

= 8.41

pKb= 14.00 - 5.59 = 8.41

+ 1-0.63)

= 7.78

Drug Stability C,,the

following reactions wcw:

Clg= [HA] + [A-I = So + [A-I

so

Example-Above what pH will free m e begin to precipitate from a solution initially containing 0.0294 mol of m a k e h y d d o ride per liter? The pKb of cmaine is 5.59, and its molar solubility is 5.60 x lo-'.

PHARMACEUTICAL SIGNIFICANCE

Drug Solubility If a salt, NaA,is added to water to give a -ntration

[H@+lli = K,,

(94)

where K, is the ionization constant for the conjugate acid, HA, and [HaO+lprefers to the hydronium-ion concentration a b v e

One of the most diversified and f i t f u l areas of study is the investigation of the effect of hydrogen-ion concentration on the stability or, in more general terms, the reactivity of pharmaoeutical systems. The evidence for enhanced stability of systems when these are maintained within a narrow range of pH, as well as of progressively decreasing stability as the pH departs from the optimum range, is abundant. Stability (or instability) of a system may result from gain or loss of a proton (hydrogen ion) by a substrate moleculmften accompanied by an electronic rearrangementthat reduoes (or increases) the reactivity of the molecule. Instability results when the s u b s t a m desired to remain unchanged is converted to one or more other, unwanted, substances. In aqueous solution, instability may arise through the catalytic effect of acids or b a s e e t h e former by transferring a proton to the substrate molecule, the latter by accepting a proton. Specific illustrations of the effect of hydrogen-ion conoentration on the stability of medicinals are myriad; only a few will h given here, these b i n g chosen to show the importanoe of pH adjustment of solutions that require sterilization. Morphine solutions are not decomposed during a 60-min exposure at a temperature of 100" if the pH is less than 5.5; neutral and alkaline solutions, however, are highly unstable. Minimum hydrolytic decomposition of solutions of cmaine

CHAPTER 17: IONIC SOLUTIONS AND ELECTROLYTE EQUILIBRIA

w

s in the range of pH of 2 to 5; in one study a solution of m a i n e hydrcchloride, initially at a pH of 5.7, remained stable during 2 months (although the pH dropped to 4.2 in this time), while another solution b u f f e d to a b u t pH 6 underwent approximately 30% hydrolysis in the same time. Similarly, solutions of p w a i n e hydrcchloride containing some hydrochloric acid showed no appwiable decomposition; when dissolved in water alone, 5% of the prmaine hydrmhloride hydrolyzed, whereas when buffered to pH 6.5, h m 19 to 35% underwent deoomposition by hydrolysis. Solutions of thiamine hydrcdoride may be sterilized by autmlaving without appreciable decomposition if the pH is blow 5; a b v e this, thiamine hydrcchloride is unstable. The stability of many disperse systems, and especially of certain emulsions, is oRen pH dependent. Information concerning specific emulsion systems, and the effect of pH upon them, may be found in Chapter 21.

Drug Activity Drugs that are weak acids or weak base-and

hence may exist in ionized or nonionized form (or a mixture of b t h t m a y be active in one form but not in the other; often such drugs have an optimum pH range for maximum activity. Thus, mandelic acid, bnzoic acid, or salicylic acid have pronounced antibacterial activity in nonionized form but have practically no such activity in ionized form. Amrdingly, these substances require an acid environment to function effectively as antibacterial agents. For example, s d i u m bnzoate is effective as a wemative in 4% concentration at pH 7, in 0.06 to 0.1% concentration at pH 3.5 to 4, and in 0.02 to 0.03% concentration at pH 2.3 to 2.4. Other antibacterial agents are active principally, if not entirely, in cationic form. Included in this category are the auidines and quaternary ammonium compounds.

249

Drug Absorption The degree of ionization and lipoid solubility of a drug are two important factors that determine the rate of absorption of drugs from the gastrointestinal tract, and indeed their passage through cellular membranes generally. Drugs that are weak organic acids or bases, and that in nonionized form are soluble in lipids, apparently are absorbed through cellulm membranes by virtue of the lipoidal nature of the membranes. Completely ionized drugs, on the other hand, are absorld poorly, if a t all. Rate8 of absorption of a variety of drugs are related to their ionization oonstants and in many cases may b predicted quantitatively on the basis of this relationship. Thus,not only the degree of the acidic or basic character of a drug, but also consequently the pH of the physiological medium (eg, gastric or intestinal fluid, plasma, oerebmspinal fluid) in which a drug is dissolved or disper8$d-bcarne this pH determines the extent to which the drug will be converted to ionic or nonionic formh m e important parameters of drug absorption. Further information on drug absorption is given in Chapter 58.

REFERENCES 1. Benet LZ,Goyan JE.J Pharm Sd 1966;64:1179. 2. Riegelman S et al. J Phwm Sci 1962;61:129. 3. Niekgall PJ et al. J P h w m Sd 1972;61:232.

Conway BE.Ionic Hydmf on in Chemistry and Bwphysics. Amsterdam: Elsevier, 1980. Denbigh K The Principles of Chemicd Equilib&rn, 4th ed. London: Cambridge University W,1981. Freiser H. Fernando Q. Ionic E a u i l i b ~ ain AnalvtM Chemistns New York Wiley, 1966.Harned HS,Owen BB.The Physical Chemispy ofElectmlyf c S d u f ons. New York, Reinhold, 1958. ACKNOWLEDGMENTSpaul J Niebergall, PhI3 is a h o w l edged for his & o h in previous editions of this work

If a solution is placed in contact with a membrane t h a t is permeable to molecules of the solvent, but not to molecules of the solute. the movemellt of solvent throueh tthe membrane is called osn~osrs.Such a membrane often is called S P ~ Tr -pcbl-n~rw I blc. 11s the several types ofmembranes ofthe body vary in their permer ~ ~ ~ l ~ y .\.lost ability, it is well to note t h a t they a r e s ~ ~ l t ~ c t rpermeable normal livinpcell membranes maintain various solute concentration gradients h selectir~elypermeable membrane may be defined either as one t h a t does not permit free, ullhampered diffusiol~of all the solutes present, or a s one t h a t maintains at least one solute collcel~tratiol~ gradient across itself Osmosis, then, is the diffusiol~of water through a membral~ethat maintains at least one solute concentration gradient across itself rissume t h a t Solutiol~h is on one side ofthe membrane. and Solution U of the same solute but of a higher concentration is on the other side, the solr~entwill tend to pass into the more concentrated solution until equilibrium has been established 'rhe pressure required to prevent this movement is t h e osmotic pressure It is defined a s t h e excess pressure, or pressure greater than that above t h e pure solvent, t h a t must be applied tu Solution I3 to prevent passage of sulvent through a perfect semipermeable membrane from ri tu U The concentration of a solution with respect to effect U H osmotic pressure is related to t h e number of particles (unionized molecules, ions, macromolecules, aggregates) of solute(s) in solutiol~and thus is affected by t h e degree of ionizatiol~or aggregation of the solute See Chapter 16 for review of culligative properties of sulutiolls Body fluids, illcludil~gblood and lacrimal fluid, normally have an osmotic pressure t h a t often is described a s corresponding to t h a t of a 0 9: solutiol~of sodium chloride The body also attemnts to keen the osmotic nressure of the contents of the gastrointestinal (GI)tract at about this level, but there the normal range is much wider than t h a t of most body fluids 'rhe 0 9 5 sodium chloride solution is said to be rso-osn~otrt.with physiological fluids In medicine, the term rsofonrt., meaning equal tone, is commonly used interchangeably with iso-osmotic IIowever, terms such as isotonic and tonicity should be used on1.v with reference to a physivlogical fluid lso-osmotic actually is a physical t e r m t h a t compares t h e osmotic pressure (or another colligatir~eproperty, such as freezing-point depression) of two liquids. neither of which may be a pl~ysiologicalfluid, or which may be a physiological fluid only under certain circumstances For example, a solutiol~ofburic acid t h a t is iso-osmotic with both blood and lacrimal fluid is isotunic only with the lacrimal fluid 'rhis solutiol~causes hemolysis of red blood cells because molecules of boric acid pass freely through tthe erythrocyte membrane regardless of concentration ' r ~ u s , isotrll~icityinfers a sense of physiological compatibility where iso-osmoticity need not 11s another example, a t.h~~n1rt.ul1.v deb-

sidered a physiological fluid, or suitable for parentera1 use h solutiol~is isotonic with a living cell if there is no net gain or loss of water by the cell, or other change in the cell. when it is in contact with t h a t solution Wysiolugical solutions with an osmotic pressure lower t h a n t h a t of body fluids. or of 0 9: sodium chloride solution, are referred to commonly as being h.vpotonrt. Physiological solutiol~shaving a greater osmotic pressure are termed hypcrtonrt.. Such qualitative terms are of limited value, and it h a s become necessary to state osmotic properties in quantitative terms To dv so. a term must be used that will represent all the particles t h a t may be present in a given system The term used is os1~1o1: t h e weight. in grams, of a solute, existing 111 a solutiol~ a s molecules (and/or ions, macromolecules, aggregates, etc), which is osmotically equivalent to a mole of a11 ideally behaving nonelectrolyte Thus, t h e osmol weight of a nonelectrolyte, in a dilute solution, generally is equal to its gram molecular weight h 1~1rIlros~~101, abbreviated mOsm, is t h e weight stated in milligrams If one extrapolates this concept of relating a n osmol and a as being equivalent, then one also may mole of a l~ol~electrolyte define a n osmul in t h e followingways It is the amount of solute t h a t will provide 1rivogadrv's number (6 02 x 10' '1 of particles in solutiol~and it is the amount of solute that. on dissolution in 1 k g of water, will result in an osmotic pressure increase of 17,000 torr at 0' or 19,300 torr at 37' One mOsmol is 1/1000 of an osmol For example, 1mol of anhydrous dextrose is equal to 180 g One osmol of this nonelectrolyte is also 180 grams One mOsmol would be 180 mg ' r ~ u s 180 , mg ofthis solute dissolved in 1k g of water will produce an increase in osmotic pressure of 19 3 torr at body temperature For a solution of an electrolyte such as sodium chloride, one molecule of sodium chloride represents one sodium and one chloride ion IIence, 1mulwill represent 2 osmol of sodium chloride theoretically riccordingly, 1 osmol NaC'l - 58 5 g/2 or 29 25 g This quantity represents the sum total of 6 02 x 10'' ions as t h e tutal number of particles Ideal solutiolls infer very dilute solutiol~sor infinite dilutiol~ IIowever, a s t h e concentration is increased. other factors ent e r With strong electrolytes, interionic attraction causes a decrease in their effect on colligatir~eproperties In addition, and in opposition, for all solutes, including nonelectrolytes, solvation and possibly other factors operate to intensify their colligative effect Therefore, it is v e y difficult and often impossible to predict accurately t h e osmoticity of a solutiol~It may be possible to do so for a dilute solution of a single pure and wellcharacterized solute. but not for most parentera1 and enteral medicinal andlor nutritional fluids, experimental determination likely is required

CHAPTER 18: TONICITY, OSMOTICITY, OSMOLALITY, AND OSMOLARITY

THERAPEUTIC CONSIDERATIONS

251

It generally is accepted that osmotic effects have a major place in the maintenance of homeostasis (the state of eauilibrium in the living M y with respect to various function; and to the chemical composition of the fluids and tissues, eg, temperature, heart rate, b l d pressure, water content, or b l d sugar). To a great extent these effects occur within or between cells and tissues where they cannot be measured. One of the most troublesome problems in clinical medicine is the maintenance of adequate M y fluids and proper balance htween extracellular and intracellular fluid volumes in seriouslv ill ~ a t i e n t s I. t

tion Osmoglyn (Alcon) and isosorbide solution Ismotic (Alcon) are oral osmotic agents for reducing i n t r a m l a r pressure. The osmotic principle also applies to plasma extenders such as polyvinylpyrrolidone and to saline laxatives such as magnesium sulfate, magnesium citrate solution, magnesium hydroxide (via gastric neutralization), durn sulfate, s d u m phosphate, and d i u m biphosphate oral solution, and enema (Fleet). An interesting osmotic laxative that is a nonelectrolvte is a lactulose solutioi. Lactulose is a nonabsorbable d i s a c a r i d e that is colon-specific, wherein colonic bacteria degrade some of the disaccharide to lactic and other simple organic acids. These, in toto, lead to an osmotic effect and laxation. An extension of

should h kept in mind, however, that fluii a n i electrolyte

this therapy is illustrated by Cephulac (Marion Merrell Dow)

abnormalities are not diseases, but are the manifestations of disease. The physiological mechanisms that control water intake and output appear to respond primarily to serum osmoticity. Renal regulation of output is influenced by variation in rate of release of pituitary antidiuretic hormone (ADH) and other factors in response to changes in serum osmoticity. Osmotic changes also serve as a stimulus to mderate thirst. This mechanism is sul3ciently sensitive to limit variations in osmoticity in the normal individual to less than about 1%.B d y fluid continually oscillates within this narrow r a n g . An increase of plasma osmoticity of 1%will stimulate ADH release, result in reduction of urine flow, and, at the same time, stimulate thirst that results in increased water intake. Both the increased renal reabsorption of water (without solute) stimulated by circulating ADH and the increased water intake tend to lower serum osmoticity. The transfer of water through the cell membrane mcurs so rapidly that any lack of osmotic equilibrium between the two fluid compartments in any given tissue usually is corrected within a few seconds and, a t most, within a minute or so. However. this r a ~ i dtransfer of water does not mean that com~lete equilibration occurs between the extracellular and intracellular compartments throughout the entire M y within this same short perid of time. The reason is that fluid usually enters the M y through the gut and then must he transported by the circulatory system to all tissues before complete equilibration can occur. In the normal person it may require 30 to 60 min to achieve reasonably g o d equilibration throughout the b d y after drinking water. Osmoticity is the property that largely determines the physiological acceptability of a variety of solutions used for therapeutic and nutritional purposes. Pharmaceutical and therapeutic consideration of osmotic effects has been, to a great extent, directed toward the side effects of ophthalmic and parenteral medicinals due to abnormal osmoticity, and either to formulating to avoid the side effects or to finding m e t h d s of administration to minimize them. More recentlv this consideration has been extended to total (central) pareiteral nutrition, to enteral hyperalimentation ('tube" feeding), and to concentrated-fluid infant formulas.' Also, in recent years, the importance of osmometry of serum and urine in the diagnosis of many pathological conditions has been recognized. There are a n u m h r of examples of the direct therapeutic effect of osmotic action, such as the intravenous (IV)use of mannitol as a diuretic that is filtered at the glomeruli and thus increases the osmotic Dressure of tubular urine. Water must then be reabsorbed agAnst a higher osmotic gradient than otherwise, so reabsorption is slower and diuresis is observed. The same fundamental principle applies to the 1V administration of 30% urea used to affect intracranial pressure in the control of cerebral edema. Peritoneal dialysis fluids tend to be somewhat hyperosmotic to withdraw water and nitrogenous metabolites. Two to 5%sodium chloride solutions or dispersions in an oleaginous base (Muro, Bausch & Lomb) and a 40% glucose ointment are used topically for corneal edema. Ophthalgan (WyethAyerst) is ophthalmic glycerin employed for its osmotic effect to clear edematous cornea to facilitate an ophthalmoscopic or goniosoopic examination. Glycerin solutions in 50% mncentra-

solution, which uses the acidification of the colon via lactulose degradation to serve as a trap for ammonia migrating from the blood to the colon. The conversion of ammonia of b l o d to the ammonium ion in the colon ultimately is coupled with the osmotic effect and laxation, thus expellingundesirable levels of b l d ammonia. This prduct is employed to prevent and treat frontal systemic encephalopathy. Osmotic laxation is observed with the oral or rectal use of glycerin and sorbitol. Epsom salt has been used in baths and comDresses to reduce edema associated with wrains. Another appioach is the indirect application of the osmoic effect in therapy via osmotic pump drug delivery systems.2

It is necessary to use several additional terms to d e h e expressions of concentration in reflecting the osmoticity of solutions. The terms include osmolality, the expression of osmolal concentration, and osmolarity, the expression of osmolar concentration. OSMOLALITY-A solution has an osmolal concentration of one when it contains 1osmol of solute/kg of water. A solution has an osmolality of n when it contains n osmolkg of water. Osmold solutions, like their counterpart mold solutions, reflect a weight-to-weight relationship between the solute and the solvent. Because an osmol of any nonelectrolyte is equivalent to 1 mol of that compound, then a 1osmolal solution is synonymous to a 1mold solution for a typical nonelectrolyte. With a typical electrolyte like d i u m chloride, 1 osmol is approximately 0.5 mol of sodium chloride. Thus, it follows that a 1osmolal solution of s d i u m chloride essentially is equivalent to a 0.5 mold solution. Recall that a 1osmolal solution of dextrose or sodium chloride each will contain the same particle concentration. In the dextrose solution there will be 6.02 X 10'" moleculedkg of water and in the d i u m chloride solution one will have 6.02 X 102%tal ion@ of water, one-half of which are Na+ ions and the other half C1-ions. As in mold solutions,osmolal solutions usually are employed where quantitative precision is required, as in the measurement of physical and chemical properties of solutions (ie, colligative properties). The advantage of the w / w relationship is that the concentration of the system is not influenced by temperature. OSMOLARlTY-The relationship observed between molality and osmolality is shared similarly between molarity and osmolarity. A solution has an osmolar concentration of 1when it contains 1 osmol of solute per liter of solution. Likewise, a solution has an osmolarity of n when it contains n osmols/L of solution. Osmolar solutions. unlike osmolal solution. reflect a weight in volume relation$hip between the solute gnd final solution. A 1 molar and 1 osmolar solution would be identical for nonelectrolytes. For d i u m chloride a 1 osmolar solution would contain 1 osmol of s d i u m chloride per liter which approximates a 0.5 molar solution. The advantage of employing osmolar concentrations over osmolal concentrations is the ability to relate a specific number of osmols or milliosmols to a volume, such as a liter or milliliter. Thus, the osmolar concept is simpler and more practical. Volumes of solution, rather than weights of solution, are more practical in the delivery of liquid dosage forms.

252

PART 2: PHARMACEUTICS

Many health professionals do not have a clear understanding ofthe difference between osmolality and osmolarity, l n fact, the terms have been used interchangeably, 111 osmolar solution of a solute always will be more concentrated t h a n a 1 osmolal solution. With dilute solutiolls the difference may be acceptably small. For example, a 0 . 9 5 rulr< solutiol~of sodium chloride in water col~taills9 g of sodium chloride/L of solution, equivalent to 0.308 osmolar; or 9 g of sodium chloride/996.5 g of water, equivalent to 0.309 osmolal, less than a 15 error. For concentrated solutiol~sthe percent difference between osmolarity alld osmolality is much greater alld may be higllly siplificant; 3.5:; for 5?$ rr: / I < dearose solutioll and 25q: for 2 5 5 rr: / r<

dearose solut.ion. One should be alerted to t.he sizable errors that may occur with col~cel~trated solutiolls or fluids, such as those employed in total parentera1 nutrition, enteral hyperalimentation, and oral nutritiollal fluids for infants. Reference has been made to t h e terms hypertonic and hypotonic, rlnalogous terms are hyperosmotic and hypo-osmotic. Assuming- normal serum osmolality to be 285 mOsmolkg, as serum osmolality increases due to water deficit, t h e followu~g signs and symptoms usually are found to accumulate progressively at approximately these values: 294 to 298-thirst (if the patient is alert and communicative); 299 to 313-d~y mucous membranes; 314 to 329-weakness, doughy sku]; above 330disorientation, postural hypotension, severe weakness, fainting, CYS changes, stupor, and coma, 11s serum osmolality decreases due to water excess the followil~gmay occur: 275 to 261-headache; 262 to 251-drowsiness, weakness; 250 to 233-disorientation, cramps; below 233-seizures, stupor, and coma. As indicated previously, t h e meehal~ismsof t h e body actively combat such major changes by limiting the variatiol~in osmolality for normal individuals to less t h a n about 15 (approximately in the range 282-288 mOsmol/kg, based on the above assumption). The value given for normal serum osmolality above was described as an assumptiol~because ofthe variety ofvalues found in the literature. Serum osmolality often is stated loosely to be about 300 mOsmol/L. Various references report 280 to 295 mOsmol/L, 275 to 300 mOsmol/L, 290 mOsmol/L, 306 mOsmol/L, and 275 to 295 mOsmolkg. l n recent years, much attention has been directed a t determining osmoticity of total parentera1 nutritiol~solutions, enteral formulas, and parentera1 and enteral medications:'-:' IIyperosmoticity of parentera1 and enteral formulas and medications sen7es as an indicator for potential risks, il~cludil~g tl~rombophlebitis,pain at injectiol~site, diarrhea, and abdominal cramping. IIowever, the terms osmolality and osmolarity often have been used u~terchangeablyand caused much confi~sion for practitioners. Often, when t h e term osmolarity is used, one cal~notdiscern whether this simply is incorrect terminology, or if osmolarity actually has been calculated from osmolality. Another current practice t h a t can cause col~fusiol~ is t h e use of the terms nornla/ or ~ ~ . v s ~ o / ofor ~ ~isotonic c u / sodium chloride solutiol~(0.9':;). The solution surely is iso-osmotic. IIowever, a s to being physiological, t h e concentration of ions are each of 154 mEq/L whereas serum colltaills about 140 mEq of sodium and about 103 mEq of chloride. ' r l e range of mOsmol values foulld for serum raises t h e questioll as to what really is meal11 by t h e terms hypotollic and hypertonic for medicinal and nutritional fluids. One can f i l ~ d the statement that fluids with an osmolality of 50 mOsmol or more above normal are hypertonic; and, if they are 50 mOsmol or more below normal, tlley are hypotonic. Olle also call filld tile statemellt t h a t peripheral illfusiolls should llot have an osmo. larity exceedillg 700 to 800 m O s m o l / ~ ,~~~~~l~~ " ofosmol con. centrations ofsolutiolls used in peripheral illfusiolls are (U5W) 5% dextrose solution, 252 mOsmol/L; (UlOW) 1 0 9 dearose solution, 505 mOsmol/L; and Lactated Ringer's 5 9 'rextrose, 525 mOsmol/L. When a fluid is hypertonic, undesirable effects often can be decreased by using relatively slow rates of infusion, and/or relatively short periods of infusion. For example, 255

dextrose solutiol~('r25M:&4,25rt Amino Acids is a representative of a highly osmotic hyperalimentatiol~solution. It h a s been stated t h a t when osmolal loading is needed, a maximum safe tolerance for a normally hydrated subject would be an approximate increase of 25 mOsmol/kg- of water over 4 hours.'

COMPUTATlON OF OSMOLARlTY Several methods are used to obtain numerical values of osmolarity. The osmolar concentration, sometimes referred to as the throrctical o s n ~ o l a r i t .is~ ,calculated from the rr: / r< collcentratiol~

using the follo~vingequation: g 1,

rru)ls x

osnlul 1 IlOf rr~(lsrr~ot 111(1sr11ol x x rnul o~irnol 1.

g

(1)

The number of osmol/mol is equal to 1for nonelectrolytes and is equal to t h e number of ions per molecule for strong electrolytes. of factors such as This calculatiol~ omits col~sideratiol~ solvatiol~and interionic forces. Uy this method of calculation, 0.9X sodium chloride h a s a n osmolar c o l ~ c e l ~ t r a t i oofl ~308 mOsmol/L and a concentration of 154 mOsmol/L in either sodium or chloride ion. Two other methods compute osmolarity from values of osmolality. The determination of osmolality will be discussed later. One method h a s a strong theoretical basis of pl~ysicalchemical p r u ~ c i p l e s ~ ~ s i ~ ~ g vofa lt hu e spartial molal volume(s) of tile solute(s),Il0.9:; sodium chloride solution, found experi. mentally to have an osmolality of 286 mOsmolkg, was calculated to have an osmolarity of 280 mOsmol/L. rather different from t h e value of 308 mOsmol/L calculated a s above. The method, using partial molal volumes, is relatively rigorous, b u t many systems appear to be too complex and/or too poorly defilled to be dealt with by tllis metllod, The other method is based on calculating- the weight of water from t h e solution density and col~cel~tratiol~ g water.

fi sol UI inn

I ~ I [ solu[ , io11

-

g 5rllute

1111. soluIit>11 1~11.so111ii(11,

then 1110s!1u>l; r > 5 r ~ l o ~it!; 4I!,I, 1 so1111 [o11! I

i rnllsruol =

,

wntrr

osmolalit>- I: I OIIII g r v a r ~ r l r n ~snla+lnn .

'rleesperimelltal

value for the osmolality of 0,gr; sodium chloride solutioll was 292.7 mOsmol/kg; t h e value computed for osmolarity was 291.4 m(jsmol/L, This method uses easily tailled values of density of tile solutioll and of its solute content and can be used with all systems. For example, the osmolality of a llutritiollal product was determilled by tile freezing-point depressioll method to be 625 m(jsmol/kg-'O; its osmolarity was calculated a s 625 x 0.839 - 524 mOsmoVL. klonograpl~siin the LSP for solutiolls provide 1C: replenishment offluid, nutrients, or electrolytes, and for osmotic diuretics be such as klannitol Injection, require the osmolar collcel~tratiol~ stated on the label in osmol/L; however, when the colltellts are less than 100 mL, or when the label states the article is not for direct illjeetion but is to be diluted before use, tile label alterllaLively may state tile total osmolar eoncentration jll mOsmoVmL, An rxnmplr n f t h r use nfthc first nlcthnd dcscrilrd nhnvc is the cnnlputntinn of the npprnximntc nsnlnlnr cnnccntrntinn [throrc,t~c,olosrnol o r 1 t ~ d1 n L n c t n t d Ringer's 5'2 Dcxtrnsr Snlutinn [Ahhott~:which is l n h d r d to contain: per liter: drxtrnsr [hydrnus150g: sndiunl chloride (i g: pntnssium chlnridr :iOO mg, cnlciunl chlnridr 200 mfi, nnd sodium Inct n t r 2.1 g. Also stntcd is t h a t t h r tntnl nsnlnlnr cnncrntrntinn n f t h r snlUtinnis npprnxinlntrly 524 mr)snlnln, in cnntrii,utcd iIJ7 1: kacid.If abaseWU& k d , then, at 2s0, fie expected minimum rate of the reaction would expected to cwxur at pH 7. A reaction may be catalyzed not only by hydrogen ion and hydroxide ion, but also by other Brijnsted acids or bases such as the solvent water. This is referred to as general acidhase catalysis. In this case, the observed rate canstant is given by

kobs

= kwater

+ kacid lB+l + kbase [OH-]

(65)

where kwabr is a pseudo-order rate oonstant that has the concentration of water, which is in large excess, incorporated into it. Figure 19-7 shows how a plot of the logarithm Bob, versus pH might appear in such a case. The flat region, where the rate of reaction apparently is not pH dependent, is the region where the solvent is much more important as a catalyst than either the hydrogen or hydroxide ions. For compounds that are weak acids or weak bases, which can therefore exist in b t h ionized and nonionized species, the pH rate profiles h a m e even more oomplex. W n , b t h the ionized and nonionized species are subject to decomposition and catalysis by hydrogen and hydroxide ion; but each of these species may react a t a different r a h . For example, the hydrolysis of the weakly basic drug prwaine can be represented by1 -dGPrltotddt = k1[0H-lGPrl

+ ka[OH-lGPrH+l

(66)

where P r is the nonionized procaine molecule and PrH+ is the protonated form. The concentration of each species can be related to the total pmaine concentration by the relationships [Pd =

[OH-]

~ Kb+ [OH-] * [ ~ r l ~ ~ ~ (67)

[PrH+l = Kb+Kb [OH-] *[filroari

(68)

where % is the classical dissociation oonstant for the weak base prccaine. The oomplete rate expression for prccaine hydrolysis is given by Equation 69. -

dY[Kb+ =

kl[oH-la [OH-]

+

ka[oH-Yb ] [ ~ r ] & ~ ~ (69) i

Kb+ [OH-]

The pH dependency of prccaine hydrolysis is illustrated graphically in Figure 19-as by a plot of logarithm Bob, versus pOH for the pH region 7 to 13.

274

PART 2: PHARMACEUTICS

Upon substitution of Equation 70 into the rate equation, the initial rate, uo, (ie, The rate at time equal to zero) is given by Equation 7 1. kfkdElo urn (71) kr + kz Km kf + - 1 +[Slo [Slo where Km,the Michaelis-Mentenconstant, is equal to (k,+kz)/ k1 and urn, the maximum initial velmity of the reaction, is equal to kz [Elo.The rate constant kz is often referred to as the turnover number which represents the n u m b r of molecules of prduct P created per second per mole of enzyme. Equation 70 dws not lend it self well to analysis as plots of uo vs. [Sl0 only asymptotically approachs the maximum velmity, [Sl0. Rearrangement of Equation 71 into Equation 72, known as the Lineweaver-Burk Equation, lends itself more readily to analysis as shown in Figure 19-9. Uo

--

'e E V

d

=

-1 =UO

-

C

1

1

2

I

3

4

5

6

7

POH

Figure 19-8. Apparent first-order rate of hydrolysisof procaine m a function of hydroxide-ion concentration at 40". (Fmrn Higuchi T, Lachrnan L. J APM kiEd 1955; 44: 52.)

1 +- Km um

(72)

um[s1o

An important area of study in enzyme kinetics is enzyme inhibition. There are two basic mechanisms in which an inhibitor, I, can inhibit and enzyme-catalyzed reaction. Competitive inhibition occurs when the inhibitor competes with the substrate, S, for the active binding site on the enzyme and blmks the catalytic action of the enzyme. In such a case, the formation of the enzyme-inhibitorcomplex is assumed to he in rapid equilibrium with the enzyme and inhibitor.

E+IoEI

General Acid or Base Catalysis Acid or base catalysis is not restricted to the effect of hydrogen or hydroxide ion. Undissmiated acids and bases often can he demonstrated to produce a catalytic effect, and in some instances metal ions and various anions can serve as catalysts. Mutarotation of glucose in acetate buffer is catalyzed by hydrogen ion, hydroxide ion, acetate ion, and undissmiated axtic acid. Also, the rate of barbiturate hydrolysis in ammonia buffers is increased by increasing buffer concentration at constant pH as a result of catalysis by NHs. Hydrolysis of the amide function of chlorampheniool exhibits, in addition to solvent and specific acid-base catalysis, *nerd acid-base catalysis in phosphate and citrate buffers. General acid-base catalysis is to be anticipated if there is evidence of a significant solvent catalysis, as illustrated in the pH-rate profile of Figure 19-7.

Equation 73 shows the resulting Lineweaver -Burk Equation for the case of a competitive inhibitor. Km

(73)

the dissmiation oonstant for the enzyme-inhibitor plex, [E][I]/[EI]. Figure 19- 10 shows a typical LineweaverBwk graph for competitive inhibition. Each plot represents a different concentration of the oompetitive inhibitor. ~ ~thatt e all three plots intersect at the same point on the y-axis indicating that the reactions all have the same maximum velmity. H ~ since they ~ do ~ not intersect ~ at~the same ~ point, on the x-axis then they have different Michaelis-Menten constants, K,.

K,

Emyme Catalysis In biological systems, catalytic molecules, called enzymes (E), reversibly bind to a substrate (S)to form an intermediate (X)which then decomposes to give a prduct (P) and the original enzyme. kf E+SoX kr and kz X+P+E The rate of this reaction, u, will he given by d[PYdt = kz@]. However, this is an improper rate equation as X is an intermediate. Michaelis and Menten used a steady state approximation (ie, a t sometime during the reaction the time rate of change of the intermediate will he zero) to calculate the concentration of X.

IX1

=

kr[Elo[Slo kf[SIo + k . + ka

Figure 199. Lineweaver-Burk plot of modified Michael&-Mentenequation (Equation 72).

CHAPTER 19: CHEMIC4L KINETICS

275

However, since the plots do not intersect a t the same point on the y-axh, then the r e a d o m have diffeent maximum velocities.

OTHER EFFECTS Ionic Strength In general, the effects of increasing concentrations of electrolytes on reaction rate can Iw predicted by consideration of the influence of ionic strength on interionic attraction. The Deby+Hiickel equation may be used to demonstrate that incl-eased ionic strength would be expected to decl-easethe rate of reaction btween oppositely charged ions, and i n c r e w the rate of reaction btween similarly charged ions. Thus, the hydrogenion catalyzed hydrolysis of sulfate esters is inhibited by increasing electrolyte concentration. H+ 0

14Sh Figure 19-10. Lineweaver-Burk plot for competitiw enzyme inhibition (Equation 73).

ROSOs-+Ha0 + ROH+ HSO4Reactions btween ions and dipolar molecules, and reactions btween neutral molecules generally are less sensitive to ionic strength effects than are reactions btween ionic compounds. However, reactions that result in formation of oppositely charged ions as prcducts may exhibit considerable increase in rate with increasing ionic strength.

The other type of enzyme inhibition is noncompetitive inhibition. In this case the inhibitor d m not bind to the active site

oftheenzymebutratherbindstoanotherpartoftheenzymeor to the enzyme-substrate complex, X. E

+IoEI

and X+IoXI In this case, the equilibrium constant, &, is given by both ~I~Y[E and I I[XIKl/[xrl. The resulting Lineweaver-BurkWuation is given by Equation 74.

[-

1 = 1 UO

urn

] p + E]

+ urn[Slo

(74)

Figure 19-11 shows a typical Lineweaver-Burk graph for noncompetitive inhibition. Each plot represents a different concenNote that all plots intration of the mmpetitive *itor. brsect at the same point on the x-axis indicating that the reactions all have the same Mihaelis-Menten constant, K ~ .

DielectricComtantof Solvent Reactions involving ions of opposite charge are awlerated by solvents with low dielectric constants. For example, the rate of hydrogen ion-catalyzed hydrolysis of sulfate esters is much greater in low dielectric constant solvents, such as methylene chloride, than in water . Reaction btween similarly charged species is favored by high dielectric constant solvents. Reaction btw, neutral molecules, which *due a highly palm tran&ion state, such as the reaction of triethylamine with ethyl iodide to p d u m a quaternary ammonium salt, also will be enh a n d by high dielectric constant solvents.

H y d r o l ~s i(Solvolysis) Hydrolysis of esters, such as pmaine, aspirin,or atropine, r e p merits one of the more common types of drug instability. Ester hydrolysis is either hydrogen- or hydroxide-ion catalyzed, although the catalysis that is important from the viewpoint of drug-product stability depends upon the spec%c oompound and the pH of the solution. Amides generally are more stable than esters but are subject to catalysis by hydrogen and hydroxide ions, and oRen by general acids and bases. Some examples of the kinds of functional groups subject to hydrolytic cleavage

IIv,

-

'AS,

I 0.1

o

e

lmo Figure 19-11. Lineweaver-Burk plot for noncompetitive enzyme inhibition (Equation 74).

4

e a 1012 pH

Figure 1912. Apparent first-order rate of hydrolysis of aspirin as a function of pH at 17. (From Edwards U. Trans Farday Soc 1950; 46: 723.)

276

PART 2: PHARMACEUTICS

and species shuwl~to be catalysts for the reactiuns are presented below.

>

-

-0) -

('t12()11 I ;;--

0

!

I

Hz0

1I

4t[.~lll111'

ll-Y-('[l.<

ii TH',OH Q

+

-;:I{

C'-

110-c--

glycol acetate is formed; and in a solutiol~c o l ~ t a i l ~ i serum l~g albumil~(both in rjtro and in rp11r>hir g r o u p on t h n~l o l ~ r 1 1 1is~ in ;I lowpr s t ; i t ~of ~ n - form mieelles no furthertelldelley to reduee sur. p r p :it t h ~~n t ~ r f i iWtI ~I P ,~ P it no I o n g ~ is r :is s ~ ~ r r o ~ ~ nhyr iw:i~ri face tension ,rhe topic of micelles will be discussed later in t ~ DrI ~ I P ~ I I I P t11:in S , 1%-11~11 i t 1s In t h t~n ~ l k - s r > l ~ ~ tp11:is~ ir>n Chapter 2 1 r n t r ~ ; i s ~i nd t ~ ~ i i r t i ot w n t m - ~ ~film n n l o l ~ r ~;ilsr> ~ l ~\%-ill s rontritn~t~ If one plots t h e values of surface concentration, I versus conto this prorpss centratiol~e, for substances adsorbing to t h e vapor-liquid and h further reduction in free e n e r n occurs up011 adsorptiol~beliquid-liquid interfaces, using data such a s those given in Figcause of the gain in entropy associated with a change in water ure 20-13, olle gellerally obtaills an adsorptioll isotllerm shaped structure Water molecules, in the presence of dissolved alkyl like tllose 111 Figure 20-9 for vapor adsorptioll Indeed, it call be chains are more highly organized or rctb-lrh~than they are as a shown t h a t ~ 1 Lallgmuir 1 ~ equatioll (Equation 20) call be fitted pure bulk phase, hence, the entropy of such structured water is to such data when written in the form lower than t h a t of bulk water The process of adsorptiol~requires t h a t the ice-like structure ! ? -r',, (26) I - F - ~ nlrblf as the c h a u ~ sgo to the interface, and thus an increase UI the entropy of water occurs The adsorption of molecules diswhere I',,, , is t h e maximum surface concentration attained solved in oil can occur but it is by water structure with iilcreasing concentration and h' is related to h in Equachanges, and hence. only the first factors mel~tionedare importion 20 Combining Equations 24 and 26 leads to a widely used t a u t here relationship between surface-tension change I1 (see Equatiol~ It is very rare that significant adsorptiol~can occur a t the 23), and solute col~cel~tratioll c, kllowll as t h e Syszkowski hydrocarbon-air interface as little loss in free enern comes equation about by bringing hydrocarbon chains with polar groups attached to this interface O n t h e other hand, a t oil-water interI1 - I ,,, , RT In (1+ h'cj (27) faces, t h e polar portions of t h e molecule can interact with Tvater at the interface, leading to significant adsorptiol~ 'I'l~us,whereas water-soluble fatty acid salts are adsorbed Mixed Films from water to air-water and oil-water interfaces. their undisIt would seem reasollable to expect t h a t the properties of a sursociated counterparts, t h e free fatty acids, which are water inface film could be varied greatly if a mixture of surface-active soluble, form illsoluble films at t h e air-~vaterinterface, are llot agents were in the film As an example, consider that a mixture adsorbed from oil solutioll to an oil-air interface, b u t show sigof short- and long-chain fatty acids would be expected to show n i f i c a ~ tadsorptioll a t t h e oil-~vater illterface whell dissolved a degree of conclrnsafron varjlng from t h e gaseous state when in oil t h e short-chain substallce is used in high amoullt to a highly From tllis discussioll it is possible also to collclude tllat adcolldellsed state when t h e lollger chain substallce predomisorptiol~from aqueous solutiol~requires a lower solute coneentration to obtain the same level of adsorptiol~if t h e hydrophobic chain length is increased or if t h e polar portiol~of t h e molecule is less hydrophilie O n t11e other hand. adsorptiol~ from nonpolar solvents is favored when t h e solute is quite -. polar Because soluble or adsorbed films c a l ~ n o tbe compressed, z there is no simple, direct way to estimate t h e number of molecules/unit area coming- to the surface under a given set of z

z

col~ditiolls mate this value For relatively by applicatiol~ simple of tsystems h e Gibbsitequation, is possible which to estirelates surface collcel~tratiol~ to t h e surface-tension change produced a t different solute activities The derivation of this equation is beyond the scope of this discussion, but it arises from a classical t l ~ e r m o d j ~ ~ a m treatment ic of the change 111 free e n e r n when molecules col~celltrateat the boundary between two phases The equation may be expressed as '

ir rl? --

HT rlr)

\)L ll :T :SO

w

f

E40-

=2 e

"

30

-

20

-b

L

I

-5

I

LOG

(24)

where I ' is the moles of solute adsorbed/unit area, R is the gas constant, T is the absolute temperature and cly is the change 111 surface tension with a change in solute activity, d a , at activity o

1

-4

-3

h

-1

C

Figure 20-13. The effect of increasing cha~nlength on the surface a c t ~ i ity of a surfactant at the alr-aqueous solut~onInterface (each curie d ~ f fers from the preced~ngor succeed~ngby h v o methylene groups w ~ t hA, the longest cha~n,and

D,the shortest)

CHA!TER 20: INTERFACIAL PHENOMENA

k--k-+k--k--

---

Figure 2@14. A mixed monomolecular film. 2,a longxhain ion;

a 9

-m O,

a

long-chain nonionic compound.

8

4

6E e

nates. Thus, each oomponent in such a case would operate independently by bringing a proportional amount of bhavior to the system.

*

More often, the ingredients of a surface W do not bhave independently, but rather interact to prcduce a new surface

*.

An obvious example would be the combination of organic amines and acids which are charged oppositely and would Iw expected to interact strongly. In addition to such polar-group interactions, chain-chain interactions strongly favor mixed condensed films. An important example of such a case murs when a long-chain a h h o l is intrcduoed along with an ionized long-chain substance. Together the molecules form a highly oondensed film despite the presence of a high number of like charges. Pre8umably this cnxurs as seen in Figure 20-14, by arranging the molecules so that ionic groups alternate with a l w hol however' ifchain4ain interactions are not strong' the ionic species ORen will by the more unionized specie8 and will "de80rbn into the bulk solution. On the other hand, sometimes the more soluble surface-active agent prduoes surface pre8sures in exom of the oollappse pressure of the insoluble film and displaces it h m the surface. This is an important ooncept h a u s e it is the underlying principle behind cell lysis by surface-active agents and some drugs, and bhind the important p r m ~ of ~ detergency. s

B

k P

s

-E 0 m

1 2 z

*

li 1

0 0

1

2

3

bncrntrotbn, Moles par Lltlr

Figure 20-15. The relation between admrption and molecular w i g h t of fatty acids. (From Weiser HB. A Textbook of Colloid Chemistry. New York: Elsevier, 1949.)

sorption that cwxum h m water. This is seen in Figure 20-15, where adsorption of various fatty acids &om water onto c h m a l increases with increasing alkyl chain length or nonpolarity. It is difficult to predict these effects, but, in general, the more chemically unlike the solute and wlvent and the more alike the wlid surface group and solute, the greater the extent of adsorption. Another factor that must be kept in mind is that charged wlid Adsorption from Solution on to Solid surfaces, such as polyelectrolytes, will strongly adsorb oppositely Surfaces charged solutes. This is similar to the strong s p d c binding Adsorption to solid surfaces h m solution may c~xurif the d i ~ seen in gas chemiwrption, and it is characterized by ~ignificmt monolayer adsorption at very low concentrations of wlute. See solved molecules and the solid surface have chemicalgroups caFigure 20-16 for an example of such adsorption. pable of interacting. Nonsp&c adsorption also will cHxur if Adsorption onto activated c h m a l has h e n &own to he exthe solute is surface active and if the surface area of the solid is tremely useful in the emergency treatment of acute overdosage high. This latter case would b the same as w s at the vaof a variety of drugs taken by the oral route.'' Overall effecpor-liquid and liquid-liquid interfam. As with adsorption to tiveness of commercially available activated-chmal suspenliquid interfaces, adsorption to solid surfaces from solution generally leads to a monomolecular layer, oRen descrikl by the Langmuir equation in the form:

XlM

=

[(diW)rnk*cY(l+ k*c)

(28)

where x is the amount of adsorkl solute, M is the total weight of solid, d M is the amount of solute adsorbed per unit weight of solid at ooncentration c, k* is a oonstant, and MMhn is the amount of solute per unit weight covering the surface with a oomplete monolayer. However, as Gilesmhas pointed out, the variety of oombinatiom of solutes and solids, and hence the variety of possible mechanisms of adsorption, can lead to a number of more oomplex isotherms. In particular, adsorption of surfactants and polymers, of great importanoe in a number of pharmaceutical systems, still is not understood well on a fundamental level, x multilayed. and may in some situations even l Adsorption h m solution may be measured by separating solid and solution and either estimating the amount of adsorbate adhering to the solid or the loss in oonoentration of adsorbate h m solution. In view of the possibility of solvent adsorption, the latter approach really only gives an appmnt adsorption. For example, if solvent adsorption is great enough, it is possible to end up with an i n c r e d ooncentration of solute aRer mntact with the solid; here, the tern negative adsorption is used. Solvent not only influence8 adsorption by oompeting for the surfaoe,butmdiBCUBBedinoonnectionwitha&orptionatliquid surfam, the solvent will determine the escaping tendency of a solute; for example, the more polar the molecule, the less the ad-

Figure 2@16. The adsorption of a cationic surfactant, LN+, onto a negative~chargedsil~aorglalssurface,exposingahydmphobicsurfaceas the solid is exposed to air. (From Ter-Minmsian-Saraga L Adv Chem Ser 1964; 43: 23 2 .)

290

PART 2: PHARMACEUTICS

sions as an antidote in oral poisonings appears to be directly related to the total charcoal surface area. "rug adsorption to charcoal tends to follow b t h the Langmuir model as well as the Freundlich model. In addition, a drug that is un-ionized at gastric pH will adsorb to c h m a l to a greater extent than will the ionized form of the drug, probably hcause of less repulsive interactions in the adsorhd state of neutral molecules. Great care must be exercised in the formulation of activated-chmal suspensions hcause pharmaceutical adjuvants employed in suspensions have the potential to adsorb to the c h m a l and blwk sites for drug adsorption.

SURFACE-ACTIVE AGENTS

Table 20-7. Effect of Aerosol OT Concentration on the Surface Tension of Water and the Contact Angle of Water -th Magnesium Stearate

-

CONCENTKA I ION (M 3 106)

rsv

em

1.O 3.0 5.0 8.0 10.0 12.0

60.1 49.8 45.1 40.6 38.6 37.9

120 113 104

15.0

35.0

63

20.0 25.0

32.4 29.5

M

89 80 71

w

Throughout the discussion so far, examples of surface-active agents (surfactants) have been restricted primarily to fatty acids and their salts. It has been shown that b t h a hydrophobic portion ( a l k ~chain) l and a h~drophific portion ( c a h x y l and sulfate, which is used widely as an emulsifier and solubilizer in carbxylate groups) are required for their surface activity, the pharmaceutical systems. Unlike the sulfonates, sulfates are relative degree of polarity determining the tendency to accususceptible to pH-dependent hydrolysis leading to the formamulate at interfaces. I t now becomes important to look at some tion of the longmchainalcohol. of the specific types of surfactants available and to see what CATIONIC AGENTS-A number of long-chain cations, such as amhe salts ammonium salts, are structural features are required for different pharmaceutical applications. used as surface-active agents when dissolved in water; howThe classification of surfactants is quite arbitrary, but one their use in pharmaceutical preparations is limited to that ,,, based on chemical structure appears best as a means of intro,timicrobial preservation rather than as surfactants. qy,is ducing the topic- It is generally convenient to categorize surfacshes because the cations adsorb so readily at cell membrane tants amrding to their polar portions because the nonpolar structures in a nonspecific manner, leading to cell lysis (eg, ~ortionusuall~ismadeupofalk~lorar~l@oups-Themajorpo-hemolysis), as do anionics to a lesser extent. I t is in this way lar groups found in most surfactants may be divided as follows: that they act to destroy bacteria and fungi. anionic, cationic, amphoteric, and nonionic. As shall be seen, Since anionic and nonionic agents are not as effective as the last group is the largest and most used for phmapreservatives, one must conclude that the positive charge of ceutical systems, so that it will h emphasized in the discussion these compounds is important; however, the extent of surface that follows. activity has been shown to determine the amount of material needed for a given amount of preservation. Quaternary ammonium salts are preferable to &ee amine salts as they are not subject to effect by pH in any way; however, the presence of orTypes ganic anions such as dyes and natural polyelectrolytes is an imANIONIC AGENTS-The most commonly used anionic portant source of incompatibility and such a combination surfactants are those containing carboxylate, sulfonate, and should avoidedsulfate ions. Those containing carbxylate ions are known as AMPHOTERIC AGENTS-The major groups of molecules soaps and generally are prepared by the saponificationof natufalling into the mphoteric category are those containing carral fatty acid glycerides in alkaline solution. The most common box~lateor phosphate groups as the anion, and amino or quacations associated with soaps are sodium, potassium, ammoternary ammonium groups as the cation- The former group is nium, and triethanolamine ; the chain length of the fatty acids represented by various polypeptides, proteins, and the alkyl be ranges &om 12 to 18. taines; the latter group consists of natural phospholipids such The extent of solubility in water is iduenoed greatly by the as the lecithins and ce~halins-In general, long-chin a m ~ h o length of the alkyl chain and the presence of double bonds. For terics, which exist in solution in zwitterionic form, are more example, sodium stearate is quite insoluble in water a t room surface active than are ionic surfactants having the same hytemperature, whereas s d u m ole ate under the same conditions drophobic group, because in effect the oppositely charged ions is quite water soluble. are neutralized. However, when compared to nonionics, they Multivalent ions, such as calcium and magnesium, produce marked water insolubility, even at lower alkyl chain lengths; appear somewhere between ionic and nonionic. thus, soaps are not useful in hard water that is high in content PROTETNMonsidering the rapidly growing importance of these ions. Soaps, being salts of weak acids, are subject also of proteins as therapeutic agents, the unique surface characto hydrolysis and the formation of free acid plus hydroxide ion, teristics of these biological macromolecules deserve some spe particularly when in more concentrated solution. cial attention. Therapeutic proteins have h e n shown to be exTo offset some of the disadvantages of soaps, a number of tremely surface active, and they adsorb to clinically important long alkyl chain sulfonates, as well as alkyl aryl sulfonates such surfaces such as glass bttles and syringes, sterile filters, and as s d i u m dodecylbenzene sulfonate, may be used; the sulplastic IV bags and administration sets; the result is treatment fonate ion is less subject to hydrolysis and precipitation in the failures. In general, proteins can adsorb to a whole variety of presence of multivalent ions. A popular group of sulfonates, surfaces, both hydrophobic and hydrophilic. From the standwidely used in pharmaceutical systems, are the dialkyl sodium point of the surface, protein adsorption appears to be maxisulfosuccinates,particularly d i u m bis-(2-ethylhexy1)suIfosuc- mized when the electrical charge of the surface is opposite that cinate, best known as Aerosol OT or d m s a t e sodium. This comof the protein or when the surface is extremely hydrophobic. pound is unique in that it is soluble b t h in oil and water, and From the standpoint of the protein, the extent of adsorption de hence forms micelles in b t h phases. I t reduces surface and inpends on the molecular weight, the number of hydrophobic side terfacial tension to low values and acts as an excellent wetting chains, and the relative distribution of cationic and anionic side agent in many types of solid dosage forms (Table 20 -7). chains. The effect of ionic strength is usually to enhance adA number of alkyl sulfates are available as surfactants, but sorption by shielding adjacent proteins &om repulsive electriby far the most popular member of this group is d i u m lauryl cal interactions. Adsorption is also maximized when the pH of

the protein solution is equal to the pI (isoelectricpoint) of the molecule, again due to minimized electrical repulsion. When different proteins compete for adsorption sites on a single surface, the effect of molecular weight hecomes most striking. Early in the adsorption process the protein with the smaller molecular weight, which can diffuse to the surface more rapidly, initially occupies the interface. After some time, it is found that the larger molecular weight protein has displaced the smaller protein since the larger molecule has more possible interaction points with the surface and thus greater total energy of interaction. The most important consequence of therapeutic protein ad-

mption is the loss of bioactivity, the reasons for which include loss of therapeutic agent by irreversible adsorption to the surface, possible structural changes in the proteininduced by the interface, and surface-associated aggregation and precipitation of the rotei in. Each of these conseauences is related to the structureladopted by the protein in th;! interfacial region. The native three-dimensional structure of a protein in solution is the result of a complex balance between attractive and repulsive forces. Surface can easily disrupt the balance of forces in proteins residing in the interfacial region and cause the molecule to undergo a change, unfolding from the native to the extended codguration. As it is unlikely that the extended mdguration will refold back to the native state upon release fiom the interface, the protein is considered to he denatured. Like other polymers, the unfolding of the protein at the interface is thought to minimize the contact of awlar amino acid side chains with water. k addition, electrical interactions, both within the protein and between the protein and the surface, strongly mdulate the configuration assumed at the interface. Motion of the interface, such as comes about during shaking of a solution, appears to accelerate the surface-associated denaturation. Some rotei ins appear to be rather vulnerable to surface-induced struiural alterations, whereas others are very resistant. Algorithms for predicting those proteins most vulnerable to the structuredamaging effects of interfaces are not yet available. Empirical observations suggest that those proteins easily denatured in solution by elevated temperatures may also be most sensitive to interfacial denaturation. The best defense against untoward effects on the structure of proteins induced by surfaces appears to be prevention of adsomtion. Research in the field of biomaterials has shown that sukaces that are highly hydrophilic are less likely to serve as sites for protein adsorption. Steric hindrance of adsorption by handing hydrophilic polymers, such as polyethylene oxide, to a surface also appears to be successful in minimizing adsorption. Formulations of rotei ins intended for ~arenteraladministration &equently contain synthetic surfactants to preserve bioactivity. The specific molecular mechanism of protection is not understood and can involve specific blocking of adsorption to the interface or enhanced removal &om the interface before protein unfolding can occur. In support of the former mechanism is the observation that surfactants most successful at protecting proteins &om interfacial denaturation contain long polyethylene oxide chains capable of blocking access of the protein to the surface. PHOSPHOLIPIDS-All lecithins contain the L-aglycerophosphoylcholine skeleton esterzed to two long-chain fatty acids (often oleic, palmitic, stearic, and linoleic). Typically, for pharmaceutical use, lecithins are derived &om egg yolk or soyhean. Although possessing a polar zwitterionic head group, the twin hydrocarbon tails result in a surfactant with verv low water solubilitv in the monomer state. With the exception of the skin, phospholipids make up a vast majority of the lipid component of cell membranes throughout the M y . As a result, the bimmpatibility of lecithin is high, accounting for the increasing popularity of use in formulations intended for oral, topical, and intravenous use. Egg yolk lecithins are used extensively as the main emulsifjhg agent in the fat emulsions intended for intravenous use.

The ability of the lecithins to form a tough but flexible a m between the oil and water phases is responsible for the excellent physical stability shown the IV fat emulsions. In aqueous media, phospholipids are capable of assembling into concentric bilayer structures known as liposomes. The therapeutic advantage of such a lipid assembly for drug delivery depends upon the encapsulation of the active ingredient either within the interior aqueous environment or within the hydrophobic region of the bilayer. Deposition of the liposome within the M y appears to be dependent upon a number of factors, including the composition of the phospholipids employed in the bilayer and the diameter of the li~osome.

The uni&e surface properties of phospholipids are critical to the function of the pulmonary system. Pulmonary surfactant is a mixture of phospholipids and other associated molecules secreted by type lI pneumocytes. In the absence of pulmonary surfact ant (as in a neonate h r n prematurely), the high surface energy of the pulmonary alveoli and airways can he diminished only by physical collapse of these structures and resulting elimination of the air-water interface. As a consequence of airway collapse, the lung fails to act as an organ of gas exchange. Pulmonary surfactant maintains the morphology and function of the alveoli and airways by markedly decreasing surface energy through decreasing the surface tension of the air-water interface. The most prevalent component of pulmonary surfactant, dipalmitoylphosphatidylcholine (DPPC), is uniquely responsible for forming the very rigid surface a m necessary to reduce the surface tension of the interface to a value near 0. Such an extreme reduction in surface tension is most critical during the process of exhalation of the lung where the air-water interfacial area is decreasing. Although DPPC does form the rigid film, in the absence of additives it is unable to respread over an expanding interface typical of a lung during the inhalation phase. An anionic phospholipid, phosphatidylglycerol, in conjunction with a surfactant-askated protein, SP-C, appears to aid the respreading of DPPC and to maintain mechanical stability of the interface. A truly remarkable feature is that pulmonary surfactant is able to carry out the cycle of reducing surface tension to near 0 during exhalation and then reexpanding over the interface during inhalation at whatever rate is necessary by the respiratory pattern. Commercially available pulmonary surfactant replacement preparations contain DPPC as the primary ingredient. Agents that aid in the respreading of DPPC may differ depending upon the source of the surface-active material. NONKiNIC AGENTS-The major class of compoundsused in pharmaceutical systems are the nonionic surfactants, as their advantages with respect to compatibility, stability, and potential toxicity are quite significant. I t is convenient to divide these compounds into those that are relatively water insoluble and those that are auite water soluble. The maior tmes of compounds making up A s first group are the long-;hairfatty acids and their water-insoluble derivatives. These include: Fatty alcohols such as lauryl, cetyl (16 carbons), and stearyl alcohols Glyoeryl esters such as the naturally wcuning mone, di-, and triglycerides Fatty acid esters of fatty alcohols and other alcohols such as pmpylene glycol, polyethylene glycol, sorbit an, sucrose, and cholesteml. Included also in thi 5 general class of nonionic waterinsoluble compounds are the free steroidal alcohols such as cholesterol.

To increase the water solubilityof these compounds and to form the second group of nonionic agents, polyoxyethylene groups are added through an ether linkage with one of their alcohol groups. The list of derivatives available is much too long to cover completely, but a few general categories will he given. The most widely used compounds are the polyoxyethylene sorbitan fatty acid esters, found in pharmaceutical formulations that are to be used both internally and externally. Closely related compounds include polyoxyethylene glyceryl and

292

PART 2: PHARMACEUTICS

steroidal esters, as well as the comparable polyoxypropylene esters. I t is also possible to have a direct ether linkage with the hydrophobic group, as with a polyoxyethylene-stearyl ether or a polyoxyethylene-alkyl phenol. These ethers offer advantages hecause, unlike the esters, they are quite resistant to acidic or alkaline hydrolysis. Besides the classification of surfactants according to their polar portion, it is useful to have a method that categorizes them in a manner that reflects their interfacial activity and their ability to function as wetting agents, emulsifiers, and solubilizers. Variation in the relative polarity or nonpolarity of a surfactant significantly influences its interfacial behavior, so

some measure of polarity or nonpolarity should k~ useful as a means of classification. One such approach assigns a hydrophile-lipophile b a l a m (HLB) n u m b r for each surfactant; although the methcd was developed by a commercial supplier of one group of surfactants, it has received widespread application. The HLB value, as originally conceived for nonionic surfactants, is merely the percentage weight of the hydrophilic group divided by 5 in order to reduce the range of values. On a molar basis, therefore, a 100% hydrophilic molecule (polyethyleneglycol) would have a value of 20. Thus, an increase in polyoxyethylene chain length increases polarity, and hence the HLB value; at constant polar chain length, an increase in alkyl chain length or numher of fatty acid groups decreases polarity and the HLB value. One immediate advantage of this system is that to a first approximation one can compare any chemical type of surfactant to another type when both polar and nonpolar groups are different. Values of HLB for nonionics are calculable on the basis of the proportion of polyoxyethylene chain present; however, to determine values for other types of surfactants, it is necessary to compare physical chemical properties reflecting polarity with those surfactants having known HLB values. Relationships btween HLB and phenomena such as water solubility, interfacial tension, and dielectric constant have h e n used. Those surfactants exhibiting values greater than 20 (eg, s d u m lauryl sulfate) demonstrate hydrophilic behavior in ex-

cess of the polyoxyethylene groups alone. Refer to Chapter 22 for further information. Acknowledgment-The author is grateful to Professor George Z e grafi for his continuing mentorship and support.

REFERENCES 1.Semat H. Fundamentals of Phvsics. 3rd ed. New York: Holt Rinehart Winston, 1967. 2. Michaels AS. J Phvs Chem 1961; 66:1730. 3. Ring T A Powder ~ e c 1991; h 66:196. 4. Elamin AA, et al. I& J Pharmaceut 1994; 111:169. 6,Dirkson JA, Ring TA Chem Eng Sci 1991; 46;2389, 6. Zisman WA. Adv Chem Ser 1964; 43: 1. 7. Putz G, et al. JAppl Physiol 1994; 76: 1426. 8. Titoff Z. Z Phys Chem Leipzig 1910; 74:641. 9 . Brittain HG. Phvsical Chamcterization of Pharmaceutical Solids. New York: ~ekk;?r,1996. New York: 10. Osiaow LI. Surface Chemistry: Theory and hnlicationss. -~ e & h o l d 1962: , 11.Langmuir I. J A m Chem Soc 1917; 39:1848. 12. Giles CH. In: E H Lucassen-Reynders, 4.Anionic Suqfactants. New York: Dekker, 1981, Chap 4. 13. Weiser HB. A Textbook of Colloid Chemistry. New York: Elsevier, 1949. 14. Ter-Minassian-Saraga L. Adv Chem Ser 1964; 43:232. 16. C ~ n e DO. y Activated Charcoal in Medical Applications, Dekker, New York, 1996. 16. Modi NB, et al. P h a ~ mRes 1994; 11:318. .

<

,

BIBLIOGRAPHY Adamson AW. Physical Chemistry of Surfaces, 6th ed.New York: Wiley Interscienoe, 1990. David JT,Rideal EK. Interfacial Phenomena, 2nd ed. New York: Academic Press, 1963. Hiemenz PC. Principles of Colloid and Surface Chemistry, 2nd ed. New York: Dekker, 1986. MacRitchie F. Chemistry at Inteflaces. San Diego: Academic Press, 1990. Shaw DJ. Intmduction to Colloid and Su&ce Chemistry, 4th ed. London: Butterworths, 1992.

Bill J Bowman, PhD Clyde M Ofner Ill, PhD Hans Schott, PhD

The British chemist Thomas Graham applied the term "colloidn (derived from the Greek word for glue) ca 1850 to polypeptides such as albumin and gelatin; polysaccharides such as acacia, starch, and dextrin; and inorganic oompounds such as gelatinous metal hydroxides and Prussian blue (ferric fe-anide). Contemporary colloid and surface chemistry deals with an unusually wide variety of industrial and biological systems. A few examples include catalysts, lubricants, adhesives, latexes for paints, rubbers and plastia, soaps and detergents, clays, ink, packaging films, cigarette smoke, liquid crystals, drug delivery systems, ell membranes, blood, muoous secretions, and aqueous humors.14

DEFINITIONS AND CLASSIFICATIONS Colloidal Systems and Interfaces Except for high molecular weight polymers, most soluble substmoe8 can b prep& as either low r n o l d a r weight mlutions, oolloidal dispersions, or coarse suspensions depending upon the choioe of dispersion medium and dispersion techn i q ~ eColloidal .~ dispersions consist of at least two p h a s e ~ n e or more dispersed or internal phases, and a oontinuous or external phase called the dispersion medium or vehicle. Colloidal dispersions are distinguished h m solutiom and coarse dispersions by the particle size of the dispersed phase, not its wmposition. Colloidal dispersions contain one or more substances that have at least one dimension in the range of 1-10 nm at the lower end, and a few pm at the upper end (covering about three orders of magnitude). Thus blood, e l l membranes, thinner neme fibrs, milk, rubber latex, fog, and foam oolloidal systems. Some materials, such as emulsions and sus~ensionsof most o r g d c drugs, are coarser than true colloidal s ~ k mbut s exhibit similar behavior. Even though serum albumin, acacia, and povidone form true or ~ o solutions ~ in water, ~ the@size of the individual solute molecules places such solutions in the colloidal range (particle size > 1nm).1",510 Several features distinguish colloidal dispersions from ooarse suspensions and emulsions. Colloidal particles are usually too small for visibility in a light microscope h a u s e at least one of their dimensions measures 1 pm or less. They are,however, oRen visible in an ultramicroscope and almost always in an electron microscope. Conversely, ooarse suspended particles are usually visible to the naked eye and always in a light microscope. In addition, oolloidal particles, as opposed to coarse particles, pass through ordinary mter paper but areretained by dialysis or ultrdltration membranes. Also, unlike coarse partides, colloidal particles diffuse very slowly and undergo little or no sedimentation or creaming. Brownian motion maintains the dispersion of the oolloidal internal phases.

An appreciable frachon of atoms, ions, or mol&s of oolloidal particles are h a t e d in the bundary layer between the particle and the dispersion medium. The bundary layer b tween a particle and air is oommonly r e f e d to as a surface; whereas, the boundary layer btween a particle and a liquid or solid is oommonly r e f e d to as an interface. The iondmolecules within the particle and within the medium are surrounded on all side by similar ionsbnolecules and have balanced form fields; however, the iondmolecules a t surfaoes or interfaces are subjected to unbalanced forces of attraction. Consequently, a surface free energy oomponent is added to the total free energy of oolloidal particles and becomes important as the particles h m e smaller and a greater fraction of their atoms, ions, or molecules m h a t e d in the surface or interfacial region. As a result, the solubility of very k e solid particles and the vapor pressure of very small liquid droplets are greater than the corresponding values for o o m particles and drops of the same materials. SPECIFIC SURFACEAREA-Decreasing particle size increases the surfaoeto-vO1ume expmsed as the 'pecific surface area Specific surface area may expressed as the area cma) per unit (v Or per unit mass Pam). For a sphere, A = 4 d and V = 4 / 3 d , thend, is:

a,).

(Mj

-

A

-A-A&-3d--3-crn-1 V

-

4/3d

-

r cmS - r

I d ) of the material expreaA as g/cmg, the spefllC

surfam

is:

A A 4 d A, P-M-Vd-#3,,&

3 cma rd g

Table 21-1 the of comminution on the specific surfaOem a of a initially rnnsisting of Onesphere having a 1-cm radius. The sp&c surfam m a increases as the material is broken into a lsrger numbr of smaller and smaller Activated charcoal and kaolin are golid adsorbents 106 cma/g and 104 having spefllC surfam areas of about cma/g, respectively. One gram of activated charwal has a sur,f , quai to V6 acl.e hause of its extensive porosity and internal voids.

Physical States of Dispersed conti Phases

d ,

A useful classification of oolloidal systems is based upon the state of matter of the dispersed phase and the dispersion medium (ie, whether they are solid, liquid, or g a s e o u ~ ) . ~ , ~ , ~ Common examples and various oombinations are shown in Table 21-2. The terms sols and gels are oRen applied to wlloidal dispersions of a solid in a liquid or gaseous medium. Sols tend 293

294

PART 2: PHARMACEWICS

-

Table 21-1. Effect of Comminution on the Specific Surface Area of a Volume of 4 ~ 1 3cm3, Divided into Uniform Spheres of Radius Ra NUMBEROF SPHERES

R

A,, (rm2krn3

1 o9

1 cm 0.1 cm = 1 mm 0.1 mm 0.01 m im --

3 3 x 10 3 x lo2 x lo3

1d3

0.1 nm

3x

1

103 106

highly hydrated ions (eg, carbxylate, sulfonate, and alkylammonium ions) andlor organic functional group that bind water through hydrogen bonding (eg, hydroxyl, carbnyl, amino, and imino groups). Hydrophilic colloidal dispersions can be further sukdivided a8:

True soluiions: water-soluble polymers (eg, acacia and povidone). Gelled solutwns, gels, or jellies: polymers p r m t at eufficiently high wnoentrations andlor at temperatures where their water solubility is low. Examplea include relatively wnoenkated eolutions of gelatin and starch (which set to geLs upon cooling) and methylcellulose (which geLs upon heating).

I

Prarbkulate dkpersbns; solids that do not form molecular aolutions but

lo8

* Shaded region wrresponds to colloidal particle-size range.

to have a l o w e r v i w i t and ~ are fluid. If the solid particles form

bridged structures ~os*skng some mechanical 5t=ngthg the system is then called agel. Prefixes typically designate thedis~ e r s i o nmedium. For example, hydrosol (or hydrogel), alcoml (or alcogel), and aerosol (or aerogel), designate water, alcohol, and air,respectively.

Interaction Between Dispersed Phases and Dispersion Mediums

remain as discrete though minute particlea Bentonite and microcrystalline d u l o a e are examples of t h h y~d m l s .

Lipophilic or oleophilic substanoes have a strong affinity for oils. Oils are nonpolar liquids consisting mainly of hydrocarbons having few polar groups and low dielectric constants. Examples include mineral oil, benzene, c a r b n tetrachloride, vegetable oils (eg, cottonseed or peanut oil), and essential oils (eg, lemon or peppermint oil). Oleophilic colloidal dispersions include polymers such as polystyrene and unvulcanized or gum rubber dissolved in benzene, magnesium, or aluminum stearate dissolved or dispersed in cottonseed oil, and activated charcoal which forms sols or particulate dispersions in all oils.

LYOPHOBIC DISPERSIONS

Ostwald originated another useful classification of colloidal dispersions based on the af~mityor interaction between the dispersed phase and the dispersion medium?"u8 This classification refers mostly to solid-in-liquid dispersions. Colloidal dispersions are divided into the two broad categories, lyop hilic and lyophobic. Some soluble, low molecular weight substances have molecules with bath tendencies and asmiate in solution, forming a third category called association colloids.

LYOPHILIC DISPERSIONS The system is said to be lyophilic (solvent-loving) if there is considerable attraction between the dispersed phase and the x liquid vehicle (ie,extensive solvation). The system is said to l hydrophilic if the dispersion medium is water. Due to the presence of high concentrations of hydrophilic group, solids such as bntonite, starch, gelatin, acacia, and povidone swell, disperse, or dissolve spontaneously in water to the greatest degree pessible without breaking covalent hnds. Hydrophilic colloids oRen contain ionized groups that disswiate into

The dispersion is said to be lyophobic (solvent-hating) when there is little attraction between the dispersed phase and the dispersion medium. Hydrophobic dispersions consist of particles that are only hydrated slightly or not at all h a u s e water molecules prefer to interact with one another instead of solvating the particles. Therefore, such particles do not disperse or dissolve spontaneously in water. Examples of materials that form hydrophobic dispersions include organic compounds consisting largely of hydmarbon portions with few, if any, hydrophilic functional groups (eg, cholesterol and other steroids); some nonionized inorganic substances (eg, sulfur); and oleophilic materials such as polystyrene or gum r u b b r , organic lipophilic drug^, p a r 6 wax, magnesium stearate, and cottonseed or soybean oils. Materials such as sulfur, silver chloride, and gold form hydrophobic dispersions without being lipophilic. There is no sharp dividing line between hydrophilic and hydrophobic dispersions. For example, gelatinous hydroxides of polyvalent metals (eg, aluminum and magnesium hydroxide) and clays (eg, bentonite and kaolin) possess some characteristics of bth.2","8 Common lipophobic dispersions include water-inoil emulsions, which are essentially lyophobic dispersions in lipophilic vehicles.

Table 21-2. Classification of Colloidal Dispersions According to State of Matter DISPERSE PHASE

SOLID

LIQUID

GAS

DISPERSION MEDIUM (VEH KLE) MLlD

LOU ID

Zinc Oxide Paste USP, toothpaste (dicalcium phosphate or cakium carbonate with aqueous sodium carboxymethylcellulosebinder), and pigmented plastics (titanium dioxide in polyethylene).

SQIS Bentonite Magma NF,

Absorption bases (aqueous medium in Hydrophiiic Petrolatum USP), emulsion bases (oil in Hydrophitic Ointment USP, Lanolin USP), and butter Solid foams (foamed plastics and rubbers) and pumice

Trisulfapyrimidines Oral Suspension USP, Alumina and Magnesia Oral Suspension USP, Tetracycline Oral Suspension USP, Betamethasone Vaterate Lotion USP, and Prednisolone Acetate Ophthalmic Suspension USP. E i w h i a Mineral ~ Oil Emukion USP, Benzyl Benzoate Lotion USP, and soybean oil in water for parenteral nutrition, milk, and mayonnaise. Foams, carbonated beverages, and effervescent salts in water.

GAS

Epinephrine Bitartrate Inhalation Aerosol USP, Isoproterenot Sulfate Inha tation Aerosol USP, smoke, and dust.

aeroMetaproterenol Sulfate Inhalation AerosoI USP, Povidone-Iodine Topical Aerosol USP, mist, and fog. No colloida I dispersions.

CHAPTER 21: COUOI DAL DISPERSIONS

1

ASSOCIATION COLLOIDS Organic compounds that contain large hydrophobic moieties on the same molecule with strongly hydrophilie groups are said to b amphiphilic. The individual molecules are generally too small to be in the colloidal size range, but they tend to asmiate into larger aggregates when dissolved in water or oil. These compounds are designated association colloids h a u s e their aggregates are large enough to qualify as oolloidal particles. Examples include surfactant molecules that assmiate into mimlles a b v e their critical mioelle concentration (CMC)and phospholipids that assdate into cellular membranes and liposomes, which have k n used for drug delivery.

PROPERTIES OF COLLOIDAL DISPERSIONS

295

1

Partide Shape Particle shape depends upon the chemical and physical nature of the dispersed phase and the methcd employed to prepare the dispersion @reparation methods are described in later sections). Primary particles exist in a wide variety of shapes, and their aggregation produces an even wider variety of shapes and structures. hpwation such as mechanical Olmminuand precipitation generally prcduoe shaped parthe precipitating possess pronounoedWstallization habits or the solids b i n g ground possess strongly developed cleavage planes. For example, micronized particles of sulfonamides and other organic powders and precipitated aluminum hydroxide gels typically have irregular random shapes. An exmption is bismuth subnitrate; bigmuth nitrate solutions with s d i u m carbnate precipitates lath-shaped pmticles. In addition, precipitated silver chloride particles show their cubic nature under the electron miuosoope. Lamellar or plate-like solids oRen pwerve their lamellar *ape during mechanical Imause milling m~~ micronization break up the stacks of thin plates, in addition to fragmenting plates in the lateral dimensions. In these materials, the molecular cohesion between layers is much weaker than the cohesion within layers. Examples of such materials include graphite, mica, and kaolin (Fig 21-11. In a like manner, macroscopic a s h t o s and cellulose films consist of bundles of microscopic and submicroscopic fibrils that have very small diameters. Mechanical comminution splits these bundles into their component fibrils as well as cutting them shorter. Figure 21-2 shows the individual, needle- or rcd-shaped cellulose crystallites formed aRer breaking up the aggregated bundles of microcrystalline cellulose. These crystallib averae 0.3 pm in length and 0.02 pm in width, which pkoes them in the colloidal size range. Micmrystalline cellulose is a fibrous thickening agent and tablet additive made by the controlled hydrolysis of oellul~~e. Its manufacture is described in the 1618th editions of this text, which also contain an electron micrograph of the porous, spongy, and compressible fibril bundle aggregates used in tableting. Except in the special cases of clay and cellulose just mentioned, regular shaped particles are typically p d u o e d by condensation rather than disintegration methds. For example, colloidal silicon dioxide is a white powder consisting of submicroscopic spherical particles of rather uniform size (ie, narrow particle size distribution). It is manufactured by hightemperature, vapor-phase hydrolysis of silicon tetrachloride in an oxy-hydrogen flame (ie, a flame p d u o e d by burning hydrogen in a stream of oxygen). It is commonly r e f e d to as fumed or pyrogenic silica because of this manufacturing p r o w . Different grades are produced by different reaction conditions. Figure 21-3 shows the relatively large, single spherical particles of colloidal silicon dioxide. Their average diameter of 50 nm corresponds to the comparatively small s p a c surface area of 50 ma/g. Smaller spherical particles

Figure 21-1. Transmission electron rnicrograph of a well-crystallized, f ine-particle kaolin. Note hexagonal shape of the clay pbtelets (courtay, John L Brown, Engineering Experiment Station, Georgia Institute of T ~ ~ ~ ~ ~ ~

have a larger surfaoe m a . For example, the grade with the averse diameter, nm, has a spdc fam ma of 380 ma/g. The ker-grade psrticles tend to sinter or grow together into chain-like aggregates wembling pearl necklaces during the manufacturing pmss (Fig 21-4). Latexes of polymers, such as latex-based paints are aqueous dispersions prepared by emulsion polymerizati;n. Their p ~ c l e s

Figure 21-2. Transrnksion electron micrograph of Avicel RC-591 thickening grade rnicrocflalline cellulow. The needles are individual cellulose crystallites; some are aggregated into bundles (courtesy, FMC Corporation; Avicel is a registered trademark of FMC Corporation).

2 96

PART 2: PHARMACEUTICS

*

..

I L

-

- ,

14

Figure 21-3. Trdnsm~ss~on electron m~crographof Aeros~lOX 50, ground and dusted on The spheres dre trdnslucent t o the electron bedm, cduslng overldpp~ngportlons t o be ddrker owlng t o dn ~ncredsedth~ckness(courtesy, Degussd AG of Hdndu, Germdny; Aeros~l1 5d reg~steredtrddemdrk of Degussd) The suff~x50 ~nd~cdtes the spec~f~c surfdce dred In m'/g

Figure 21-4. Trdnsmlsslon electron mlcrogrdph of Aerosll 130, ground

are spherical because polymerizatioll of the solubilized liquid monomers takes place inside spherical surfactant micelles, Some c.1a.y~ grow as plate-like particles possessu~gstraight edges and hexagollal angles (eg, bentonite and kaolin) (Fig 211).Other clays have lat11-shaped (nontronite) or rod-shaped particles (attapulgit e). I Emulsificatiol~produces spl~ericaldroplets to minimize the oil-water interfacial area. Cooling an emulsiol~below t h e meltillg poult of t h e dispersed pllase freezes the dispersed particles in a spherical shape. For instance, paraffin may be emulsified in 80',Cwater and then cooled to room temperature to produce a hydrosol c o l ~ t a i l ~ i spherical l~g particles. Sols of viruses and globular proteins, which are hydrophilie, con tail^ compact particles possessing definite geometric shapes. For example, the poliomyelitis virus is spherical, the tobacco mosaic virus is rod.shaped, alld tile serum albumills alld g l o b u l ~ l sare prolate ellipsoids of revolutiol~(football-shaped).

uid or gaseous suspending medium and represents a three-dimellsiollal random walk. Suspended colloidal particles and solute molecules undergo both rotatiollal and trallslatiollal B r o w l ~ i a lmovements, ~ For trallslatiol~almotion, E u ~ s t e i derived l~ the equation:

Diffusion and Sedimentation The rnolem~lesof a gas or liquid are engaged 111 a perpetual and random thermal motiol~causing collisio~~s with one another and with t h e colltauler wall billions of times per second. Each collisiol~ changes t h e direction and t h e velocity of these molecules. 'I'l~ecolltinuous motiol~of molecules of a dispersiol~ medium randomly buffets any dissolved molecules and suspended colloidal particles. The random bombardment imparts an erratic movement called Rrownian wotion to solutes and particles. This p h e l ~ o m e l ~ is ol~ named after the botanist Robert Browl~who first observed it under t h e microscope in an aqueous pollen suspension. The Brownian motiol~of colloidal particles magnifies the random movements of molecules 111 the liq-

and dusted on The spheres dre fused together Into chd~n-l~ke dggregdtes (courtesy. Degussa AG of Hdndu. Germdny; Aerosll 15 a registered trddemdrk of Degussd) The suff~x130 ~nd~cdtes the spec~f~c surfdce dred In m'/g

F - \I5T3t ,here, is tile displacemellt in tile x.direction in time, t, and T3 is tile diffi~,si(~n r(lpffic.ipnt. Eillstein also showed t h a t for spherical particles of radius, r, ullder collditions valid for stokes7law alld ~ i law ofr+.cosity: ~ ~ ~ ~

T3

-

RT 6;rrIrN

where I? is gas 'Onstant, is is rir~ogadro'snumber, and is the viscosity of the suspending medium. h commol~measure of the mobility of a dissolved molecule or suspended particle in a liquid medium is the diffusion eoefficient, At room temperature, using units of cm2/sec, t h e value of sucrose in water is 4.7 x l o - " and the value of serum albumin in water is 6 . 1 x lo-'. Uiffusiol~is a slow vrocess on a macroscopic scale. U s i l ~ g t l ~ e v a l uofe 1 x l o - ' em-/see, Brownial~motion causes a particle to move in one direction an average distallee of 1em in 58 days, 1mm in 14 hours, or 1 pm UI 0.05 seconds, As seen in the above equation, smaller molecules diffuse faster in a given medium. The radius of a sucrose molecule is smaller t h a n t h a t of a serum a l b u m u ~molecule; t h e calculated values are 0.44 nm and 3 . 5 nm, respectively (assuming a spherical shape). Steroids have only slightly higher molecular weights than sucrose; however, their diffusiol~coeficiel~ts111 petrolatum-based absorptiol~bases are in t h e 10-'[) to l o - "

h

CHAPTER 21: COLLOIDAL DISPERSIONS

cmz/sec range. These much smaller diffusion coefficients are caused by the much higher vehicle visoosity. Passive diffusion (driven by a concentration gradient and carried out through Brownian motion)is imPdant in the release ofdrugs from topical preparations and in the gastrointestinal absorption of

The concentration of inorganic and organic colloidal dispersions and of bacterial suspensions can be measured by their Tyndall effect or turbidity. Turbidity, .r, is defined by an e ua tion analogous to Beer's law for the absorption of light!,"' namely:

drugs-

Brownian motion and convection currents maintain dissolved molecules and small colloidal particles in suspension indefinitely. This is true for all intrinsically stable systems when dissolution or dispersion m u r s spontaneously and the come sponding free energy change is negative (see below). In metastable or diuturna dispersions, Brownian motion pre-

297

7

1In b = --

1 It where b and I, are the intensities of the incident and transmitted light beams, and 1 is the length of the dispersion through which the light passes. The concentration of dispersed particles may he measured in two ways using turbidity. In turbidimetry,

vents sedimentation and may extend their life for years.

a spectrophotometer or photoelectric colorimeter is used to

As particle size or r increases, Brownian motion decreases as seen by the T proportionality to r-"'. Larger particles have a greater tendency than smaller particles of the same material to settle to the bottom of the dispersion, provided the densities of the dispersed phase, dp, and the liquid vehicle, dL, are s a ciently different (sedimentation, when dp > d ~ )On . the other hand, larger particles will rise to the top of the dispersion when dp < dL. This is known as creaming. The Stokes equation reflects the rate of sedimentation/creaming; it is expressed as:

measure the intensity of the light transmitted in the incident direction. The theoretical and practical aspects of determining the particle size of suspensions by turbidimetry and the feasibility of estimating their particle-size distribution are discussed in two chapters by Kourti et al.'"the dispersion is less turbid, the intensity of light scattered a t 90" to the incident h a m is measured with a nephelometer. Both methods require careful standardization, using suspensions that contain known amounts of particles similar to those being studied. The turbidity of hydrophiliccolloidal systems such as aqueous solutions of gums, proteins, and other polymers is far weaker than that of lyophobic dispersions. These solutions appear clear to the naked eye; however, their turbidity can be measured with a phohlectric celllphotomultiplier tube and used to the molecular weight of the solute. The theory of light scattering was developed in detail by Lord Rayleigh. For white, nonabsorbing noncondu&,rs or dielectrics like sulfur and insoluble organicoompounds,the equation obtained for spherical particles whose radius is small oompared to the wavelength of light is:^,^

2(dp - dL)rzgt 971 where h is the height (or distanix) that a spherical particle moves in time, t, and g is the acceleration of gravity. The equation illustrates that this rate is proportional to rZ. Consequently, as Brownian motion diminishes with increasing particle size, the tendency of particles to sediment or cream is increased. At a critical radius, the distance, h, that a particle settledcreams equals the mean displaixment, 2, due to Brownian motion over the same time interval, t, and therefore, the two are equal.'' Intravenous vegetable oil emulsions have little tendency to cream h a u s e their mean droplet size, -0.2 pm, is smaller than the critical radius. In most pharmaixutical suspensions, sedimentation prevails. h =

4aznoz(nl- no)' (1 + oosZ0) ,i4dZc b is the intensity of the unpolarized incident light; I , is the intensity of light scattered in a direction making an angle, 0, with the incident beam and measured at a distance, d. The scattered light is largely polarized. The concentration, c, is expressed as Light Scattering the number of particles per unit volume. The refractive indices, nl and no, refer to the dispersion and the dispersion medium, The optical properties of a medium are determined by its rerespectively. Since the intensity of scattered light is inversely fractive index. Light will pass through the medium undefle&d proportional to the fourth power of the wavelength, blue light when the refractive index is uniform throughout. However, 450 nm) is scattered much more strongly than red light when there are discrete variations in the refractive index from (A the presence of particles or caused by small-scale density flue(A 650 nm). Colloidal dispersions of colorless particles appear blue when the incident white light is viewed in scattered light tuations, part of the passing light will be scattered in all direc(ie, in lateral directions such as 90" to the incident beam). Loss tions. When a narrow beam of sunlight is admitted through a of the blue rays due to preferential scattering leaves the transsmall hole into a darkened room, bright flashing points reveal mitted light yellow or red. Preferential scattering of blue radiathe presence of the minute dust particles suspended in the air. tion sideways accounts for the blue color of the sky, sea, A beam of light striking a particle polarizes the atoms and cigarette smoke, and diluted milk and for the yellow-red color molecules of that particle and induces dipoles, which act as setof the rising and setting sun viewed head-onondary sources and reemit weak light of the same wavelength The particles in pharmaceutical suspensions, emulsions, as the incident light. This phenomenon is called light scatterand lotions are generally larger than the wavelength of light, Aing. The scattered radiation propagates in all directions away When the particle size exceeds hfl0, destructive interference from the particle. In a bright room, the light scattered by the htween the light scattered by different portions of the same dust particles is too weak to be noticeable. particle lowers the intensity of the scattered light and changes Colloidal particles suspended in a liquid also scatter light. its angular de~endenix-Ra~leigh'stheory was extended to When an intense, narrowly defined h a m of light is passed large and strongly absorbing and conducting particles by Mie through a suspension, its path becomes visible because of the and to nonspherical particles by Gans.l-Z-"sIt is possible to delight scattered by the in the beam. This Tyndall Beam termine the average particle size and even the particle size disis characteristic of colloidal systems and bemmes most visible tribution of colloidal dispersions and coarser suspensions by when viewed against a dark background in a direction perpenmeans of turbidity measurements using appropriate precaudicular to the incident beam. The magnitude of the turbidity or tions in experimental techniques and interpretationsopalescence depends upon the nature, size, and concentration DYNAMIC LIGHT SCATI'ERIPlG-Light scattered by a of the dispersed particles. For example, when clear mineral oil moving particle undergms a Doppler shift; its frequency inis dispersed in an equal volume of a clear, aqueous surfactant creases slightly when the particle move s towards the hoto odesolution, the resultant emulsion is milky white and opaque due to light scattering. However, microemulsions containing emdmtector and decreases slightly when it moves away. This shift is so small that it can only be detected by very intense, strictly sified droplets that are only a b u t 40 n m in diameter (ie, much monochromatic laser light. Because they are engaged in ransmaller than the wavelength of visible light) are transparent dom Brownian motion, a set of colloidal particles scatters light and clear to the naked eye.

I,

= I0

CHAPTER 21: COLLOIDAL DISPERSIONS

propylene glycol) that does not swell the polymer. The solvent should be added in a proportion of 3-5 parts of solvent to one part of polymer. If other nonpolymeric, powdered adjuvants are to he incorporated into the solution, they are dry-blended with the polymer powder and should comprise only U4 or less of the blend for the best results. Large increases in the concentration of polymer solutions may lead to precipitation and gelation. One way of effectively increasing the concentration of aqueous polymer solutions is to add inorganic salts. The salts will bind part of the water in the solution in order to become hydrated. Competition for water of hydration dehydrates the polymer molecules and precipitates

them. This phenomenon is called salting out and may cause the polymer to separate as a concentrated, viscous liquid solution, a simple coacervate, or a solid gel. Because of its high solubility in water, ammonium sulfate is often used to precipitate and separate proteins from dilute solutions. However, salting out is reversible and subsequent addition of water redissolves the precipitated polymers-and liquefies their gels. HOFMEISTER OR LYOTROPIC SERIES-The effectiveness of electrolytes to cause salting out depends upon their extent of hydration. The Hofmeister or lyotropic series arranges ions in order of increasing hydration and increasing effectiveness in salting out hydrophilic colloids. The series for monovalent and divalent cations are

and

The Hofmeister series governs many colloidal phenomena, including the effect of salts upon the temperature of gelation, the swelling of aqueous gels, and the viscosity of hydrosols, and the permeability of membranes towards salts. The series is observed in many phenomena involving small atoms or ions and true solutions, including the ionization potential and electronegativity of metals; the heats of hydration of cations; the size of hydrated cations; the viscosity, surface tension, and i&ared spectra of salt solutions; and the solubility of gases in salt solutions. This series also arranges cations in order of increasing ease in displacement from cation-exchangeresins based on the smaller hydrated specie size (eg, K+ displaces Na+ and Li+).Adsorption in the Stern layer of particles (see below) also illustrates the series. The lithium ion is more extensively hydrated, and therefore, Li+ (aq), including the hydration shell, is larger than Cs+ (aq). Due to its smaller size, the hydrated cesium ion can approach a negative particle's surface more closely than the hydrated lithium ion. Moreover, because of its greater electron cloud, the Cs+ ion is more polarizable than the Li+ ion. Therefore, the Cs + ion is more strongly adsorbed in the Stern layer. For anions, in order of decreasing effectiveness in salting out, the lyotropic series is F- > &rate"- > HPO4'- > tartrate2- > S04'- > acetate- >

Iodides and thiqanates, and to a lesser extent bromides and nitrates, actually tend to increase the solubility of polymers in water (ie, salt them in).1-2-bsThese large polarizable anions reduce the extent of hydrogen bnding among water molecules, and thereby, make more of the hydrogen-handing capacity of water available to the solute. Most salts, except for nitrates, bromides, perchlorates, iodides, and thiocyanates, raise the temperature of precipitation or gelation of most hydrophiliccolloidal solutions. Exceptions among hydrophilic colloids are methylcellulose, hydroxypropyl cellulose, and polyethylene oxide, whose gelation temperatures or gel melting points are lowered by salting out. Most hydrophilic sols require electrolyte concentrations of 1 M or higher to induce precipitation or gelation. In addition,

299

hydrophilic colloids disperse or dissolve spontaneously in water and their sols are intrinsically stable. Therefore, the polymer may be redissolved by removing the coagulating salt through dialysis or by adding more water. Whenever hydrophilic colloidal dispersions undergo irreversible precipitation or gelation, chemical reactions are involved. Neither dilution with water, heating, nor attempts to remove the gelling or precipitating agent by washing or dialysis will liquefy these gels. Most of the hydrophilic and water-soluble polymers mentioned previously are only slightly soluble or insoluble in alcohol. Addition of alcohol to their aqueous solutions may cause precipitation or gelation because it lowers the dielectric con-

stant of the medium and tends to dehydrate the hydrophilic solute. Alcohol also lowers the concentrations a t which electrolvtes salt out hvdro~hilic colloids. Therefore. alcohol is often ,. referred to as a nonsolvent or precipitant. However, the addition of alcohol to an aqueous polymer solution may cause coacervation (ie, the separation of a concentrated viscous liquid phase) rather than precipitation or gel formation. Sucrose also competes for water of hydration with hydrophilic colloids and may cause phase separation. However, most hydrophilic sols tolerate substantially higher concentrations of sucrose than of electrolytes or alcohol. Lower viscosity grades of a given polymer are usually more resistant to the effects of electrolytes, alcohol, and sucrose than grades having higher viscosities and molecular weights. The gelation temperature or gel point of gelatin is highest at its isoelectric point, where the attachment of adjacent chains through ionic b n d s hetween carboxylate ions and alkylammonium, guanidinium, or imidazolium groups is most extensive. Since carboxyl groups are not ionized in strongly acidic media such as gastric juices, interchain ionic bonds are practically nonexistent in this environment and interchain attraction is limited to hydrogen bonds and van der Waals forces. Therefore, the combination of an acidic pH that is considerably below the isoelectric point and a temperature of 37" C completely prevents the gelation of gelatin solutions. Conversely, if a polymer owes its solubility to the ionization of these weakly acid groups, reducing the pH of its solution below 3 may lead to precipitation or gelation. This is observed with carbxylated polymers such as many gums, d i u m carboxymethylcellulose, and carbomer. Adjusting the media to higher pH values returns the carbxyl groups to their ionized state and reverses the gelation or precipitation. However, gelation temperatures typically depend more upon temperature and concentration than Hydrogen carbxymethylcellulose swells and disperses but does not dissolve in water. Only the s d u m , potassium, ammonium. and triethanolammonium salts of carboxvlated ~olvmers are well soluble in water. In the case of carboxðy~liulose, salts with heavy metal cations (eg, silver, copper, mercury, lead) and trivalent cations (eg, aluminum, chromic, ferric) are practically insoluble. Salts with divalent cations, especially of the alkaline earth metals, have borderline solubilities. Generally, higher degrees of substitution tend to increase the tolerance of carbxymethyloellulose toward salts. When inorpanic salts of heavv or trivalent cations are mixed with alkali mital salts of car&xylated polymers in solution, precipitation or gelation m u r s due to metathesis. For instance, if a soluble copper salt is added to a solution of d i u m carhaxymethlycellulose, the double decomposition can be schematically written as: 1

R1 and R2represent two car~xymethylcellulosechains, which are cross-linked by a chelated copper ion. Dissociation of the cupric carbxylate complex is negligible.

300

PART 2: PHARMACEUTICS

Electric Properties ORIGIN OF ELECTRIC CHARGES-Particles can acquire charges &om several sources. Inproteins, one end group of the polypeptide chain and any aspartic and glutamic acid units contribute carbxylic acid groups, which are ionized into negatively charged carbxylate ions in neutral to alkaline media. The other chain end group and any lysine units contribute amino groups, while arginine units contribute guanidine groups, and histidine units contribute imidazole groups. The nitrogen atoms of these groups become protonated in neutral to acid media. These covalently attached anions and cations confer a negative and positive charge to the molecule, respectively.Therefore, proteins may be referred to as polyelectrolytes (polymeric electrolytes or salts). However, they are not the only organic polymers that contain ionic groups, and thus, many substances may be considered to be polyelectolytes. For example, natural polysaixharides of vegetable origin such as acacia, tragacanth, alginic acid, and pectin contain carkmxylic acid groups, which are ionized in neutral to alkaline media. Agar and carrageenan, as well as the animal polysaccharides heparin and chondroitin sulfate, contain sulfate groups, which are strongly acidic and ionize even in acid media. Cellulosic polyelectrolytes include sodium carbo~methylcellulose,while synthetic carboxylated polymers include carbomer, a copolymer of acrylic acid. Counterions are reauired for electroneutralitv of the ionizing groups on polyelectrolytes. Counter-ions disscciate &om ionogenic functional groups and can be replaced by other ions of like charge. For example, in neutral and alkaline media, Na+, K+, CaZ+,and MgZ+are among the counterions neutralizing the negative charges of the carbxylate groups, and if hydrochloric acid was used to make the medium acidic and to supply the protons, C1- is present to neutralize any of the cationic groups mentioned previously. These counterions are not an integral part of the protein particle but are located in its immediate vicinity. Alternatively, at a specific intermediate pH value (4.5-7 for most proteins), the carbxylate anions and the alkylammonium, guanidinium, and imidazolium cations on the same molecule neutralize each other exactly. There is no need for counterions because the ionized functional groups are in exact balance. At this pH value, called the isoelectric point, the protein particle or molecule is neutral; its electrical charge is neither negative nor wsitive . but z e r ~ . ~ - " ~ " Most inorganic particulate compounds are also charged. Aluminum hydroxide, AI(OH),, may be dissolved by acids and alkalis to form aluminum ions, Al"+, and aluminate ions, Al(OH)4-, respectively. In neutral or weakly acid media (ie, acid concentrations too low to cause dissolution), an aluminum hydroxide particle has some positive charges attributed to Al"+ valences that have not h e n completely neutralized. The schematic below re~resentsa wrtion of the surface of an aluminum hydroxide &uticle t h i t has one such positive charge neutralized by a C1- counterion:

In weakly alkaline media (ie, base concentrations too low to transform the aluminum hydroxide particles completely into aluminate and dissolve them), the aluminum hydroxide particles bear some negative charges due to the presence of a few aluminate groups. The schematic below repre sent s a portion of

the surface of an aluminum hydroxide particle that has one such negative group neutralized by a Na+ counterion:

g

HO

\

AI-OH

At a pH of 8.5 to 9.1, there are neither Al(O&+ nor AI(OH)4ions on the particle surface but only neutral Al(OH)R molecule^.'^^'^ Therefore. the articles have no charge " and do not need counterions for charge neutralization. This pH is considered to be the isoelectric point. In the case of inorganic particulate compounds such as aluminum hydroxide, it also is called the zero point of charge. Bentonite clay is a lamellar aluminum silicate. Each lattice layer consists of a sheet of hydrated alumina sandwiched between two silica sheets. Isomorphous replacement of Al"+ by MgZ+or of Si4+by Al"+ confers net negative charges to the thin clay lamellas in the form of cation-exchange sites resembling silicate ions built into the lattice. The counterions producing electroneutrality are usually Na+ ( d i u m hntonite) or CaZ+ (calcium bentonite). Silver iodide sols can be prepared by the reaction: In the bulk of the silver i d d e particles, there is a 1:l stoichiometric ratio of Ag+:I- ions. If the a b v e reaction is carried out with an excess of silver nitrate, there will he more Ag+ ions than 1- ions in the surface layer of the particles. The particles will then be positively charged and the counterions surrounding them will be NO3-. If the reaction is carried out using an exact stoichiometric 1:l ratio of silver nitrate to sodium iodide or with an excess sodium i d d e , the surface of the particles will contain more I- ions than Ag+ ions."+ The particles will then be negatively charged and the counterions surrounding them will be Na+. An additional mechanism through which articles acquire electric charges is by the adsorption of including ionic surfact ants. This is discussed in more detail in a later section. ELECTRIC DOUBLE LAYERS-As described previously, the surface layer of a silver i d i d e particle prepared using an excess of s d i u m iodide contains more I - ions than Ag+ ions; whereas, the bulk of the particle contains the two ions in an equimolar proportion. The aqueous solution in which such particles are suspended contains relatively high concentrations of Na+ and NO3-, a lower concentration of I-, and traces of H+, OH-, and Ag+.The negatively charged particle surface attracts positive ions &om the solution and repels negative ions. Therefore, the solution immediately surrounding the particle surface contains a much higher concentration of Na+ (counterions) and a much lower concentration of NOs- ions than in the bulk solution. A number of Na+ ions equal to the number of excess 1ions in the surface (ie, the number of I - ions in the surface layer minus the number of Ag+ ions in the surface layer) and equivalent to the net negative surface charge of a particle are pulled towards its surface. These counterions tend to approach the particle surface as closely as their hydration spheres permit (Helmholtzdouble layer); however, thermal agitation of the water molecules tends to disperse them throughout the solution. Consequently, the layer of counterions surrounding the particle is spread out. The Na+ ion concentration is highest in the immediate vicinity of the negative surface, where the ions form a

CHAPTER21:COUOIDALDISPERSIONS

compact layer called the Stern layer. The Na+ ion concentration decreases with distance h m the surface, throughout a diffuse layer called the Guy-Chapman layer. Therefore, the sharply d e k e d , negatively charged particle surface is surrounded by a cloud of Na+ counterions required for electroneutrality. The oombination of the two layers of oppositely charged ions constitutes an electric double layer, which is illustrated in the top part of Figure 21-5. The electric potential of a plane is equal to the work required to bring a unit electric charge from i n k i t y (in this case, h m the bulk of the solution)to that plane against electrostatic f o m . If the plane is the surface of a particle, the potential is called surface or Jro potential, which measures the total potential of the double layer (Fig 21-5). This is the thermcdynamic potential that operates in galvanic cells. Upon moving away h m the particle surface towards the bulk solution in the direction of the horizontal axis,the potential drops rapidly across the Stern layer h a u s e the Na+ ions in the immediate vicinity of the particle surface screen Na+ ions that arefarther removed in the d i E w part of the double layer h m the effect of the negative surfacecharge. The decrease in potential across the GouyChapman layer is more gradual. As the composition of the diffuse double layer gradually approaches that of the bulk liquid, where the anion concentration equals the cation concentration, the potential asymptoticallyapproaches zero. In view of this indefinite end point, the thickness of the d i E w double layer (6) is arbitrarily d e k e d as the distance over which it takes the potential at the bundary btween the Stern and Gouy-Chapman layers to drop to 0.37 (equal to 1 / e j of its value (Fig 215).13,4,610 The thickness of double layers usually ranges from 1 to 100 nm and decreases as the concentration of electrolytes in solution increases. This o m s more rapidly for higher valence counterions. The value of 6 is approximatelyequal to the w i p meal of the Debye-Hiickel theory parameter ( K). The electrokinetic or (zeta) potential has practical import a m h a u s e it can IH measured experimentally. In aqueous dispersions, organic particles containing polar functional groups, and even relatively hydrophobic inorganic particles, are surrounded by a layer of water of hydration, which is associated with the particles through iondipole and dipole-dipole interactions. When a particle moves, this shell of water, and all of the ions h a t e d inside it, moves along with the particle. Conversely, if water or an aqueous solution flows through a fixed bed of these solid particles, the hydration layer surrounding each particle remains attached to it. The electric potential at the plane of shear or slip separating the b u n d water h m the frw water is the I; potential. It dws not include the Stern layer and includes only the part of the Gouy-Chapman layer that lies outside the hydration shell (Fig 21-51. STABIIJZATION BY EIJN3"I'OSTATIC REPULSIONWhen two uncharged hydrophobic particles are in close proximity, they attract each other by van der Waals secondary valenoes, mainly London dispersion forms. For individual atoms and molecules, these forces decrease with the seventh power of the distance btween them. In the case of two particles, every atom of one particle attracts every atom of the other particle. Because the attractive forms are nearly additive, they decay much less rapidly with interparticle distance, approximately with the second or third power of the distance btween them. Therefore,whenever two particles approach each other closely, the attractive forces take over and cause them to adhere. Coagulation murs as the primary particles aggregate into increasingly larger secondary particles or flm.If the dispersion consists of two kinds of particles, one having positive and the other negative charges, the electrostatic attraction between such oppositely charged particles is superimposed on the attraction by van der Waals f o m and coagulation is amlerated. If the dispersion contains only one kind of particle with the same surface charge and charge density (the most common case) then electrostatic repulsion tends to prevent the particles h m approaching closely enough to come within the effective

rangeofeachother'svanderWaalsattractivefomes.Thissta-

301

b u s the dispersion against interparticle attachments or COagulation. The electrostatic repulsive energy has a range in the order of 6. A quantitative theory of the interaction between lyophobic disperse particles was worked out independently by Derjaguin

0 O

Distancefrom particle surface

Figure 21-5. Electric double layer at the surface of a silver iodide particle (upper pas and the corresponding potentials (lower part). The distance from the particle su dace, plotted on the horizontalaxis, r e f e to ~ both the upperandlowerportionsofthefigure.

302

PART 2 PHARMACEUTICS

and Landau in the L'SSIt a n d by Verwev and Overbeek in the Yetherlands in t h e early 1940s I - ' i 7 - q o Detailed c a l c u l a t i o ~ ~ s may be found in Chapter 21 of RPS-17 The so-called ULVO theo v predicts a n d explail~smany, but not all, experimel~taldata, its refinement to accoul~tfor discrepal~ciesis ongoing The ULVO theory is summarized in F i p ~ r e21-6, where cun7e IW represents t h e van der Waals attractive energy, which decreases approximately by the secolld power of t h e illterparticle distance, and curve E R represents the electrostatic repulsive energy, which decreases expol~el~tially with ii~terparticledistance Because ofthe combination ofthese two opposing effects, attractioll predominates a t small and large distances, whereas

the absolute value of tile 5 potelltial is small, t h e resultallt potel~tialenergy is negative and va11 der Waals forces of attractioll predomillate over electrostatic repulsioll a t all interparticle distallees Such sols coagulate rapidly The two identical particles, whose illteractioll is depicted in Figure 21-6, have a large (positive or negative) 5 potential, resulting in an appreciable positive or repulsive potential energy at intermediate distances Iiowever, h - o w l ~ i a motion, l~ convection currents, sedimentation, or stirring of the dispersion will evelltually put tllem on a collisio~course As tile t y ~ oparticles approach each other, the two counterion atmospheres begin to illterpelletrate or overlap a t point A, correspolldillg to the

repulsiol~may predominate at intermediate distances Nega-

distance, d z 'rhis produces a net repulsive (positive) energy be-

tive energy values indicate attraction and positive values indicate repulsion The resultallt cun7e DPRAS, obtained by algebraic additioll of curves I:A a n d E R , gives the total, net energy of illteractioll between two particles interparticle attraction depends mainly up011 the chemical nature a n d particle size of the dispersed material Once these have been selected, t h e attractive energy between particles is fixed and cannot be readily altered Electrostatic repulsiol~depends up011 t h e 11ro potential, or t h e density of t h e surface charge, a n d up011 the thickness of t h e double layer, both of which goverll the magnitude ofthe 5 potel~tial' r ~ u s dis , ersion stability correlates to some extellt with this potel~tial'The 5 potential can be widely adjusted using additives, especially ionic surfactants, water-miscible solvents, and electrolytes lf

cause of tile work illvolved in distortillg the diffuse double layers and pushing water molecules a n d coul~teriol~s aside If the particles continue to approach each other, t h e repulsion between their surface charges illcreases the net potential energy of u ~ t e r a c t i otlo~ its maximum positive value at R , where most of have been displaced lf the intervening water and coul~teriol~s the height of the potential energ?: barrier R exceeds t h e kinetic energy of the approachil~gparticles, they will not come any closer to each other than the distance dl v ~ n l t~ iofn tlnp t>r>l~nri;iry fornmpd t>pt\\-ppin :i sol or sr>ll~t~r>in :inri tlnp IjlIrP d l s p ~ r s i o nn l ~ d l l l n l111 :in ~ l ~ r : t r ~ r , fipld is stl~dipd.rf tlnp dispprspd p1n:isp is ~ : I > I I > ~ ItPl sns~t>ollnd:iry , is lor,:it~rit > , ~t l n ~r ~ f ~ i r : t i vn ~& ~gr:irii~ntI T ~ S P I ~ iipp:ir:itl~s, IIS fr~rll~~ntly 11spd \\-it11 protpun sr>ll~tir>ns). rf spvpr:il S ~ P ~ : of ~ Pp:irtir:I~s S or S O I I I ~ P S witln difY~rpntmot>ilitips:irp prpspnt, p:ir:In \\-ill fornm :i t>r>unri:irymoving \\-it11 ;i r:ln:ir:ir:t~ristir,vplr>r,it:. I Tnlikp mir:rr>pI~r:trr>plnr>r~sis, this mptlnod pprnmits tlnp idpntitit::itir>in of difY~rpintr,r>llr>id:ilr,r>mpr>npnts in :i m i x t l ~ r p , tlnp n l ~ : i s ~ ~ r ~ nofl ~t linn~~t I ~ r : t r o p l n o r ~ tnlot>ility ir, of ~:it:ll,:inri :in pstim;itir>inof t l n ~r ~ l : i t i viinlo111nts ~ pr~s~int. Capillary Elcctrophorcsi~(:;ipill:iry~ I ~ r , t r o p l n o r ~Is(i:sE ~ ~ " " " is :i W I ~ P II I~S P I ~ s~p:ir:itloin t~r,Ininlrll~~ twst s l ~ i t ~fi>r r i r,lniirg~d,w : i t ~ r along- while the counterions in the diffuse double layer outside s o l l ~ t >~l I~I I I P ~ : I I I1n:iving PS nlr>l~r,l~l:ir \\-pigInts r:inging from tlnosp of the plane of slip, in the free or mobile solvent, move toward the :iminr>:ir:ids ;ind ppptidps to inl~r,I~ir: :ir:iris. (:E 1n:is t l n ~fi>llr>\\-ing :idv:inother electrode This phenomenon is called ~ ~ l ~ ~ c f r o l ~ hIfo r ~ ~ t:igps: s r s . i t provirips Eist :ind ~ f f i r : i ~ spp:ir;itir>ns, nt rprllllrps only munl~tp the charged surface is immobile, as is the case with a packed : i m r > l ~ nr>fs:implp, ts is :ipplir:;it>lp to :i \\-idp r:ingp r>f:in:il,vt~s, :inri l un v,r>inbed of particles or a tube filled with water, applicatiol~of an tr;ist to HPI.(:) pmploys ~ ~ I ~ ~ I nP lO~ d~ iI: ~ iS i t l n t1n:in ~ r r>rg;inir,s r > l v ~ n t s . E I ~ t : t r ~ ~ p l niso r:iirri~ri r ~ ~ i ~ 011t in In~~rizointiil t::ipilI:ir~~s of f i l s ~ ds1lir,:i electric field causes t h e counterions in t h e free water to move 1\~1nir,lnis t~iiinsp:ir~int to I I I ~ E ~ V I I I I P of ~ ) 20 to 100 pnl t>r>rp:ind 20 to 100 towards t h e opposite electrode, dragging solvent with them r:m I~ngtln.Rot11 r,:ipill:iry pnds ;irp hpn t rirn\-in\\-:ird. E:ir,ln pnd is in]This flow vf liquid is called ~ ~ l ~ ~ c f r o o s n and ~ o s rt sh,e pressure mprspri in :i vi:il fi llpd \\-it11 :i t>l~ffpr sr>ll~tir>n t1n;it [:on t;iins ;in p1pr:trodp produced by it is called rlc~cfroosn~ofrc prcssurc. Conversely, if ;isspmhly. Thp p[pt:trorips :irP r:onin~t:t~d to :in i i d j l ~ s t : i h lnigln-vo[t:ig~ l~ dr, the liquid is made to flow past charged surfaces by applying hypo\\-pr s l ~ p p l y AS . t l n ~d i s s o l v ~ d: i n : i I > t ~ nligr:it~ s p:ist :i ri~t~r:tioin \\-indrostatic nressure. disnlacement of the counterions in the free rir>\\-in t l n ~r:;ipill;iry, tlnpir r,r>nt:~intr:itir>ins :irp m ~ : i s l ~ i - t>y ~ r i111tr:iviol~t water produces a potential difference between the two ends of :it>sorptir>nor t>y ~ottpinl;is~r-iinril~r:~d) f l l ~ r > r ~ s r : ~Tn lr n: ~~sllir,:i . t::ipill:irthe tube or bed called s f r c o ~ u r n gpofcntral These three pheIPS iirp oft~inr,o:it~d~ ~ t ~ r i n i iwltln l l y :i w r y tlnun I:iypr of pr>lyimlripto rpd l l r : ~t l n ~ fr:igility. ~r Tlnis pl:istir, r:r>:itung is t>llrnpri off un tlnp wlndr>\\nomena depend upon the relative motion ofthe charged surface iirp:i. and the diffuse double layer outside the plane of slip surroundTlnp r,:ip~ll:iryis fillpd \\-it11 tnlffpr soll~tion,tlnp s:implp i s injprtpri :it ing t h e surface Actually, most of the diffuse double layer lies onp pnd, ;inri :i r,onst:int lnigln pr>tpnti;il diffprpinr,~15 IS : i p p l i ~ d ,\\-lnirln within the free sulvent and, therefore, can move along the surp r o d ~ ~ii tp:o~t ~~n t i i i lp ~ i d i ~ ior n tf i ~ l ds t r ~ n g t l nin tlnp r;ingp of 300 to ,100 face All three electrokinetic phenomena measure t h e V/r,nl. rf 15 20,000 V :ind tlnp tr>t:il r,:ipill;iry I~ngtln(i, 37 r,m, t h ~ n same potential. which is the potential a t the plane of slip 15 I 350 V/r:m. Tlnp vplr>r,ityof migr:itir>n,I!, is tlnp r::ipiIl:iry lpngtln to h ~ i c r o c l c c t r o p h o r c s i ~ T lp:irtlrlps n~ of p1n;irm:it p11tir :il s l ~ s p ~ i n - tlnp dptpr:tor, (I(I., riiviri~dhy t l n ~nligriitlon tinw, t. of t l n ~:iin:iIyt~fronl tlnp sions :ind ~ m l ~ l s l r > tn>s :, i r t ~ r ~~r>tInror.ytw :i, :ind o t l n ~ lr s ~ > l i i tr~~dl l s 1:i, r,:ipill;iry iinjpr,tion pnri to tlnp r i ~ t ~ r : t i r\\-indo\\-. >n rf(iL 50 r:m ;ind t 10 ~ P K p:irtir:l~s,:ind m:iny r:r>nt:imin:int p:irtir,lps in pln:irnm:iv,~l~tir:iilSOIIImiin 600 spr,, thpn I! .50/600 0.083 r,m/spr:. Tlnp ~ l ~ r t r o p l n o r ~nlotlr, tions :irp visihlp in ;i mit:rr>st:r>pp.Tlnprpforp, tlnpir pot~inti:iIs:irP i tI 1 1 is I 'n/s:/130 c n 2.4 X 10 " r:m2/~spr:. r,r>nv~inipn tly r n ~ : i s l ~ rt>y ~ dr n ~ c ~ r o u l u c ~ t r o { ~ I!\' opotpn ~ ~ , s ~ti;il difY~rpnr:~, [in :idditir>nto ~ l ~ r : t r r > p l n r > r~ ~ls~i sr,: t r ~ > - ~ > sm:iy n l o spI:iy i s :in 1mport;int 15, : i p p l ~ ~~ >dP ~ \ \ - P . Pt\\-o P I ~~ P I c t r o d ~ t1n:it s :irP r i i p p ~ dinto :i disp~rsloiniind rolp 111 (:E. Tlnp ~ s o ~ l ~ r tpoint r i r , of In,~rir:itprisilit:;~1s ; i p p r r > ~ i m : i t ~1.8. ly s ~ p : i r ; i t ~ t>y r i ii dist:iinr~,(i, p r o d l ~ r ,t l~n~~pot~1nti:ilg r : i d i ~ n tor f i ~ l d Tlnp \\-p:ikl,~:ir:idir, sil:inr>l groups t>pr,r>mpinr,r~:isingIyionizpri \\-~tlninstrpngtln, 15/(i, p~prpsspri:is V/r,nl. Tlnp :ivPr:igP v~lor:ity,I!, of t l n ~p:irtir,rp;ising pH. (:r>nditir>ningtlnp r,:ipill:iry with ;i N:iOH sr>ll~tir>n :ind thpn r h s in rpsponsp to tlnp : i p p l i ~ dpot~intl:ild i f f ~ r ~ i ni rs :d~~ t ~ r n l i i nl~siing ~d witln tlnp t > l ~ f Ypnsllrps ~r t1n;it i t s \\-:ill is r:ln:irg~d111nifornlIywltln p:irtiiilIy ionlzpd sil;inr>l groups. Tlnpsp inpg;itivpI,~r,ln:irg~ds i t ~ :ittr:it:t s r:iitloinir, r,r>l~ntprir>ns from tlnp t n l f f ~ rto filrnl :iin ~ l ~ r : t r idr o, l ~ h l i~i y ~ r .Vv71npin :in plpt:trir, p o t ~ n t i i i lis :ipplipd, tlnp r::itir>nsin tlnp riiffllsp p:irt of tlnp rir>llt>lp I:iypr t>p,vr>ndtlnp pl:inp of s1np:ir I Fig 21 -5)migr:itp to\\-;irri tlnp npg;itivp pIpr,trodp, pintr:iiniinp\\-:it~r~>fIn,~dr:itioin. R P ~ , : ~ I IofS Pt l n ~snliill t > o ro~f t l n ~ r,:ipiIl:irl~sr,r>mp:irpdto tlnp diffllsp rir>llt>lp 1:iypr tInir.knpss, tlnp pIpr.trr>-usTlnp ~ l ~ r : t r o p l n o r ~mobility, tir, p, is ~rl11:ilto 1!/(15/(i) :ind 1s tlnp v~Iot:ity motir, flow I F O F ) r,:in t>p sl~t>st:inti:il.Tlnp E O F movps in :i plug p r o f i l ~ r::il~spdt>y:i pr>tpnti:ilgr:idipnt of 1 V/r:m. !\r:r:r>rriing to tlnp Srnr>ll~r,lnr>wski r:itln~rin tlnp r:l~str>m;iry p:ir:ihr>lir:p r o f i l ~1>fl:in111niir flow. At lnigln pH, tlnp prl~xition,p i r t i t : I ~S ~ Z Piind slniip~ria not :ifY~r,tt l n ~ pot~intiiil.HII\\.PVP~, if E O F 1s strong ~>PI,:~IISP t l n ~siI:iinol ~ T I I I I ~:irP S P K ~ P I ~ S ~i oVnPi z~~~d .Anltlnp p:irtir:lp r:idil~sis s m : i l l ~ rt1n:in or r,r>mp:ir;it>lpto & 11111%-lniv,lnr::isp t l n ~ plnotprir: p ~ p t l d iirp ~ s n ~ p i i t i v ~r,lniirg~ri ly iiinri try to n l i g r i i t ~to\\-tirri t l n ~ pirtirlps r:;innr>tt>p dptpr,td in :i nlir:rosr,op~),:i f:ir,tor of 6 r ~ p 1 : i t : ~t lsn ~'1. positlvp pIpr,trodp or :iinori~.TInisn~r>t~r>n is o t t ~ nr > v ~ n \ - I n ~ l rt>y n ~;ir istrong T l n ~visr,r>sity, q, ;ind tlnp riiplpr,trlr, r,onst:int, I ) , r ~ f to~ trl n ~:~IIIIPI>IIS :inri oppositp EOF, \\-lnir,ln rir:igs t l n ~ n lto\\-:ird t l n ~i n ~ g i i t i v~~1 ~ r : t r oord ~ rnpd111m within tlnp rir>llt>lpI;iypr :ind r.:innot t>p r n ~ : i s l ~ rriir~r:tly.~"y d r:iitlnori~.TIIPSPiin:iIyt~sn l o w fronl tlnp injpr,tir>npoiin t in tlnp :inr>ripr,r>m11sing tlnp v i i l l ~ ~ f isr \\-:it~r:it 2,SC(:, PKprPsslinp t l n ~v~Ior,ityin pnlfs~r:and p:irtmpnt tr>w:irri tlnp r,:itlnod~.Tlnp ordpr r>f;irriv:il;it tlnp riptpr,tir>in\\-intlnp ~ l ~ r : t r o p l n o r ~ nlot>llity tir, 111 ~ ~ m / s ~ r : ) / ~ v r > l t s /:ind r : m )rxjnvprting , into dew 1s: r,:itlr>nu,;in:ilyt~sI \ ~ - ] ~ I I S~Pl ~ ~ t r o p l n o r nl1gr:itloin ~tlr, t o ~ : i r r it l n ~ t l n ~:ippropri:it~llnlts, t l n ~S n l o l l ~ r , I n ~ > ~1111:itioin ~ski is ~ P I ~ I I ~ to ,PI~ 12.9 r,:itlnr>d~ is s l ~ p ~ r i m p r >:ind s ~ d: i r , r : ~ I ~ r : i t>y t ~ dt l n ~EOF), inr>nir>nir,:iin;ilyt~s p \\-it11 g v p n :is millivr>lts1n3V). Z ~ t ; ipr>tpnti:ils ;is lnigln :is 180 mV 1\\-1nit:Inmigr;itp P K ~ : I I I S ~ hy V PEOF), I~ a n d ;inionir, ;in;ilyt~s1\\-1nr>sp npt mi1n;ivp t>ppin rpportpd.' ""l rf tlnp p i r t i r l ~s11rf:ir.~Iniis :ippr~r,i:it>l~ r:onrillr:gr:itir>nv~Ior:ityI S t1n:it of t l n ~E O F min11s t l n ~ i ~r I ~ t : t r ~ ~ p l nmigr:itir>n ~~r~tir: v~111r:ity to\\-tirri t l n ~:inori~). At lo\\- pH, t l n ~E O F is sm:il l :ind t l n ~ppptidps :irP p o s i t i v ~ l yr:ln:irg~d. Tlnpir rnigr:itlr>in to\\-:ird tlnp t::itlnod~ is tlwn s l ~ p ~ r i n ~ p :ind o s ~ iir,r:~I~rd :itpri h , tlnp ~ E O F in tlnp s:imp dirpr:tir>n.Tlnp dirprtion of tlnp E O F r:;in t>p rpvprspd hy :idding :i r,:itlr>nir:sl~rf:ir,t:int,sl~r,ln:is r : ~ t y l t r ~ n ~ ~ t l n y l i i n ~ n ~ o 1. El~r.trr>r>smr>sis r:;illsps lirll~idto flrnv ;ilr>ngtlnp \\-;ills of tlnp r:pll r,r>innium t>rr>mldp,to tlnp t>l~ffpr.r t \\-ill rp;ir,t ;inri n ~ 1 1 t r ; i l i ztlnp ~ s~l:inr>l t:iining tlnp rilspprsion. Tlnis un t11rn prr>rillr,ps;i rpt11i-n flrnv in to t l n ~ groups, :ind P K ~ , P S S s~~rf:irt:iint :irisort>~don t l n ~sil11:ii ~ l l r,oinf~r l ii ~ I I S I t:pntpr of tlnp v,pll. Tllprpfi>rp,t l n ~nlir,rosr:op~nlllst t > fi>v,l~s~d ~ 1111 t l n ~ tivp r:ln:irg~to it. Tlnp R r rr>l~ntprir>ns r,:illsp :in E O F to\\-:ird tlnp ;inr>ri~. st:itir>n:iryt>r>l~nd:iry t>pt\\-ppn tlnp t\\-o liql~idI:iy~i-s t1n:it :irP flrn\-ing Tlnp E O F r:;in t>p s l ~ p p r ~ s hs ~, r,r>;itiing d~ tlnp silit::~r:ilpill:iri~s\\-it11 :i p01,~in oppositp riir~r:tionsin o r d ~ rto n l ~ i i s l l rt ~l n ~t r l l ~v~111r:ity of t l n ~ mpr or h , usung ~ T ~ f l o nr,:ipill:irips. p:irtir,I~s. I!11 lpss tlnp 1np:it gpinpr:itpd t > , t~l n ~~ l ~ r , t r ir~sist:iinr,~ t: of t l n ~h l l f f ~ rSO2. Fr>llr>\\-ingtlnp motion of sunglp p1rtir:lps un :i mir,rr>sr,r>pit: fipld :ind Il~tionI.JOIIIP In~iitiing)is d i s s i p i i t ~ d ,it ~ . : ~ I I St Pl nS ~t ~ n l p ~ r i i t l to l r ~111r n ~ : i s l ~ r i ntlnpir g vplov,ity IS only pr>ssit>lpusing w r y dilutp dlspprr,rP:isP mi tln tlnw ;ind p r o m o t ~ st ~ n l p ~ r : i t gr:irii~n l ~ r ~ t s iir,ross t l n ~r:iipllslons. Tlnprpforp, m:iny rilspprsions m11st t>p riill~tprit>pfi>rpm;iking I:iry. Tlnis i i n t p r f ~ r p s\\-~tlnr~proril~v,ihi lit? :ind s1n:irpn PSS of tln P (:I? s11~:lnd~t~rnmin:itir>ns. S i n t : ~tlnp pr>tpnti:il d ~ p ~ n 1:irgply ds upon tlnp spp:ir;itions. T l n ~:irnr>l~nt of 1np:it gpinpr;itpd is d i r ~ r , t l yproportir>n:il to n:itllrp, ionir, strpngtln, :inri pH of t l n ~s l ~ s p ~ n d i nmpriil~m, g dlspprtlnp srl1I;irp of tlnp fi pld strpngtln 1\\-11ir:In is 1;ii-g~);ind to tlnp r,r>ndl~r,ti\i ty sions slnr>l~ld not t>p dill~tpdwitln w:itpr tmt \\-it11 sr>ll~tlr>ins 1n:iving of tlnp t>l~ffprsr>ll~tir>n. Vv71nilp d ~ r , r ~ : i s i nt lgn ~volt:ip~,usung Ioingpr or r,r>mpr>sitir>ns idpntir,:il to tlnpir r,r>ntinl~r>l~s p1n:is~I P ~witln , tlnpir rn\-n s m : i l I ~ r - t > or::ipill:iri~s r~ iiinri/~>r nlorp rii111t~t > l ~ f Ysoll~tioin ~r \\-t.l>l~ld r~dllr,~ sprllm t1n:it 1n:is ~ > P PsI ~~ p : i r : i t ~hy d 11Itriifi1tr:itioin or r,~intrifi~g:itioin). t l n ~r:itp of 1np:it gpnpr:itir>n;it \\-r>l~lri :ilsr>inr,rp:isp tlnp s~p:ir;itir>n tinws.

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CHAPTER21:COUOIDALDISPERSIONS

Shod separation timea reduce the band broadening due to analyte diffusion, improving the re~olution.Therefore, the caflary is cwled with a tbermostatted liquid. A variation of CE is m i d a r elechkinetic (capillary) ehromatography (MEKC)zeb The analytw are mlubilized in m i d e s of an ionic surfactant, such as s d u m ddecyl sulfate, which is added to the buffer solution at a conoenkation well above its critical m i d e concentration of 8 x 104M. MEKC is suited garticularly to separate neukal analytw of limited water solubility, which are extensively partitioned into the mioelle~,but is also a ~ ~ l k a btol eionic anal*. Anionic a n a l ~ k sb, i n g well soluble in water, either do not padition into tbe m i d w or form mixed midw the anionic s u r f a h t . Cationic anal* ofh form precigitatw with anionic surfactanb. Therefore, their separation by MEKC is best carried out with cationic surfactan&. The combination of a nonionic and an ionic surfactant g d u c e s mixed m i d w . Theae have lower surfwe charge densitiw and larger sizw than the m i d w of ionic surfactants, and henoe they have lower electrophoreticmobilitiw. Thus,addition of a nonionic to an ionic eurfactant narrows the migration time window, which is the differenoe b tween the migration timw of the bulk solution in EOF and of the mid ~and o, h shortens the analysis time. Analytea with molecular weighb of 5000 or higher are not solubilized by m i d l ~Therefore, . while they can b analyzed by CE, they cannot be analyzed by MEKC. Although anionic m i d w tend to migrate toward the a n d e , a strong EOF in neukal or alkaline media will drag them toward the cathode, but with a velocity retarded by tbeir own migration velocity. If a neukal analyte is partly mlubilized in mioellw and partly dissolved molecularly in tbe buffer solution, the latter portion has a shorter migration time h a u s e ita velmity is that of the EOF. C a p i l l q gel e l e c b r o p h ~ r eemploys s ~ ~ ~ capillaria fded with a gel of rns-linked polyacrylamide, which s u p p EOF. ~ ~Isotachopboreais and d e 6 c f o c u a i ~ gdwcribd ,~ in previow editions of this text, are other m&tiw of CE.

LYOPHlLlC DISPERSIONS Lyophilic dispersions oonsist either of polymers dissolved in a good solvent or of insoluble but extensively solvated particles dispersed in a liquid medium that has a high afEnity or attraction for them. The free energy of dissolution or dispersion is AG, = AH, - TAS, where AH, and AS, are the heat or enthalpy change, and the entropy change of dissolution or dispersion, respectively. For dissolution of polymers and dispersion of par ti^ d a t e solids to cwxur spontaneously, AG, must b negative. Since bath of these prooesses are exothermic (ie, occur with the evolution of heat), their AH, is negative. Since the number of available conformationsof the polymer chains increases oonsiderably upon dissolution, and the number of positions and orientations of the solid particles increases considerably upon their dispersion in the liquid, their AS, is positive (ie, there is an increase in randomness). The negative enthalpy change and the positive entropy change of dissolution/dispersion b t h contribute to making AG, negative. Therefore, bath types of oolloidal systems are formed spontaneously when powders of solid polymers and particulate solids are brought into oontact with the liquid dispersion medium. They are thermodynamically stable and reversible (ie, they are easily reoonstituted aRer the dispersion medium has k n removed). The van der Waals energies of attraction btween dissolved macromolecules or between dispersed lyophilic solid particles are smaller than AG, and are therefore insufficient to cause flocculation or coagulation of the dispersed phase. Furthermore, the solvation layers surrounding dissolved macromolecules and dispersed lyophilic particles form a physical barrier preventing their close approach. Most liquid dispersed systems of pharmaceutical interest are aqueous. Therefore, most of the lyophilic oolloidal systems discussed blow consist of hydrophilicsolids dissolved or dispersed in water. Most of the prcducts mentioned blow areofficialin the USP or NF, where more detailed descriptions may be found; they are also discussed in detail elsewhere in this text. Hydrophilic colloids can be divided into two classe8 (ie, soluble and particulate materials). Solutions of water-soluble polymers molecularly dissolved in water may be classi&d as oolloidd dispersions because the individual molecules are in the colloidal particle size range: the diameter of a randomly ooiled polymer

305

chain commonly exoeeds 10 nm. Particulate or ooquscular hydrophilic oolloidal dispersions are formed by solids that swell and are peptized in water but whose primary particles do not dissolve or break down into individual molecules or ions.

Water-Sol uble Polymers Most of the hydrophilic oolloidal systems used to prepare pharmaceutical dosage forms are molecular solutions of water-soluble, high wei&t polymers. These polymers are either line@ or slightly branched but not cw-linked. Water-soluble according to their pOlymers may divided into three OFigin: Natuml polynsers i d u d e polysawharidea (acacia, agar, heparin s d u m , peetin, sodium alginate, kagacanth, xanthan gum) and polypegtidea (mein, gelatin, protamine sulfate). Of these, agar and gelatin are only soluble in hot water. Cellulose derwafves are p d u d by chemically m d f y i q oellulose obtained fiom w o d pulp or cotton to p d u c e soluble polymers. Cellulose is an insoluble, linear polymer of glucose unite in the ring or pyranose form joined by 8-1,4 gluwsidic Each gluwse unit (except for the two at the terminal chain ends) w n t a i n ~a primary hydroxyi group on the No. 6 carbon and two secondary hydroxyb on the No. 2- and 3+3rhna. Chemical m d ification of d u l o s e involves substitutions at these hydroxyl group with the primary hydroql group bing tbe most reactive. The extent of such reactions is e x p r w d as degree of substit utwn DS), the n u m h of substituted hydroxyl group per glucose residue. The highest value for DS is 3. Fractional value^ are m a common b w e the DS is averaged over a multitude of glucose reBiduw. A DS value of 0.6 indicatw that some glucose repeat units are not substituted while others substituted once or even twice. Some soluble cellulose derivatives are listed below. Their DS valuea cornpond to their reapeetive pharmaoeutical grad=; the group shown replace the hydrogen atoms of the cellulosichydmxyls. Official derivativea i d u d e nsethylcellulose D S = 1.65-1.93); (-0-03,) and s o d i m crarboxy~hylcelluloseD S = 0.60-1.00); (--0-CHgOO-Naf 1. Hydmxyethylcellulose (DS= 1.0);(4(CH,CH20),H) and hydmxypropylcellulose D S = 2.5);

w.

-o+-cH--CHro-)nH

CH, are manufactwed by adding ethylene oxide and propylene oxide, respectively, to alkali-hated d u l o a e . The value of n is about 2.0 for hydroxyethyloellulose and not much greater than 1.0 for hydroxypropyldulose. Hydmxypropylnsebhylcelluloseis prepared by reacting alkali-hated d u l o s e first with methyl chloride to inkoduoe methoxy groups (DS = 1.1-1.8) and then with propylene oxide to introduce propylene glycol ether groups (I38 = 0.1-0.3). In general, the inbduction of hydroxypmpyl groups into oellulose slightly reduoes ite water solubility while promoting its alcohols, solubility in polar organic solvenb such as &orglycols, and some ethers. The molecular weight of native d u l o s e is so high that soluble derivatives of approximately the same degree of polymerization would b m l v e too slowly and their solutions would b egcemively viscous even at comenkations of 51%. To overcome thwe aculties, wnkolled degradation is wed to break the celluloee chaina into shorter segments. Commercial grades cellulose derivativw, such as s d u m carboxymethyldlulose, wme in variow molecular weights or vkcoeity gradea as well as with variow degrees of substitution. Official cellulose derivatives that are insoluble in water but soluble in some organic solvents include ethylcellulose (D8 = 2.2-2.7); (-OCaH5); cellulose acetaie phthdaie D S = 1.70 for acetyl and 0.77 for phthalyl); hydmxypropyltnethylcellulosephthdate; and polyvinyl acetate phthalaie. Collodwn, a 4.0% (wh) solution of pyroxylin ( d u l o s e dinikate) in a mixture of 75% (vh) ether and 25% (v/v) ethyl alcohol, is also a cellulose based, lyophhc colloidal system. Water-soluble synthetic polymers conskt mostly of high mole cular weight polyethylene glycols, or polyethylene oxides, and vinyl derivativw such as polyvinyl alcohol, povidone or golyvinylpyrmlidone, and carbomer (Cwbopol), a wpolymer of acrylic acid.

PART 2: PHARMACEUTICS

h second classificatio~~ of hydropl~ilicpolymers is based upon their charge. Xonionic or uncharged polymers illelude methylcellulose, hydroxyetl~yland hydroxypropyl cellulose, ethylcellulose, pyroxylin, polyetl~yleneoxide, p o l j ~ ~ i n alcohol, yl and poridone. Anion,ic or negatively charged pol.v~~lrctrol.vtt~s include carboxylated polymers (eg, acacia, alginic acid, pectin, tragacanth, s a n t h a n gum, and carbomer) at pII values that result of their carbosyl groups. Sodium alginate, in t h e iol~izatiol~ sodium carbosymet~~ylcellulose, and polypeptides leg, sodium caseinate) a t pII values above their isoelectric points are also anionic. Sulfuric acid is a stronger acidic group t h a t exists a s a monoester in agar and heparin and as a monoamide in heparin. Cu tionic or positively charged pol.vt~l~~c trol.vt(bs are rare. Esamples illelude chitin, a polysaccharide found in the shells of beetles and crustaceans, and polypeptides at pII values below their isoelectric points. Protarnines such a s protarnine sulfate are strongly basic due to their high arginine colltellt and have isoelectric points around pII 12.

Particulate Hydrophilic Dispersions The dispersed phase of these sols collsists of solids that swell 111 water and spol~tal~eously break up into particles having colloidal dimensions ' r l e dispersed particles have high specific surface areas and are extensively hydrated RcnfonrfebXF is a hydrated a l u m u ~ u msilicate that crystallizes in a layer structure with UIdividual lamellas 0 94 nm thick Their top and bottom surfaces collsist of sheets of oxygen ions from silica and an occasional sodium ion neutralizing a silicate ion-exchange site ' r l e clay narticles con tail^ stacks of these lamellas Water nenetrates between these lamellas to hydrate the oxygen ions and causes extensive swelling ' r l e bentonite particles 111 bentonite magma collsist of single lamellas or packets of a few lamellas with intercalated water Their specific surface area amoullts to several hundred square meters per gram Kaolrn LTSP is also a hydrated a l u m u ~ u msilicate having a layer structure In kaolin, hydrated alumilla lattice layers alterllate with silica layers 'r~erefore,one of the two exterllal surfaces of a kaolin nlate collsists of a sheet of oxygen ions from silica whereas the other is a sheet of hydroside ions from hydrated alumina. Both surfaces are well hydrated but water cannot penetrate into t h e individual lattice layers. 'rherefore, the particles do not swell in water or exfoliate into thin plates, As a result, kaolin plates dispersed in water are much thicker than those ofbentonite, about 0.04 to 0.2 pm. !lIugncsir~,nlAlr~,nlinr~,nl Silicatr NF, also known as C'eegumG, is a clay similar to bentonite but col~taulsmagnesium; it is white whereas bentonite is gray. Colloiclol Actirwttd Attapr~,lgit~ LTSP also consists of magnesium alumil~umsilicate. IIowever, rather t11an having a lamellar habit like the other three clays, it crystallizes in the form of long needles approximately 20 nm in widt11,l.'" ' r l e followil~gadditional hydropl~ilicparticles can also produce colloidal dispersions in water. Titanir~,nldioxid(b is a white pigment with eesellel~tcovering power. Colloidal silicon d i o x i d ~ collsists of rougl~lyspherical particles t h a t are covered with silosane and silanol groups, illicrocrystallin~~ ccllr~~losr is hydrophilic because of the hydroxyl and ether groups on the surface of the cellulose crystals. Gelatinous precipitates of hydrophilie compoul~dssuch as a l r ~inr~,nl , ~ ~ hydroxid~~ gcl, alr~mlinrml ph.ospha t~ grl, and nlagnt~sir~,nl hydroxid(b collsist of coarse floes produced by agglomeratiol~of the colloidal particles formed in the initial stages of precipitation.

LYOPHOBIC DISPERSIONS Lyophobic dispersions are intrinsically unstable and irreversible because of the lack of attraction between t h e dispersed and continuous phases Lnlike lyophilic dispersions, their large surface free energy is not lowered by solvation, their dispersiol~ process does not take place spontaneously, and they are not easily recol~stitutedFor lyopl~obicdispersions, I C ; , is positive

because of a positive (endothermic)1H, term, which makes the reverse process (agglomeration)the spontaneous one rlqueous dispersions of hydrophobic solids or liquids can be prepared by physical means that supply a n appropriate amount of energy to the system IIowever, they are unstable ' r l e van der Waals attractive forces between t h e particles are stronger than the solvation forces t h a t promote particle dispersal, and therefore, the particles tend to aggregate Most of the discussiol~of lyopl~obic dispersions deals with hydrosols consisting of hydrophobic solids or liquids dispersed in an aqueous media because water is the most widely used vehicle Such hydrosols consist of aqueous dispersions of illsoluble organic and inorganic compounds, which usually have low degrees of hydration Organic compounds t h a t are preponderantly hydrocarbol~in nature and possess few hydrophilie or polar groups are hydropl~obic,and therefore, il~solublein water Like all lyopl~obicdispersions, hydrophobic dispersions are intrinsically ullstable In their most t~~ermodynamically stable state, the dispersed phase h a s coalesced into large crystals or drops, so t h a t t h e specific surface area and surface free energy are minimized Therefore, mechanical, chemical, or electrical energy must be supplied to break u p t h e dispersed phase into smaller particles and overcome the resulting increase 111 surface free energy that occurs from the parallel increase in specific surface area IIydropl~obicdispersions can be prepared by either dispersion methods (the redueti011 of coarse particles to colloidal dimellsiolls t11rougl1 c o m m u ~ u t i oor~ peptization) ~ or condensation methods (the aggregatiol~of small molecules or ions into particles haring colloidal dimensions) Uispersiol~metl~ods tend to produce sols that have wide particle size distributions Conversely, c o l ~ d e l ~ s a t i ometl~ods l~ w a y produce essentially monodisperse sols provided specialized techniques are employed Methods of purificatiol~to remove low molecular-weight, water-soluble impurities from hydrosols have been reviewed 111 the corresponding chapter of the previous Rcnl rngfon edition

Preparation by Dispersion Methods ' r l e first method, nlr~chanrcaldrsrnf~~grafron of solids and liquids into smaller particles before or during dispersiol~within a fluid vehicle, is frequently carried out by the input of mechanical energy via shear or attrition Equipment such as colloid and ball mills, microl~izersand, for emulsions, homogenizers is described elsewhere in this text and in Reference 27 U y grinding with inert, water-soluble diluting agents also produces colloidal dispersions For example, sulfur hydrosols may be prepared by triturating t h e powder with urea or lactose followed by shaking with water Lltrasonic generators provide exof energ?: IIowever, t h e succeptionally high col~cel~tratiol~s cessfi~ldispersiol~of solids by means of ultrasol~icwaves can only be achieved with comparatively soft materials such as many organic compounds, sulfur, talcum, and graphite 1n cases where fine emulsiol~sare mandatory, such a s soybean oilin-water emulsiol~sfor intravenous feeding, emulsificatiol~by ultrasound waves is the method of choice " ' r l e formati011 of aerosols is described elsewhere in this text Pt~ptrzafronis a second dispersion method used to prepare colloidal dispersions ' r l e term is defined as t h e breaking up of aggregates (or secondary particles) into smaller aggregates (or primary particles) t h a t are within the colloidal size range Primary particles are those particles t h a t are not formed from smaller ones Peptizatiol~is synonymous with d~~ffocculafron. I t can be brought about by t h e removal of flocculating agents, usually electrolytes, or by the addition of deflocculatil~g or peptizing agents, usually surfactants. water-soluble polymers, powor ions t h a t adsorb onto the particle surface ""\'hen dered activated charcoal is added to water wit11 stirring, the aggregated grains cal~notbe completely broken up and the resulting suspel~siol~ is gray and trallslucel~t The addition of

CHAPTER 21: COLLOIDAL DISPERSIONS

50.1% s d i u m lauryl sulfate or octoxynol 9 deflocculates the grains into h e l y dispersed particles and results in a deep black and opaque dispersion. Ferric or aluminum hydroxide that has been freshly precipitated with ammonia can be peptized with small amounts of acids which reduce the pH helow the isoelectric points of the hydroxides. Even washing the gelatinous precipitate of Al(OH)3 with water tends to peptize it. Therefore, in quantitative analyses, the precipitate is instead washed with dilute solutions of ammonium salts that act as flocculating agents.

Preparation by Condensation Methods Sulfur is insoluble in water but somewhat soluble in alcohol. When an alcoholic solution of sulfur is mixed with water, a bluish-white colloidal dispersion results. In the absence of added stabilizing agents, the particles tend to agglomerate and precipitate upon standing. This technique of first dissolving a material in a water-miscible solvent such as alcohol or acetone and then prducing a hydrosol by precipitation with water is applicable to many organic compounds. I t has been used to prepare hydrosols of stearic acid, natural resins like mastic, and the so-called pseudo-latexes. Another less common physical condensation m e t h d is to introduce a current of sulfur vapor into water, which prduces colloidal particles. Alternatively, the very fine powder produced by condensing sulfur vapor onto cold solid surfaces (sublimed sulfur or flowers of sulfur) can be dispersed in water by the addition of a suitable surfactant to produce a hydrosol. Organic compounds that are weak bases, such as the alkaloids, are usually much more soluble at lower pH values, where they are ionized, than a t higher pH values, where they exist as the free base. Therefore, increasing the pH of their aqueous solutions a b v e their pKa may cause precipitation of the free base. Conversely, organic compounds that are weak acids, such as the barbiturates, are usually much more soluble at higher pH values, where they are ionized, than at lower pH values, where they exist as the free acid form. Therefore, lowering the pH of their aqueous solutions well below their pKa usually causes precipitation of the free acid. Depending upon the supersaturation (defined helow) of the unionized bases or acids and the presence of stabilizing agents, the resultant dispersions may be within the colloidal range. Chemical condensation m e t h d s include the reaction between hydrogen suKde and sulfur dioxide (eg, by bubbling H2S into an aqueous SOz solution): The same reaction occurs when aqueous solutions containing s d u m s a d e and s a t e are acidified with an excess of sulfuric or hydrochloric acid. Another reaction is the decomposition of sodium thiosulfate by sulfuric acid, using either very dilute or very concentrated solutions to obtain colloidallydispersed sulfur:

307

Double decompositions that prduce insoluble salts can also lead to colloidal dispersions. An example is silver chloride: NaCl

+ AgNOs + AgCl + NaNOs

In addition, the reduction of gold, silver, copper, mercury, platinum. rhodium. and ~alladiurnsalts with formaldehvde. ,. , hvo drazine, hydroxylamine, hydroquinone, or stannous chloride forms hydrosols of the metals, which are strongly colored (eg, red or b l ~ e ) . ~ ~ ' - ~ ~ KINETICS OF PARTICLE FORMATION-When the solubility of a compound in water is exceeded, its solution becomes supersaturated and the compound may precipitate or

crystallize. The rate of precipitation, the resulting particle size (whether colloidal or coarse), and the particle size distribution (which can be narrow for mono- or homodispersed particles or broad for p l y - or heterdispersed particles) depend upon two successive and largely independent processes. These are nucleation and crystallization (ie, growth of nuclei). When a solution of a salt or sucrose is supermled or when a chemical reaction prduces a salt in a concentration exceeding its solubility p r d uct, the separation of excess solid fiom the supersaturated solution is far from instantaneous. Clusters of ions or molecules called nuclei must exceed a critical size before they become stable and capable of growing into colloidal size crystals. These embryonic particles have much more surface for a given weight of material than larger and more stable crystals. Therefore, they have a higher surface free energy and greater solubility. The m e n c e of nucleation d e ~ e n d us w n the relative supersaturation. If C is the actual c o k n t r a i o n of the solute hefore crystallization and C, is its solubility limit, then C - C, is the supersaturation and (C - C$ / C, is the relative supersaturation. Von Weimarn recognized that the rate or velocity of nucleation (number of nuclei formed per liter per second) is proportional to the relative supersaturation. Nucleation seldom occurs a t relative supersaturations below 3. However, this statement refers to homogeneous nucleation, where the nuclei have the same chemical composition as the crystallizing phase. If the solution contains solid impurities, such as dust particles in suspension, these may act as nuclei or centers of crystallization (heterogeneous nucleation). Once nuclei have formed, crystallization hegins. Nuclei grow by the aggregation of ions or molecules fiom solution. Crystallization continues until the supersaturation is relieved (i-e.until C = C,) and may result in the formation of either colloidal or coarse particles. The rate of crystallization or growth of nuclei is proportional to the supersaturation:

This equation is similar to the Noyes-Whitney equation that governs particle dissolution except that C < C, for the latter process, making drnldt negative. In b t h equations, m is the mass of material crystallizing out in time t , D is the diffusion coefficient of the solute molecules or ions, 6 is the length of the diffusion path or the thickness of the liquid layer adhering to the growing particles, and A, is their specific surface area. The Both reactions also prduce pentathionic acid (HzSlj06)as a by Dresence of dissolved i m ~ u n t ise mav affect the rate of crvstalproduct. The preferential adsorption of the pent athionate anion iization and even changl the crystafhabit, provided that k e s e onto the surface of the sulfur particles confers a negative elecimpurities are surface-active and become adsorbed onto the nutric charge to the particles, thereby stabilizing the ~ o l . ' - ~ ~clei ~ or growing crystals." For inst a m , 0.0 05%polysorbate 80 or When powdered sulfur is hiled with a slurry of lime, it disoctoxynol 9 significantly retards the growth of methylpredsolves with the formation of calcium pentasulfide and thiosulnisolone crystals in aqueous media. fate. Subseauent acidification ~roducesthe colloidal "milk of Von Weimarn found that the particle size of the crystals desulfur," whiih upon washing A d drying yields Precipitated pends strongly upon the concentration of the precipitating subSulfur USP. stance. At verv low concentrations and slight " relative su~ersatSols of ferric, aluminum, chromic, stannic, and titanium hyuration, diffusion is quite slow because the concentration droxides or hydrous oxides are produced by the hydrolysis of gradient that drives the p r m s s is very small. S a c i e n t nuclei the corresponding chlorides or nitrates: will usually form to relieve the slight supersaturation. However, crystal growth is limited by the small amount of excess AlCl, + 3 Hz0 AI(0H)s + 3 HCI dissolved material available to each particle and, therefore, the particles cannot grow beyond colloidal dimensions. This condiHydrolysis is promoted by hailing the solution andlor adding a tion is represented by points A, D, and G of the schematic plot base to neutralize the formed acid.'

308

PART 2: PHARMACEUTICS

of von Weimarn (Fig 21-7),rit ii~termediateconcentrations. the extent of nucleation is somewhat greater and much more material is available for crystal growth. Therefore, coarse crystals form rather t h a n colloidal particles. This condition is represented by points U, E,and 11 in Figure 21-7, rlt high concentrations, nuclei appear so quickly and in such large numbers t h a t supersaturatiol~is relieved before any appreciable diffusion can occur. The high viscosity of the medium also slows down t h e diffusiol~of excess dissolved ions or molecules, retarding crystal growth ~vithoutsubstal~tiallyaffecting t h e rate of nucleation, 'rherefore, a large number ofvery small particles results which, because of their proximity, tend to 1 ~ 1 kand produce a translu-

cent gel. This condition is represented by points C and F in Figure 21-7. Lpon subsequent dilutiol~with water, such gels USUally yield colloidal dispersions. Thus, colloidal systems are usually produced at very low and high ssupersaturations. Low solubility is a necessary condition for producing colloidal dispersions. lf t h e solubility of t h e precipitate is increased, for i l ~ s t a l ~ cbye h e a t u ~ g t h edispersion, a new family of cun7eswill result similar in shape to those shown in Figure 217 but are displaced to the right (towards higher concentrations) and upwards (towards larger particle sizes).',".'".'" additional phenomennon illustrated in Figure 21-7 is t h a t aging increases particle size. Curves riUC?,UEF, and GI11 correspond to il~creasil~g time periods after mixing the reagents, namely, 10-30 minutes, several hours, and weeks to years, respectively, This gradual increase in the particle size of crystals in their mother liquor is a recrystallization process called Ostruald riprbnin,g. V e y small particles have a higher solubility t h a n large particles of the same substallce due to their greater specific surface area and higher surface free e n e r n , ln a saturated solutioll containing precipitated particles with a wide range of particle sizes, t h e very smallest particles dissolve spontaneously and deposit onto the larger particles. The growth of the larger crystals a t t h e expellse of t h e small olles occurs because this process lowers t h e free e n e r n of t h e dispersion, ridding small amounts of surface-active compoul~dst h a t adsorb a t t h e particle surface slows down the process. l l ~ c r e a s i l ~the g solubility of t h e precipitate accelerates the spontaneous coarsening of colloidal dispersions UPOH aging. For instance, barium sulfate precipitated by mixing concentrated solutiol~sof sodium sulfate and barium chloride is largely in the colloidal size range and passes througll filter paper. ' r l e colloidal particles gradually grow in size by Ost~valdripening. forming large cr?..stals t h a t call be removed quantitatively by filtration. IIeatingthe aqueous dispersiol~speeds recrystallization by increasing the solubility of barium sulfate in water.

Conversely, the addition of ethyl alcohol lowers t h e solubility of barium sulfate and slows Ostwald ripening, which allows the dispersiol~to remain in t h e colloidal state for years. The relationship between particle size and solubility is given by t h e Ostwald-Freundlich or Kelvin equation which, for nonionic solutes, is',".": s 2T!11 ln -- - -S , rdRT where S and S , are tile solubility of havillg a radius r alld t h e solubility of large, flat ( r - Y,), respectively,For the meall iollie activity is included, 'rhe solid/solvent illterfaeifil free e n e r n , 7,Call ollly be determilled indirectly (for instance, by means of tllis 'rle ratio of the weigllt of tile to its dellsity ($I/d) equals its molar volume, rissuming M - 500 g/nlol, d - 1.00 g/,,,~,,alld - 3 0 6brg/cn7.', and usillgthe values of8,3~.i :< 10' 6brg/fl10/-K for t h e gas collstallt R alld 298 K for the absolute temperature T, dispersed having radii of 1 x lo--" cm (10 nm). 1 x lo--:'em (0.1pm), 1 x 1 0 - em (1pm), alld 1 x lo-,$ em (10 p m ) correspolld toS / S , ratios of 3.36, 1.13, 1,012, and 1.0012 respectively. 'rherefore, while particles having sizes at tile lower elld o f t h e rallge are more sol. llble than coarser of t h e same tile solubility of fillely groul~ddrug or excipiel~tpowders (particle radii typically in the 1-10 ~m range) is ollly illcreased by loreover, they call be spray-dried or freeze-dried and recol~stitutedmuch more successfully, Any surfactants present in the dried powders aid redispersion ofthe l~al~oparticles in saline.

CHAPTER 21: COLLOIDAL DISPERSIONS

317

Like liposomes, intravenously injected nanoparticles are readily taken up by the RES phagmytic cells of the liver, spleen, and lungs. Also like liposomes, surface modification may extend the b l d circulation time of nanoparticles or target them to specific tissues. DRUG-POLYMER CONJUGATES-Polvmer s have also been used to produce soluble drug-polymer conjugates, which are formed by chemical reactions to prcduce covalent hands hetween a drug and a polymeric molecule.47These polymer conjugates include synthetic polymers as well as biological polymers such as globular and fibrous proteins, antihadies and polysaixharides. For example, Mylotarg for Injection (gemtuzumab ozogamicin)

Colloids are also used as pharmaceutical excipients for a variety of purposes including thickening agents. Colloidal thickening agents or visoosity builders belong to four chemical categories. Semi-syntheticcellulose derivatives include methylcellulose,carbxymethyldlulose s d u m , hydroxypropyl methyloellulose, and hydroxypropyl cellulose. Natural polymers include acacia, tragacanth, xanthan gum, s d u m alginate, and carrageenan. Synthetic polymers include carbmer, a co-polymer of acrylic acid; poloxamer, a block copolymer of ethylene oxide and propylene oxide; polyvinyl alcohol; and povidone (polyvinylpyrrolidone).Particulate colloids include bentonite, colloidal silicon dioxide, and microcrystalline cellulose. These visoosity builders may be used

consists of a conjugate between an IgG monoclonal antibody and

to decrease the dissolution rate of controlled release dosage forms,

to decrease the sedimentationor creamingrates of dispersed syscalicheamicin, a chemotherapeutic agent. These conjugates are tems, to improve the taste-masking abilities of liquid vehicles, administered by 1V infusion and the antihdy targets the CD33 and to provide consistency to ointments. Many of the waterantigen found on the surface of leukemic blasts and immature soluble viscosity builders mentioned ahave are surhce-active and normal cells of myelomonmytic lineage, but not on normal are also used as emulsifjhg and suspending agents. Even parhematopoietic stem cells. The antibdy-drug conjugate is heticulate colloids are used to stabilize emulsions and suspensions. lieved to have a lysomotropic mechanism of action, ie, the antiColloidal silicon dioxide is a white powder consisting of subMy-antigen complex is internalized into the cell through endomicroscopic spherical particles of fairly uniform size in the cytosis and entrapped within endosomal compartments. These range of 5-50 nm or higher. It is used to thicken liquid dosage endosomes merge with primary lysosomes to form secondary forms and in tablets. The surface of colloidal silicon dioxide parlysosomes, where the drug-antihdy hands are presumably broticles contains siloxane (Si-0-Si) and silanol (Si-OH) groups. ken by the acidic environment or cleaved by certain lysosomal When colloidal silicon dioxide powder is dispersed in nonpolar enzymes. Once cleaved from the antihdy, the drug is able to difliquids, the particles tend to adhere to one another through hyfuse out of the lysosome and exert its pharmacological effect. drogen hands between these surface groups. The spherical parIn-111and Y-90 Zeualin consists of a conjugate hetween an ticles of finer grade colloidal silicon dioxide are linked together ibritumoab antibdy (a murine IgG) and either an indium-111 into short chain-like aggregates as shown in Figure 21-4. This or yttrium-90 radioisotope. These conjugates are administered creates loose three -dimensional networks that increase the by IV infusion and attach to the CD20 antigen found on the surviscositv of the liauid vehicles even at levels as low as a few Derface of normal and malignant B-lymphwykes. However, the cent. Ti;e hydrogen-bonded structures are torn apart by Atirantihdy-antigen complex is not internalized. The attachment ring but rebuilt while at rest, conferring a thixotropic nature to of the antibcdy induces cell apoptosis and the close proximity of the thickened liquids. the radioisotope creates free radicals that damage nearby cells. Aerosil200 is the grade most widely used as a pharmaceutiPEG-Intron Powder for Injection also consists of a conjugate. In cal adjuvant. Its primary spheres, which are extensively sinthis case, interferon a-2b is conjugated with a PEG derivative. tered together, have an average diameter of 12 nm. At levels of The conjugates are injected subcutaneously. The PEG deriva8 to lo%,it thickens liquids oflow polarity such as vegetable and tive prevents detection by the RES and, therefore, decreases mineral oils to the consistency of ointments, imparting considthe clearance of interferon a-2b from the body. erable yield values to them. Hydrogen-bonding liquids such as The actively targeted conjugates described a b v e may be alcohols and water solvate the silica spheres, thereby reducing contrasted to passively targeted macromolecular conjugates for the hydrogen handing between particles. Therefore, the higher solid tumor tissue. Passively targeted macromolecular conjusilicalevels of 12-18% or more are required to gel these solvents. gates have shown preferential accumulationin solid tumors heThe grades that consist of relatively large and unattached cause of the EPR effect. The preferential accumulation reduces spherical particles, such as those in Figure 2 1-3,are less efficient systemic toxicity by reducing damage to non-canoerous organs. thickening agents hcause they lack the high specific surface In addition, the EPR effect is more effective for macromolecules area and asymmetry of the finer grades. The consistency of ointgreater than 40 kDa but negligible for smaller molecules that are cleared more rapidly from the tumor i n t e r ~ t i t i u m . ~ ~ments . ~ ~ thickened with colloidal silicon dioxide is not a ~ ~ r e c i a b l v reduced at higher temperatures. Incorporation of colloidal silicon These macromolecular coniupates have also demonstrated the dioxide into ointments and pastes, such as those of zinc oxide, potential to overcome drug resistance. The large conjugate can also reduces the syneresis or bleeding of the liquid vehicles. be taken up into cells by endocytosis, bypassin a drug resisColloidal silicon dioxide is also used in dry dosage forms. tance mechanism of deficient drug transportJ This uptake The spherical particles are nonporous and have a density of process may also avoid ATP-driven efflux pumps for the free 2.13 g/cm? However, the bulk density of their powder is a d r u g 1 as well as blmk overexpression of these pumps."2 mere 0.05 glcm? Because the powder is extremely light, it is A doxorubicin-HPMA[N-(2-hydroqpropyl)methacrylamidel frequently used to increase the f l a n e s s or bulk volume of conjugate has h e n studied in phase 1clinical trials. The maxipowder formulations. In addition, the high porosity of colloidal mum tolerated dose of this conjugate is several times higher than silica enables it to absorb a variety of liquids from fluid frathat of the free drug. This observation was ascribed to the EPR grances to viscous tars, transforming them into free-flowing effed" A methotreQate-albumin conjugate was investigated to powders that can h incorporated into tablets or capsules. The overcome the short in uiuo half-life and low tumor accumulation porosity in colloidal silicon dioxide is due entirely to the enorrates of the free drug in phase I and I1 clinical trials in Germous void mace between the ~articles.which themselves are many.rj4-m A camptothecin PEG conjugate has been evaluated in solid. when k e s e u l t r a h e p&cles are incorporated at levels a phase lI clinical trial.MOther macromolecular drug conjugates as low as 0.1-0.5% into a powder consisting of coarse particles under investigation include ampolfistyrene-co-maleicacid-halfor granules, they coat the surface of the granules and act as n-buty1ate)-conjugatedne~arzinostatin,"~ dextran-mitomycin tiny ball bearings and spacers. This improves the flowability C,ljs and gelatin-methotrexateT9 of the powder and eliminates caking, which is important in tableting. In addition. colloidal silicon dioxide is used to improve tailet disintegration. I t is also used as a glidant and as Exapients a moisture absorber. Most of the excipients, adjuvants or non-therapeutic ingredients Microcrystalline cellulose is manufactured by controlled hyof dosage forms listed helow are monographs in the NF or USP. drolysis of purified native cellulose, which dissolves the amor1 1

0

"

318

PART 2: PHARMACEUTICS

12. Schntt 11. Mnrtin AN. I n Dittcrt LW: cd, rlrnrr~c~urt Plrc~rrnc~c:~, 7th rd. Philndrlphin: .JB Lippincntt, 1974. 12. Prnvdcr T: cd. Portlc.lr S I I PI11str1hrltlort I I I ~ s s ~ ~ (~rtci s s ~I'hc~r(~c,J ~ P ~ ~ ~ trr~zcltlort:ACS S~rmpnsiunlS r r i c s 472: llmcricnn Chrmicnl Sncictj~: Wnshinfitnn, DC: 199 1. 14. Rnss D J ~c: t nl. d I1o11~11(i Irrtvrfe~(,r, S ~ .1978; I (j4:S:i:i nnd 1980; 76:478. 15. Mnrnwctz 11. :Vlnc~rt)rnol~~c~~~lt~s Irt Solrltlort: 2nd rd. N r w Ynrk: WilryIntcrscirncr: 1975. l(i. Vcis 11. T k :l.ioc~romolrc~~~lc~r I'hurnlstn. of I:rlc~t~rt. Nrw Ynrk: 11cndrnlic, lY(i4. 17. Wnrd AG. Cnurts 11. cds. Thp Se~~(,rtc~v c~rtdTvc~/~,r~ology of I:r,lc~t~rt. Chnp (i. N r w Ynrk: Acndcnlic Press: 1977. 18. P n r k s G J ~I'hprn . Krf!lY(i5; ( i 5 : l i i . 19. Schntt 11. .I Phorrn S ( , I1977; (j(j:1548. such as oir~,minr~~31 h,.~droriclvpvI, air~,minr~,m phospha tv pvI, and 20. Snnntnji 11: Strrnjic K. ('c)e~grrlot~or~ clrtd Atel h11lt? o f I ) I S ~ PA?s~S(, n~agntbsir~m~ h.vclroxicle~collsist of coarse floes produced by the trrns. N r w Ynrk: IInlstcnd, 1972. agglomeratiol~of colloidal particles formed in the initial stage 21. IIuntcr R.J. %(,toPotrrttlol ~ r ('01101(i t Sc,~prte,(,. New Ynrk: llcndrmic al areas, of precipitation. 'I'hey possess large i n t e r ~ ~ surface Prcss, 1981. 22. Dnl-irs ,IT, Ridcnl EK. Irrtc,rfoc,lcll Phrrtc)rnurtc~,2nd rd. N r w Ynrk: which is one of the reasons why t h e first two are used as subAcndrnlic Prrss: lI)(i:i. strates for adsorbed vaccines and toxoids . Alr~mina o nd n~agn,e~23. Birr M. cd. ISlpc,trt)r)horc,s,s.vnls I nnd 11. New I'nrk: ~lcndrnlic.1959 sia oral sr~,spebnsions,a mixture of gelatu~ousprecipitated alunnd lY(j7. minum a n d m a e l ~ e s i u mhvdroxides. as well a s a l u m i l ~ u m 24. Shnw D.J. ISlpc,trt)nlrorc,s~s. New Ynrk: ~1cndrmic.1969. hydroxide gel, are used as antacids 25. Pr~rnrrort I'oplllnry ISluc.trophorr,sls: vnls I-VII. Fullrrtnn, CA: Ge~latronis used to mal~ufacturethe followil~gsuppository Brcknlnn Instrunlrnts. 1YY:i-1995. bases glycerinated gelatin suppositories, glycerin supposito3;. Cnnlillcri P. I'clplllon. ISlre~trophorc~s~s: 2"" cd. Bncn Rntnn, FL: CRC ries (in which glycerin is solidified with sodium stearate t h a t Prcss, 1998. 27. Lnchnlnn L: Liclcrmnn ILI: Knniji ,JL. Thr Thror?.ortd hoc,t~c,r of crystallizes out as a network of needles up011 coolil~gthe hot soIrr~irrstr~cll I'/rx~rrnoc:~. :I"' rd. Philndrlphin: Len $ Fchijirr. 1Yifi. lution), a n d polyethylene glycol suppositories (in which low 28. O v r r l c c k ,JThG. rlciv ( ' ~ l l o l dIrtt~rfc~c,(, S ~ ,1982; I 15:251. molecular-weight liquid PEGS, such as PEG 400, a r e stiffened 29. LnhIcr VK: D i n r ~ RII. r .I rlrn I'hrrn Sot, 1950; 72:4847. by high molecular-weight P E G such a s 3350 or 4000, which :In. Mntijrvic E. r1e.c.I'hrrn Krs 1981; 14:22 nnd ~lrrr'KPI!:Vl(~tt,r.Sc~~ 1985; are waxy solids) h pharmaceutical application of gelation in a 15:48:i. l ~ o l ~ a q u e medium o ~ ~ s is the mal~ufactureof Plastrbase~or J(~le~ne~ 31. Schick M,J: rd. :Vorrlortlc. Srlrfi~c~torrts-P/~ys~c~c~l I'hprn 1 s t ~ New . (Syurbb),which is prepared using 5 5 of a low-molecular-weigl~t Ynrk: Drkkcr: 1987. polyethylene a n d 9 5 5 of mineral oil 'I'l~epolymer is soluble in 32. Vincrnt B. ~ l d I101l~11ci v Irttprf(~c,r, .%I 1974; 4:lY:I. :i:i. Schntt 11. d Phornm Se.1 1980; (jY:852. mineral oil above 90'C, which is close to its melting point 34. Shinndn K: N n k n ~ w nT: Tnnlnnlushi B-I: Iscnlurn T. I'c)llo~dolSrrrWhen the solutiol~is cooled below 90'U. the nolvmer nrecinifoc,torrts. New Ynrk: Acndrnlic Prcss: l W i . tates and causes gelati011 The mineral oil is immobilized in the 35. httwnnd D. Flnrrncr 11T. Srrrfoe,tclrrtS~stroms.Lnndnn: Chnpnlnn $ network of entangled, adhering, il~solublepolyethylene chains, I I d l : 198:i. which probably eve11 associate into small crystallu~eregions :Gj. Rnscn M,J. Srlrfoc,tc~rttsc1rtd Irrtc,rfi~c,~ol Phurtornrrto. 2nd rd. New Cnlike petrolatum, this gel call be heated to about 60' C withYnrk: Wile>;, 1 9 h . out any substantial loss in consistency 37. Mukrrjcc P: M~rsclsK.J. I'r~tlc.ol:l.l~c~rllr I'c)rr~~vrttrot~orrs of A(~rluorls Crosnovidone a n d croscarmellose sodium a r e crosslil~ked Srlrfc~e,tclrtt .S?stt,rns, NSRDS-NBS :Hi. Washinfiton DC: Nntl B u r Std: 1I)il. povidone a n d carboxymethylcellulose sodium, respectively :is. Shinndn K. cd. .Sol~!rrrtPrortln~rtlusof Solrrt~orts.New Ynrk: 'I'hese crosslil~kedpolymers swell rapidly a n d extensively in . Srlsfoc,tc~rtt . Drkkcr, l k i . aqueous media and, therefore, are frequently used a s tablet dis:1Y. Bnurrrl M. Schcchtcr RS. :l.l~c~roprnrrls~orts clrtd K p l < ~ t S ~ dT S ~ P I J ~ S . integrants Starch performs t h e same function, its major eonNrw ~ n r k : ' ~ r k k c1988. r: stituent, amylogectin. is highly branched and il~solublein wa40. Snlnns C: Kunirdn 11. rds. Irrdrlstrlol rlppl~c~ot~orrs of :l.I~c,ro~r~~rllt e r but swells considerably Because crosslinked hydrophilie slorts. New Ynrk: Drkkcr: 1996. polymers swell extensively without dissolution, they are also 41. Schntt 11. In: Grnnnrn AR: cd. Kurnl rr,gtc)rt:Tht, Sc,~rrtc,v clrtd Prclc,tlc,r used a s matrices for controlled-release dosage forms of Phorrnoc:~. 19"' cd, Chnp 20. Enstnn: Mnck: 1995. 42. Ruckcnstcin E. I'hrrn P/tys I,utt 1978; 57:517 nnd .I ('01101ci Irtft,rfi~e,~ 51 1978; (3;::i(iI). 42. K r c u t r r .J: rd. I'ollo~dolIlrrlg Ilpll l ! p S?strrns. ~ Nrw Ynrk: Dckkrr: REFERENCES 1994. 1. L~rklcmn.J. Frlrrdornr,rrtc~lsof Irttrrfoc,r clrtci ('ollold S ~ , rre,v: I Y vnls 44. Rnsnff M: rd. l'r~s~c~lrs. New Ynrk: Drkkcr: 1996. 1-111. Snn Dirjin: Acndrnlic Press: 1YY:C2000. 45. Owunwnnnc A: Pntrl M: S n d r k S. T/ri, Horrxihook of Kr~d~ophc~rrnc~2. I I u n t r r R,J. F~)rrrtdot~orts o f I1~1l1~11ci .Sc~~(,rtc~(v: vnls I nnd 11. Oxfnrd: c,rrltlc,nls.Lnndnn: Chnpmnn $ IInll, 1995. Clnrrndnn Prrss: 1987 nnd 1991. 4(i. B u r p s s D.J: 1Iickc~;A.J.I n Swnrlrick ,J: Bnjdnn ,JC: cd. ISrrt,c~loprd~o :I. E v r r c t t DII. K(lslc. Pr~rtc,~plus of I3oll{)leiS ~ , I P I ~ Lnndnn: ~ , P . : Rnj~nlSnc of Phnrrnoc~rrrt~c~d 75,c~hrtolog,~, 2"" rd. Nrw Ynrk: Drkkcr: 2002. C h r m , 1988. 47. Putnnnl D: Knpncrk .J. rldv Polyrn 5 1 1995; 12255. 4. vnn Wcimnrn PP. I n Alcxnndcr .J: cd. ('01101d ('hvr~m~str?.: vnl I. New 48. Mncdn 11: Wu ,J: Snwn T: hlntsunlurn Y: IInri K. .I I'c)rrtrt)lKrl 2000; Ynrk: Chrnlicnl Cntnlnji Cn [ R c i n h n l d ~ 1Y2(j. : S r r nlsn I'hprn KPI! (j5:271. 1926; 2217. 41). , J n n ~SII. Wirntjrs MG, Lu D: 11u .JL-S. P/r,epending on the densities o i the disperse and continuous phases. This is undesirable in a pharmaceutical product where homogeneity is essential for the administration of the correct and uniform dose. Furthermore, creaming, or sedimentation, brings the particles closer together and may facilitate the more serious problem of coalescence. The rate at which a spherical droplet or particle sediments in a liquid is governed by Stokes' law (Equation 3). Other equations have been developed for bulk systems, but Stokes' equation is still useful because it points out the factors that influence the rate of sedimentation or creaming. These are the diameter of the suspended droplets, the viscosity of the suspending medium, and the difference in densities between the dispersed phase and the dispersion medium. Usually, only the use of the first two factors is feasible in affecting creaming or sedimentation. Reduction of particle size contributes greatly toward overcoming or minimizing creaming, because the rate of movement is a square-root function of the particle diameter. There are, however, technical difficulties in reducing the diameter of droplets to hlow about 0.1 pm. The most frequently used approach is to raise the visoosity of the continuous phase, although this can be done only to the extent that the emulsion still can h removed readily from its container and spread or administered conveniently. AGGREGATION AND COALESCENCE-Even though " creaming and sedimentation are undesirable, they do not necessarily result in the breakdown of the emulsion, as the dispersed droplets retain their individuality. Furthermore, the droplets can be redispersed with mild agitation. More serious to the stability of an emulsion are the processes of aggregation and code scence. In aggregation (flocculation) the dispersed droplets come together but do not fuse. Coalescence, the com-

335

plete fusion of droplets, leads to a decrease in the number of droplets and the ultimate separation of the two immiscible phases. Aggregation precedes coalescence in emulsions; however, coalescence does not necessarily follow from aggregation. Aggregation is, to some extent, reversible. Although it is not as serious as coalescence, it will accelerate creaming or sedimentation, because the aggregate behaves as a single drop. Aggregation is related to the electrical potential on the droplets, but malescence depends on the structural properties of the interfacial film. As discussed previously, it has been recognized that combinations of emulsifiers produce more stable emulsions than a single emulszer alone. One reason for this

synergy, as suggested by Shulman and Cockbain, is that appropriate combinations of surhctants form densely packed complex flms at the oil-water interface. Additional beneficial effects of mixed emulszer flms could result from an increase in viscosity of the interfacial emulsifier film. A viscous interfacial film could enhance emulsion stability because thinning of the film at the points of droplet to droplet contact would h inhibited. An additional explanation for the hneficial effect of mixed-film emulsifiers suggests that appropriate mixtures of surfactants provide a more elastic interfacial film. A more elastic interfacial film would resist r u ~ t u r euwn collision of emulsion dro~lets. It ha; also h e n observed that when ekulsifiers are combined in certain concentrations and proportions, liquid crystalline phases can be formed. The preparation of emulsions with surfactants that form liquid crystalline states can have greater stability against coalescence compared to emulsions that are formulated in the absence of liquid crystalline states. Friberg and Larsonz have explained the enhanced stability of emulsions due to liauid crvstals in terms of a reduced van der Wads attraction beiween lmulsion droplets. Such an effect depends upon the formation of layers or lamellae around the emulsion droplets. Each layer of liquid crystal contributes to a further reduction in the van der Wads attractive force. An additional effect of liquid crystals may be related to the high visoosity that often is observed upon their formation. Liquid crystals possess a visoosity that is on the order of 100-fold greater than most oil-water interfaces. The high viscosity may result in reduced rates of coalescence. A key factor that may he important for the stabilizing effect of liquid crystals is the location of the liquid crystalline phase in relation to the dispersed droplets. To effectively inhibit coalescence, the liquid crystals should concentrate a t the interface between the droplet and the continuous phase. This may not wcw with all oil-water-surfactant combinations. Particle-size analysis can reveal the tendency of an emulsion to aggregate and coalesce long before any visible signs of instability are apparent. The methods available have been reviewed by Groves and F r e ~ h w a t e r . ~ ~ INVERSION-An emulsion is said to invert when it changes from an O/W to a WIO emulsion, or vice versa. Inversion sometimes can h brought about by the addition of an electrolyte or by changing the phase-volume ratio. For example, an O/W emulsion having d i u m stearate as the emulsifier can h inverted bv the addition of calcium chloride. hecause the calcium stearate formed is a lipophilic emulsifier and favors the formation of a WIO prduct. Inversion often can h seen when an emulsion, prepared by heating and mixing the two phases, is being cooled. This takes place presumably because of the temperature-dependent changes in the solubilities of the emulsifjhg agents. The phase inversion temperature (PIT) of nonionic surfactants has been shown by S h i n d a and KuniedaZsto be influenced by the HLB numher of the s u r f a c t a n t t h e higher the PIT value, the greater the resistance to inversion. Apart from work on PIT values, little quantitative work has been carried out on the process of inversion; nevertheless, it would appear that the effect can be minimized by using the proper emulsifjhg agent in an adequate concentration. Wherever possible, the volume of the dispersed phase should not exceed 50% of the total volume of the emulsion.

336

PART 2: PHARMACEUTICS

BlOAVAlLABlLlTY FROM COARSE DISPERSIONS All dosage forms must h capable of releasing the drug in a known and consistent manner following administration to the patient. Both the rate and extent of release are important. Ideally, the extent of release should approach loo%,while the rate of release should reflect the desired properties of the dosage form. For example, with products designed to have a rapid onset of activity, the release of drug should be immediate. With a long-acting prduct, the release should take place

over several hours or days, depending on the type of prduct

pensions to gain information as to the bioavailability of drugs from this type of dosage form. The viscosity of the vehicle used to suspend the particles has h e n found to have an effect on the rate of absorption of nitrofurantoin but not the total bioavailability. Thus Swi and Parrottm were able to maintain a clinically acceptable urinary nitrofurantoin concentration for an additional 2 hr by increasing the viscosity of the vehicle. BIOAVAILABIIXI'Y FROM EMULSIONSThere are indications that improved bioavailability may result when a poorly absorhd drug is formulated as an orally administered emulsion. However, little research appears to have h e n done to directly compare emulsions and other dosage forms such as suspensions, tablets, and capsules; thus, it is not possible to draw uneqUivCiCd con~l~Si0nS as advantages of emulsions. If a drug with low aqueous solubility can be formulated So as to in solution in the oil phase of an emulsion, its bioavailability may be e ~ h a ~I t~must d - be recognized, however, that the drug in such a system has several barriers to pass bfore it arfives at the mucosal surfam of the GI tractFor example, with an OIW emulsion, the drug must diffuse through the oil globule and then pass across the oil-water interface- This may be a difficult p r m s s , depending on the characteristics of the interfacial film formed by the e m u l s i ~ n g agent. In spite of this potential drawback, Wagner et als" found that indoxole, a nonsteroidal anti-idammatory agent, wassignificantly more bioavailable in an O/W emulsion than in either a Or a hard gelatin Bates and Sequeiras7 found significant increases in maximum plasma levels and total bioavailability of micronized griseofulvin when in a corn WI' emulsion- In this case, however, the enhanced effect was not due to emulsification of the drug in the phase per se, but more probably hcause of the linoleic and oleic acids present having a specific effect On G1motility-

used. The rate and extent of drug release should k reproducible from batch to batch of the product, and should not change during shelf-life. The on which biopharmaoeutics is based are dealt with in some detail in Chapters 57 to 59. Although published work in this area has been concerned with the bioavailability of solid dosage forms administered by the oral the rate and of release from both suspensions and emulsions are also import ant and so must be considered in some detail. BIOAVAILABILITY FROM SUSPENSIONSSuspensions of a drug may be expected to demonstrate improved bioavailability to the same drug formulated as a the suspension already contablet or capsule. This is hause t i n s discrete drug particles, whereas tablet dosage forms must invariably undergo disintegration in order to maximize the necessary dissolution process. Frequently, antacid suspensions are as k i n g more rapid in action and therefore more effective than an equivalent dose in the form of tablets. Bates et a129 observed that a suspension of salicylamide was more rapidly bioavailable, at least during the first hour following administration, than two different tablet forms of the drug; this study was also able to demonstrate a correlation k t w e e n the initial in vitro dissolution rates for the several dosage forms studied and the initial rates of in viva absorption. A similar argument can be developed for hard gelatin capsules, where the shell must rupture or dissolve hfore drug particles are released and can b g i n the dissolution REFERENCES prmess. Such was observed by Antal e t also in a study of the 1. Hiestand EN. J P h ~ r mSci 1964; 63:1. bioavailabili ty of several doxycycline products, including a 2. Haines BA, Martin A. J Pharm Sci 1961; 60:228,763,766. suspension and hard gelatin capsules. sansom et a181 found 3. Matthews BA, Rhodes CT. J Pharm Pharmaml 1968; XO(Supp1): that mean plasma phenytoin levels were higher aRer the ad204s. ministration of a suspension than when an equivalent dose 4. Matthews BA, Rhdes m. J pharm sci 1968; 67:669. was given as either tablets or capsules. I t was suggested that 6. Matthews BA, ~ h CT.Jd Pharm ~ sci 1970; 69:621. this might have h e n due to the suspension having a smaller 6. Schneider W et al. Am J Pharm Ed 1978; 42:280. particle size. 7. Scheer M.Drug Cosmet Ind 1981; (Apr):40. 8. Kellaway LW, NGib NM. Int J Pharm 1981; 9:69. In common with other prducts in which the drug is present 9. Martin AN et al. P h y s h l Pharmaq, 3rd d.Philadelphia: ~ e &a in the form of solid particles, the rate of dissolution, and thus Febiger, 1983, p 661. potentially the bioavailability of the drug in a suspension, can GE et al. Int Pharm 1992; 83: 163. te affected by such factors as particle size and shape, surface 114 et PhQrm Sci 1973; 62:1361. characteristics, and P ~ ~ YStrum ~ et~ ~conducted P ~ a ~ 12.~Eocleston ~ -GM. In Encyclopedia of Pharnaace titical Technology, vol6. comparative bioavailability study involving two commercial New York: Dekker, 1992, p 137. brands of sulfamethiazole suspension (Prduct A and Prduct 13. Davies JT.In: Proceedings of the International Congress on Surface Acf vity, 2nd 4.London: ButterworthlAcademic, 1967, p 426. B). Following administration of the prducts to 12 normal indi14. Sherman P. In: Emulsion Science. New York: Academic Press, 1968, viduals and blood samples taken at times over a Chap 4. p e r i d of 10 hr, the Strum study found no statistically signifi16. Rogers JA. Cosmet Toiletrks 1978; 93(7):29. cant diff in the extent of drug absorption from the two 16. Griffin WC. J Soc Cosmet Chem 1949; 1:311. suspensions. The absorption rate, however, differed, and from 17. ~ * fW,-. i ~J sot cosnaet ,-hem 1964; 6:249. in vitro studies it was concluded that prduct A dissolved faster 18. D a ~ e sJT, ~ j d EK ~ dIntel)rQcia[Phenomena. ~e~ york: Academic than Prduct B, and that the former contained more particles Press,196 1, Chap 8. 19. Schott J. J Pharm Sci 1971; 60:649. of smaller size than the latter, differences that may h respon20. Swarbrick J. J SOCCosmet Chem 1968; 19:187. sible for the more rapid dissolution of particles in h d u & A. 21. Garrett EB J PhQrm Sci 1966; 60:1667. h d u c t A also provided higher serum levels during in vivo 22. Kitchener JA, Mussellwhite PR In: Emulsion Science. New York: tests 0.5 hr hradministration. me results showed that the Academic Press, 1968, Chap 2. rate of of sulfamethiazole o ' m a sus~ensionde23. W4derbum DL. In: Advances in PhaFmaceua*ml Sciences, vo] 1. pended on the rate of dissolution of the suspended particles, London: Academic Press, 1964, p 196. which in turn was related to particle size. Previous s t u d i e s S 3 ~ ~ 24. Burt BW. J Soc Cosmet Chem 1966; 16:466. had shown the need to determine the dissolution rate of sus26. Eocleston GM. Cosmet Toilet~ies1986; 101(11):73.

CHAPTER 22: COARSE DISPERSIONS

26. Friberg S, Lmmn K In: Brown GH, ed.Advances in Liquid Crysbds, vol2. New York Academic W,1976, p 173. 27. Grove& MJ, Freshwater DC.J P h w m S d 1968,67:1273. 28. Shin& 4 Kunieda H. In. Encyclopedia of Emlsion Techndogy. New York Dekker, 1983, Chap 5. 29. Bat= TR et al. J P h m S d 1969; 581468. 30. Antal E J et al. J Pharm Sci 1975; W.2015. 31. W r n LN et al. Med J Aust 1976; 2:593. 32. Stnun JD et al. J P h w m S d 1978; 67:1669. 33. Bat- TR et al. J P h w m S d 1973; 62:2057. 34. Howard SA et al. J P h w m Sci 1977; BB.667. 36. S& MM, Parrott EL. J Phwm Sci 1980,69403. 36. Wagner J G et al. Clin P h a m d Thw 1 W , 7:610. 37. Bate8 TR,Sequeira JA. J P h m S d 1976; 64:793.

Adamson AW. Physical Chemism of Surfaces, 4th ed. New York WileyIntereeience, 1980.

337

A t t w o d D, Florence AT. In: Surfractant Systems; Their Chemistry, P h w m c y and Bwlogv. London: Chapman & Hall, 1983, p 469. Becher P. E m b w n s : Theorv and Practice. 2nd ed. New York Reinbold. 1966. Becher P. Encyclopedia of E m b w n Technology, vols 13. New York I h k . 1983-1988. Davis JT;Rideal EK. Interfmial Phenomena. New York Academic %, 1963. E d e s t o n GM. In. Encyclopedia of Phwmaceutical Techndogv, vol6. New York DeHHer, 1992, p 137. Hiemenz PC. fiinciples of Cdloidd and Surface Chemistry, 2nd ed. New York D h , 1986. Matijevic E, ed. Surfrace and Colloid Science, wls 14.New York Wiley, 1971. O&pw U.SurfraceChemistry. New York Reinhold, 1962. Par6tt G. Dispei-swn ofPowders in Liquids. New York Applied Science, 1973. Sherman P. Emulsion S&nce. New York Academic W,1964. Sherman P. Rheology of Emul&m. New York Macmillan, 1963. Vold RD,Vold MJ. Colloid and Interfuce Chemi&y. Reading MA. Addimu-Wdey, 1983.

Itheology is t h e branch of physics t h a t deals with deformation, includingflow, ofmatter rilthougl~this defil~itiol~ was pruposed in 1929, t h e recognition of r~~eological phenomena dates back to antiquity ' The earliest applicatiol~of rheolog?: (ca 1600 UCE) is associated with t h e E e p t i a n rimenemhet who made a 7' correction to the drainage angle of a water clock in order to account for the temperature dependent variation in water flow during the course of a day Archimedes's claim (co 250 UCE&"'C;ive me but one firm spot on which to stand, and 1 will move the earth "-was based on the annlication of solid mechanics. the oldest branch of the physical sciences ' Iteiner' describes a simple mechanical experiment 111 which he lets three different materials-a pencil, a ball of plasticine, and a known mass ofwater-fall from some height onto the surface of a table Yewton's second law tells us t h a t F- 111 a. where F is the force acting- LIPOH each of these materials of mass n7, and a is t h e acceleration of the center of mass of each material S u ~ c eF is pruportiollal to n7. a is t h e same for each of these materials Conseauentlv. these three bodies fall towards t h e table in exactly the same manner Their material differences do not become apparent until they reach the table top rit that point, the pencil rebounds somewhat, the plasticine stays put, and the water spreads over the tabletop and, on reaching t h e edge, fluws off These v e y different outcomes-which mechanics is unable to explain-are the focus of rheology The ubiquity of rl~eologicalphenomena in pharmacy is e v dent 111 t h e levig-ation or mixing of ointments on slabs, t h e use of a mortar and pestle to prepare s u s p e l ~ s i o ~and ~ s emulsions, the flow of emulsions through colloid mills and pumps. the use of roller mills for compacting powders or processing ointments, and the mechanical properties of glass or plastic containers and of rubber or polymeric closures Squeezing ointments. creams, ur toothpaste from a collapsible tube, spreading- loti011 on the skin, or spraying liquids from atomizers ur aerosol cans all involve rl~eoloeicalnhenomena 'rhe fluiditv of solutiolls to be injected by syringe or infused intravenously, t h e flexibility of tubing used in catheters, and t h e strength of sutures and ligatures are important rl~eologicalproperties Drug release from dosage forms and delivery systems is often col~trolledor modulated by the rl~eologicalproperties of t h e formulatiol~matrix Although at a molecular level, diffusion is governed. in part. by t h e rheological behavior of the environment Itl~eolo$calprillciples g-overn the circulatiol~ofblood and lymph through capillaries and large vessels, the flow of mucus, t h e transit of the lumillal contents through the gastrointestinal tract, the bending of bunes, the stretching of cartilage, and the cvntraction of muscles The fundamentals of rheology are presented in the followingseeti011 in the sequence t h a t underscores their temporal recognition and applicatiol~in pharmacy rather t h a n their historic development in physics L L

L.

FUNDAMENTALS The jargon of rheology can be problematic for the uninitiated For example, a s Scott Blair1 notes, strcss and sfrarn, in everyday English, have virtually t h e same meaning Itheologists, however, use t h e word sfrcss to refer to a system of forces, ~ s s r r ~ ~ ~ or , shcol- mode, whether applied in a c o ~ ~ ~ p r ~ cxfcnsronol. and sfmrn, to a change in size or shape Itl~eologicalprinciples stem from two fundamental laws derived in the late 17th century Itobert IIooke's law vf elasticity (eo 1676) and lsaac Yewton's law of flow (1687) The corresponding equations, which embody these laws, characterize IIookean and Yewtonian materials, respectively When a force is applied to a body, the two r~~eological extremes of behavior are t h e pure elastic deformatiol~of a IIookean solid and the pure viscous flow of a Yewtonian liquid Pure (ideal) elasticity means t h a t t h e body returns to its origulal form once the stress is remuved, while pure (ideal) viscosity means that t h e liquid flows even under the smallest stress and does not return to its original shape or form once the stress is removed" The resistance to deformation, or flow, is described by the modulus of elasticity ur Young's modulus. E , for an elastic body undergoing extension, and by T, the coeficiel~tof viscosity for a liquid Elastic deformation of solids is described by IIooke's law,

where d l is t h e elastic deformation ur extension in length I caused by t h e applicatiol~of stress rr 'rhis is illustrated in Figure 23-1 Viscous deformation. i e viscous flow, occurs in accorda~~ce with Yewton's law,

k

wherein the applied stress rr results in flow with a velocity gradient, u or rate uf s h e a r T h e proportionality constant is termed r~rscosrfy,while its reciprocal is calledflurdrfy. Viscosity h a s also been described as the rnft~malfrrcfron in the fluid as it correspol~dsto the resistance of the fluid to t h e relative motiol~ of adjacel~tlayers of liquid This is illustrated in Figure 23-2 lmagine a liquid contau~edbetween two very large, parallel plates a s being divided into a stack of very thin, parallel layers much like a deck of cards. as shown in Figure 23-2 Shear is applied to the liquid by pulling or pushing- the top plate with a constant force F per unit area A. ie F/A. or rr. while holdingthe bottom plate s t a t i o n a y The top liquid layer, in contact with the moving plate, adheres to it and moves with the same velocity as t h e plate 'rhe secund layer, adjacent to the top one, is dragged

CHAPTER 23: RHEOLOGY

339

Table 23-1. Approximate Shear Rates for PharmaceuticalOperations

C

o

c

EkmnatJon

R

Figure 23-1. Elastic deformation in accordance with Hwke's Law.

along by friction, but its velocity is r e d u d somewhat by the resistanceofthelayersbneathit.Eachlayerispulledforwardby the layer moving a b v e it but is held back by the layer underneath it, over which it moves and which it drags along. The farther the liquid layers sl.e from the moving plate, the smaller their vehities. The b t t o m layer adheres to the stationary plate and has zero velocity. ~ h - , the velocity of the liquid layers hmases in the d s o n x perpendicular to the direction of flow y. The shear strain or deformation in shear, -y, is the displacement y divided by the height, X, of the or deform4 portion of the liquid, as shown in Figure 23-2. I t equals the tangent of the displacement angle 0 that, a t low 0 values, is approximately equal to 0 expressed radians: = Z = tm 0 x = 0. In due time, all layers except the bttom one undergo finite deformation.What distinguishes one liquid from another is the rate at which the deformation increases with time- Tb is

OPERATDN

RATE OF SHEAk SF1

Pouring from a bottle Spreading lotion on skin Levigating ointment on slab with spatula Injecting through hypodermic syringe Dispensing nasal spray from plastic squeeze bottle Processing in colloid mill

50 400-1000 400-1000 4,000 20,000 l0~-10~

shearing stress, T, have l m n replaced by +? and cr, wpectively, in acoordance with more widely ampted nomenclature r m m mendati0ns.8,~ Characteristic shear r a h for pharmacy-related activities are listed in Table 23-1. Even for a given prmms, the shear rate can vary within wide limits, depending on the scale of the pmoess and the processing rate. Thus, when a lotion is rubbed into the skin, if the hand (moving surface) slides across the skin (stationary surface) with a velocity v = 45 cm/s and if the thickness of the lotion film is x = 0.05 cm, then, awarding to Equation 3, the rate of shear is +? = (45 cm/sY(0.05 cm) = 900 8-l. For a given form and a oonstant vis&ty, the rate of shear is uni-

formthrou&outthela~eroflotion. The flow of liquids by parallel layers moving past each other and dragging adjsent layers along (a8 in Fig 23-21 is called laminar or streamline flow. At higher velocities andlor if the plates h a w rough surfaces, eddies Or swirls develop whereby mass transfer m r s h m one layer or lamina to another. Theoretically, this complex phenomenon-refed to as turbulent flow-may b describd by a set of p@tid differential Wuati0n8, known as the Navier-Stoke8 equations, which govern fluids in motion. However, explicit solutions of these nonlinear ~ u a t i o n s originally , derived in the 1840s On the basis of laws of c o n ~ m a t i o nof mass, momentum, and energy, remain elusive. From a historic rheological viewpoint, deformation of matter waS in ideal terms. differentiations were made among perfect, rigid Euclidean bodies (solids), ideal Hookean elmtic solids, PasCalian,or in*cid, liquids, and Newtonian liquids. For ideal Euclidean mlids, only maM (or density) is relevant; rigid bdies do not undergo deformation under stress. When stress is applied to an ideal Hmkean elastic solid, the deformation indud is recoveredwhen the is re moved. Inviscid liquids exhibit no resistance to flow when stre~sed,whereas Newtonian liquids undergo flow at a rate that is proportional to the stapplied. Unfortunately, most solids and fluids encountered in pharmacy do not exhibit ideal behavior oonsistent with the classical models that evolved with Hooke, Pascal, or Newton. By the 19th century, evidence for more complex, nonided rheological bhavior b g a n to accumulate and the clear-cut dividing line htween Hookan Or elastic solid8 and Newtonian or v j g ~ ~ u s liquids h a m e inmasingly b l u d . Some system that bhave as elastic solids when subjected to small stresses, or tO mcderate stre8ses of short duration, will undergo permanent deformation, wembling very visoous liquids, if the stresses are larger andlor applied for longer periods of time. For many materials, the temporal dependence of their rheological properties neoessitates careful oonsideration of their handling prior to and during the prmess of rheological evaluation. Nonetheless, an understanding of ideal rheological behavior is n e w my b fore deviations h m ideality can IE considered.

~the $ ~ ~ ~ ~ ~ zg$Js t ~ f zzg dthe e !d,":;~:; f ~ ~ ~ ~ rate at velocity gradient, ie, the which velMity, v, changes with the diskam, x, perpendicular to the direction of flow:

dr

dv

?=dt=dx The rate of shear or velmity gradient, .i. indicates how fast the liquid flows when a shear stress is applied to it. Its unit acwrding to b t h definitions is s-l, since Y is dimensionlw, velccity is expressed in mlsec, and x in m. It should be noted that the symbols used in the past in the pharmaceutical literature for the rate of shear, D, and for the

v

Elastic Solids Figure 2 1 2 . Laminar flow of a liquid contained between two parallel plates.

In the stretching or extension of an elastic solid, the deformation is said to IX in tension. The deformation or strain of the strekhed b d y , or its elongation, is the difference between i h

340

PART 2: PHARMACEUTICS

Table 23-2. Values of Mdulus of Elasticity"of Representative Solids of Pharmaceuticalor Biomedical Interest YOUNG5 MODU WS (DYNEvcM3

MATERlAL

2.2 x 10l2

Steel Glass Potassium chloride Silk, viscose rayon Microcrystalline cellulose Polystyrene Polyethylene (low density)

6x 2.3 x 1.5 x 1.3 x 3.4 x 2.4 x

10'' 10" 10'' 10" 1O1O

lo9

is called permanent set. Many materials undergoing such "mld

2 x lo7

Rubber (vulcanized)

4.7 x 10''

Tooth enamel Bone Tendon Muscle Soft tissue Gelatin gels 10% solids 20% solids 30% solids

2.2 x 10" 1.3 x lo9 6 x lo6 7.5 x 104 2.4

law of proportionality btween stress and strain is obeyed throughout the linear portion OL. The elastic mdulus of the solid is the slope of OL or the tangent of the angle LOC. The material hehaves elastically up to the yield point Y , where the stress is called yield stress. When stresses helow the yield stress are applied to the sample and then released, it stretches and contracts along the same curve OLY. Beyond Y , the material bhaves as aplastic, rather than as an elastic solid. Along the (nearly) horizontal portion YAH, the material is ductile; it flows or creeps under practically constant stress like a viscous liquid. If the stress is released at A, the sample retracts along AC. The nonrecoverable deformation 0 C

x lo5

1.0 x 106 1.5 x 106

*At room temperature.

length while under tension, 1, and its original length, 1, which is equal to the length ahr the stress is expressed as a fraction of the original length, namely, - 1) 11. Other m d e s of deformation are by hending or flexure, torsion, compression and shear. For an ideal elastic solid, Hooke's law (Equation 1) states that the stress is directly p r o p o ~ o n a to l the strain. This relationship is obyed by real solids a t mcderate stresses and strains sustained for short periods of time. The modulus of elasticity or Young's modulus, E, is a measure of the stiffness, hardness, or resistam to elongation. There is also a modulus of shear or rigidity and a compression or bulk mcdulus. Tensile compliance is the reciprmal of Young's mdulus, or the ratio of strain to stress. In the CGS system, the units of stress are dynes/cm2 or, since force = mass X acceleration, (g-cm/sec2X/cm2= g/(cm sec2).To convert dynes/cm2to the SI unit, Newton/m2or Pascal, divide by 10. Since strain is dimensionless, Young's mcdulus has the same dimensions as stress. Mdulus values for a range of solids of pharmaceutical or biomedical interest are listed in Table 23-2. Figure 2 3-3 shows representative stress-strain curves in tension, also called load-elongationcurves. The cross-sectional area, A, of the solid hcomes smaller as it is stretched. Therefore, to calculate the actual or true tensile stresses, the forms are divided by A,, the cross-sectional area at each appropriate elongation. Stress-strain curves oRen are plotted with the strain or extension, the dependent variable, on the abscissa while consistency or flow curves (see blow) usually are plotted with stress, the independent variable, on the abscissa. The practiix followed here is to plot stress on the ordinate for b t h stress-strain and consistency curves, in order to make mdulus and visoosity, respectively, the slopes of these curves. The characteristic portions in the representative stressstrain curve OLYAHB in Figure 23-3 are as follows. Hcmke's

a,

flow" are strengthened by some change in structure, causing an upturn HE in the stress-strain curve. This is called work (or strain) hardening. It may result &om the elimination of flaws, fiom a reduction in crystal size as in the case of metals, or &om reversible crystallization on stretching, as in the case of homo polymer elastomers. At B, the sample ruptures; R is the elongation at the break or the ultimate elongation, and the stress correspondingto B is the ultimate strength or tensile strength. These values, as well as the load-elongation curve heyond Y , depend on the rate at which the sample is stretched. The area OLYAHBRCO under the stress-strain curve is the energy or work required to break or rupture the material- It measures its toughness or brittleness. Glass is hard hecause of its high elastic mcdulus- Owing to the absenm of a yield point and to a very low elongation to break, it is brittle as opposed to steel, which undergces work hardening, has a high elongation to break, and is tough. Plastics are medium-hard or ~ f iThose . that exhibit comparatively high elongations a t break, like polyethylene but unlike polystyrene, are tough- Vulcanized rubhers are tough even though they are soft (low elastic m d u lus) hecause their elongation to break is very high, namely, 600-800%-

Newtonian Fluids The viscosity of simple liquids, ie, pure liquids consisting of small molecules and solutions where solute and solvent are small molecules, depends only on composition, temperature, and pressure. It increases mderately with increasing pressure and markedly with decreasing temperature. For solutions of solid solutes, the viscosity usually increases with conmntration. Simple liquids follow Newton's law (Equation 2) of direct proportionality btween she ar stress and rate of shear, so that their vimsity is independent of the shear stress or the rate of shear. Their flow behavior is thus referred to as Newtonian. Representative Newtonian viscosities are listed in Table 23-3.

Table 23-3. Newtonian Vismities and Activation Enelylies for Viscous Flow4 ACTIVATION ENERGY FORVISCOUS FCOW TEMPERATURE (=c)

Water

20 50 99

0.0100 0.0055 0.0028

4.2 3A 2.8

20 50 20

0.01 20 0.0070 0.0291 0.01 13 0.0024

3.3 3.3 6.8 5.3 1.65

;a

Ethanol Absolute

F

40%wlw

A

B

c

Figure 23-3. Stressstrain curves in tension. Loads or tensile stresses are corrected for actual cross-sectional areas.

VISCOSITY (W KE)

MATERM

Ethyl ether Glycerin Anhydrous 95%wlw

50 20 20 20

aAt 1 atm pressure.

15.00 5.45

(KCALIMOLE)

12.5 t 0.6

CHAPTER 23: RHEOLOGY

341

flow, b t h must be evduated at the same lmation. Using the values at the wall of a cylindrical tube, dividing Equation 5 by Equation 4, and rearranging gives

V - R4AP t

Figure2S4. Larninarflowof a liquid through acylindricalduct. A.Three dimensional view of telescoping layers. B. Cross-section showing radial distribution of wlociiy. C. Cros~sectionshowing radial distribution of velociiy gradient.

flow cylindrical pipesor capil1Sries is lamh=, ie, Newtonian, at low velocities, for smdl tube radii, or for liquids of high vimit~. The liquid layers are very thin cylinders ooncentric with the duct?'. During flow, they telmcope past one another as shown in Figure 23-4.. The arrows in Figure 23-4.E represent the velmity u of the individual cylindrical layers of radius r; v is maximal in the center of the t u b and decreases in the radial direction, ie, in the direction r (previously xj perpendicular to the direction of flow y. The velmity is zero in the outermost liquid layer adjaoent to and adhering to the wall, whose radius is equal to the inside radius of the t u b R. In the center of the tube, where u is maximum, the velmity gradient d u /dr = p is zero. This is shown in Figure 23-4C, where the arrows rep w e n t .3 and the velmity gradient is maximum at the wall. If V is the volume of liquid flowing through a cylindrical t u b of radius R in time t, the volumetric flow rate is V/t, and the shear rate at the wall is 4 = -(V/t) (4)

81q

(6)

This is Poiseuille's law, found experimentally by this French physician while studying the flow of liquids through capillary tubes representative of blood vessels. [The poise is also named in his honor.] In the human b d y , the pumping action of the heart supplies the driving pressure for the flow of blood, which is the difference btween the arterial and venous pwsure. Digitalis g l y w sides increase the form of oontraction of the heart muscle and make the heart a more efficientpump. This increases bP and, hence, the rate of flow of blood V/t. Vawdilator drugs like nitroglycerin or hydralazine hydrochloride increase the radius of blood vessels by relaxing the vascular smooth muscles. Sinoe the flow rate varies with the fourth power of the radius of the blood vessel, a mere 5% increase in radius causes a 22% increase in the flow rate at oonstant blod pressure, because (l.05)4 = 1.22. Plots of shear s t m (on the y-axis)as a function of the rate of shear (on the x-axis) are referred to as flow curves or rheograms. The rheograms of typical Newtonian liquids, like those of Figure 23-5, are straight lines going through the origin. Viscosity is the slope of such a line or the tangent of the angle it makes with the horizontal axis. Of the two liquids shown in Figure 23-5, A has a higher visoosity than B h a u s e ol >p, so that q ~ ( t=a n a ) > q~ (= tan p; qn = ~ & a = crdjl and q~ = crJ?, = U&Z. A given shear stress, crl, produces a greater rate of shear, 93, in the more fluid Liquid B than j l in the more visoous Liquid A. Alternatively, to prduce a given rate of shear, pa, in the two liquids require8 a higher shear stre58, ux,for the more visoous Liquid A than crs for the more fluid Liquid B. In the CGS system, viscosity is d e k e d as the tangential force per unit area, in dynedcma,required to maintain a difference in velmity of 1cm/s between two parallel layers of liquid 1 cm apart. Its unit is therefore dynedcma-see-' or g/cm-s, which is called a poise. Bemme many common liquids including water have visoositie8 of the order of of a poise, their viscosexpmsed in ,-entipoise. In the SI system, the ity is of vi8M)8ity is ~ ~ ~ ~ or Ps9cal a - ,s, ~which - equals 1 Typical Newtonian visoosities are listed in Table 23-3. The variation of visoosity with temperature often is descriM by an Arrhenius equation: q = AeE./RT or I n q = l n A + -E a RT

7rRs The shear stress is zero in the center of the t u b and maximum at the wall: RAP uwaU = (5) 21

The liquid flows through the tube due to pressure, either caused by its own weight (hydrostatic)or p d u o e d by a pump. This pressure exoeeds the innate visoous friction of the liquid and is oonverted into heat. The p w s u r e drop, AF, dong a length I of the tube is the difference between the p w u r e at the bginning and at the end of the t u b . As visoosity is shear stress divided by rate of shear, and as b t h vary in the xdirection perpendicular to the direction of

Figu~e23-5. Rheograms or flow curves of two Newtonian liquids.

342

PART 2 PHARMACEUTICS

where A and E,, are cunstants. T is the absolute temperature and R is the molar gas col~stallt Values of B,,, the at.frr~afrt~n cbn6brg.v for visenus flow, are listed in Table 23-3 Large values of B,, indicate that the viscosity decreases substantially with rising temperature riccording to Equation 7, plots of In -q as a f u n tion of the reciprocal of t h e absolute temperature should be straight lii~eswith slopes of B,, / R . For associated, eg, hydrogen-bonded, liquids such plots are often somewhat curved riceording to Eyring's " h o l ~fhcory," liquids contain vacancies or holes t h a t are essential to flow The activation energy is used largely t u form these holes ' E,, is about 1/3 to 1/4 vf the latent heat of vaporizatiol~for nonassociated liquids

Non-NewtonianFluids Fluids t h a t do not obey Yewton's law (Equation 2) are described as non-Xcrutonran flurcls The r~~eological behavior of non-Yewtonial~fluids may be characterized either as time-rnclcpcnclcnf or time-clcpcnclcnf non-Yewtonian fluids TIME-INDEPENDENT NON-NEWTONIAN FLUIDSB Shtbor-fhrnnrngflurds. Many colloidal systems, especially polyFigure2*7m Three randomly coiled plymer in solution. AmAt mer solutiol~sand flocculated solidAiquid dispersions, become re' ; In shear field. more fluid the faster they are stirred This shebar-fhrnnrng behavior is often referred to as p s ~ ~ u d o ~ ~ l a s f rbut t . r t t~h, e latter term is outdated and potentially misleading Shear-thinning behavior is an example of non-Yewtonian flow because the visin sheaths uf water of hydration Additional water is mechanitemperature a n d c o m p o s i t i o ~is, con. cosity, at cally trapped inside the open coils The coiled macromolecules, stant as required by Yewton's law of viscous flow (Equation 2). 1" constant segmental motion, become entangled (Figure 23but decreases with increasing- shear 11s tile increase in shear 7A) Lpon the applicatiul~ofshear, a unidirectional lamillarmorate is greater thall the illcrease in the corresponding shear tion is superimposed on t h e random thermal motion of t h e wastress, the flow cun,e of yigure 23.6 is collcave toward the t e r molecules and chain segments T h e randomly coiled, shear-rate axis entangled macromolecules tend to disentangle themselves and ,rlere is an apparent viscosity for each value of shear rate or to align tl~emselvesin the direction of flow, as showl~in Figure shear stress, which call be expressed in two differellt ways 23-7B. The viscosity of the solution-its resistance to flow-depuillt p in yigure 23.6, the r+.cosity can be taken as pends on the size and shape of the flow units The imposition of the slupe secallt to the flow at p, ur tall H, which is increasing shear in these systems enables the macromolecule the viscosity of a yeTvtonian liquid whose flow cun,e passes "chains" to uncoil progressively and become streamlined or elonthroudl P, Jrlis is equal to the ratio rrl,/ v,, Jrle secolld method gated, tllereby offerillg less resistallce 10 flow thall the original, defilles the apparel11 viscosity as t h e slope o f t h e tallgellt tothe " ~ ~ ' ~ " i m a t spherical, el~ shapes 111Ithe same time, the amoullt flow curve a t P, ie, drr,, /d ,, - tall S inee both H and 1;less commonly encounted are dilatant fluids for which n < 1.Shear-thinning and dilatant liquids frequently follow this empiricalpower law or (Equation 8) over a wide range of shear rates. OTHER EMPIRICAL EQUATIONS AND M O D E L S Many empirical equations and models have been developed b flow behavior of nonover the years in an effort to d e ~ c r i the Newtonian systems. One of the more sucmssfulrelationships is the Herschel-Bulkley mcdel, cr = k t n + no

E3

I B

c

Figure 2S15. Elements of mechanical models for vixoelastic behavior. A. Maxwell element. B. Voigt-Kelvin element C. Burges' model. Arrows show applied force or bad.

I

I

o

D

n

I

I

0

f ime

G Time

A

B

,

(15)

in which wo is the yield stress and k is a consistency mfficient. For dilatant or shear thickening systems, k > 0, 1 < n < m, and WO = Q for shear-thinning systems, k > 0, 0 < n < 1, and uo = 0; and, for Bingham plastia, k > 0,n = 1, and no > 0. VISCOELASTIC MATERIALSVisccelastic behavior is oRen represented in terms of a mechanical mcdel. Two of the basic elements used in such a mcdel are a helical spring (which Hmke7s law and is characterized by a modulus~j and a dashpot (ie, a cylindrical container with a loosely fitting piston f l e d with a Newtonian liquid, characterized by its visoosity, v). When the deformation is in shear rather than in tension, Young's E is repla& with the rigidity or she. modul m G.When a spring and a dashpot sl.e oonnecw in series, they form a Maxwell element (Figure 23-154); when they are they form a ~ ~ i ~ element ~ pigure - ~ ~ o o n n e c in ~ 23-15B). Several Maxwell and/or Voigt-Kelvin elements can combined in pardlei and/or in series to ~ ~ - n the t complex vismlastic hhavior of solutions and semisolids. A simple Cornbination is Burgers7mcdel, which oonsists of a Maxwell and a Voigt-Kelvin element in series (Figure 23-15C) and is characterized by two elastic moduli and two vi8008itie8. When a constant load or stress, w0, is applied to a Maxwell element, the elastic spring extends immediately to the recoverable strain or elongation, yet = OA = no/E (Figure23-1M). The

A

I

347

0

G Time

c

Figure2S16. Deformationof three heological models at constantapplied stress. A. Maxwell element. 0. Voigt-Kelvin element. C. Burgers' body.

piston in the dashpot pulls upwards gradually; thispermanent deformation, Y Vis~ M , y proportional to time, t. he two deformations are additive: = r,l + x8. At time D, 7 = ED = BCl + ~CD = OA + CD. When the stress is removed at time D i ~ (Poht 31, the spring retracts immediately and fully, and the specimen contracts h m 3 to C by a length, rel= BC = OR he ~ e r m w n or t omc cover able deformation, Or w p , is %is = CD = u O t / w In plots like those of Figure 23-16, compliance (ie, strain per unit s t w s ) oRen is used instead of strain. Compliance (eg, shear Or is the recipmal of mcdulus. If the Maxwell element is stretched to a given deformation, m,the stre88 required to maintain this deformation constant decreases gradually. As the piston of the dashpot is pulled gradually upwards and the dashpot extended, it increasingly relieves the stress on the spring, which gradually contracts. ARer a long time, as + %is, cr + 0. If the initial stress is wo and the stress at time, t, is W , the stress relaxation is cr = croe-(mtn~ = cr$(-tte~

(16)

The exponent W / q iB dimensionless and the ratio 0 = q / E , which has the dimension of time, is the relaxation time. When a constant stma uo is applied to a Voigt-Kelvin el& ment (Figure 23-16B), the spring can stre# only as fast as the slow extension of the visoous dashpot permits. The greater the visoosity of the liquid in the dashpot, the greater is this retardation. The stress is shared by spring and dashpot, ie, no = E r + v t . A8 wo stretches the springdashpot assembly, the retarded elastic deformation of the specimen increases with time until, at t = m, the spring reaches the full extension corresponding to the applied stress: 7, = no /E. No additional deformation then takes place. When the 8-8 is removed at time G, the specimen retracts fully to its original shape where 7 = 0, h a u s e of the elasticity of the spring, but the motion is damped along the exponential curve ED, which is the mirror image of 0 3 , h a u s e the plunger is pulled back only slowly to its origi-

348

PART 2: PHARMACEUTICS

nal positiol~thruugl~the viscuus liquid in the dashpot, h retardation time, H,,, analogous to t h e relaxation time, is t h e time required for strain to relax to 1 / of ~ its initial value when stress is removed and is defined as #,, - E l I,. Along the retarded elastic deformatiol~branch O R (70 ?, - -

F

:

(1- (>

y.,Jl - 6b-l;lv,,)

-I;#$,,) -

(17)

CT3is de-

Il,71en the stress is removed, the exponential scribed by -

fro

E

--l;'v,, -

y-, P -I;#,,,

-

RG

-

JG

+

+ RE

--(I E,j

(TI> - [ T O - --

E?

-

eb -I;",,)

TI? -

-

I--

TI

TI?- T I

-

2.5r!>

TI

(20)

The Newtonial~viscosities T 1 2 and T I are those of the dispersion and of t h e liquid vehicle or solvent, respectively; T.!, represents the specific viscosity of t h e dispersion, ie, the increase in viscosity of t h e dispersiol~over t h a t of the solvent, expressed as a multiple of the viscosity of the solvent; r!) is the volume fractiul~o f t h e disperse phase [Blood contains 4 5 5 r 2.5, i f t h e solvation layer ofsolvated spherical particles is illeluded in r!>,their dispersions may obey ti^^^ 20, Examples of the latter are solutiolls of globular proteills at their isoelectric point, where their net electric charge is zeru, Furthermore, t h e "ideal" dispersions addressed by Einlaw are collsidered to be so dilute that tile distortioll of t h e larnillar streamlines ofthe solvent a t the surface of one particle does not Overlap alld reillforce the distortiolls aroulld its neighbors. IIowever, a t higher disperse phase concentrations, the perturbation of laminar flow produced by one particle reaches into tile fields of otller particles, ,rlis produces addi. tional resistance to flow and increases T.[, and T~? above t h e values gi,e, by ~~~~~i~~~ 20, L)eviations from these conditions result in higher dispersiol~ viscosities thall those calculated by ~ i law except ~ tllat, ~ ,he, tile disperse phase is fluid, the calculated viscosity is too h i g h rhl example of an extreme positive deviation is found in aqueous sodium bentonite dispersiolls. Their specific viscosity is about 70 times greater than that calculated from Equatiol~ 20. The particles are thin plates, deviating considerably from spherical shape. They are hydrated, and their negatively charged faces attract the positively charged edges but repel the negatively charged faces of other particles. Polymer solutiolls with their thread-like, highly solvated, and entangled macromolecules also deviate considerably from Einstein's law. Several variations on Einstein's law express the specific viscosity as a polynomial in r!>thereby broadenu~gitsapplicability, for example. to more conientrated dispersiolls. Cusson Model-One of the more successful relationships applied to dispersions with a high solids contellt is t h e Casson"' model, -

k[)+ k l j, IP2 ,

(21)

where hI, and hl are constants which depend on t h e properties of the dispersiol~medium and the disperse phase, Although the

~

CHAPTER 23: RHEOLOGY

Casson equation has been used empiricallyin mdelingthe rheological properties of a wide range of concentrated dispersions, it was originally derived from basic principles with the assumption that the disperse phase behaved as rigid r d s .

Computational Rheology E m ~ i r i c drelationshi~saside. numerical methods for the characterization of non-Newtonian flow were developed in the 1960s, but it is only relatively recently that computational rheology has emerged to address previously intractable problems such as three-dimensional transient flows of polymeric liquids, non-isothermal non-Newtonian flows, or turbulent flow of generalized Newtonian and viscoelastic materials.21 Com~uter software, in consort with modern rheometer design, has also facilitated the development of more complex m d e l s of deformation and flow under flow regimes ranging &om the laminar to the turbulent, even encompassing the transitional flow regime in which flow is neither completely laminar or completely turbulent. In all likelihood, the net effect of these advances is to d e m y s t i ~rheological principles and allow the a priori estimation of the mechanical properties of the living and nonliving systems with which we contend.

349

12-15pm. This phenomenon is known as the FahraeusLindqvist or Sigma E f f e ~ t . ~ 'Three , ~ ~ possible contributory came8 are: 1. The hematwit value is lower for blood in capillaries. For in-

stance, blood flowing through a capillary of 5OPm diameter has only 70% of the red blood d l s of blwd flowing through large

ve8&.

2. Red blood oells are biconcave dim with an average diameter (dl of 7.5pm. Their size k by no means negligible compared to the radius of capillaries. Thie leads to a reduction in the apparent viscosity by a factor of (1+d/Ra) aoeording to the so-called S k m

m)

EffeCt.S1 3. The tubular ainch effect comkta of an awumulation of red cells in an annu& region located at a dktance of about 60% of the t u b radius from the t u b axis during laminar flow of b l d through cylindricalcapillaries.Almost wlorlesa plasma flows in the vieinity of the capillary wall. Blwd flowingin the center of the tube is aLso deficient in red cells. This phenomenon commonly is o b served when swpensione of spherical or a s y m m e ~ cparticlea flow through ducts whose diameter k only a low multiple of the particle size?'

In the diameter range btween 30cl.m and 300pm the effective blood viscosity can be predicted usin the hemahait reduction resulting from the Fahroeus effect!'

The apparent viscosity

can Iw determined in macro-visoometers?'

The flow properties of blood are determined by the hematw i t (Hct) value, plasma visoosity, red e l l aggregation, and BIORHEOLOGY d e f ~ r m a b i l i t ~ ? 'The , ~ studies of blood visoosity factors present an important mechanism to b t t e r understand the pathBiorheolom is the study of deformation and flow in biological ways of cardiovascular disorders. I t also allows utilization of systems. Biological fluids are generally both elastic and visblood viscosity tests in diagnostics, prognostic, and preventive cous. Hence they are vismlastic materials. Biological fluids medicine?%levated Hct levels have h e n aswiated with adare rheologically complex due to their multicomponent nature. verse cardiovascular outoomes including arteriosclerosis, oomThe altering effects of disease compound the complexity of evalnary heart disease (CHD), angina pectoris, mymardial infarcuating the rheology of physiological fluids. Several journals tion, and CHD i n c i d e n ~ e . ~Individuals -~~ who exercise cover issues related to rheological characterization of biological regularly have h e n found to have d u d blmd and plasma fluids and tissues and the effect of disease and drugs on these visoosity compared with n~nexercisers.~~ On the other hand, properties. These include Biorheology, Journal of BiomechanaRer heavy exercise or during severe asthma attacks, serum ics, and Clinical Hemorheology and Microcirculation. It is immean lactate levels increase. In high concentrations, lactic aciportant to under stand the rheological properties of biological dosis prcduoes erythrccyk swelling, increasing the Hct level materials for a greater understanding of their implications in and increasing whole-blood visoosity at high and low shear b t h the healthy and diseased state. Rheological of . - parameters rates." biological matehals are also important in successful drug deArtificial Blood Substitutes (ABS) offer an alternative to livery to the b d y . blood transfusion. They have the ability to replace temporally the volume expansion and oxygen transport functions of transfused blood?M0 In the normal circulation system, vascuHemorheology lar m p t o r s have k e n calibrated to wpond to a determined The main function of b l o d is to act as a transport medium. It premure and shear form exerted by normal b h d . When ABS are intrcduced, new biorheological properties of the blood mixtransports almost everything that is essential for the various organs of the b d y . Blcmd is composed of solid particles (red ture can mur. Depending on the flow properties of the spcells, white cells, and platelets) suspended in a fluid medium ABS, peripheral resistance of the circulatory system, and vas(plasma).22Early investigators conceptualized b l d as a viscular m p t o r responses might be altereds8 ABS can b divided in 3 classes: hemoglobin based prcducts, p e r f l m a r b n cous fluid, assuming that the viscosity controls its flow properties.23However, b l d is not a fluid in the ordinary sense; it is based p d u c t s , and volume plasma expanders. Hemoglobinbased pmducts include conjugates of hemoglobin with larger a fluidized suspension of elastic cells, which characterizes its rheological behavior. B l d is a non-Newtonian fluid with vismolecules (dextran or polyethyleneglyool), intramolecular cross-linked hemoglobins, polymerized hemoglobins, and lipomlastic properties. At low shear rates, blood visoosity is higher hecause of the tendency of erythrocytes to aggregate. At high some encapsulated hem~globin.'~ Perfluormarbn-based products have the ability to dissolve significant quantities of shear rates, which are typical for the arterial side and capillaries, b l d visoosity is lower and constant because of erythrocyte oxygen. Perfluodemicals are immiscible with water, oonsequently must h e m u l s a d bfore introduction to the blocdd e f o r m a t i ~ n . Comprehensive ~~,~~-~ studies show that the shear dependence of the viscosity of b l d may be attributed exclustream?Es7 Due to the small size of the emulsion particles (