FOURTH E DITION
`
`Physical Pharmacy
`
`PHYSICAL CHEMICAL PRINCIPLES IN THE PHARMACEUTICAL SCIENCES
`
`AlfredJY!artin, Ph.D.
`Emerit1ts Coulter R. Sublett P1·ofessor
`Drug Dynamics Institute,
`College of Pharmacy,
`University of Texas
`
`with the participation of
`PILAR BUSTAMANTE, Ph.D.
`Titular Prof essm·
`Depa1-t1Mnt of Pharmacy
`and Pharmaceutical Technology,
`University Alcala de Henares,
`Mad1·id, Spain
`
`and with illustrations by
`A. H. C. CHUN, Ph.D.
`Associate Research Fellow
`Phannaceutical Products Division,
`Abbott Laboratcnies
`
`LEA & FEBIGER
`
`PHILADELPHIA, LONDON
`
`1993
`
`'!lfh;·7~39
`
`DRL - EXHIBIT 1008
`DRL001
`
`

`
`L&A & F~;urCER
`Box SO~
`£00 Chesttr Field Parkway
`Malvem, PA 19955-9725
`(215)251 ·f290
`
`Executive Editor: George H. Mundorff
`Production Manager: 'fhomas J. Colaiezzi
`Project Editor: Denise Wilson
`
`Library of Congress Cataloging-in-Publication Data
`
`Martin, Alfred N.
`Physical pharmacy : physical chemical principles
`in the pharmaceutical sciences I Alfred Martin ; with
`ibe participation of Pilar Bustamante and with
`illustrations by A.H.C. Chun.-4th ed.
`p. cm.
`Includes index.
`ISBN 0-8121-1438-8
`1. Pharmaceutical chemistry. 2. Chemistry,
`I. Bustamante, Pilar.
`Physical and theoretical.
`II. TiUe.
`[DNLM: 1. Chemistry, Pharmaceutical. 2.
`Chemistry, Physical. QD 453.2 M379p)
`RS40S.M34 1993
`541.S'024'615-dc20
`DNLM/DLC
`for Library of Congress
`
`92-49751
`CIP
`
`NOTE: Although the author(s) and the publisher have taken
`reasonable steps lo ensure the accw·acy of the drug information
`included in this text befot·e publication, drug information may
`chango without notice and readers are advised to consult the
`manufacturer's packaging inserts before prescribing medications.
`
`Reprints of chapters may be pm·chased from Lea & Febiger in
`quantities of 100 or more. Contact Sally Grande in the Sales
`Department.
`
`Copyright C 1993 by Lea ,~ Febigcr. Copyright under the Interna(cid:173)
`tional Copyright Union. All rights rese1·ved. This book is protected by
`copyright. No pai·t of it may be i·eproduced in any mannei· or by any
`means without written permission from, the publisher.
`PRINTED IN THE UN~TED STATES OF AMERICA
`
`r1int No. 6 4 3 2 1
`
`DRL - EXHIBIT 1008
`DRL002
`
`

`
`Contents
`
`ix
`
`1. Introduction 1
`2. States of Matter 22
`-z-: ~Thermodynamics 53
`4. Physical Properties of Drug Molecules 77
`5. Solutions of Nonelectrolytes 101
`6. Solutions of Electrolytes 125
`7 .. Ionic Equilibria 143
`8. Buffered and Isotonic Solutions 169
`9. Electromotive Force and Oxidation - Reduction 190
`10. Solubility and Distribution Phenomena 212
`11. Complexation and Protein Binding 251
`/12. Kinetics 284 - 2. 41 '.l :',· I I~ ·· .•:.<·!
`'I ).-
`::'~ A~ Diffusion and Dissolution 324 .- ~ .( (
`.,;
`\14) lnterfacial Phenomena 362
`,
`v
`1.:>'t
`'*5,l Colloids 393
`\16. Micromeritics 423
`'·'
`\.,171 Rheology 453
`~: Coarse Dispersions 477
`19. Drug Product Design 512
`'/'~·O'•/
` v~·!.\' ,,
`\,.;20. Polymer Science 556
`-;;1 U
`3-Prfendix: Calculus Review 595
`Index 603
`~-
`''*"
`
`6.
`
`. (
`-¥-~.
`
`<;<t~ <Jell--
`
`DRL - EXHIBIT 1008
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`

`
`16
`M icromeritics
`
`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 the name micro?'l'te'titics by Dalla Valle. 1
`Colloidal dispersions are characterized by particles that
`are too small to be seen in the ordinary microscope,
`(whereas the particles of pharmaceutical emulsions and
`suspensions and the "fines" of powders fall in the range
`of the optical microscope) Particles having the size of
`coarser powders, tabie't'"" granulations, and granular
`salts fall within the si~ge. The approximate size
`ranges of particles in pharmaceutical dispersions are
`listed in Table 16- la.. The sizes of other materials,
`including microorganisms, are found in Tables 16-lb
`and c. The unit of particle size used most frequently in
`~cromel·itics is the micto~eter, µ.m, also called the
`micron, µ., and equal to 10- m, 10- 4 cm, or io-3 mm.
`One must not confuse µ.m with mµ., the latter being the
`symbol for a millimicron or io-9 m. 'l'he millimicro11 now
`is most commonly referred to as the nanometer (nm).
`(Jcnowledge 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€fi\
`pa1;J.icle size of a drug can affect its release from dosageV
`forms that are administered orally, parenterally, rec-
`
`tally, and topically. The successful formulation of
`suspensions, emulsions, and tablets, from the view-~\
`points of both physical stability and pharmacologi&
`response, also depends on the particle size achieved in
`the product. In the area of tablet and capsule manu(cid:173)
`facture, control of the particle size is essential in~
`achieving the necessary flow properties and properlY
`mixing of granules and powders. These and other
`factors reviewed by Lees2 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 polydisperse sample), two properties are impor(cid:173)
`tant, namely (1) the shape and smface area of the
`individual particles, and (2) the size range and number
`or weight of particles present and, hence, the total
`surfa,ce area. Particle size and size distributions will be
`considered in this section; shape and suxface area will
`be discussed subsequently.
`The size of a S]~.re is readily expressed in terms of
`its diameter. As the degree of assymmetry of particles
`
`-
`
`TABLE 16- 1 a. Particle Dimensions in Pharmaceutical Disperse Systems
`
`Particle Size
`
`Micrometers
`(µm)
`
`0. 5-10
`10- 50
`
`50- 100
`150- 1000
`1000- 3360
`
`Millimeters
`
`0.0005- 0.010
`0.010-0.050
`
`0.050-0.100
`0.150- 1.000
`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
`
`.
`
`423
`
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`430 Physical Phcmnacy
`
`also equals 1.43. Customarily, the prime is dropped
`since the value is independent of the type of distribu(cid:173)
`tion. The geometric mean diameter (the particle size at
`the 50% probability level) on a weight basis, d~, is 10.4
`µm, whereas d0 = 7.1 µm.
`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 r eadily computed by use of the l'Clevant
`equation. The Hatch-Choate equations are listed in
`Table lG-5.
`Examfl/B 16- 1. 1"rom the number distribution data in 'l'ablo 16-4
`and Figure lG-5, it is found thal <Lu = 7.l 11m and "u = 1.113, 01· log
`<Tu = 0.1553. Using the relevanl llalch-Choate equation, calculate
`d1n and d~.
`The cqualion for the length-number mean, d1", is
`log d1• = log d0 + 1.151 log? <Tp
`- 0.8513 I 1.161(0.1653)2
`= 0.8513 ·~ 0.0278
`= 0.87!H
`d1. = 7.57 11m
`To calculate cl~, we must subslilutc into the following llalch(cid:173)
`Choale equalion:
`
`log cl1• = log ct; - 6.757 logZ cr11
`0.8791 = log cl;
`6.757(0.1653)2
`
`OI'
`
`log ct;= 0.8791 I· 0.1388
`= 1.0179
`<1; = 10.4 11m
`One can also use an equation suggest.eel by Rao,'
`cl~ = du CTo(3 In "rl
`(16- 2)
`lo readily obtain d;, knowing clu and uu. In the present example,
`d~ = 7. I (1.43)<3 In 1.43)
`= 10.42
`'!'he sludenl should confirm lhat substitution of the relevant data
`inlo lhe remaining Halch-Choatc equations in Table 16-5 yields the
`following slalistical diamet.ers:
`d, .. = 8.60 µm;
`d,. = 8.07 µm;
`ct • .,,.= 11.11 µm
`cl,.,= 9.78 µm;
`Particle Number. A significant expression in particle
`technology is the nmnber Of 7Ja?·tictes ver unit weight N,
`which is expressed in terms of dvw
`The number of particles per unit weight is obtained
`as follows. Assuming that the particles are spheres, the
`volume of a single particle is 'TTdv~/6, and the mass
`
`(volume x density) is 7Tdv}p16 g per particle. The
`number of particles per gram is the11 obtained from the
`proportion
`
`(7Tdv,/1p)/6 g _ !_g
`1 particle - N
`
`and
`
`(lG-3)
`
`(16-4)
`
`Example 16-2. The mean volume number diameter of the powder,
`the data for which are given in Table 16-2, is 2.41 µm or 2.111 x 10- 4
`cm. If the dcnsily of the powder is 3.0 g/cm3, what is the number of
`particles per grnm?
`
`N =
`
`6
`3.14 x (2.41 x 10- 4)3 x 3.0
`
`= 4.56 x 1010
`
`METHODS FOR DETERMINING PARTICLE SIZE
`
`Many methods are available for determining particle
`size. Only those that are widely used in pharmaceutical
`practice and are ty1)ical 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 Eclmundson5 and by Allen, 10 and
`the references given there to other sources. The
`methods available to determine the size charactel'istics
`of submicrometer particles have been reviewed by
`1 S uch methods apply to colloidal clispe1·sions
`Groves. 1·
`(sec Chapter 15).
`Mi~opy, s~ng, se~tion, and the rletermi(cid:173)
`r-ation of Aarticle volume arc discussed in the following
`section.
`one of t he measurements are tl'llly direct
`/, ~~ethocls. Although the microscope allows the observer
`UC' view the actual particles, the results obtained arc
`probably nQ more "direct" than those resulting from
`other methods since only two of the three particle
`dimensions are ordinarily seen. The sedimqnkat.ion
`methods yield a particle size relative to"" the rate at
`I~ which particles settle through a suspending medium, a
`\!' measurement important in the development of emul(cid:173)
`sions and suspensions. The measurtJWept of particle
`volume, using an apparatus called the Cq,u,Ucr cappter,
`allows one to calculate an equivalent volume diameter.
`However, the ~mjgue "ivcs no informatjon as to the
`sha_pe 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
`
`TABLE 16-5. Hate//- Choate Equations for Computing Statistical Diameters from Number and Weigflt Distributions
`
`Diameter
`
`Length- number mean
`Surface- number mean
`Volume-number mean
`Volume- surface mean
`Weight - moment mean
`
`Number Distribution
`
`log d, + 1.151 log2 a.
`log d1n -
`log a11 + 2.303 log2
`log d.,.
`"•
`log a, + 3.454 log2
`log dvn
`"•
`log d,,. ~ log d11 ·I- 5.757 log2 a11
`log dwm -
`log dR t 8.059 log2 cr11
`
`Weight Distribution
`
`log d1n = log d;. - 5. 757 log2
`"•
`log d.,. = log ~f - 4.606 fog2
`IT/I
`- 3.454 log2 a11
`log d.,. = log d8
`log d_, = log d~ -
`l.151 log'- IT11
`log di + 1.151 log2 cr1
`log dwm
`
`DRL - EXHIBIT 1008
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`

`
`directly applicable to the analysis for which it is
`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 µ.m to about 100 µ.m. 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 by which the size of the
`particles may 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, generally made 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. 13
`Martin's diameter is the length of a line that bisects the
`particle image. The line may be drawn in any direction
`but . must be in tte same direction for all particles
`measured. The Martin diameter is identified by the
`number 1 in Figure 16-7. Feret's diameter, corre(cid:173)
`sponding to the nwnber 2 in the figure, is the distance
`between two tangents on opposite sides of the particle
`parallel to some fixed direction, 'the y-direction fo the
`figure. 'fhe thfrd measurement, number 3 in Figure
`16- 7, is the projected area diameter. It is the diameter
`of a circle wjth the same area as that of the particle
`ich the
`observed perpendicular to the su · ace on
`part~.
`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. E le.c.l:.wnic
`
`Ch<t7Jter 16 • Micromeritics 431
`
`scanners haye been cleyeloped to remove the necessity
`of measuring the particles by visual ob
`rvation.
`Prasad and Wan14 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(cid:173)
`methylcellulose, sodium starch glycolate, and methyl(cid:173)
`cellulose. The projected area of the particle profile,
`Feret's diameter (p. 432), and various shape factors
`(elongation, bulkiness, and surface factor) were deter(cid:173)
`mined. The video recordjng technjgue was found to be
`simple and convenient for microscopic examination of
`excipients.
`A disadvantage of the microscopic method is that the @
`dii.uneter is obtajped from only two dimensio.ps of the
`~tide: length and breadth. No estimation of the depth
`ickness) of the particle is ordinarily available. In
`addition, the number of particles that must be counted ~ "
`(300 to 500) to obtain a g-ood estimation of the.ilistribu-~
`tion makes !'he methar] somewhat slow and tedious.
`But, 'i'nicroscopic 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 standard sieves
`calibrated by the Natjopal Illll'eau ofStanclards. Sieves
`are generally used for grading coarser particles; if
`extreme care is used, however, they may be employed
`for screening material as fine as 44 H:m (No. 325 sieve).
`$ieves produced by photoetching and electroforming
`techniques are now available with apertures from 90
`p,m clown to as low as 5 p,m. According to the method of
`the U.S. Pbarmacopeia for testing powder finenessJ
`cle,tipile mass qf sample is placed 011 the proper sieve in
`a mechanical shaker. The powder is shaken for a
`
`Electron microscope
`
`Optical microscope
`
`Ultracentrifuge
`
`Sedimentation "'
`
`Sieving
`
`., I
`
`Coulter counter
`
`Adsorption
`
`II
`
`Air Permeability
`
`1 A
`
`10 A
`
`100 A
`0.01 /.LITI
`
`0. 1 µ.m
`
`1 µ.m
`
`10 µ.m'
`
`100 µm
`
`1000 µ.m
`1 mm
`
`10,000 µm
`1 cm
`
`Particle size
`
`Fig. 16-6. Approximate size ranges of methods used for particle sille and specific surface analysis.
`
`DRL - EXHIBIT 1008
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`

`
`432 Physical Phannacy
`
`3
`
`f
`l
`
`f
`
`2
`
`Sedimentation. The application of ultracentrifugation
`to the determination of the molecular weight of high
`polymers has already been discussed (p. 403). The
`particle siz~jn th!'! sqhpie..)!Sl range may be obtained by
`gravity seqimentation as expresseqjn -~.tol~es' law,
`
`h
`v = - =
`t
`
`d8i2(Ps - Po)g
`18'T]0
`
`or
`
`dst =
`
`(16-5)
`
`(16- 6)
`
`in which v is..tbe rate of settling, /~is the distance .91' fall
`i)1 time l, cl8t is th_~eaJ1_diamet.er of the particles based
`on the velocity of sedimentation, Psis the clensity_gf the
`particles and p0 that of t he dispet'§iO!l.fl'!~9fo]i1, ~-~he
`accfilID:ation.due-to gravity, and !loi~._t_he viscosity of the
`J'!lil.dium. The equation holds exactly only for spheres
`falling freely without. hindrance and aL a cunslanL raLe.
`The law is applicable to irregularly shaped particles of
`various sizes as long as one realizes t hat the diameter
`{
`I obtained is a relative particle size equivalent to that of
`sphere falling at the same velocity as that of the
`1 particles under consideration. The particles J!!USt no.t be It
`• ag_gregated or clumped together in the-suspension since V
`such clumps would fall more rapidly than the individual
`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 setUe under the acceleration of gravity, 981 cm
`sec-2, at 25° C. The rate of settling, v, is 7.30 x 10- 3 cm/sec; the
`density of the medium is l.Ol g/cm3, and its viscosity is 1 cp = 0.01
`poise or 0.01 g cm- 1 sec- 1. Calculate the Stokes' diameter of the zinc
`oxide powder.
`
`'I
`
`y
`
`Fig. 16-7. A general diagram providing definitions of the Feret,
`Martin, and projected diameters. (From 'I'. Allen, Particle Size
`?11eas1i1·emen~s, 2nd Edition, Chapman & Hall, London, 1974, p. 131,
`reproduced with permission of the copyright owner.)
`
`definite period of time, and the material that passes
`through one sieve and is retained on the next finer sieve
`is collected and weighed.
`Another custom is to assign the particles on the lower
`(M. sieve the arithmetic or gegmetr jc mean size oU he two
`\!:I ~t'e,fills. Arambulo and Deardorff15 used tfos method of
`size classification in their analysis of the average weight
`of compressed tablets. Frequently the powder is as(cid:173)
`('D, signed the mesh number of the screen through which it
`\!) passes or on which it is retained. King and Becker16
`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 arran1Xd in.A nest of about five with the ~t at
`carefully weighed sample of the powder is
`t~.
`plac.IU! on the top sieve, and after tJJe sjeyes are shaken
`for a predetermined period of time, the powder re(cid:173)
`tained on each sieve is weighed. Assuming a log-normal
`distribution, the cumulative percent by ~1t of
`powder retained on the sieves is plotted on the
`prol:}ability scale against the logarithm of the al'ithmetic
`mean size of the openings of each of two successive (
`screens. As illustrated in F igure 16-5, the geometric
`·\
`mean weight diameter d~ and the geometric standard
`9 can be obtained directly from the straight
`deviation c:r
`line.
`According to Herdan, 17 sieving errors can arise from
`
`COa number of variables including siru::e !99ding and
`
`dw;a.tion and in.tensity 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.
`
`18 x 0.01 g cm-1 sec- 1 x 7.30 x 10-a cm sec- 1
`(5.60 - 1.01) g cm- 3 x 981 cm sec- 2
`= 5.40 x 10- 4 cm or 5.40 1.1.m
`
`For Stokes' law to apply, a further requirement is
`that the flow of dispersion medium around the particle
`as it sediments is lamiinar or streamline. In other
`words, the rale of sedimentation..of_a _P..art!c)~..l!!!!§.t not
`be so rapid_that turbulence is set_up, si11Ce this in turn
`will affect the sedimentation of the particle. Whether
`the flow is turbulent or laminar is indicated by the di(cid:173)
`mensionless Reynolds number, R0 , which is defined as
`
`R·~_ vdpo
`
`v
`
`(16- 7)
`
`'TJo
`in which the symbols l1ave the same meaning ·as in
`equation (16-5). According to Heywood, 19 Stokes' law
`cannot be used if R e is g~an Q.2,..sinc~­
`lence appears at this value. On this basis, the limiting
`particle sjze under a given set of conditions may be
`calculated as follows:
`
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`

`
`Rearranging equation (16-7) and combining it with
`equation (16-5) gives
`
`RoTJ
`v = -
`dpo
`
`d2(Ps - Po)g
`= -------'-
`18TJ
`
`and thus
`
`(16-8)
`
`(16-9)
`
`Under a given· set ofd.;nsity a~d vi;cosity conditions,
`equation (16- 9) allows calculation of the maximum
`PJ:rticle diamet~..:_v.-rh0:.~~ sedil!J_~nt~tion will Q~_g9v,e1:ned
`l?.t§W~{es'._l!!~, that is, when Re.does not exceed 0.2.
`Example 16-4. A powdered material, density 2.7 g/cm3, is
`suspended in water at 20° C. What is the size of the largest particle
`that will settle without causing turbulence? 1'he viscosity of waler at
`20° C is 0.01 poise, 01· g/(cm sec) and the density is 1.0 g/cm3.
`From equation (16- 9):
`
`cl3 =
`
`(18)(0.2)(0.01)2
`(2. 7 - 1.0)1.0 x 981
`d = G x 10-3 cm = 60 lkm
`Example 16-5. If the material used in Example 16-4 is now
`suspended in a syrup containing 60% by weight of sucrose, what will
`be the critical diameter, that is, the maximum diameter fo1· which R.
`does not exceed 0.2? The viscosity of the syrnp is 0.567 poise that is,
`and the density 1.3 g/cm3 .
`d3 =
`
`(18)(0.2)(0.567)2
`(2. 7 - 1.3)1.3 x 981
`d =- 8.65 x 10-2 cm = 865 µm
`
`Several methods based on sedimentation are used.
`Principal among these are the pipette method, the
`b~.l!l].~~ .!!1-ethod, and the hydrometer method. Only the
`first technique is discussed here since it combines ease
`of analysis, accuracy, and economy of eqwpment.
`The Andreasen apparatus is shown in Figure 16-8.
`It usually consists of a 550-mL vessel containing a
`10-E!~iP~t~~ sealed into a ground~glass stopper.
`When the pipette is in place in the cylinder, its lower tip
`is 20 c~.l:>~low the surface of the suspension.
`The analysis is carried out in the following manner. A
`1 or _2%_ suspension of the particles in a medium
`containing a suitable defiocc!J!a~i.i~g agent is introduced
`into the vessel and brought 'to the 550-mL mark. The
`stoppered vess~.l is~.sha,ken to distribute the particles
`J,miforinly throughout the suspension and the appara(cid:173)
`tus, - w'ith pipette in place, is clamped securely in a
`c~stant-~~!n.pe1:ature bat,h. At various time intervals,
`10-mL samples are withdrawn and discharged by
`means of the two-way stopcock. The samples are
`evaporated and weighed or analyzed by other appropri(cid:173)
`ate means, correcting for the deflocculating agent that
`has been added.
`'I'he 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 encl of the pipett,e at the time each s:.mple is
`removed. The residue or dried sample obtained at a
`
`Chapte1' 16 • MiC1·omcwitics· 433
`
`,. l
`
`Fig. 16- 8. Andreasen apparatus for determining particle size by the
`gravity sedimentation method.
`
`paiticular 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
`undersize, and the sum of the successive weights is
`known as the curn.u,lative weighl unclersize. 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, 16-3, and 16- 4. The cumulative
`percent by weight unclersize may then be plotted on a
`probability scale against the particle diameter on a Jog
`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 16-4, p. 450.
`The Micromeritics Instrument Co., Norcross, Ga.,
`offers the SediGraph 5100 for particle-size analysis
`based on the seclin1entation principle. Since particles
`are not usually of uniform shape, the particle size is
`expressed as equivalent spherical diameter or Stokes'
`diameter.
`A low-energy x-ray beam passes through the suspen(cid:173)
`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
`temperature-controlled, and Lhe data are analyzed
`under computer software control. Particle diameters
`are measured from 0.1 to 300 µ,m at temperatures from
`10° to 40° C. The Micromeritics Co. also manufactures
`equipment for· the measurement of powder density,
`surface area, adsorption and desorption, pore volume,
`
`DRL - EXHIBIT 1008
`DRL008
`
`

`
`434 Physica.l Phm·nuicy
`
`pore size, and pore size distribution (see pp. 440-
`442 for a discussion of pore size).
`MATEC Applied Sciences, Hopkinton, Mass., has
`developed a particle-size measurement system for
`subniicron particles in the range of 0.015to1.1 µm . The
`particles in suspension are caused to pass through
`capillary tubes, the larger particles attaining greater
`average velocities than the smaller ones. The instru(cid:173)
`ment applies this principle to the determination of
`average particle size and size distribution by number or
`volume of particles. The operation, from the time of
`sample injection to graphics output, requires a maxi(cid:173)
`mum of 8 minutes. '£he liquid medium consists of 1 mL
`of water containing a surfactant and the suspended
`particles in the concentration of 2 to 4% solids. The
`particles to be analyzed are prefiltered through a 5-µm
`or smaller pore size filter. A computer terminal and
`program, printer, and plotter are available to calculate
`and display the size and si:r,e 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
`occurs.~ 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 calibl'ated in terms of particle
`size~l'he instrument records electronically all those
`particles producing pulses that are within two threshold
`values of the analyzer. By systematically varying the
`tlu-eshold 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 par ticles 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. 1'he 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 dissolution20
`21 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 repor ted by Beaubien and
`Vanderwielen23 for the automated particle counting of
`milled and micronized drug-s. Samples of spectinomycin
`hydrochloride and a micronized steroid were subjected
`to particle-size analysis, together with polystyrene
`spheres of 2.0 to 80.0 µm diameter which were used to
`calibrate the apparatus. The powders showed log(cid:173)
`normal distributions and were well characterized by
`geometric volume mean diameters and geometric stan(cid:173)
`dard deviations. Accurate particle sizes were obtained
`between 2 and 80 µm diameter with a precision of about
`0.5 µ.m. The authors concluded that the automated
`
`Mercury
`
`Electrolyte
`solution and
`particles
`
`Main
`amplifier
`
`Threshold
`circuit
`
`Pulse
`amplifier
`
`Counter
`drive
`
`Digital
`register
`
`~ ...... 0-- ---------------'
`~Counter
`switch
`
`fig. t 6-9. Schematic diagram of a Coulter counter, used to determine particle volume.
`
`DRL - EXHIBIT 1008
`DRL009
`
`

`
`17
`Rheology
`
`Introduction
`Newtonian Systems
`Non-Newtonian Systems
`Thixotropy
`
`Determination of Rheologic Properties
`Viscoelasticity
`Psychorheology
`Applications to Pharmacy
`
`INTRODUCTION
`1'he term rheology, from the Greek rheo (to flow) and
`logos (science), was suggested by Bingham and Craw(cid:173)
`ford (as reported by Fischer1) 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(cid:173)
`geneous dispersions are more complex, however, and
`cannot be expressed by a single value.
`In recent years, the fundamental principles of rheol(cid:173)
`ogy have been used in t he study of paints, inks, doughs,
`road building materials, cosmetics, dairy products, and
`other materials. 'I'he 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-Blair 2 recognized the impor(cid:173)
`tance of rheology in pharmacy and suggested its
`application in the formulation and analysis of such
`pharmaceutical products as emulsions, pastes, suppos(cid:173)
`itories, and tablet coatings. The manufacturer of me(cid:173)
`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(cid:173)
`ing manufacture to determine its "feel" and "body .11 The
`variability of subjective tests at different tinles under
`varying environmental conditions is, however, welJ
`recognized. A more serious objection, from a scientific
`standpoint, is the fai lm·e 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(cid:173)
`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 containers, and their
`removal prior to use, wbether this is achieved by
`pouring from a bottle, extrusion from a Lube, 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(cid:173)
`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(cid:173)
`cussed by Martin et al. 3
`When classifying materials according to the types of
`flow and deformation, it is customary to place them j.n
`one of two categories: Newtonian or non-Newtonian
`systems. The choice depends on whether or not their
`flow properlies 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 ii1 place. If the top plan