IPR2016-1096
`
`Luye v. Alkermes
`IPR2016-1095 & IPR2016-1096
`
`ALKERMES EXh. 2017
`
`Luye V. Alkermes
`
`ALKERMES Exh. 2017
`Luye v. Alkermes
`IPR2016-1096
`
`

`

`11TH
`
`EDITION
`
`Remington’s
`
`ALFONSO R GENNARO
`
`Editor, and Chairman
`of the Editorial Board
`
`
`
`

`

`. Pharmaceutical .
`
`Sciences
`
`e1985
`
`EMACK PUBLISHING COPMANY
`
`

`

`Entered according to Act of Congress, in the year 1885 by Joseph P Remington,
`in the Office of the Librarian of Congress, at Washington, DC
`
`Copyright 1889, 1894, 1905, 1907, 1917, by Joseph P Remington
`
`Copyright 1926, 1936, by Joseph P Remington Estate
`Copyright 1948, 1951, by‘The Philadelphia College of. Pharmacy and Science
`Copyright © 1956, 1960,.11965,1970, 1975, 1980, 19:85, by The Philadelphia College ofPharrnacy and
`Science
`‘
`..
`'
`'
`‘
`.,
`_'
`.
`
`All Rights Reserved
`
`Library of Congress Catalog Card No 60—53334
`ISBN 0-912734-03-5
`
`l
`
`;
`ll
`
`The use of portions of the text of USP XX, NF XV, and USAN and the USP Dictionary of Drug
`Names is by permission of the USP Convention. The Convention is not responsible for any
`inaccuracy of quotation or for any false or misleading implication that may arise from
`separation of excerpts from the original context or by obsolescence resulting from
`publication of a supplement.
`
`NOTICE—This text is not intended to represent, nor shall it be interpreted to be, the equivalent
`of or a substitute for the official United States Pharmacopeia (USP) and/or the National
`Formulary (NF).
`In the event of any difference or discrepancy between the current official
`USP or NF standards of strength, quality, purity, packaging and labeling for drugs and
`representations of them herein, the context and effect of the official compendia shall
`prevail.
`
`Printed in the United States of America by the Mach Printing Company, Easton, Pennsylvania
`
`
`
`

`

`Table of Contents
`
`part1
`
`orientation
`
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`
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`Scope
`1
`.
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`2 Evolution of Pharmacy
`3Ethics..................
`4 Pharmacists in Practice
`.
`.
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`.
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`'5
`PhOImOCIS'SInIndUSNY -
`-
`-
`-
`-
`-
`-
`-
`-
`a
`-.
`6 Pharmacists in Government
`.
`.
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`7 Drug Information .
`.
`.
`.
`.
`.
`.
`.
`-
`-
`-
`-
`-,
`8Research.................‘
`
`Part2
`
`Pharmaceutics
`
`-
`-
`-
`-
`-
`-
`-
`-
`-
`9 MeirOIOQY and COICUIO‘ion -
`-
`-
`-
`-
`-
`-
`-
`-
`-
`10 Statistics
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`11 ComputerSdence
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`12
`COICUIUS
`-
`-
`-
`-
`-
`-
`-
`13 Molecular Structure, Properties, and States of
`MOI'ef
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`.
`14 Complexation .
`.
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`15, Thermodynamics .
`.
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`'16 Solutions and Phase Equilibria
`.
`.
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`.
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`17
`Ionic Solutions and Electrolytic Equilibria
`.
`.
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`.
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`18 Reaction Kinetics .
`.
`.
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`.
`.
`.
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`19
`Interfacial Phenomena
`.
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`.
`.
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`20 Colloidal Dispersions
`.
`.
`.
`.
`.
`.
`.
`.‘ .
`..
`21
`Particle Phenomena and Coarse Dispersions
`.
`.
`22 Rheology .
`.
`'.
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`.
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`.
`.
`.
`
`.
`
`3
`8
`19
`27
`34
`42
`49
`59
`
`69
`104
`14°
`148
`
`161
`186
`I198
`207
`230
`249
`258
`271
`301
`330
`
`Pa";
`
`PharmaceuticalChemistry
`
`.
`Inorganic Pharmaceutical Chemistry .
`23
`.
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`.
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`24 Organic Pharmaceutical Chemistry
`.
`.
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`25 Natural Products
`.
`.
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`.
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`.
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`26 Drug Nomenclature_un"ed States Adopted
`Names..................428
`27 Structure-Activity Relationship and Drug Design
`
`349
`374
`397
`
`435
`
`.
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`’44 Respiratory Drugs
`.
`;
`.
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`45 Sympathomimetic Drugs .
`.
`46 Cholinomimetic(Parasympathomimetic) Drugs
`47 Adrenergic and Adrenergic Neuron Blocking Drugs
`
`.
`.
`
`866
`876
`894
`
`.
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`.
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`.
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`.
`
`911
`46 Antimuscarinic and Antispasmodic Drugs
`921
`49 Skeletal Muscle Relaxants
`.
`.
`.
`.
`.
`933
`.
`.
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`.
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`.
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`50 Diuretic Drugs
`.
`.
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`.
`.
`946
`.
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`.
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`51 Uterine and Antimigraine Drugs
`. ....951
`.
`.
`52Hormones....... .
`.
`.
`.
`,
`.
`.
`1002
`.
`.
`53 VitaminsandOther Nutrients .
`.
`.
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`.
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`1035
`.
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`.54 Enzymes
`.
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`.
`.
`1039
`.
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`55 General Anesthetics
`.
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`1048
`.
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`56 Local Anesthetics .
`.
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`1059
`.
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`57 Sedatives and Hypnotics.
`.
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`1075
`.
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`58 Antiepileptics
`.
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`1084
`.
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`59 Psychopharmacologic Agent
`.
`.
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`1099
`.
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`60 Analgesics and Antipyrefics
`.
`.
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`.
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`1124
`.
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`61 Histamine and Antihistamines
`.
`.
`.
`.
`.
`1133
`.
`62 Central Nervous System Stimulants
`63 Antineoplastic and Immunosuppressive Drugs .
`.
`1139
`64 Antimicrobial Drugs .
`.
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`1158
`65 Porositicides .
`.
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`1234
`66 Pesticides .
`.
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`1241
`67 Diagnostic Drugs
`.
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`1264
`68 PharmaceuticalNecessities
`.
`.
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`.
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`1276
`.
`69 Adverse Effects of Drugs .
`.
`.
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`1321
`.
`70 Pharmacogenetics
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`1336
`71
`Pharmacological Aspects of Drug Abuse
`.
`.
`.
`.
`1341
`72
`Introduction of New Drugs
`.
`.
`.
`.
`.
`.
`.
`.
`.
`1357
`
`.
`
`p9"7
`
`DIOIOQIWIPWdu‘“
`
`73
`74
`
`'
`'
`'
`'
`'1'
`'
`'
`'
`'
`PIInCIpIIesI‘OfImmunOIOgy
`Immunrzmg Agents and Diagnostic Skin Anti-
`gens'j""""""""'1380
`75 AIIergemc Extracts '
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`'
`1396
`
`1671
`
`Part 8
`
`Pharmaceutical Preparations and Their
`“mu'mtu'e
`.
`'
`'
`I
`'T'
`:IefomIIUIgaan ' é”:
`'
`l'
`'
`IQOVOIF my on
`Ioequwo ency esnng '
`78 Separation
`79 Sterilization .
`.
`.
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`
`.
`
`'
`'
`.
`
`'
`'
`.
`
`1429
`4 4
`1432
`1443
`
`Part 4
`Radioisotopes in Pharmacy and Medicine
`28 Fundamentals of Radioisotopes.
`.
`.
`.
`.
`.
`.
`.
`453
`29 Medical Applications of Radioisotopes
`.
`.
`.
`.
`.
`471
`
`\
`
`pa" 5
`
`Testing and Analysis
`
`503
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`30 Analysisof Medicino|5
`550
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`31 BiologicolTesfingI
`I
`559
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`I
`32
`cnnico|Ano|y5is
`I
`I
`33Chromatography..............593
`34
`Instrumental Methods ofAnaIysis
`.
`.
`.
`.
`.
`.
`.
`619
`35 Dissolution
`.
`.
`.
`I
`_
`I
`,
`.
`I
`,
`I
`_
`I
`I
`I
`I
`653
`
`.
`_
`I
`Pharmaceutical and Medicinal Agents
`Part6
`'36’Diseases‘ Manifestations and Pathophysiology
`‘
`.
`.
`.
`.
`’\ 37 Drug Absorption, Action, and Disposition
`.
`.
`.
`.
`38 Basic Pharmacokinetics
`.
`.‘
`.
`.
`.
`.
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`.
`.
`.
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`39 PrinciplesofClinicalPharmacokinetics
`.
`-
`-
`-
`-
`4°
`TOPICOID'UQS
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`.
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`.
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`41 Gastrointestinal Drugs .
`.
`.
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`1681
`.
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`.
`.
`94 Ambulatory PatientCare
`42 Blood, Fluids, Electrolytes, and Hematologic
`1702
`.
`.
`.
`.
`.
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`.
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`.
`.
`95
`InstitutionaIPatientCare
`816
`Drugs
`.
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`1723
`.
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`96 Lon -Term Care Facilities
`4
`43 Cardiovascular Dru s
`.
`.
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`
`
`1
`
`1
`I
`
`K
`i
`I
`I
`
`I
`
`I
`
`80 Tonicity, Osmoticity, Osmolality, and Osmolarity .
`81
`Plastic Packaging Materials
`.
`.
`.
`.
`.
`.
`.
`.
`.
`82 Stability ofPharmaceuticaI Products
`.
`.
`.
`.
`.
`.
`83 QualityAssurance andControl
`.
`.
`.
`.
`.
`.
`.
`.
`84
`Solutions, Emulsions, Suspensions, and Extrac~
`"VeS-----------_--------1492
`55 Po'ememIP'ePOmfiOnS -
`-
`-
`-
`-
`-
`-
`-
`-
`-
`-
`1518
`86
`Intravenous Admixtures
`1542
`.
`.
`.
`.
`.
`.
`.
`87 Ophthalmic Preparations
`1553
`.
`.
`.
`.
`.
`.
`.
`.
`88 Medicated Applications
`1567
`I
`I
`I
`I
`I
`I
`I
`I
`N39 powders
`I
`I
`I
`I
`I
`I
`1535
`'
`'
`'
`l
`'
`'
`I
`omI.S°IId Dosage Forms '
`1603
`.I 91 Coating of Pharmaceutical Dosage Forms .
`1633
`I92 Susta‘ de seDruDeliverSstems
`1644
`713 L93 Agog]:
`.e-e°_
`_
`_
`'y y
`1662
`741
`762
`773
`792
`
`1455
`1473
`1478
`1487
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`.
`I
`'
`.
`_
`
`.
`.
`I
`'
`.
`_
`
`.
`.
`I
`'
`-.
`_
`
`Part9
`
`Pharmaceutical Practice
`
`

`

`1737;
`1749
`1757
`1764
`1778
`1796
`1617
`
`1824
`
`.
`.
`.
`'105 “surgical Supplies .
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`106
`Poison Control
`.
`.
`.
`.
`.
`.
`.
`.
`.
`107 Laws Governing Pharmacy
`.
`.
`.
`.
`.
`.
`.
`108 Pharmaceutical Economics and Management
`109 DentalServices
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`
`.
`.
`
`.
`.
`.
`.
`_.,
`
`.
`.
`.
`.
`.
`
`1869
`1879
`1690
`1917
`1935
`
`Alphabeticlndex
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`1946
`
`Index
`
`'.
`.
`.
`. ,.
`.
`97 The Pharmacist and Public Health .
`.
`.
`.
`98 The Patient: Behavioral Determinants .
`.
`.
`.
`.
`99 Patient Communication .
`.
`.
`.
`.
`.
`.
`.
`.
`.-.
`.
`100 PatientCompliance .
`.
`.
`.
`.
`.
`..
`.
`_;
`.
`.
`.v
`101 The Prescription
`.
`.
`.
`.
`.
`.’-.
`.
`. -. .
`.
`.
`102 Drug Interactions .
`.
`.
`».
`.
`.
`.
`.‘ ._
`.
`.
`_.
`103 Utilization ,and Evaluation of Clinical Drug
`Literature .
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`.
`,.
`.
`.
`
`.
`
`.
`
`.-
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`.
`
`..
`
`104 Health Accessories
`
`is
`it
`IE
`IE
`I:
`{I
`
`.
`
`
`
`.q“,
`L_.
`
`a
`
`1‘???”
`
`
`
`

`

`.r.
`
`CHAPTER 21
`
`Particle Phenomena and Coarse
`Dispersions
`/———_—‘-‘_——————\
`
`William I lllguchl, PhD
`Distinguished Professor and Chalrman
`Department of Pharmaceutics
`College of Pharmacy
`University of Utah, Salt Lake City, UT 64112
`
`Anthony P Slmonelli, PhD
`Professor of Pharmaceutics
`School of Pharmacy 6 Institute of Material Sclence
`University of Connecticut
`Storrs, CT 06268
`
`James Swarbrlck, DSc, PhD
`Professor and Chairman
`Division of Pharmaceutics
`School of Pharmacy. Unlverslty of North Carolina at Chapel Hm
`Chapel Hlll, NC 27514
`
`Alfred Martin, PhD
`Coulter R Sublett Professor
`Drug Dynamics lnstltute, College of Pharmacy
`University of Texas
`Austln, TX 78712
`
`Norman F H Ho. PhD
`Professor of Pharmacy, College of Pharmacy
`The University of Michigan
`Ann Arbor, MI 46104
`
`Understanding particle phenomena and concepts of dis-
`persion techniques is important in many areas of pharma-
`ceutics and biopharmaceutics.
`In the formulation and
`manufacture of dosage forms such as powders, capsules,
`tablets, suspensions, emulsions, and aerosols, knowledge of
`particle technology is essential. Also, it is becoming in-
`creasingly important to consider such factors as particle size
`and degree of deaggregation in drug utilization by the pa-
`tient.
`.
`
`This chapter will discuss the formation of suspensions and
`emulsions, and the time behavior involving flocculation, co-
`alescence, crystal growth, and caking. The “theory” is in-
`tended to give readers qualitative or semiquantitative
`guidelines, rather than quantitative directions for manufac-
`turing procedures. Many of the equations and concepts
`presented cannot be used directly for the purpose of formu-
`lation; rather they are meant to provide understanding of the
`interactions involved in the preparation of, for example, an
`emulsion or a suspension. '
`t
`For the purposes of the present discussion, a dispersed
`system will be regarded as a two-phase system in which one
`Phase is distributed as particles or droplets in the second, or
`c°ntIHUOUS, phase. Since each phase can exist insolid, liquid, ‘
`0r gaseous state,
`there are nine possible combinations.
`_ °WeV§r, since gases are miscible in all proportions, there are
`m refillty Only eight combinations. The treatment will be
`festlflctefl to a discussion of those solid—liquid and liquid—
`lqmd dispersions that are of pharmaceutical significance,
`Edmeb’: suspensions and emulsions.
`In these systems the
`Oisipersed phase is frequently referred to as the discontinuous
`ter:tlemal phase, and the continuous phase is called the ex—
`Afi cfihase or disperSion medium. .
`asis flsperslons may be ClaSSlfled into three groups on the
`with 00 the Size of the dlspersed'particlles. Chapter 20 deals
`of the :11? “Ch group—colloidal dispers10ns—in which the Size
`A to 0 Slspersed particles is in the range of approxrmately 1_0
`classific 1311- Molecular dispersions, the second group in this
`group ca 101}, are discussed in Chapters l6 and 17. The third
`SiZe eicezalSlgtmg ofcoarse draperszons in which the particle
`of coarse dis -5 fli’n, isthe subject of this chapter. Knowledge
`pharmammt_pcrs10ns is essential for the preparation of both
`emulsio
`$081; Suspensmns (solid—liquid dispers10ns) and
`“3 (holuid—liquid dispersions).
`
`The Dispersion Step
`
`The pharmaceutical formulator is primarily concerned with
`producing a smooth, uniform, easily flowing (pouring or
`spreading) suspension or emulsion, one in which dispersion
`of particles can be effected with minimum expenditure of
`energy.
`
`In preparing suspensions, particle—particle attractive forces
`-
`among powder particles present a problem. These forces may
`be overcome by the high shearing action of such devices as the
`colloid mill, or by use of surface-active agents. The latter
`greatly facilitate wetting of lyophobic powders and assist in
`the removal of surface air that shearing alone may not remove;
`thus the clumping tendency of the particles is reduced.
`Moreover, lowering of the surface free energy by the adsorp-
`tion of these agents directly reduces the thermodynamic
`driving force opposing dispersion of the particles.
`In emulsification a similar situation exists. Frequently high
`shear rates are necessary for dispersion of the internal phase
`into fine droplets. The shear forces are opposed by forces
`operating to resist distortion and subsequent breakup of the
`droplets. Again surface-active agents help greatly by lowering
`interfacial tension, which is the primary reversible component
`resisting droplet distortion. Surface-active agents also may
`play an important role in determining whether an oil-in-water
`or a water-in-oil emulsion preferentially survives the shearing
`action.
`
`For thermodynamic reasons, once the process of dispersion
`begins there develops simultaneously a tendency for the sys-
`tem to revert to an energetically more stable state, manifested
`by flocculation, coalescence, sedimentation, crystal growth,
`and caking phenomena.
`If these physical changes are. not
`inhibited or controlled, successful dispersions will not be
`achieved or will be lost during shelf life.
`
`Wetting
`
`Wetting of a solid by a liquid is best illustrated by the be-
`havior of a small droplet of liquid placed on a flat surface of
`a solid.
`If the droplet spreads over the solid, the liquid is said
`to wet the solid completely, and the contact angle, 0, measured
`through the liquid is zero (see Fig 21-1). The term nonwetting
`is somewhat arbitrary but may be applied to a liquid when 6
`301
`
`
`
`

`

`
`
`302
`
`CHAPTER 21
`
`'yL
`
`_‘———
`
`—|.-
`75
`_' 73L
`Fig 21-1. A drop of liquid on a flat solid surface. Forces and the
`contact angle, 0, are shown.
`
`> 90°. For the nonspreading region, 0 < 0 < 90°, the term
`partial wetting may be applied.
`For a better understanding of the wetting process, the
`Young equation
`
`(1)
`’Ys = ’YSL + ’YLCOS 0
`deduced from analysis of the force vectors (see Fig 21—1) at
`equilibrium may be instructive. Here 73, 75L, and 7;, are the
`surface tension of the solid, the interfacial tension of the solid
`liquid, and the surface tension of the liquid, respectively.
`Rearranging Eq 1 gives
`
`'YS — ’YSL
`7L
`
`cos '0 =
`
`(2)
`
`Hence, cleansurfacesofsuchsolids aregenerallymuchmore
`wettable by solvents listed in Table I. As Zisman has pointed
`out, however, there are instances when a relatively low-energy
`liquid does not spread on a high—energy solid.1 This behavior
`occurs when molecules of the liquid or a constituent in it ad-
`sorb on the high-energy surface. Sometimes surface con-
`tamination of high-energy surfaces by hydrophobic materials
`significantly lowers 7,9, with the result that wetting does not
`occur; for example, very low concentrations of cationic sur-
`face-active agents render glass nonwetting toward water.
`
`"Intermolecular Forces
`
`All interactions involving molecules and ions, and aggre-
`gates of molecules and ions include both attractive and re-
`pulsive forces. These forces depend on the nature ofspecies,
`the diStance of separation, the orientation of the molecules,
`and the nature of the medium.
`_
`I‘on—Iou Electrostatic Interactions—The interionic in-
`teraction of two polarizable ions (see Fig 21-2) obeys the fol-
`lowing laws:
`
`and
`
`Energy = E = ——-q1q2
`er
`
`Force = F = - q1q—22
`er
`
`(3)
`
`(4)
`
`l
`‘
`
`I
`
`I
`
`‘
`
`i
`
`‘
`
`which states the dependence of 0 on 73, 75L, and 7L. From
`this equation it is obvious that wetting is favored if 75 is large,
`7L is small, and 73L is small. Complete wetting results if the
`right—hand side of Eq 2 equals one.
`The practical significance of wetting may be illustrated by
`the preparation of methylprednisolone suspensions. Mi-
`cronized methylprednisolone, is not wetted (6 > 90°) by water
`in the absence of a surfactant, but if a small amount of poly-
`sorbate 80 is added the contact angle is reduced to nearly zero '
`and a fine dispersion may be prepared.
`Low-Energy Solids—The particle surface of many organic
`substances is hydrophobic because there are few polar func-
`tional» groups in the molecules of the substances. For such
`low-energy solids the surface tension may be relatively small,
`in the range of 20 to 40 ergs/cmz. From Eq 2 it is evident that
`such surfaces will be poorly wetted by highly polar liquids (of
`relatively large surface tension) such as water or glycerin.
`Less polar liquids wet the surfaces more readily. Table I
`shows that as 'yL decreases, 0 decreases in accordance with Eq
`2.
`'
`Wetting agents are surface-active substances used to reduce
`contact angle and thus improve wetting. They function by
`adsorbing at air/liquid and solid/liquid interfaces, reducing
`both 7L and 751,. Eq 2 shows that for wetting of low—energy
`solids by water, reduction of 7;, is necessary even when 751,
`is small.
`V
`High-Energy Solids—Metals, silica, clay minerals, and
`water-insoluble salts are among the substances with 73 values
`ranging from several hundred to thousands of ergs/cmz.
`
`Table l—Contact Angles of Various quuids at 20° on Low-
`Energy Solids
`
`Paraffin
`Polyethylene
`
`Water (7L = 73)
`108
`94
`Glycerol (7L = 63)
`96
`79
`Formamide (71, = 58)
`91
`77
`Bis(2-ethylhexyl) phthalate (71, = 31)
`36
`5
`Benzene (7L = 29)
`24
`spreads
`n-Hexadecane (’yL = 28)
`28
`spreads
`Di(n-octyl)ether (’yL = 28)
`23
`spreads
`
`7n—Decane ('71, = 24) spreadsfl
`
`
`where qi and q:; are the charges on ions 1 and 2, respectively,
`r is the distance of separation of the ions, and e is the dielectric
`constant of the medium. As can be seen, if q1 and q2 are of
`the same sign, the force, F, is negative and therefore repulsive
`in nature. On the other hand, if the charges are of opposite
`sign, the interaction is attractive. It shOuld be noted that the
`distance dependence for this situation isinversely propor-
`tional to the first power in r for E and second power for F.
`This difference in the distance dependence results from the
`fact that
`
`(5)
`E = J: Fdr
`which states that the energy is equal to the work, W, of
`bringing together, the two ions from infinity to a distance r
`from each other.
`'
`An example calculation for sodium chloride can be used to
`illustrate the magnitude of the ion—ion interaction. For the
`sodium chloride molecule in the vapor state, r is about 2.5 X
`10‘8 cm, qNa+ = —q01"— = electronic charge = 4.8 X 10~10 esu
`(electrostatic units), and the dielectric constant may be as-
`sumed to be unity. Therefore,
`
`(4.8 X 10‘10)2
`2.5 X 10‘8
`
`N 10‘11 erg/ion pair
`
`W =
`
`Interionic interactions of two polarizable ions. Like charges
`Fig 21-2.
`repel and unlike charges attract.
`
`
`
`

`

`or
`
`since
`
`W = 120,000 cal/mole
`
`cal/mole =
`
`(erg/molecule)No
`4.18 X 107 ergs/cal
`
`The value for the work, W, represents the amount of work
`required to separate one mole of sodium chloride molecules
`in the vapor state into one mole of sodium and one mole of
`chloride ions.
`.
`_
`Other Electrostatic Interactions—In addition to the
`ion—ion interaction other electrostatic interactions may be
`possible involving ions, dipoles, and induced dipoles.
`A permanent dipole moment exists in a molecule when the
`“center of gravity” of the negative charges does not coincide
`with that for the positive charges.
`'
`The field of an ion or permanent dipole temporarily may
`polarize molecules which may not have a permanent dipole.
`When this occurs, the resulting polarization leads to an in-
`duced dipole in the molecule.
`Various pair combinations of ions, permanent dipoles, and
`induced dipoles give rise to higher order electrostatic inter-
`actions such as the idn—dipole, the ion~induced dipole, the
`dipole—dipole, and dipole—induced dipole. These interactions
`are weaker and generally more short—range than the ion—ion
`interaction, the distance dependence for the energies ranging
`from r‘2 to r‘6 (see Table II). Furthermore, all of these in-
`teractions usually are directionally dependent.
`Hydrogen-Bonding—A hydrogen atom attached to an
`electronegative atom such as oxygen or nitrogen effectively
`produces a dipole with a highly exposed positive end. As a
`result, the proton end can participate in unusually strong di-
`pole—dipole interactions with other strongly electronegative
`centers. Each water molecule has two such hydrogen-bonding
`protons and therefore water molecules in liquid water and ice
`are highly associated. The hydrogen-bonding capabilities of
`water also partially explain its unusually good solvating ability
`for other polar molecules.
`London Dispersion Forces—These attractive forces arise
`from the fact that at any given instant the electron distribu-
`tion around an atomic nucleus may not be symmetrical and
`consequently this leads to the formation of a'temporary d‘ipOle
`moment. Such temporary dipoles in neighboring atoms are
`correlated so as to produce an effective induced dipole—in-
`duced dipole interaction.
`‘
`The characteristics of the dispersion forces are that they
`are approximately additive, they are not directionally de-
`pendent, and they follow the 1/r6 dependence in energy. As
`will be seen later, the London Forces, along with hydrogen-
`bonding forces, are generally the most important in describing
`the intermolecular and the‘interparticulate behavior of non-
`lonic compounds in solutions and dispersions. '
`Born Repulsive Forces—If molecules or ions are brought
`very close together, the outer electron clouds of the atoms will
`begin to overlap. This gives rise to a mutual repulsive force
`that increases very rapidly (~1/r12) as the atoms are brought
`
`Table lI—Distance Dependence of Various Electrostatic
`Interactions
`\—______—
`
`Distance dependence
`Force
`Energy
`Type interaction
`x—“—__—___
`
`1/r
`1/r2
`Ion—ion
`l/r2
`1/7‘3
`Ion—dipole
`l/r3
`1/r4
`Dipole—dipole
`l/r6
`l/r7
`Dipole—induced dipole
`l/r6
`l/r7
`London dispersion forces
`\______—____‘_—
`
`PARTICLE PHENOMENA AND COARSE DISPERSIONS
`
`303
`
`closer together such as one might expect when two hard rubber
`balls touch and are pressed together.
`
`Particle-Particle Interactions
`
`The interaction between particles may be analyzed by the
`same type of forces responsible for interatomic and intermo-
`lecular interactions. Let us consider first the interaction of
`two arbitrary particles as shown in Fig 21-3.
`The kinds of interactions contributing to the particle—
`particle bindingenergies are:
`
`s1ve .
`. 1.) The various electrostatic contributions (attractive and repul-
`2. The London dispersion forces between the atoms of one particle
`with those in the other (attractive).
`3. The covalent bonds (attractive).
`4. The Born repulsion forces.
`
`The latter two can contribute only when the two particles are
`touching.
`A rigorous quantitative treatment of the above contribu-
`tions to particle—particle binding is beyond the scope of this
`text. However, considerable insight into the magnitude,
`nature, and the applications of these forces can be gained by
`“order of magnitude” theoretical calculations using approx-
`imate theories and simplified models.
`Charge—Charge Interactions—Let us examine the pos—
`sibility of electrostatic interactions between two particles, A
`and B (see Fig 21-3). While contributions from charge—di—
`pole, charge—induced dipole, and dipole—dipole interactions
`between an atom, ion, or molecule of one particle and that in
`the other may occur, generally these are probably of much less
`importance than the charge—charge interactions. Therefore,
`as a first approximation let us consider only the charge—charge
`forces between the two particles.
`The energy of coulombic interaction may be written as the
`summation of Eq 3 (assuming 6 = 1) over all possible ion—pair
`combinations between the two particles; ie,
`M N --
`“22%
`i=1j=1rij
`
`(6)
`
`where q,- is the charge on the ith ion in Particle A which con-
`tains M ions, qj is the charge on the jth ion in Particle B which
`contains N ions, and r,-1- is the distance between ions i and j.
`If it is assumed that the particles are spheres and that charges
`on each sphere are uniformly distributed, Eq 6 simply reduces
`
`
`
`Parameters used to describe the interactions between
`Fig 21-3.
`particles where a and b are the particle radii of the particles involved,
`R is the intercenter distance of separation of the two particles, and H
`is the distance of separation between the two surfaces of the interacting
`particles.
`
`
`
`

`

`r—-—-—_&-—————¥—'7
`
`304
`
`CHAPTER 21
`
`to
`
`E =
`
`
`QA QB
`R
`
`(7)
`
`where QA and Q3 are the net charges on Particles A and B and
`R is the intercenter distance between the two spheres (see Fig
`21-4). The corresponding equation for the force is
`
`-Q Q
`(8)
`F= RA,”
`It is both instructive and useful at this point to examine the
`magnitude of maximum energies and forces that might arise
`from purely electrostatic contributions and compare them to
`the gravitational forces on the particles. The maximum
`charge on a given particle in air is limited by the electric
`breakdown field of about 60 esu, which corresponds to a charge
`of
`
`Q = 60a2
`
`(9)
`
`where a is the radius of the sphere.
`Table III tabulates the results of calculations for E and F
`based on Eqs 7-9 for different—sized particles.
`It must be kept
`in mind that these values represent the maximum electro-
`static interaction limited by surface electrical discharge in
`air.
`
`It can be noted that for small particles, electrostatic effects
`may be important. For example, two 1-um particles with the
`same maximum charge may repel each other with a force that
`is 20,000 times greater than the gravitational force, D. These
`calculations explain why certain dry powders that become
`charged during trituration in the mortar defy the laws of
`gravity.
`Interestingly, as the particle size is reduced, this
`phenomenon increases in accordance with the predictions of
`Table III, which shows that the relative importance of the
`electrostatic force as compared to the gravitational force
`should increase with decreasing particle size.
`London Dispersion Forces—The London dispersion force
`contribution to the particle—particle interaction may be es-
`timated by summing the attraction over all possible atom pair
`combinations between the two particles (see Fig 21-5). Thus,
`we may write
`
`01'
`
`M N.
`2, eij
`r=1j=1
`
`E =
`
`u
`Al N
`E = z Z 5‘11
`i=1j=1 rij
`
`(10)
`
`(11>
`
`where kij, the London constant, is characteristic of the atom
`pair involved and is a function of the polarizabilities and the
`ionization energies of the atoms.
`
`Table lll—Maxlmum Electrostatic Energy and Force ot
`Interaction between Uniformly Charged Spheres Near
`Contacta (R z 23 and Field = 60 esu) as a Function of
`Particle Size"
`Electrostatic
`
`Gravitational
`force
`Force
`Energy
`Radius
`(dynes)
`(dynes)
`(ergs)
`(cm)
`_______.__—..._———
`
`4.1 X 10‘9
`9 X 10‘6
`1.8 X 10‘9
`10—4 (1 pm)
`4.1 x 10—6
`9 x 10-4
`1.8 x 10—6
`10—3
`4.1 X 10’3
`9 X 10‘2
`1.8 X 10‘3
`10‘2
`4.1
`9
`1.8
`10‘1 (1 mm)
`___—_______———————————-—
`1
`1.8 X 103
`9 X 102
`4.1 X 103
`
`a For these calculations the particles are assumed to be touching. These
`values approximately apply for particles not touching if distances of separation
`are not comparable to the particle radius.
`5 Density of 1 is assumed.
`
`
`
`Fig 21-4. Electrostatic interactions between two particles containing
`M and M ions, respectively. The distance r],- is the distance between
`the ith ion of one particle and the jth ion of the other particle.
`
`
`
`Fig 21-5. The London dispersion force contribution to the particle—
`particle interaction. This may be estimated by summing the attraction
`over all possible atom-pair combinations between the two particles,
`containing M and N atoms, respectively. The above illustrates the
`interaction of the ith atom of one particle with jatoms of the other
`particles where iand [are 1, 2, 3, 4, 5, etc.
`
`In the case of two equal-sized spheres of the same substance
`the summations in Eq 11 may be transformed to double in-
`tegrals and the following equation is obtained for energy:
`_ —A
`2a2
`2a2
`(R2 — 4112)]
`_ m
`R2
`6 R2 — 4a2
`
`(12)
`
`where A = 7r2n2k, n is the number of atoms/cm3, k is the
`London dispersion force constant, R is the particle—particle
`intercenter distance, and a is the radius of the sphere. A more
`rigorous equation may be deduced which takes into account
`the so—called “retardation effect,” but it would not signifi—
`cantly contribute to the present discussion.
`.
`It is worthwhile to present the limiting forms of Eq 12.
`First, when R is much greater than 2a (ie, when the intercenter
`distance is large compared to the sphere diameter), one can
`show that the energy and force would be inversely propor—
`tional to the 6th and 7th power of R, respectively. On the
`other hand, when the closest distance, H, between the surfaces
`of the two spheres is much smaller than the sphere radius, one
`can show that
`
`-Aa
`‘ rm
`
`“3’
`
`and
`
`
`_ Aa
`_ 12H2
`where H = R —- 2a and H <<< a (see Fig 21-3).
`In order to gain an appreciation for the magnitude of the
`London attraction between two particles one can compute the
`energies and forces using Eqs 13 and 14 employing the ap-
`propriate values for A. Table IV gives a list of A values.
`These may be used in the present calculations. As can be seen
`from the A values, the London forces do not differ too greatly
`among materials with widely differing properties. The results
`
`(14)
`
`
`
`

`

`Table IV—Tabulation of A Values
`
`PARTICLE PHENOMENA AND COARSE DISPERSIONS
`
`305
`
`M atoms
`
`Fig 21-6. The interaction of two particles based on the flat-plate
`model. For symbolism, see Figs 3 and 5.
`
`Nonspherical Particles—The above discussion was re-
`stricted to uniform spheres which do not generally represent
`real powders. Real powder particles are also subject to both
`plastic and elastic deformation which would provide larger
`areas of contact between them. The actual situation for
`powders would be expected to lie somewhere between the
`interaction between uniform spheres and that for parallel
`plates and is much more complicated than either of the above
`cases. _ Thus, for example, the interaction of two contacting
`cubes in contrast to that for two spheres, also depends upon
`their relative orientation (face to face, face to edge, corner to
`face, edge to edge, etc).
`In addition to the mutual orientation
`and shape effects for real powders, one must consider the
`particle-size distribution and the important factor of whether
`or not the particle is deformable (plastic and/or elastic) under
`the prevailing conditions.
`It would be beyond the scope of this text to attempt detailed
`considerations of the above factors. However, in order to gain
`an appreciation for the magnitudes of the possible London
`force interactions between real powder particles it is helpful
`to examine the limiting case of two interacting flat plates (see
`Fig 21-6).
`For two parallel flat surfaces separated by a distance, H, the
`equations for the London Force interacting energy and
`force/unit area are
`'
`—A
`E = 127rH2
`
`(15)
`
`and
`
`
`+A
`(16)
`F — (“HS
`Table VI tabulates the results of calculations for the same two
`distances of separation used in Table V for comparison pur-
`poses.
`Tables V and VI show that suitably oriented flat plates or
`
`Material
`
`A X 1012 ergs
`
`w H
`
`0.31
`20
`0-.35
`Paraffin
`0.50
`Polyethylene
`0.63
`Polystyrene
`1.4
`Fe
`1.6
`Graphite
`1.8
`Silica
`2.1
`Rutile
`
`Mercury 2.9
`
`of using Eqs 13 and 14 and an A value of 10‘12 erg are pre-
`sented in Table V for two distances of separation, 5 X 10’8 and
`5 X 10‘7 cm. For other A values the reader may make the
`appropriate adjustments using Table IV information. The
`H value of 5 X 10‘8 should be a reasonable limiting distance
`of closest approach (within a factor of two) for two atoms in-
`volved in the contact of the two macroscopic spheres.
`An examination of the results presented in Tables III and
`V reveals several important relationships. First, as was the
`case with electrostatic interactions, London forces decrease
`much more slowly than the gravitational forces with de-
`creasing particle size. Thus, as can be seen at a distance of
`separation of 5 A, 1-p.m particles exhibit London attractive
`forces that are approximately one million times stronger than
`gravity, but 1-mm particles have approximately the same
`forces. For this reason fine particles tend to be “stickier” than
`coarse particles.
`Secondly, the London attractive forces decrease more slowly
`than the electrostatic forces with decreasing particle size.
`Thus, a 10-fold decrease in particle size corresponds to only
`a 10—fold decrease in the London forces but to a 100-fold de-
`crease in electrostatic forces. Thus, for 1-/.Lm particles or
`smaller, it is likely that London forces are always more im-
`portant than electrostatic forces when the particles are near
`contact. However, as the distance of separation is increased,
`the electrostatic forces remain relatively constant while the
`London forces decrease rapidly. For example, as the distance
`of separation is changed from 5 to 50 A, the London forces are
`decreased by a factor of a hundred while the electrostatic
`for