33
`
`J N Staniforth
`
`Particle size analysis
`
`PARTICLE SIZE AND THE LIFETIME OF A DRUG
`
`PARTICLE SIZE
`Dimensions
`Equivalent diameters
`Particle size distribution
`Statistics to summarize data
`Influence of particle shape
`
`PARTICLE SIZE ANALYSIS METHODS
`Sieve methods
`Equivalent diameter
`Range of analysis
`Sample preparation and analysis conditions
`Principle of measurement
`
`Alternative techniques
`
`Automatic methods
`Microscope methods
`Equivalent diameters
`Range of analysis
`S ample preparation and analysis conditions
`Principle of measurement
`
`Alternative techniques
`
`Automatic methods
`
`Electrical stream sensing zone method
`
`( Coulter'
`
`counter)
`Equivalent diameter
`Range of analysis
`S ample preparation and analysis conditions
`Principle of measurement
`
`Alternative techniques
`Laser light scattering methods
`Equivalent diameters
`Range of analysis .
`Sample preparation and analysis conditions
`Principles of measurement
`Alterntive teèhniques
`. Automatic methods
`
`564
`
`Sedimentation methods
`Equivalent diameters
`Range of analysis
`S ample preparation and analysis conditions
`Principles of measurement
`Alternative techniques
`
`Automatic methods
`
`SELECTION OF A PARTICLE SIZE ANALYSIS
`METHOD
`
`PARTICLE SIZE AND THE LIFETIME OF
`A DRUG
`
`The dimensions of particulate solids are of import-
`ance in achieving optimum production of effi-
`cacious medicines. Figure 33.1 shows an outline
`of the lifetime of a drug; during stages 1 and 2
`when a drug is synthesized and formulated, the
`particle size of drug and other powders is deter-
`mined . and influences the subsequent physical
`performance of the medicine and the pharmaco-
`logical performance of the drug.
`Particle size influences the production of formu-
`lated medicines (stage 3, Fig. 3'3.1) as solid
`dosage forms. Both tablets and capsules are
`produced using equipment which controls the
`,mass of drug and other particles by volumetric
`filling. Therefore, any interference with the
`uniformity of fill volumes may alter the mass of
`drug incorporated into the tablet or capsule and
`
`thus reduce the content uniformity of the medi-
`cine. Powders with different particle sizes have
`different flow and packing properties which alter
`the volumes of powder during each encapsulation
`or tablet compression event. In order to avoid
`such problems the particle sizes of drug and other
`
`MYL_BUP00094689
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`Mylan v. MonoSol
`IPR2017-00200
`MonoSol Ex. 2019
`
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`

`PARTICLE SIZE ANALYSIS . 565
`
`2
`
`3
`
`Drug
`synthesis
`
`Development of
`formulated
`medicine
`
`Production of
`formulated
`medicine
`
`il
`
`Drug
`removed from
`body
`
`..----
`
`Drug in
`body
`
`Administration
`..--- -- of
`medicine
`
`6
`5
`Fig. 33.1 Schematic representation of the lifetime of a drug
`
`4
`
`size, since a reduction in size generally increases
`the specific surface area of particles. Thus,
`particles having small dimensions wil tend to
`increase the rate of solution. For example, the
`drug griseofulvin has a low solubility by oral
`administration but is rapidly distributed following
`absorpti0n; the solubility of griseofulvin can be
`greatly enhanced by particle size reduction, so that
`blood levels equivalent to, or better than, those
`obtained with crystalline griseofulvin can be
`produced using a microcrystalline fòrm of the
`drug. Similar examples of a reduction in particle
`size improving the rate of solution include tetra-
`cycline, aspirin and some sulphonamídes. A
`reduction of particle size to improve rate of
`solution ~ind hence bioavailability is not always
`beneficial. For example, small particle size nitro-
`furantoin has an increased rate of solution which
`produces toxic side effects because of its' more
`rapid absorption.
`It is clear from the lifetime of a drug outlined
`above that a knowledge and control of particle size
`is of importance both for the production of
`medicines containing partIculate solids and in the
`efficacy of the medicine followinR administration.
`
`(33.1)
`
`(33.2)
`
`where C is the concentration of solute in solution
`at time, t; Cs is the solubility of solute and c is, a
`constant which can be determined from a knowl-
`edge of solute solubility. The constant c was more
`precisely defined by Danckwerts, who showed
`that the mean rate of solution per unit area under
`
`turbulent conditions was given bydx ,
`
`dt = Do (Cs - C)
`
`(33.3) PARTICLE SIZE
`Dimensions
`
`where'D is a diffusion coefficient and 0 is the rate
`of production of fresh surface. Do can be inter-
`preted as a liquíd film mass transfer coeffcient
`which wil tend to vary inversely with particle
`
`When determining the
`
`size of a relatively large
`solid it would be unusual to measure fewer than
`three dimensions, but if the same solid was broken
`
`. =+
`
`i
`
`i
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`566 PHARMCEUTICAL TECHNOLOGY
`
`up and the fragments miled, the resulting fine
`particles would be irregular with different
`numbers of faces and it would be difficult or
`impractical to determine more than a single
`dimension. For this reason a solid particle is often
`considered to approximate to a sphere which can
`then be çharacterized by determination of its
`diameter. Because measurement is then based on
`a hypothetical sphere which represents only an
`approximation to the true shape of the particle,
`the dimension is referred to as the equivalent
`diameter of tn.e particle.
`
`Equivalent diameters
`It is possible to generate more than one sphere
`which is equivalent to a given irregular particle
`shape. Figure 33.2 shows the two-dimensional
`projection of a particle with two different diam-
`eters constructed about it. The projected area
`diameter is based on a circle of equivalent area to
`that of the projected image of a solid particle; the
`projected perimeter diameter is based on a circle
`having the same perimeter as the particle. Unless
`the particles are unsymmetrical in three dimen-
`sions then these two diameters will be inde-
`pendent of particle orientation. This is not true for
`Ferets and Martin's diameters (Fig. 33.3) the
`values of which are dependent on both the orien:'
`tation and the shape of the particles. These are
`statistical diameters which are averaged over many
`different orientations to produce a mean value for
`each particle diameter. Ferets diameter is deter-
`mined from the mean distance between two
`
`Projected perimeter
`diameter, dp
`
`Projected area
`diameter, da
`
`Fi~. 33.2 Different equivalent diameters constrcted around
`tlesaie particle
`
`'" ." ., .. - ---..
`
`Reörientation
`
`-- .. ..
`
`dF
`
`dF
`
`dF
`
`Frg. 33.3 Influence of particle orientation on statistical
`diameters. The change in Ferets diameter is shown by the
`distances, dF; Martins diameter dM corresponds to the
`dotted lines in the mid-part of each image
`
`parallel tangents to the projected particle peri-
`meter. Martin's diameter is the mean chord length
`of the projected particle perimeter, which can be
`considered as the boundary separating equal
`particle areas (A and B in Fig. 33.3).
`It is also possible to determine particle size
`based on spheres of, for example, equivalent
`volume, sedimentation volume, mass or sieve mass
`of a given particle. In general, the method used
`to detérmine particle size dictates the type of
`equivalent diameter which is measured although
`interconversion may be carried out and this is
`sometimes done automatically as part of the size
`analysis.
`
`Particle size distribution
`
`A particle poputltion which consists of spheres or
`equivalent spheres with uniform dimensions is
`monosited and its characteristics can be described
`by a single diameter or equivalent diameter.
`However, it is unusual for particles to be
`completely monosized; most powders contain
`particles with a large number of different equiv-
`alent diameters. In order to be able to define a size
`distribution or compare the characteristics of two
`or more powders consisting of particles with many
`different diameters, the size distribution can be
`bróken down into different size ranges which can
`be presented in the form of a histogram plotted
`from data such as that in Table 33.1. Such a
`histogram presents an interpretation of the particle
`size distribution and enables the percentage of
`particles having a given equivalent diameter to be
`determined; A histogram representation allows
`
`c
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`

`rl'"¡;f
`;'\
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`.'
`
`Table 33.1 Frequency distribution data
`Per cent particles in each
`Number of particles
`diameter range (per cent
`in each diameter
`range (frequency)
`frequency)
`
`Equivalent
`particle
`diameter
`(p,m)
`
`2
`4
`6
`8
`10
`12
`14
`
`1
`2
`4
`8
`4
`2
`1
`
`4.5
`9.1
`18.2
`36:4
`18.2
`9.1
`4.5
`
`diferent parcle size distrbutions to be compared;
`for example, the size distribution shown in
`Fig. 33.4(b) contains a larger proportion of fine
`particles than the powder in Fig. 33.4(a) in which
`the ,partides are normally distributed. The peak
`frequency value, known as the mode, separates the
`normal curve into t~o identical halves, because
`the size distribution is fully symmetriqil. Not
`all particle populations are characterized by
`symmetrical normal size distributions and the
`frequency distributions of such populations
`exhbit skewness (Fig. 33.4(b)). A frequency
`curve with an elongated tail towards higher size
`ranges is positively skewed (Fig. 33.4(b)), the
`reverse case exhbits nègative skewness. These
`cart sometimes be normalized
`by replotting the equivalent particle diameters
`using a logarithmic scale and are thus usually
`referred to as log normal distributions. In some
`size distributions, more than one mode occurs;
`Fig. 33.4(c) shows bimod~lJrequency distribution
`for a powder which has been subjected to miling.
`Some of the coarser particles from the unmilled
`population remain unbroken and produce a mode
`towards the highest particle 'size, whereas the frac-
`
`skewed distributions
`
`PARTICLE SIZE ANALYSIS 567
`
`Table 33.2 Cumulative frequency distribution data
`
`Equivalent
`particle
`diameter
`(p,m)
`
`Per cent
`frequency
`(from
`Table 33.1)
`
`Cumulative per cent frequency
`
`Undersize
`
`Oversize
`
`2
`4
`6
`8
`10
`12
`14
`
`4.5
`9.1
`18.2
`36.4
`18.2
`9.1
`4.5
`
`4.5
`13.6
`31.8
`68.2
`86.4
`95.5
`100
`
`100
`95.5
`86.4
`68.2
`31.8
`13.6
`4.5
`
`tured particles have a new mode which appears
`lower down the size range.
`An alternative to the histogram representation
`of a particle size distribution is obtained by
`sequentially adding the per cent frequency values
`as shown in Table 33.2, to produce a cumulative
`per cent frequency distribution. If the addition
`sequence begins with the coarsest particles; the
`values obtained will be cumulative, per cent
`frequency undersize; the reverse case produces a
`cumulative per cent oversize. Figure 33.5 shows
`two cumulative per cent frequency distributions.
`Once again it is possible to compare two or more
`particle' populations using the cumulation distri-
`bution representation. For example, the size
`distribution in Fig. 33.5(a) shows that this powder
`has a larger range or spread of equivalent diam-
`eters in comparison with the powder represented
`in Fig. 33.5(b). The particle diameter corre-
`sponding to the point which sep~rates the cumu-
`lative frequency curve into two equal halves,
`above and below which 50% of the particles lie
`(point a in Fig. 33.5(a)). Just as the median divides
`a symmetrical cumulative size distribution curve
`into two equal halves, so the lower and upper
`
`(b)
`
`(c)
`
`;:
`CJ
`c:
`Ql
`:J
`C"
`
`Ql..0+..c:
`
`Ql
`
`CJ..
`Q)a.
`
`Particle diam.
`Particle diam.
`distrbution, (b) a positively skewed distrbution and
`
`~c
`
`:
`Q)
`:J
`C"
`
`Ql..0+..
`c:
`Q)
`CJ..
`Qla.
`
`(a)
`
`Mode
`
`Particle diam.
`
`;:
`CJ
`c:
`Ql:J
`0-
`
`Ql..-..c:
`
`Ql
`
`CJ..
`Qla.
`
`Fig. 33.4 Frequency distribution cures correspondig to (a) a normal
`
`(c) a bimodal distrbution
`
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`568 PHARMACEUTICAL TECHNOLOGY
`
`(a)
`
`(b)
`
`100
`
`75
`
`50
`
`25
`
`... .........!I-.. ..-. .
`
`..,
`,.
`
`.,..,......
`
`b a c
`
`Particle diam.
`
`Particle diam.
`
`;:()c
`. CD::
`eT
`
`CD......c
`~~CD
`.. N
`CD .-0. ~
`;: i:
`CD CD
`.- C
`.§ -2
`::
`:u
`
`E:
`
`Fig. 33.5 Cumulative frequency distribution curves. Point a corresponds to the median diameter; b is the lower quartile point and
`c is the upper quartile point
`
`quartile points at 25% and 75% divide the upper
`and lower ranges of a symmetrical curve into equal
`parts (points band c in Fig. 33.5(a)).
`
`Statistics to summarize data
`Although it is possible tò describe particle size
`distributions qualitatively it is always more satis-
`factory to compare particle size data quantitat-
`ively. This is' made possible by summarizing the
`distributions using statistical methods.
`In order to quantify the degree of skewness of
`a particle population, the interquartile coefficient
`of skewness (IQCS) can be determined
`
`(33.4)
`
`IQCS = (c - a) - (a - b)
`. (c - a) + (a - b)
`where a is the median diameter and band c àre
`the lower and upper quartile points (Fig. 33.5).
`The IQCS can take any value between -1 and
`+ 1. If the IQCS is zero then the size distribution
`is practically symmetrical between the quartile
`points. To ensure unambiguity in interpreting
`values for IQCS a large number of size intervals
`is required.
`To quantiy the degree of symmetry of a
`particle size distribution a property known as
`kurtosis can be .dètermined. The symmetry of a
`distribution is based on a comparison of the height
`
`or thickness of the tails and the 'sharpness' of the
`peaks with those of a normal distribution. 'Thick'
`tailed, 'sharp' peaked curves are described as
`leptokurtic whereas 'thin' tailed, 'blunt' peaked
`curves are platykurtic and the normal distribution
`.Îs mesokurtic.
`;
`The coeffcient of kurtosis, k (shown below),
`
`has a value of 0 for a normal curve, a negative
`value for curves showing platykurtosis and posi-
`tive values for leptokurtic size distributions
`
`(33.5)
`
`k = n L(x - i)4 -3
`(L(x - X)Z)2
`where x is any particle diameter, i is mean particle
`diameter and n is number of particles.
`Again, a large number of data points is required
`to provide an accurate analysis.
`The mean of the particle population referred to
`above in Eqn 33.5, together with the median
`(Fig. 33.5) and the mode (Fig. 33.4) are all
`measures of central tendency and provide a single
`value near the middle of the size distribution
`which represents a central particle diameter.
`Whereas the mode and median diameters can be
`obtained for an incomplete particle size, distribu-
`tion, the mean diameter can only be determined
`when the size distribution is complete and the
`upper and lower size limits are known. It is also
`possible to defie and determine the mean in
`
`-
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`MYL_BUP00094693
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`~".
`
`Table 33.3 Hatch-Choate relationships
`
`In do = In M + 0.5 In2 Og
`
`In ds = In M + In2 Og
`
`In dv = In M + i.5 In2 Og
`
`lndsv = In M + 2.5 ln2 ogk1
`
`In M = In dg + 2.5 In2 01-1
`
`In do = In dg - 2.5 In2 0w
`
`In ds = In dg - 2.0 In2 0w
`
`In dv = In dg - i. 5 In2 0w
`
`In dsv = In dg - 0.5 In2 0w
`
`Key: M, geometric mean diameter by number (see Eqn
`33.6); do, number mean diameter; d., surface mean diameter;
`dv, volume diameter; dSV surface volume or surface
`weighted diameter; dg, geometric mean diameter by
`weight.
`
`several ways and, for log-normal distributions, a
`series of relationships known as Hatch-Choate
`equations link the different mean diameters of a
`size distribution (Table 33.3).
`In a log-normal distribution, the frequency, f,
`of the occurrence of any given particle of equiv-
`alent diameter d is given by
`
`f = Ln
`
`21T lnag
`
`(lnd - lnM)2
`. exp (- 2l 2 ) (33.6)
`n ag
`
`where M is the geometric mean diameter (Chapter
`20) and ag is the geometric standard deviation.
`
`Infuence of particle shape
`The techniques discussed above for representing
`particle size distribution are all based on the
`assumption that particles could be adequately-
`represented by an equivalent circle or sphere.
`In some cases particles deviate markedly from
`circularity and sphericity and the use of a
`single equivalent diameter measurement may ,be
`inappropriate.
`
`For example, a powder consisting of mono
`
`fibrous particles would appear to have a wider
`
`sized
`size
`distribution according to statistical' diameter
`measurements. However, use of an equivalent
`diameter based on projected area would also be
`misleading. Under such circumstances, it may be
`desirable to return to the concept of characterizing
`a particle using more than one dimension. Thus,
`the breadth of the fibre could be. obtained using
`a projected circle inscribed within the fibre and
`the fibre' length could be measured using a
`
`Fibrous
`particle
`
`PARTICLE SIZE ANALYSIS 569
`
`Circumscribed
`circle,
`de
`
`Inscribed
`circle,
`d¡ ,
`
`Fig. 33.6 A simple shape factor is shown which can be used
`to quantify circularity. The ratio i/c of two different .
`diameters is unity for a circle and falls for acicular particles
`
`projected circle circumscribed around the fibre
`(Fig. 33.6).
`The ratio of inscribed circle to circumscribed
`circle diameters can also be used as a simple shape
`factor to provide information about the circularity
`of a particle. The ratio i/c will be i for a circle and
`diminish as the particle becomes more acicular.
`Suçh comparisons of equivalent diameters deter-
`mined by different methods offer considerable
`scope for both particle size and particle shape
`analysis. For example, measurement of particle
`size to obtain a projected area diameter, a, and an
`equivalent volume diameter, v, provides infor-
`mation concerning the surface:volume (a/v) ratio
`or bulkiness of a group of particles which can also
`be useful in interpreting particle size data.
`
`PARTICLE SIZE ANALYSIS
`
`METHODS
`
`In order to obtain equivalent diameters with
`which tò. interpret the particle size of a powder it
`is necessary to carry out a size analysis using one
`or more different methods. Particle size analysis
`methods can be divided into different categories
`based on several different criteria: size range of
`analysis; wet or dry methods; manual or automatic
`methods; speed of analysis. A summary of the
`different methods is presented below based on tht
`salient features of each.
`
`Sieve methods
`
`Equivalent diameter
`
`Sieve diameter, ds - the particle dimension x
`which passes through a square aperture as shown
`the next page.
`
`on
`
`:-#ff'è~~;:~;~l~~~iàAX\;J.;.._.,- -;
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`

`570 PHARMCEUTICAL TECHNOLOGY
`
`x
`
`Range of analysis (as shown below)
`The International Standards Organization (ISO)
`sets a lowest sieve diameter of 45 JLm and since
`powders are usually defined as having a maximum
`diameter of 1000 ¡.m, this could be considered to
`be the upper limit. In practice sieves can be
`obtained for size analysis over a range from 5 to
`125 000 JLm.
`
`S ample preparation and analysis conditions
`Sieve analysis is usually carried out using dry
`powders although, for powders in liquid
`suspension or which agglomerate during dry
`sieving, a process of wet sieving can be used.
`
`Principle of measurement
`
`Sieve analysis utilizes a woven, punched or elec-
`troformed mesh often in brass, bronze or stainless
`steel with known aperture diameters which form
`a physical barrier to particles. Most sieve analyses
`utilize a series, stack or nest of sieves which have
`the smallest mesh above a collector tray followed
`by meshes which get progressively coarser towards
`the top of the series. A sieve stack usually
`comprises 6-8 sieves with a progression based on
`between adjacent
`apertures. Powder is loaded on to the coarsest
`sieve of the assembled stack and the nest is
`subjected to mechanical vibration for, say, 20
`
`a Y2 or 2y2 change in diameter
`
`minutes. After this time, the particles are
`considered to be retained on the sieve mesh with
`an aperture corresponding to the ITinimum or
`sieve diameter. A sieving time of 20 minutes is
`arbitrary and BS 1796 recommends sieving to be
`continued until less than 0.2% material passes a
`given sieve aperture in any 5 minute interval.
`
`Alternative techniques
`Another form of sieve analysis, called air-Jet
`sieving, uses individual sieves rather"'- than a
`complete nest of sieves. Starting with the finest
`aperture sieve and progressively removing the
`undersize particle fraction by sequentially increasing
`the apertures of each sieve, particles are encour-
`aged to pass through each aperture under the
`influence of a partial vacuum applied below the
`sieve mesh. A reverse air jet circulates beneath the
`sieve mesh blowing oversize particles away from
`the me~h so as to prevent blocking. Air-jet sieving
`is often more efficient and reproducible than using
`mechanically vibrated sieve analysis, although
`with finer particles, agglomeration can become a
`problem.
`
`Automatic methods
`
`Sieve analysis is stil. largely a non-automated
`process, although an automated wet sieving tech-
`described.
`
`nique has been
`
`Range of
`
`ana
`
`lysis
`
`.
`Particle diam 0.001
`(tLm)
`
`I
`0.01
`
`I
`0.1
`
`.
`
`1
`
`r
`
`t
`10
`
`f4
`
`~--~
`ISO range ~
`
`I
`100
`
`I
`1000
`
`-
`
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`

`PARTICLE SIZE ANALYSIS 571
`
`Scanning electron microscope
`
`Light microscope
`
`j~j
`I r I
`
`100 1000
`Particle diameter (tLm)
`
`.
`10
`
`~.
`
`I 1
`
`I
`0.1
`
`,
`
`Jl.
`
`. 1--
`
`Transmission
`electron
`microscope
`
`. .
`
`0.001 0.01
`
`Microscope methods
`
`Equivalent diameters
`
`Projected area diameter, da; projected perimeter
`diameter dp; Feret's diameter dF and Martin's
`diameter dM (see above).
`
`Range of analysis (see above)
`
`Sa~ple preparation and analysis conditions
`
`Specimens prepared for light microscopy must be
`adequately dispersed on a microscope slide to
`avoid analysis of agglomerated particles. Specimens
`for scanning electron microscopy are prepared by
`fixing to aluminium stubs or planchettes before
`sputter coating to produce a film of gold a few nm
`in thickness. Specimens for transmission electron
`microscopy are often set in resin and sectioned by
`microtome before metallic coating on a supporting
`metal grid.
`
`Principle of measurement
`
`Size analysis by light microscopy is carried out on
`the two-dimensional images of particles which are
`generally assumed to be randomly oriented in
`three-dimensions. In many cases this assumption
`is valid, although for dendrites, fibres or flakes, it
`is very improbable that the particles wil orient
`with their minimum dimensions in the plane of
`measurement. Under such conditions, size analysis
`is carried out accepting that they are viewed in
`their most stable orientation.
`The two-dimensional images are analysed
`according to the desired equivalent diameter.
`Using a conventional light microscope, particle
`size analysis can be carried out using a projection
`screen with screen distances related to particle
`dimensions bya previously derived calibration
`factor using a. graticule. A graticule can also be
`
`used which has a series of opaque and transparent
`circles of different diameters, usually in a \/2
`progression (BS 3406). Particles are compared
`with the two sets of circles :lnd are sized according
`to the circle most closely corresponding to the
`equivalent particle diameter being measured. The
`field of view is divided into segments to facilitate
`measurement of different numbers of particles.
`
`Alternative techniques
`
`Alternative techniques to light microscopy include
`scanning electron microscopy (SEM) and trans-
`mission electron microscopy (TEM). Scanning
`electron' microscopy is particularly appropriate
`when a three-dimensional particle image is
`required; in addition the very much greater depth
`of field of a SEM in comparison with a light
`. microscope may also be beneficiaL. Both SEM and
`TEM analysis allow the lower particle sizing limit
`to be greatly extended over that possible wjth a
`light microscope.
`
`variable
`
`use some form of precalibrated, 'variable
`
`Automatiè methods
`. .
`Semi-automatic methods of microscope analysis
`distance
`to split particles into different size ranges. One
`technique, called a particle comparator, utilizes a
`diameter light spot projected onto a
`photomicrograph or electron photomicrograph of
`a particle under analysis. The variable iris control~
`ling the light spot diameter is linked electronically
`to a series of counter memories each corre:-
`sponding to a different size range (Fig. 33.7).
`Alteration of the iris diameter causes the particle
`count to be directed into the appropriate counter
`memory following activation of a switch by the
`operator.
`A second technique uses a double prism
`
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`572 PHACEUTICAL TECHNOLOGY
`
`r'
`
`Particle
`image
`
`Photomicrograph
`
`Fig. 33.7 Particle comparator
`
`Variable
`aperture iris
`
`Lens
`
`Light
`source
`
`arrangement mounted in place of the light micro-
`scope eyepiece. The image from the prisms is
`usually displayed on a video monitor. The double
`prism arrangement allows light to pass through to
`the monitor unaltered where the usual single
`particle image is produced. When the prisms are
`sheared against one another a double image of
`each particle is produced and the separation of the
`split images corresponds to the degree of shear
`between the prisms (Fig. 33.8). Particle size
`analysis can be carried out by shearing the prisms
`until the two images of. a single particle make
`
`touching contact. The prism shearing mechanism
`is linked to a precalibrated micrometer scale from
`which the equivalent diameter can be read
`directly. Alternatively, a complete size distri-
`bution can be obtained more quickly by subjecting
`the prisms to a sequentially increased and
`decreased shear distance between two preset levels
`corresponding to a known size range. All particles
`whose images separate and overlap sequentially
`under å given shear range are considered to fall
`in this size range and are counted by operating a
`switch which activates the appropriate counter
`
`Eyepiece or video camera
`
`¡.
`
`Split
`prisms
`
`/Cl~... Degree of rotation determines
`,,"~ " ~ount of shear produced
`
`. \ "/ ~
`
`No shear.
`Single particle
`image produced
`
`Small shear.
`. Overlapping
`double image
`
`Fig. 33.8 Image-shearing eyepiece
`
`Higher shear.
`Double image
`in touching contact
`
`-
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`11"tt,
`r~'
`
`memory. Particles whose images do not overlap in
`either shear sequence are undersize and particles
`whose images do not separate in either shear mode
`are oversize and wil be counted in a higher size
`range.
`Although semi-automatic size analysis methods
`remove some of the objectivity and fatigue
`associated with manual microscopic analysis, fully
`automatic size analysis has the advantage of being
`more objective, very much faster and also enables
`a much wider variety of size and shape parameters
`to be processed.
`Automatic microscopy is usually associated with
`microprocessor-controlled manipulation of an
`analogue signal derived from some form of video
`monitor used to image particles directly from a
`light microscope or from photomicrographs of
`particles. Alternatively, the signal from an elec-
`tron microscope can in some cases be processed
`directly without an intermediate video imaging
`system.
`Automatic microscopy allows both image
`analysis and image processing to be carried out.
`
`Electrical stream sensing zone method (Coulter
`
`counter) ~
`
`Equivalent diameter
`
`Volume diameter, dv. ~':;":'0;, ~ Pa.l"icle in
`
`"'i.~~ orifice
`
`~ Orifièe
`~-E tube wall
`
`PARTICLE SIZE ANALYSIS 573
`
`Sample preparation and analysis conditions
`
`Powder samples are dispersed in an electrolyte to
`form a very dilute suspension. The suspension is
`usually subjected to ultrasonic agitation fòr a
`period to break up any particle agglomerates. A
`dispersant may also be added to aid particle
`deagglomeration.
`
`Principle of measurement
`The particle suspension is drawn through an
`aperture accurately driled through a sapphire
`
`crystal set into the wall of a hollow glass tube.
`Electrodes, situated on either side of the aperture
`and surrounded by an electrolyte solution,
`monitor the change in electrical signal which
`occurs when a particle momentarily occupies the
`orifce and displaces its own volume of electrolyte.
`The volume of suspension drawn through the
`orifce is determined by the suction potential
`created by a mercury thread rebalancing in a
`convoluted V-tube (Fig. 33.9). The volume of
`electrolyte fluid which is displaced in the orifce
`in
`electrical resistance between the' electrodes which
`is proportional to the volume of the particle. The
`change in resistance is converted into a voltage
`pulse which is amplifed and processed electroni-
`cally. Pulses fallng within precalibrated limits or
`thresholds are used to split the particle size distri-
`bution into many different size ranges. In order
`to carry out size analysis over a wide diameter
`
`by the presence of a particle causes a change
`
`range it wil be necessary to change the orifice
`diameter used, to prevent coarser particles
`blocking a small diameter orifice. Conversely,
`finer particles in a large diameter orifce wil cause
`too small a relative change in volume to be accu-
`rately quantified.
`
`Range of analysis
`
`I
`0.001
`
`.
`0.01
`
`J
`
`!
`
`Coulter counter
`
`~I .0.1 1 10
`
`Particle diameter (t,m)
`
`i.
`
`1000
`
`t
`100
`
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`

`574 PHARMCEUTICAL TEèHNOLOGY
`
`ercury
`M. , ¡TO vacuum pump
`manométer ',~ I
`" Control tap
`
`Main
`amplifier
`
`Stop""
`
`Oscilloscope
`
`I Threshold
`
`Sapphire
`window
`Counting
`orifice
`
`s
`
`Counter
`On/off circuit
`
`Glassware unit
`
`Electronic counter
`
`Fig. 33.9 Diagram of Coulter counter
`
`Alternative techniques
`
`Since the Coulter principle was first described
`there have been sOme modifications to ¡the basic
`method such as use of alternative orifice designs
`and hydrodynamic focusing, but in general the
`particle detection technique remains the same.
`Another type of stream sensing analyser utilizes
`the attenuation of a light beam by particles drawn
`through the sensing zone. Some instruments of
`this type use the change in reflectance whilst
`the change in transmittance of light. It
`is also possible to use ultrasonic waves generated
`and monitored by a piezoelectric crystal at the
`base of a flowthrough tube containing particles in
`fluid suspension.
`
`others use
`
`Laser light scattering methods
`
`Equivalent diameters
`
`Area diameter, da; volume diameter dv following
`computation in some instruments.
`
`Range of analysis (as shown below).
`
`Sample preparation and analysis conditions
`
`DepenCling on the type of measurement to be
`carried tlut and the instrument used, particles can
`be presented either in liquid or air suspension.
`
`Principles of measurement
`
`Both the large-particle and small-particle analysers
`are based on the interaction of laser light with
`
`Fine~particle analysers
`
`.(-r
`
`.
`0.001
`
`I
`
`,0.01
`
`I
`
`0.1
`
`~-~i I
`
`Particle diameter (p.m)
`
`i
`1000
`
`-
`
`Large-particle analysers ~r
`
`,
`100
`
`f 1
`
`0
`
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`

`11,,,'
`~(
`
`particles. For particles which are much larger than
`the wavelength of light, any interaction with
`particles causes light to be scattered in a forward
`direction with only a small change in angle. This
`phenomenon is known as Fraunhofer diffraction
`and produces light intensity patterns which occur
`at regular angular intervals and are proportional
`to the particle diameter producing the scatter
`(Fig. 33.10). The composite diffraction pattern
`produced by different diameter particles may be
`considered to be the sum of all the individual
`
`1.0
`
`0.8
`
`0.6
`
`:;
`+-
`ë¡¡
`c:
`Q)+-
`c: 0.4
`+-.c
`0)::
`
`0.2
`
`o
`
`2 4 6 8 10
`Distance from centre of
`diffraction pattern
`
`Fig. 33.10 Diffraction pattern intensity distribution
`
`Particles measured
`in cell
`
`1 mW He/Ne Laser
`
`, PARTICLE SIZE ANALYSIS 575
`
`on to a photo
`
`patterns produced by each particle in the size
`distribution.
`Light emitted by a helium-neon laser is inci-
`dent on the sample of particles and diffraction
`occurs. In some cases the scattered light is focused
`by a lens directly on to a photodetector which
`converts the signals into an equivalent area diam-
`eter. In other cases the scattered light is directed
`by a lens on to a rotating filter which is used to
`convert equivalent area diameters into volume
`diameters which are quantified by final focusing
`detector using a second lens. The
`light flux signals occurring on the photodetector
`are converted into electrical current which is
`digitized and processed into size distribution data
`using a microprocessor (Fig. 33.11).
`Analysis of small particle sizes can be carried
`out based on diffraction of light or by photon
`correlation spectroscopy.
`In the former case, Fraunhofer diffraction
`theory is still useful for the particle fraction which
`is significantly larger than the wavelength of laser
`light. As. particles approach the dimension of the
`wavelength of the light, some light is stil scattered
`in the forward direction, according to Mie scatter
`theory, but there is also some side scatter at
`different wavelengths and polarizations. Use of the
`Mie theory requires a knowledge of the refractive
`index of the sample material for calculation of
`particle size distributions.
`.@",-"
`~ on detector ,
`
`1/ ~J' ,Diffraction pattern
`
`\ ' J" /i,-- '- V-..,
`
`, \ Detector
`J
`
`Data
`output
`
`Microprocessor
`
`Multiplexor
`AID converter
`
`Fig. 33.11 Schematic diagram of laser difraction pattern p;irtcle sizer
`
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`576 PHACEUTICAL TECHNOLOGY
`
`In the case of photon correlation spectroscopy
`(p.c.s.), the principle of Brownian