FOURTH EDITION
`
`Physical Pharmacy
`
`PHYSICAL CHEMICAL PRINCIPLES IN THE PHARIVIACEUTICAL SCIENCES
`
`A1fredIMa1"tin, Ph.D.
`Emeritus Coultei" R. Sublett Professor
`Drug Dynamics Institute,
`College of Pharmacy,
`University of Texas
`
`with the participation of
`PILAR BUSTAMANTE, Ph.D.
`- Titulai" Professor
`Depamtment of Phamnacy
`and~Pharmaceutical Technology,
`Univensity Alcala de Henares,
`Maclrid, Spain
`
`and with illustrations by
`A. H. C. CHUN, Ph.D.
`Associate Research Fellow
`Phanmaceutical Products Division,
`Abbott Laboratories
`
`LEA & FEBIGER
`
`‘‘
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`PHILADELPHIA, LONDON
`
`ll
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`LEA & FEBIGER
`Box 3024
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`. (215)251-2230
`
`Executive Editor: George H. Mundorff
`Production Manager: Thomas J. Colaiezzi
`Project Editor: Denise Wilson
`
`Library of Congress Cataloging-in-Publication Data
`
`Martin, Alfred N.
`Physical pharmacy 2 physical chemical principles
`in the pharmaceutical sciences / Alfred Martin ; with
`the participation of Pilar Bustamante and with
`illustrations by A.H.C. Chun.——4th ed.
`p. cm.
`,
`Includes index.
`ISBN 0-8121-1438-8
`2. Chemistry,
`1. Pharmaceutical chemistry.
`Physical and theoretical.
`I. Bustamante, Pilar.
`11. Title.
`1. Chemistry, Pharmaceutical.
`[DNLM:
`Chemistry, Physical. QD 453.2 M379p]
`RS403.M34
`1993
`541.3’024’615-—dc20
`DNLM/DLC
`for Library of Congress
`
`2.
`
`NOTE: Although the author(s) and the publisher have taken
`reasonable steps to ensure the accuracy of the drug information
`included in this text before publication, drug information may
`change without notice and readers are advised to consult the
`manufacturers packaging inserts before prescribing medications.
`
`Reprints of chapters may be purchased from Lea & Febiger in
`quantities of 100 or more. Contact Sally Grande in the Sales
`Department.
`
`'
`
`Copyright © 1993 by Lea & Febiger. Copyright under the Interna-
`tional Copyright Union. All rights reserved. This book is protected by
`copyright. N0 part of it may be 'rcp'rocluccd in any manner or by any
`means without written permission from the publisher.
`
`PRINTED IN THE UNITED STATES OF AMERICA
`Print No. 5
`4
`3
`2
`1
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`
`Contents
`
`1.
`
`introduction
`
`1
`
`2. States of Matter 22
`
`’2.:
`
`i/3./Thermodynamics
`
`53
`
`4. Physical Properties of Drug Molecules 77
`
`5. Solutions of Nonelectrolytes
`
`101
`
`6. Solutions of Electrolytes
`
`125
`
`143
`7._ ionic Equilibria
`8. Buffered and isotonic Solutions
`
`169
`
`9. Electromotive Force and Oxidation—Reduction
`
`190
`
`‘
`
`'2
`
`10. Solubility and Distribution Phenomena
`212
`11. Complexat/ion and Protein Binding 251
`A
`/1/2. Kinetics 284 my :2. ii.
`Jejgoiiiusion and Dissolution 324 4--3./i
`lntertacial Phenomena 362
`\1\5V,l Colloids 393
`‘i§i1:__C€‘3/i.VAM‘lVlicromeritics
`423
`_» ‘\....ji7,.3 Rheology 453
`Coarse Dispersions 477
`19.” Drug Product Design
`512
`
`H ‘. 0'\’/\ Vi./‘
`‘Q/20. Polymer Science 556 N
`\App"endix: Calculus Review 595 ~53]
`Index 603
`
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`
`16
`
`Micromeritics
`
`Particle Size and Size Distribution
`
`Methods for Determining Particle Size
`Particle Shape and Surface Area
`
`Methods for Determining Surface Area
`Pore Size
`
`Derived Properties of Powders
`
`The science and technology of small particles have
`been given thename micromeritics by Dalla Valle}
`Colloidal dispersions are characterized by particles that
`are too small to be seen in the ordinary microscope,
`Qv_h_ereas the particles of pharmaceutical emulsions and
`suspensionsand the “fines” of powders fall in the range
`of the optical microscope. Particles having the size of
`coarser powders,
`tab et granulations, and granular
`salts fall within the sieve range. The approximate size
`ranges of particles in pharmaceutical dispersions are
`listed in Table 16—1a. The sizes of other materials,
`including microorganisms, are found in Tables 16—1b
`and c. The unit of particle size used most frequently in
`micromeritics is the micrometer, am, also called the
`micron, pt, and equal to 10'“ m, 10“4 cm, or 10”3 mm.
`One must not confuse pm with min, the latter being the
`symbol for a rnillimicron or 10"9 m. The millimicron now
`is most commonly referred to as the nanometer (nm).
`(Knowledge and control of the size, and the size range,
`of particles is of profound importance in pharmacy)
`Thus, size, and hence surface area, of a particle can be
`related in a significant way to the physical, chemical,
`and pharmacologic properties of a drug. Clinically, th
`pa can affect its release from dosage
`forms that are administered orally, parenterally, rec-
`
`.2»
`
`formulation of
`tally, and topically. The ‘successful
`suspensions, emulsions, and tablets, from the view-
`points of both physical stability and pharmacologi
`rgs_p_9_pse, also depends on the partic_l_e_siz_e_a_chieved in
`the product. In the area of tablet and capsule manu—
`facture, control of the particle size is essential
`in
`achieving the necessary flow properties and proper@
`mixing of granules and powders. These and other
`factors reviewed by Leesz make it apparent that a
`pharmacist today must possess a sound knowledge of
`micromeritics.
`'
`
`PARTICLE SIZE AND SIZE DISTRIBUTION
`
`In a collection of particles of more than one size (i.e.,
`in a pol dis erse sample), two properties are impor~
`tant, na shape and surface area of the
`individual particles, and (2) the size range and number
`or weight of particles present and, hence,
`the total
`surface area. Particle size and size distributions_will be
`considered in this section; shape and surface area will
`be discussed subsequently.
`The size of a sphere is readily expressed in terms of
`its diameter. As the degree of assymmetry of particles
`
`TABLE 16-1a. Particle Dimensions in Pharmaceutical Disperse Systems
`
`Particle Size
`
`Micrometers
`(pm)
`.1
`O.5—10
`10—5O
`
`50-100
`150- 1000
`1000-3360
`
`Milllmeters
`
`0.0005~0.01O
`0.010~0.05O
`
`0.050—O.lOO
`O.l50—l.0O0
`1.000—3.360
`
`Approximate
`Sieve Size
`
`Examples
`
`' 325-140
`100~18
`18-6
`
`Suspensions, fine emulsions
`Upper limit of subsieve range, coarse emulsion
`particles; flocculated suspension particles
`Lower limit of sieve range, fine powder range
`Coarse powder range
`Average granule size
`
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`430 PhysicaiPiuLrnwLcy
`
`also equals 1.43. Customarily, the prime is dropped
`since the value is independent of the type of distribu-
`tion. The geometric mean diameter (the particle size at
`the 50% probability level) on a weight basis, d_;,, is 10.4
`um, whereas dg = 7.1 ‘urn.
`Provided the distribution is log-normal, the second
`approach is to use one of the equations developed by
`Hatch and Choate.8 By this means, it is possible to
`convert number distributions to weight distributions
`with a minimum of calculation. In addition, a particular
`average can be readily computed by use of the relevant
`equation. The Hatch~Choate equations are listed in
`Table 16-5.
`
`Example 16— I. From the number distribution data in Table 16—4
`and Figure 16—5, it is found that d,, = 7.1 um and U9 = 1.43, or log
`09 = 0.1553. Using the relevant Hatch~Choate equation, calculate
`db, and d_,’,.
`The equation for the Icngth—number mean, 051", is
`log d;,, = log d, + 1.151 logz Cg
`= 0.8513 ~— 1.151(0.1553)2
`= 0.8513 ~ 0.0278
`= 0.8791
`
`(l,,, = 7.57 pun
`
`To calculate d;, we must substitute into the following Hatch-
`Clioate equation:
`
`log d,,, = log (1; — 5.757 logz cg
`0.8791 = log d5’, — 5.757(0.l553)2
`
`log d,’, = 0.8791 + 0.1388
`= 1.0179
`
`C1,‘, = 10.4 pm
`One can also use an equation suggested by Rae,”
`(16-2)
`(ié = d, cg“ 1" ‘W
`to readily obtain d,’,, knowing d_,, and cg. In the present example,
`cl; = 7.1(1.43)‘3 '" M3’
`= 10.42
`
`The student should confirm that substitution of the relevant data
`into the remaining Hatcl1— Choate equations in Table 16-5 yields the
`following statistical diameters:
`d,,, = 8.07 am;
`d,.3 = 9.78 p.111;
`
`d,,.,, = 8.60 um;
`d,,.,,, = 11.11 mm
`
`Particle Number. A significant expression in particle
`technology is the number ofparticles per unit weight N,
`which is expressed in terms of aim.
`The number of particles per unit weight is obtained
`as follows. Assuming that the particles are spheres, the
`volume of a single particle is nrdjf,/6, and the mass
`
`(volume >< density) is 11dU,,3p/6 g per particle. The
`number of particles per gram is then obtained from the
`proportion
`
`('”'dvn3I3)/6 g 4 1 g
`1 particle W
`
`OGT3)
`
`N_6—
`)
`(
`Trdimgp
`Example 16-2. The mean volume number diameter of the powder,
`the data for which are given in Table 16-2, is 2.41 urn or 2.41 X 10”
`cm. If the density of the powder is 3.0 g/cm3, what is the number of
`particles per gram?
`
`16 — 4
`
`6
`N =T: 4.55 ><101°
`3.14 x (2.41 x 10*‘‘)3 X 3.0
`
`METHODS FOR DETERMINING PARTICLE SIZE
`
`Many methods are available for determining particle
`size. Only those that are widely used in pharmaceutical
`practice and are typical of a particular principle are
`presented. For a detailed discussion of the numerous
`methods of particle size analysis,
`the reader should
`consult the texts by Edmundson5 and by Allen,” and
`the references given there to other sources. The
`methods available to determine the size characteristics
`of submicrometer particles have been reviewed by
`Groves.“ Such methods apply to colloidal dispersions
`(see Chapter 15).
`Mig_o§_copy, sieying, sedimentation, and th_e_dg1;,g=_1;rni—
`nation of particle volume are discussed in the following
`section.
`one o
`the measurements are truly direct
`methods. Although the microscope allows the observer
`0 )0 view the actual particles, the results obtained are
`probably no more “direct” than those resulting from
`other methods since only two of the three particle
`dimensions are ordinarily seen. The s n
`methods yield a particle size relative to the rate at
`which particles settle through a suspending medium, a
`measurement important in the development of emul-
`sions and suspensions. The measu ticle
`v_(_>l_u_1;_1e, using an apparatus called the C ter,
`allows one to calculate an equivalent volume diameter.
`However, the Le
`'
`"
`informati
`to the
`shape of the particles. Thus, in all these cases, the size
`may or may not compare with that obtained by the
`microscope or by other methods;
`the size is most
`
`(9
`
`TABLE 16-5. Hatch—Chaate Equations for Computing Statistical Diameters from Number and Weight Distributions
`Diameter
`Number Distributon
`
`Weight Distribution
`
`Length—number mean
`Surface—number mean
`Volume—number mean
`Voiume—surface mean
`Weight—moment mean
`
`log d,, = log
`d +1.151|og2 cg
`log as, = log cf, »« 2.303 Iogz (TE
`log dw,
`log dg »— 3.454 Iogz Ug
`log d,,5 - log dg ~ 5.757 Iogz cg
`log d,,,,, = log dg + 8.059 iogz org
`
`log a’,,, = log dé ~ 5.757 logz cg
`log cs, — log a; — 4.506 mg? (J-g
`log d,', — 3.454 logz U8
`log d,,,
`log dvs ~
`log dé ~ 1.151 IOg22o'g
`log dwm = log d; + 1.151 log crg
`
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`
`is
`directly applicable to the analysis for which it
`intended. A guide to the range of particle sizes
`applicable to each method is given in Figure 16-6.
`Optical Microscopy.
`It should be possible to use the
`ordinary microscope for particle—size measurement in
`the range of 0.2 pm to about 100 pm. According to the
`microscopic method, an emulsion or suspension, diluted
`or undiluted, is mounted on a slide or ruled cell and
`placed on a mechanical stage. The microscope eyepiece
`is fitted with a micrometer byv of the
`particles ma be estimated. The field can be projected
`onto a screen where the particles are measured more
`easily, or a photograph can be taken from which a slide
`is prepared and projected on a screen for measurement.
`The particles are measured along an arbitrarily
`chosen fixed line, generallyimade horizontally across
`the center of the particle. Popular measurements are
`the Feret diameter,
`the Martin diameter,12 and the
`projected area diameter, all of which may be defined by
`reference to Figure 16-7, as suggested by Allen.”
`Martin’s diameter is the length of a line that bisects the
`particle image. The line ma be drawn '
`n direction
`but must be in the same djreeeion for all particles
`measured. The Martin diameter is identified by the
`number 1 in Figure 16-7. Feret’s diameter, corre-
`sponding to the number 2 in the figure, is the distance
`between two tangents on opposite sides of the particle
`parallel to some fixed direction, ‘the y—direction in the
`figure. The third measurement, number 3 in Figure
`16-7, is the projected area diameter. It is the diameter
`of a circle
`'
`same area as that of the particle
`observed perpendicular to the surface on which the
`particle re
`.
`A size—frequency distribution curve may be plotted as
`was seen in Figure 16-1 for the determination of the
`statistical diameters of
`the distribution. Elecmggnic
`
`C/rapier J6 - Micromeritics
`
`431
`
`scanners heye hmmdeyelepecl to remove the necessity
`ofme rvation.
`Prasad and Wan” used Video recording equipment to
`observe, record, store, and retrieve particle—size data
`from a microscopic examination of tablet excipients,
`including microcrystalline cellulose, sodium carboxy-
`methylcellulose, sodium starch glycolate, and methyl-
`cellulose. The projected area of the particle profile,
`Feret’s diameter (p. 432), and various shape factors
`(elongation, bulkiness, and surface factor) were deter-
`mined. The video reco in ‘te
`’ ue was found to be
`simple and convenient for microscopic examination of
`excipients.
`'
`A disadvantage of the microscopic method is that the
`dia
`— er is obt
`'
`"
`onl
`two dimensio s of the
`
`part le: length and breadth. No estimation of the depth
`.
`ickness) of the particle is ordinarily available. In
`addition, the number of articles that must be counted
`(300 to 500) to obtain a good estimation of the distribu-
`tion di°“S-
`But, microscopic examination (photomicrographs) of a
`sample should be undertaken, even when other meth-
`ods of particle—size analysis are being used, since the
`presence of agglomerates and particles of more than
`one component may often be detected.
`Sieving. This method uses a series of standerd sieves
`calibrated by the N ati
`1’ Standards. Sieves
`are generally used for grading coarser particles;
`if
`extreme care is used, however, they may be employed
`for screening material as fine ae 44 pm (No. 325 sieve).
`Sieves produced by photoetching and electroforming
`techniques are now available with apertures from 90
`am down to as low as 5 am. According to the method of
`the U.S. Pharmacopeia for testing powder fineness_,_a
`de mple is placed on the proper sieve in
`a mechanical shaker. The powder is shaken for a
`
`Sieving
`
`G)
`
`Electron microscope
`Optical microscope
`re——~u————————+
`
`Ultracentrifuge
`
`Sedimentation "
`
`-i
`
`ll.
`
`Coulter counter
`r——-—————-———~r
`
`Air Permeability
`Adsorption
`r—————lr——-————4
`
`1A
`
`I
`100A
`
`0.01 am
`
`,
`0.1 um
`
`,
`I am
`
`Particle size
`
`,{t,.,x.
`1000 ,um
`10,000 ,am
`10am
`l00p.m
`1 cm
`lmm
`
`Fig. 16-6. Approximate size ranges of methods used for particle size and specific surface analysis.
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`432 Physical Phmmacy
`
`C9
`
`Y
`
`Fig. 16-7. A general diagram providing definitions of the Feret,
`Martin, and projected diameters.
`(From T. Allen, Particle Size
`measurements, 2nd Edition, Chapman & Hall, London, 1974, p. 131,
`reproduced with permission of the copyright owner.)
`
`definite period of time, and the
`through one sieve and is retai
`is collecte
`'
`ed.
`
`asses
`"al that
`next finer sieve
`
`Another custom is to assign the particles on the lower
`sieve thear e two
`screens. Arambulo and Deardorff“ use
`IS method of
`size classification in their analysis of the average weight
`of compressed tablets. Frequently the powder is as-
`signed the mesh number of the screen through which it
`passes or on which it is retained. King and Becker”
`expressed the size ranges of calamine samples in this
`way in their study of calamine lotion.
`When a detailed analysis is desired, the sieves may
`be arranged in a nest of about five with the coarsest at
`the tgp. A carefully weighed sample of the powder is
`placgd on the top sieve, and after e shaken
`for a predetermined
`eriod of time, the powder re-
`tained 911 each sieve is weighed. Assuming a log—normal
`distribution,
`the cumulative percent by flfimlt of
`powder
`retained on the sieves is plotted on the
`probability scale against the logarithm of the arithmetic
`mean size of the openings of each of two successive
`screens. As illustrated in Figure 16-5, the geometric
`mean weight diameter at; and the geometric standard
`deviation og can be obtained directly from the straight
`line.
`
`According to Herdan,” sieving errors can arise from
`a number of variables including sie;Le,_],Qading and
`duration and intensity of agitation. Fonner et al.18
`demonstrated that sieving can cause attrition of gran-
`ular pharmaceutical materials. Care must be taken,
`therefore, to ensure that reproducible techniques are
`employed so that different particle size distributions
`between batches of material are not due simply to
`different sieving conditions.
`
`Sedimentation. The application of ultracentrifugation
`to the determination of the molecular weight of high
`polymers has already been discussed (p. 403). The
`Q3.If7tl_C7‘Vl_§V§VlZe in the Sl1l?..S..l§3JLe range may be obtained by
`gravity sedimentatioii as expressed ,_in_Stol<_cs’ law,
`
`: E : dsi2(ps “ Po)g
`2%
`18¢],
`
`"
`
`dst =
`
`18T|ofl,
`(ps — Polgt
`
`(16—5
`
`(15-5)
`
`in which i_;_is_the rate of settling, Ii is the distanceyof fall
`i_n'ti_m__e t, dsy__is_the:rnean diameter of the particles based
`on the velocity of sedimentation, ps is the density/_gf the
`particles and po that of the dispers’ioiil‘inefdium, g__is__the
`a_gcjeleration.due to gravity, and no is the viscosity of the
`medium. The equation holds exactly only for spheres
`falling freely without hindrance and at a constant rate.
`The law is applicable to irregularly shaped particles of
`' various sizes as long as one realizes that the diameter
`;' obtained is a relative particle size equivalent to that of
`sphere falling at
`the same velocity as that of the
`particles under consideration. The particles must not be
`3 aggregated or clumped together in théflsuspehsion since )
`such clumps would fall more rapidly than the individual
`1 particles, and erroneous results would be obtained. The
`proper deflocculating agent must be found for each
`sample that will keep the particles free and separate as
`they fall through the medium.
`Example 16-3. A sample of powdered zinc oxide, density 5.60
`g/cm3, is allowed to settle under the acceleration of gravity, 981 cm
`sec"2, at 25° C. The rate of settling, 2),
`is 7.30 X 10"’ cm/sec; the
`density of the medium is 1.01 g/cm3, and its viscosity is 1 cp = 0.01
`poise or 0.01 g cm” sec“. Calculate the Stokes’ diameter of the zinc
`oxide powder.
`
`d
`
`5!
`
`\/18 X 0.01 g cm"‘ sec” X 7.30 X 10“3 cm sec”
`(5.60 ~ 1.01) g cm'3 X 981 cm sec”
`= 5.40 X 10"‘ cm or 5.40 am
`
`3
`
`For Stokes’ law to apply, a further requirement is
`that the flow of dispersion medium around the particle
`as it sediments is laminar or streamline.
`In other
`words, the rate of sedimentation ofoa part_icle_rnu_s_t not
`be so rapid.that turbulence is, set up, since this in turn
`will affect the sedimentation of,.the particle. Whether
`the flow is turbulent or laminar is indicated by the di-
`mensionless Reynolds number,sRa, which is defined as
`: 7’ dp”
`(16-7)
`00/
`in which the symbols have the same meaning as in
`equation (16-5). According to Heywood,” Stokes’ law
`cannot be used if Re is g1*eat_eL,t,llELI.1..._0.2,..since»tprlgu—
`lence appears at this valii"e“."’C)n this basis, the limiting
`particle size under a given set of conditions may be
`calculated as follows:
`
`R.
`
`I
`
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`Rearranging equation (16-7) and combining it with
`equation (16-5) gives
`
`’
`
`_ : T596 .T_,.P9?€
`187]
`
`——-—
`(P3 — po)po.C/
`
`(16-8)
`
`(16-9)
`
`Under a given’ set of density and viscosity conditions,
`equation (16-9) allows calculation, of the maximum
`particle diameterwhose sedim_entation_will be governed
`that is, when Re does not exceed 0.2.
`is
`Example 16-4. A powdered material, density 2.7 g/cm3,
`suspended in water at 20° C. What is the size of the largest particle
`that will settle without causing turbulence? The viscosity of water at
`20° C is 0.01 poise, or g/(cm sec) and the density is 1.0 g/cm3.
`From equation (16-9):
`
`(Z3 =
`
`(18)(0.2)(0.O1)2
`(2.7 — l.0)l.0 X 981
`
`(Z = 6 x 10* em = 60 um
`
`is now
`If the material used in Ercamplc 16-1,
`Example 16-5.
`suspended in a syrup containing 60% by weight of sucrose, what will
`be the critical diameter, that is, the maximum diameter for which R‘!
`does not exceed 0.2? The viscosity of the syrup is 0.567 poise that is,
`and the density 1.3 g/cm3.
`
`(18)(0.2)(0.5G7)Z
`d, :
`(2.7 - 1.3)1.3 X 981
`'
`(Z = 8.65 X 10"2 em = 865 pun
`
`Several methods based on sedimentation are used.
`
`the
`Principal among these are the pipette method,
`balan,c_e_,,method, and the hydrometer method. Only the
`first technique is discussed here since it combines ease
`of analysis, accuracy, and economy of equipment.
`The Andreasen apparatus is shown in Figure 16-8.
`It usually consists of a 55,0-inL, vessel containing a
`10—mL pipette sealed into a groundjglass stopper.
`Whfleiiwtlie pipette is in place in the cylinder,its lower tip
`is 20 cmqbelow the surface of the suspension.
`The analysis is carried out in the following manner. A
`1 or ,2%..susp_ension of the particles in a medium
`containing a suitabledeflocculating agent is introduced
`into the vessel and brought to the 5I50—mL mark. The
`stopperedaressell is_,_shaken to distribute the particles
`.uniforrnly throughout the suspension and the appara-
`tusfwith pipette in place,
`is clamped securely in a
`cg_nstant~temperature bath. At various time intervals,
`10:ii/iliwsainples areiiwithdrawn and discharged by
`means of the two—way stopcock. The samples are
`evaporated and weighed or analyzed by other appropri-
`ate means, correcting for the deiiocculating agent that
`has been added.
`
`The particle diameter corresponding to the various
`time periods is calculated from Stokes’ law, with h in
`equation (16-6) being the height of the liquid above the
`lower end of the pipette at the time each sample is
`removed. The residue or dried sample obtained at a
`
`C/zdpter 10 -3 Mic-romcritics'
`
`433
`
`Fig. 16-8. Andreasen apparatus for determining particle size by the
`gravity sedimentation method.
`
`particular time is the weight fraction having particles of
`sizes less than the size obtained by the Stokes’ law
`calculation for that time period of settling. The weight
`of each sample residue is therefore called the weight
`imdersize, and the sum of the successive weights is
`known as the cumulative weight mzdersize. It may be
`expressed directly in weight units or as percent of the
`total weight of the final sediment. Such data are plotted
`in Figures 16-2, 16-8, and 16-4. The cumulative
`percent by weight undersize may then be plotted on a
`probability scale against the particle diameter on a log
`scale, as in Figure 16-5, and the statistical diameters
`obtained as explained previously. Data that illustrate
`the sedimentation method employing the Andreasen
`apparatus are found in Problem 16-/,., p. 450.
`The Micromeritics Instrument Co., Norcross, Ga.,
`offers the SediGraph 5100 for particle—size analysis
`based on the sedimentation principle. Since particles
`are not usually of uniform shape, the particle size is
`expressed as equivalent spherical diameter or Stokes’
`diameter.
`
`A 1ow—energy x—ray beam passes through the suspen-
`sion and is collected at the detector. Which x~ray pulses
`reach the detector is determined by the distribution of
`settling particles in the cell; and from the X-ray pulse
`count the particle size distribution and the mass of
`particles for each particle diameter are derived. The
`operation is completely automatic,
`the apparatus is
`temperaturecontrolled, and the data are analyzed
`under computer software control. Particle diameters
`are measured from 0.1 to 300 pm at temperatures from
`10° to 40° C. The Micromeritics Co. also manufactures
`
`equipment forthe measurement of powder density,
`surface area, adsorption and desorption, pore volume,
`
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`

`
`434
`
`P/z.ys‘iccz.lPlumncwy
`
`pore size, and pore size distribution (see pp. 440~
`442 for a discussion of pore size).
`lVlass., has
`MATEO Applied Sciences, Hopkinton,
`developed a particle—size measurement system for
`8'2Lb7'77/L'C7"OlZ partcles in the range of 0.015 to 1.1 inn. The
`particles in suspension are caused to pass through
`capillary tubes, the larger particles attaining greater
`average velocites than the smaller ones. The instru-
`ment applies this principle to the determination of
`average particle size and size distribution by number or
`volume of part'cles. The operation, from the time of
`sample injection to graphics output, requires a maxi-
`mum of 8 minutes. The liquid medium consists of 1 mL
`of water contaning a surfactant and the suspended
`particles in the concentration of 2 to 4% solids. The
`particles to be 'nalyzed are prefiltered through a 5pm
`or smaller pore size filter. A computer terminal and
`program, printer, and plotter are available to calculate
`and display the size and size distribution data.
`Particle Volume Measurement. A popular instrument
`to measure the volume of particles is the Coulter
`counter (Fig. 16--9). This instrument operates on the
`principle that when a particle suspended in a conducting
`liquid passes through a small orifice, on either side of
`which are electrodes, a change in electric resistance
`occursflln practice,
`a known volume of a dilute
`suspension is pumped through the orifice. Provided the
`suspension is sufficiently dilute,
`the particles pass
`through essentially one at a time. A constant Voltage is
`applied across the electrodes to produce a current. As
`the particle travels through the orifice, it displaces its
`own volume of electrolyte, and this results in an
`
`increased resistance between the two electrodes. The
`change in resistance, which is related to the particle
`volume, causes a voltage pulse that is amplified and fed
`to a pulse height analyzer calibrated in terms of particle
`size:“"g' ‘he instrument records electronically all those
`particles producing pulses that are within two threshold
`values of the analyzer. By systematically varying the
`threshold settings and counting the number of particles
`in a constant sample size, it is possible to obtain a
`particle size distribution. The instrument is capable of
`counting particles at the rate of approximately 4000 per
`second, and so both gross counts and particle size
`distributions are obtained in a relatively short period of
`time. The data may be readily converted from a volume
`distribution to a weight distribution.
`The Coulter counter has been used to advantage in
`the pharmaceutical sciences to study particle growth
`and dissolutionmzl and the effect of antibacterial
`agents on the growth of microorganisms.22
`The use of the Coulter particle—size analyzer together
`with a digital computer was reported by Beaubien and
`Vanderwielen23 for the automated particle counting of
`milled and micronized drugs. Samples of spectinomycin
`hydrochloride and a micronized steroid were subjected
`to particle—size analysis,
`together with polystyrene
`spheres of 2.0 to 80.0 um diameter which were used to
`calibrate the apparatus. The powders showed log-
`normal distributions and were well characterized by
`geometric volume mean diameters and geometric stan-
`dard deviations. Accurate particle sizes were obtained
`between 2 and 80 um diameter with a precision of about
`0.5 ptm. The authors concluded that the automated
`
`Mercury /V
`
`Electrolyte
`solution
`Y .
`
`Electrolyte
`solution and
`particles
`
`’ Orifice
`
`‘~c>
`é
`
`Lcounter
`switch
`
`Nlain
`amplifier
`
`W _!Thresho|d
`circuit
`
`proportional to
`particle volume
` '
`
`ill Ill
`
`Scope
`
`Counter
`drive
`
`—”Digltma_l—
`register
`
`Schematic diagram of a Coulter counter, used to determine particle volume.
`
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`

`
`17
`
`Rheology
`
`Introduction
`
`Newtonian Systems
`Non—Newtonian Systems
`Thixotropy
`
`Determination of Rheologic Properties
`Viscoelasticity
`Psychorheology
`Applications to Pharmacy
`
`INTRODUCTION
`
`The term rheology, from the Greek rhea (to How) and
`logos (science), was suggested by Bingham and Craw-
`ford (as reported by Fischerl) to describe the flow of
`liquids and the deformation of solids. Viscosity is an
`expression of the resistance of a fluid to flow; the higher
`the viscosity, the greater the resistance. As will be seen
`later, simple liquids can be described in terms of
`absolute viscosity. The rheologic properties of hetero-
`geneous dispersions are more complex, however, and
`cannot be expressed by a single value.
`In recent years, the fundamental principles of rheol-
`ogy have been used in the study of paints, inks, doughs,
`road building materials, cosmetics, dairy products, and
`other materials. The study of the viscosity of true
`liquids, solutions, and dilute and concentrated colloidal
`systems is of much practical as well as theoretic value.
`These points have been discussed in Chapter 15, which
`deals with colloids. Scott—Blair2 recognized the impor—
`tance of rheology in pharmacy and suggested its
`application in the formulation and analysis of such
`pharmaceutical products as emulsions, pastes, suppos-
`itories, and tablet coatings. The manufacturer of me-
`dicinal and cosmetic creams, pastes, and lotions must be
`capable of producing a product with an acceptable
`consistency and smoothness and must be able to
`reproduce these qualities each time a new batch is
`prepared. In many industries, the judgment of proper
`consistency is made by a trained person with long
`experience who handles the material periodically dur-
`ing manufacture to determine its “feel” and “body.” The
`variability of subjective tests at different times under
`varying environmental conditions is, however, well
`recognized. A more serious objection, from a scientific
`standpoint,
`is the failure of subjective methods to
`distinguish the various properties that make up the
`total consistency of the product. If these individual
`
`physical characteristics are delineated and studied
`objectively according to the analytic methods of rheol—
`ogy, valuable information can be obtained for use in
`formulating better pharmaceutical products.
`Rheology is involved in the mixing and flow, of
`materials, their packaging into coiitaihér’s"," and their
`removal prior to use, whether this is achievedby’
`pouring from a bottle, extrusion from a tube, or passage
`through a syringe needle. The rheology of a particular
`product, which can range in consistency from fluid to
`semisolid to solid, can affect its patient acceptability,
`physical stability, and even biologic availability. Thus,
`Viscosity has been shown to affect the absorption rate of
`drugs from the gastrointestinal tract.
`The rheologic properties of a pharmaceutical system
`can influence the choice of processing equipment to be
`used in its manufacture. Furthermore, lack of appreci-
`ation for the correct choice of a piece of processing
`equipment can result in an undesirable product, at least
`in terms of its flow characteristics. These and other
`
`aspects of rheology that apply to pharmacy are dis
`cussed by Martin et al.3
`When classifying materials. .acc9:.;d,i;t1,g.,tq~t~lti3a.g;’rli2e§* of
`flow and deformatigp '
`' custom.
`'
`lace‘tf'em in
`one 9f..,t.v.V9 e~§§l3§g;&1il~§§% - .
`Wtonian
`syst'”e5ih§.' T ‘e choice depends on whether or not their
`flow properties are in accord with Newton's law of flow.
`
`NEWTONIAN SYSTEMS
`
`Newtonian’s Law of Flow. Consider a “block” of liquid
`consisting of parallel plates of molecules, similar to a
`deck of cards, as shown in Figure 17-1. The bottom
`layer is considered to be fixed in place. If the top plane
`of liquid is moved at a constant velocity, each lower
`layer will move with a velocity directly proportional to
`
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