Modern Methods of
`Particle Size Analysis
`
`Edited by
`HOWARD G. BARTH
`
`Hercules Incorporated
`Wil1nington, Delaware
`
`A WILEY -INTERSCIENCE PUBLICATIOS
`
`JOHN WILEY & SONS
`I Chichester
`I Brisbane
`I Toronto
`
`New York
`
`I Singapore
`
`

`

`Copyright Cl 1984 by John Wiley & Sons, Inc.
`
`All rig.ht~ reserved. Published .. imultaneously in Canada.
`
`Reproduction or tmnslation of any part of this work
`beyond that penniucd by Section 107 or 108 of the
`1976 United States Copyright Act without the penni,sit1n
`of the copyright owner is unlawful. Requests for
`permission or further information .,huuld be addressed to
`the Permissions Department, John Wiley & Sons. Inc.
`
`Library of Congnss Cataloging in Publication IJala:
`Main entry under title:
`
`Modem methods of particle size analysis.
`
`<Chemical unalysis. ISSN 0069-28R3 : v. 73)
`" A Wiley-lntcrscicnce publication."
`Includes index.
`I. Particle size determination.
`Howard G.
`II. Seric::i.
`
`I. Barth,
`
`TA418.8.M63 1984
`ISBN 0-471-87571-6
`
`620' .43'021<7
`
`84-3630
`
`Printed in the United Stale' of America
`
`10 9 8 7 6 5 4 3 1 I
`
`

`

`CHAPTER
`
`2
`THE APPLICATION OF
`PARTICLE CHARACTERIZATION METHODS
`TO SUBMICRON DISPERSIONS AND EMULSIONS
`
`MICHAEL J. GROVES
`Pharmaceutics Department, College of Pharmacy,
`The Uni,•ersity of lllinois at Chicago.
`Chicago, Illinois
`
`Introduction
`1.
`2. The Meaning of the Term "Size" in a Submicroo Dispersion
`3. Methods of Presenting Size Data
`4. Direct Methods of Characterization-Microscopy
`5.
`Indirect Microscopy-Image Analysis and Electron Microscopy
`6. Hydrodynamic Chromatography
`7. Nephelometric and Light Scattering Methods
`8. Photon Correlation Spectroscopy and Laser Doppler Anemometer
`M~ods
`9. Centrifugal Methods
`10. Electrical Zone Sensing ()eyices
`11. Miscellan(l()us l\lethods
`12. Conclusions
`References
`
`43
`45
`48
`SO
`SO
`53
`SS
`
`~
`71
`81
`86
`88
`88
`
`1.
`
`INTRODUCTION
`
`Characterization of the siz.e of component particles in industrial disper(cid:173)
`sions is often required for research purposes and is a routine and essential
`part of the overall quality control procedures invariably applied to the
`products. Characterization methods have been extensively reviewed (l-
`3). but if the average particle in a dispersed system is at or below the
`limit of discrimination by the light microscope (about 1 µ.m), many of the
`regular sizing methods become inappropriate. Submicron dispersed sys(cid:173)
`tems have become technically more important during the past decade in
`a number of industries, and methodology for sizing has shown a parallel
`dev clopment.
`
`43
`
`

`

`44
`
`PARTICLE CHARACTERIZATION Of DISPERSIONS AND EMULSIONS
`
`The biologicaJ activity and effectiveness of pesticides and herbicides
`are critically affected by the size of the active component used for ap(cid:173)
`plication. As a result, submicron systems have been developed for com(cid:173)
`mercial use.* In pharmacy, the effect that particle size has on the bio(cid:173)
`logical activities of water-insoluble drugs has been well-recognized for
`many years (4). However, the reduction of solids to submicron-sized pow(cid:173)
`ders is expensive and counterproductive. Not only are electrostatic sur(cid:173)
`face forces exposed. which results in the aggregation of the fine particles,
`but handling such systems also inevitably leads to an increased risk of
`dust explosions and cross-contamination problems in a factory environ(cid:173)
`ment. In addition. there is an increased risk to health when workers are
`exposed to the possible inhalation and absorption of often potent bioactive
`materials. In these situations, it is more advantageous to handle the bioac(cid:173)
`tive materials as emulsions or as dispersions in solid-liquid systems. In
`these forms. manipulation and processing are facilitated.
`In the medical field, fine (submicron) emulsions of vegetable oils are
`now routinely administered to patients as parenteral calorie sources. In
`these products, it seems likely that administration of sufficient numbers
`of emulsion droplets close to or greater than the dimensions of a blood
`capillary could produce undesirable side effects (5). Quality control pro(cid:173)
`cedures applied to those systems should ideally determine that the prod(cid:173)
`ucts do not contain appreciable numbers of particles larger than a micron.
`Intravenous emulsions also offer some promise as drug delivery systems.
`and the same is true for liposomes or phos phatide vesicles varying in size
`from 10 to 1000 nm (6). In both cases. it is likely that a critical performance
`factor is size (7).
`Outside the biological and medical areas, the performance of pigment
`dispersions in terms of covering capacity and color development is also
`critically controlled by the size of the primary pigment particles and the
`number of primary particles forming aggregates (8). Although not emul(cid:173)
`sions in the strict sense of the term, polymer latex emulsions are widely
`employed as paints. Essential properties, such as covering capacity, pen(cid:173)
`etnilion, film-forming ability, "brushability. '' and stability are all criti(cid:173)
`cally influenced by the mean size and spread of size around the mean.
`Frequently. polymer emulsions are in the submicron range and much of
`the recent progress in size characterization methodology can be directly
`attributed to developments in this particular industry.
`
`' A li,t of addresses for manufacturers of commercially available instruments is given
`in the Appendix.
`
`

`

`THE MEANING OF THE TERM " SIZH" IN A SUBMICRON DISPERSION
`
`45
`
`2. THE MEANING OF THE TERM .. SIZE" L~ A SUBMICRON
`DISPERSION
`
`Intuitively, the term .. size" in a macroscopic system means the diameter
`of the average particle, and is often associated with some parameter that
`provides a description of the width of the size range from the smallest to
`the largest particle in the system. If the particles can be seen and meas(cid:173)
`ured. this concept provides little or no difficulty. and sizing methodology
`enables the appropriate parameters to be determined.
`However, when dealing with submicroscopic or subrnicron systems,
`semantic problems arise, because situations occur where a hard and fast
`definition of the term "particle''-and. therefore, of "size"-becomes
`somewhat imprecise.
`Submicroscopic particles are usually referred to as colloids. A colloid
`can be defined as a two-phase system with discrete particles of the dis(cid:173)
`perse phase that are between 1 and 100 nm (10-1000 A).
`These limits arc somewhat imprecise in themselves and are intended
`to describe particles that are smaJler than the lowest level of discrimi(cid:173)
`nation by the light microscope, but are capable of detection by the Tyndall
`beam effect. For example, Faraday prepared colloidal gold solutions that
`appeared to be clear when placed directly between the observer and a
`light source. When viewed laterally. however, the light appeared as a
`yellow track in the solution. and this was interpreted as being due to light
`scattered from the dispersed gold particles at right angles to the incident
`beam.
`The colloidal size range encompasses macromolecules as well as ag(cid:173)
`gregates of smaller molecules. The surface forces around an aggregated
`colloidal particle are less per unit mass than the forces around the con(cid:173)
`stituent molecules, if they were dispersed in a ''true" solution. The fun(cid:173)
`damental properties of true and colloidal solutions are the same quali(cid:173)
`tively, but differ quantitatively, because of the differences in particle size
`and structure. There is also a range of size in which particles between
`approximately 0.1 and 2-5 µm have properties between colloids and those
`of macroscopic dispersions or suspensions. The behavior of colloidal par(cid:173)
`ticles is influenced strongly by their environmental condition:s. This pro(cid:173)
`vides a challenge when attempting to characterize the size of particuJate
`systems with diameters anticipated to be below 5 µm, since properties
`of the systems can be readily affected by the conditions under which the
`analysis is carried out.
`In addition, it is necessary to closely consider what is actually defined
`as the .. size" of a colloidal particle, especially with particles below 50
`
`

`

`46
`
`PART IC LE C HARACTERIZATION OF DISPERSIONS AND EM ULSIONS
`
`nm in diameter. The .. particle" itself. for example, might consist of a
`hydrated protein molecule. a discrete solid particle, or a stabilized droplet
`of oil. It is preferable in this review to consider particles that have de(cid:173)
`finable , discrete surfaces. The discrete molecular fragment offered by a
`molecule of. say. hemoglobin will not be considered. but a colloidal gold
`particle would be. Emulsion droplets (e.g .. oil particles dispersed in water)
`offer larger problems of definition. since they consist in the main of a
`central hydrophobic "core" and a stabilizing exterior often comprised of
`a high molecular weight surfactant or dispersed colloidal entity. such as
`a polysaccharide (tragacanth or acacia gum) or a protein (e.g .. casein).
`Colloidal particles inevitably demonstrate a random movement even
`under steady state conditions. This is c.msed by the kinetic energy of the
`continuous constituent molecules and is known as Brownian movement.
`By applying a centrifugal field, the particles can be made to move in a
`consistent direction. Nevertheless, the particles will not move as a dis(cid:173)
`crete, easily definable entity, especially if the surface has a layer of sta(cid:173)
`bilizing counter ions around it. A proportion of the stabilizing layer will
`move with the surface, establishing a slippage plane, the Stem layer,
`around the surface. The thickness of the slippage plane is affected by
`environmental features such as the pH, temperature, and concentration
`of electrolytes, so that measured size characterization parameters may
`be influenced by the nature and conditions of a diluent prior to analysis.
`For particles larger than 50 nm, the thickness of the slippage plane be(cid:173)
`comes relatively less important.
`The stabilizing layer of emulsion particles can itself be influenced con(cid:173)
`siderably by environmental factors. especially if it comprises surface ac(cid:173)
`tive material. Surface active agents, or surfactants. form molecular as(cid:173)
`sociations with water. These associations are defined as states of matter
`in which the degree of molecular order lies between the almost perfect
`long-range positional and orientational order found in solid crystals and
`the statistical long-range disorder found in isotropic amorphous liquids
`and gases. These mesomorphic states of matter therefore have some of
`the properties of liquids, in that they may lack rigidity or resistance to
`deformation, and may also possess optical anistropy, a property associ(cid:173)
`ated with solid crystals (9, 10). With surfactant stabilized emulsions, the
`mesomorphic interfacial layer effectively forms a third phase in the pres·
`ence of two other phases (11). An emulsion is no longer defined as a
`dispersion of one liquid phase in another liquid in the form of droplets
`( 12). but rather as liquid droplets and/or mesomorphic systems dispersed
`in a liquid ( 13). Although an emulsion assumes two liquid phases dispersed
`in each other, one of the phases could solidify after the initial emulsifi(cid:173)
`cation process so that. under ambient conditions. the system is in effect
`
`

`

`THE MEANING OF THE TERM "SIZE" IN A SUBMJCRON DISPERSION
`
`47
`
`a dispersion, that is. a solid in a liquid or vice versa (14). Since emulsions
`arc inherently thermodynamically unstable. this solidification process is
`often resorted to as a means of improving long-term stability. Jnterfacial
`modification produced by adding absorbed surfactant will assist in min(cid:173)
`imizing interparticulate interactions by conferring a surface charge that
`repels particles approaching each other during Brownian movement. An
`alternative mechanism is to provide a diffuse layer of long chain molecules
`around the droplet that causes steric hindrance between adjacent parti(cid:173)
`cles.
`In either case, it becomes increasingly difficult to precisely define the
`meaning of "particle" and. therefore, of the size that can be measured.
`In a recent investigation into the properties of self-emulsifying oils, Ir(cid:173)
`anloye (15) was able to distinguish between emulsions consisting of drop(cid:173)
`lets surrounded by a visco-elastic gel network of surfactant phase and
`those whose droplets were not so protected. Similarly, emulsions stabi(cid:173)
`lized by a steric mechanism involving a long chain surfactant, protein, or
`polysaccharide system can be considered to have a diffuse interfacial
`layer. For example, some polymer emulsions have relatively rigid core
`structures and diffuse interfacial layers and others "soft" cores. but little
`in the way of interfacial material. As discussed in another section. the
`passage of these types of emulsion through a porous bed is a direct means
`of differentiating between these types of emulsion systems.
`The ''size" of two otherwise identically sized .. core" droplets-one
`with a diffuse interfacial layer and the other without-will differ in a
`centrifugal sizing method, because the size of the Stem layers differ and
`the interfacial layer has a different density from the core material. thereby
`influencing the overall density of the moving particle. The same possibility
`exists for the light scattering measurement method since, in the case of
`a diffuse interface, light may not only scatter from the core but also from
`light scattering centers in the diffuse layer itself, with the net effect that
`the particle appears to be larger. Obviously, these effects are relatively
`less important as the particle becomes larger and the thickness of the
`adsorbed layer becomes proportionally less predominant.
`Specimen calculations are usually enough to indicate the influence of
`these factors on a measured size parameter. Generally, the effect is rel(cid:173)
`atively trivial for particles larger than 200 nm, but may be influential as
`the size is decreased, depending on the thickness of the interfacial layer.
`In a system consisting of a spread of sizes around a mean. which is usually
`the case in the real world. this interfacial effect may not be relevant at
`the top end of the size range. However, the· smaller particles may be
`affected, because of the likelyhood that the interfacial layer would be of
`the same thickness and density for all particles in the system, irrespective
`
`

`

`48
`
`PARTICLE CHARACTERIZATION OF DISPERSIONS AND EMULSIONS
`
`of their droplet size. The net effect of this influence could be a distortion
`of the particle size distribution. For example, in a centrifugal analysis, it
`is quite possible that smaller particles may move less rapidly than pre(cid:173)
`dicted by Stokes' equation. although the same law is perfectly valid for
`the larger particles at the top end of the same distribution. The small
`particles may, therefore. appear to be smaller than they really are~ thereby
`increasing the apparent spread of the distribution.
`
`3. METHODS OF PRESENTING SIZE DATA
`
`Before discussing the methods of characterizing size, it is necessary to
`review the definitions of size related parameters. In an effort to define
`the term "particle, .. Heywood (16) decided that no upper limit couJd be
`placed on the size of a particle owing to its geometrical properties, but a
`lower limit was clearly defined as a molecule of the substance. since
`subatomic particles are not under consideration. Heywood suggested that
`the significant property of a particle is that it is a discrete portion of matter
`that may be small in relation to the space in which it is dispersed, but
`that is not necessarily small in absolute size. At its limiting condition, a
`particle may be defined as a point-source of matter in an unbounded
`space. This definition refers to a single particle and, in practice, we are
`generally concerned with assemblies of particles, sometimes having
`widely different sizes and shapes. From a technical standpoint, we need
`to define some parameter of a particle within the system that is descriptive
`of the whole. Although a bottle of an emulsified product may contain as
`many as 1016 particles, the physical properties of that product (such as
`viscosity or biological activity) may be adequately described in terms of
`the diameter of a single "average'' particle. with a second numerical
`parameter describing the relative width of the distribution around the
`mean particle diameter.
`In the majority of liquid-in-liquid emulsion systems, the particles are
`spherical. lf all particles were spherical in shape, the only necessary size
`measurement would be the diameter. In an imperfect world, however.
`the analyst is often concerned with particles of irregular and uneven
`shape. Heywood pointed out that irregular particles have only one unique
`dimension, the maximum separation along a straight line between two
`points on the surface (17). This is not always easy to measure and does
`not adequately describe the properties of the average particle. The size
`of individual particles is usually expressed in terms of the diameter of a
`circle or a sphere equivalent to the particle with regard to some stated
`property. This diameter. d, can be defined as follows:
`
`

`

`METHODS 01: PRESE~TING SIZE DATA
`
`49
`
`da The projected area diameter or the diameter of a circle having the
`same area as the profile of the particJe when viewed in a direction
`perpendicular to the dimension~ breadth (B) and length (l).
`dp The projected perimeter diameter or the diameter of a circle having
`the same perimeter as the profile of the particle when viewed from
`above.
`d u The volume diameter or the diameter of a sphere having the same
`volume as the particle.
`d f The surface diameter or the diameter of a sphere having the same
`surface area as the particle.
`du The specific-surface diameter or the diameter of a sphere having the
`same specific surface as the particle.
`d1 The free-falling diameter or the diameter of a sphere having the f)ame
`free-falling velocity as the particl.e. (If the diameter-to-velocity re(cid:173)
`lationship is in accordance with that predicted by application of
`Stokes' law, the symbol d\( is used.)
`
`Other dimensions for describing irregularly shaped particles include
`the equivalent size of the smalle5t square or round aperture through which
`a particle will pass. These dimensions represent other properties of the
`particles and differ considerably from each other in numerical magnitude.
`especially if the particles are flakes or are needle-shaped.
`Particles in a system arc not always the same size or shape, and a
`spread around the mean should be anticipated. To describe the spread,
`it is necessary to make some assumptions about the distribution. It may
`be sufficient to describe the upper and lower limits of the distributions
`as d min and d 0111, , or as the upper and lower quartiles. Only rarely is a
`symmetrical distribution around a mean encountered in practice; often,
`there are many more particles smaller than some defined particle with
`properties that adequately describe a system's overall properties. A form
`of exponential relationship is usually adequate to describe the properties
`of the system as a whole. and the logarithmic-probability relationship is
`a convenient approximation. This law allows an adequate definition of a
`mean size. and the spread is described as the width of one standard de(cid:173)
`viation around the mean (i.e., the ratio d.,,CY',:diw~ or dl6'~ :d50o/c). By
`convention, this standard deviation is always more than unity. a value of
`1.0 being a truly monodisperse system. One advantage of this definition
`of size spread is that the averages, as previously defined, may be nu(cid:173)
`merically related lo each other-the Hatch-Choate conversion (17). If a
`system distribution is described by the logarithmic-probability law, Che
`results obtained by one method of size analysis may be related to those
`
`

`

`50
`
`PARTICLE CHARACTERIZATION or DISPERSIONS AND EMULSIONS
`
`obtained from another. Logarithmic-probability distributions tend to fit
`materials prepared by homogenization or fracturing.
`
`4. DIRECT METHODS OF CHARACTERIZATION-MICROSCOPY
`
`The only direct or absolute method of size characterization is the optical
`or light microscope. where the operator is involved in observing the par(cid:173)
`ticles. making judgments. and taking mea'surements of their properties.
`The routine use of a light microscope is almost mandatory in any lab(cid:173)
`oratory where there is an interest in particle characterization, although
`use of the instrument may be confined to qualitatively examining the state
`of dispersion. without neces:mrily making measurements. Even llnder op(cid:173)
`timum viewing conditions. with adequate separation and contrast between
`the particles: a realistic lower limit for diameter measurement by light
`microscopy is around 2 µm. It is possible that this lower limit could be
`reduced by the use of differential interference contrast microscopy. but
`even in this case. claims to any accuracy at sizes below 1 µm should be
`treated with some caution. Generally speaking. microscopy is invaluable
`for making subjective impressions but is tedious and imperfect for making
`objective measurements. The accuracy of the measurement process has
`been considerably increased in recent years by the use of instruments
`employing image shearing techniques. for example, the Coulter .. Shear(cid:173)
`icon." the Fleming Instruments microscope, and shearing eyepiece de(cid:173)
`vices such as that made by Vickers. These devices function by shearing
`an image optically or mechanically until the two images just touch-the
`amount of shear required is a measure of the size of the object.
`Unfortunately. the reduced definition of the light microscope as the
`sample diameters approach the dimensions of the illuminating light, com(cid:173)
`bined with the increasingly violent Brownian movement as the particles
`become smaller. tend to make direct microscope observation of limited
`value for the characterization of colloidal materials.
`
`5.
`
`INDIRECT MICROSCOPY-IMAGE ANALYSIS AND ELECTRON
`MICROSCOPY
`
`Automated methods for image analysis have become very sophisticated
`in recent years and may be applied to direct images in a microscope or
`to photographs obtained indirectly. using an electron microscope. The
`image is scanned by a high resolution plumbicon or vidicon tube to convert
`the optical image into a video signal. After this stage. the manipulation
`
`

`

`INDIRECT MJCROSCOPY-IMAGE ANALYSIS AND ELECTRON MICROSCOPY 51
`
`of the signal is only limited by the capacity of the computer or the imag(cid:173)
`ination of the operator. When a large number of images are analyzed
`routinely, the high cost of the instrumentation is more than offset by the
`increased accuracy and workload. Dedicated computers attached to the
`instrument are capable of printing out features such as the number of
`particles of a predetermined size within a given portion of a field, the
`chord analysis of the dispersion, or, in a mixed system, the relative prop(cid:173)
`erties of the components. A number of instruments are available today.
`including the original Quantimet device. which has a wide variety of user
`options.
`Attention should be drawn, however, the danger of becoming over(cid:173)
`confident in data manipulation. An improved degree of sophistication does
`not necessarily improve the basic quality of the original information being
`manipulated. This comment, of course. applies to all types of instrumen(cid:173)
`tation. In the case of image analyzing instruments. all of the disadvan(cid:173)
`tages, such as insufficient discrimination or poor dispersion of the original
`image-making technique. aie retained. In addition, the method depends
`on the degree of precision with which the magnification of the original
`image is known in the first place (3).
`Electron microscopy. used in either the transmission or the scanning
`(surface) mode. is becoming more widely available as the cost of equip(cid:173)
`ment is decreasing. The method remains the onJy means available for the
`visualization. sizing, and characterization of many submicron particulate
`dispersions. However, in practical terms. mounting and staining remain
`crucial to the examination and, more to the point, interpretation. of dis(cid:173)
`persions. The use of an electron microscope becomes limited by the op(cid:173)
`erator's skill. Staining agents include osmium and molybdenum salts. The
`method requires a high vacuum. so that artifacts may be produced in a
`preparation that places limitations on the interpretation of data. The vac(cid:173)
`uum conditions may result in the shrinking of specimens. and until re(cid:173)
`cently. preparations containing water could 11ot be examined. The intro(cid:173)
`duction of the freeze fracturing technique has allowed replicas to be made
`of dispersions in water. This method is unique in the field of particle
`characterization, since the dispersion usually need not be diluted. The
`intact material, therefore. can be examined without risking untoward ef(cid:173)
`fects caused by the dilution process and the nature of the diluent. Artifacts
`may occur on occasion. when the advancing ice front squeezes particles
`together and increases the local electrolyte concentration, but one can
`guard against this effect.
`·
`Freeze fracturing as a technique has been invaluable in many areas.
`For example, earlier postulates about the nature and dimensions of in-
`
`

`

`52
`
`PARTICLE CHARACTERIZATION OF DISPERSIONS ANO EMULSIONS
`
`Figure 1. Scanning electron photomicrograph of a freeze-fractured sample of triglyceride
`droplets stabilized with phospholipid, showing the interfacial structures that suggest mul(cid:173)
`Wayers around the droplets. The fractured surface is lishtly shadowed with gold.
`
`,
`
`terfacial layers around emulsion droplets have been substantially con(cid:173)
`firmed by direct visualization (Figure l).
`It is only rarely possible or necessary to work directly from an electron
`microscope screen. and photographs are always made of any one field.
`Since it is necessary to examine a large number of fields, automatic or
`semiautomatic scanning devices are advantageous to generate sufficiently
`useful data from an electron microscope facility. These are often not avail-
`able, so that interpretation of data is either carried out manually or on a
`qualitative level. Unfortunately, to approach statistical accuracy when
`characterizing the size of particulate systems, a sufficiently large number
`of different fields (i.e .. samples), must be taken. Because a sufficient
`number of measurements is required. it is tempting to be less than thor(cid:173)
`ough. Paradoxically, sampling error becomes much higher as the particle
`diameters increase toward the realistic upper limit of the method. - 1 µm.
`because the size of the field is proportionally smaller and a large number
`of fields are examined.
`Another problem concerns estimates of size. The size of the image is
`dependent initially upon the voltage across the electron source. and there
`may be several stages of subsequent image magnification, causing addi(cid:173)
`tional sources of error. This overall error factor is partially overcome by
`calibrating the system with relatively monosized polymer latex particles
`or by diffraction gratings. However. the latex standards are themselves
`often sized by electron microscopy. Caution is therefore required in the
`
`

`

`HYDRODYNAMIC CHROMATOGRAPHY
`
`53
`
`interpretation of much of the published data on electron microscope siz(cid:173)
`ing, especially if the authors do not provide details of calibration or the
`number of samples taken.
`Scanning electron microscopy is proving to be a useful analytical tool.
`Surfaces. when bombarded by electrons, emit secondary electrons and
`x-rays that are characteristic of the surface. It has become feasible to
`unambiguously identify the elemental composition of individual particles.
`provided that the atomic number is greater than 14. The technique also
`makes it possible to derive particle mass. maximum thickness. and av(cid:173)
`erage thickness for single particles. so that characterization of particulates
`has become more intensive and valuable. Advances in this area can be
`anticipated.
`
`6. HYDRODYNAMIC CHROMATOGRAPHY
`
`Hydrodynamic chromatography (HOC) is the technique developed ini(cid:173)
`tially for the characterization of polymer latices by Small ( 19) (sec Chapter
`9 for applications to high molecular weight polymers). Column chroma(cid:173)
`tography is used to separate particles according to size. At the time the
`concept was originally tested, the chromatography was mainly confined
`to the separation of materials in a column packed with solid particles; an
`appropriate detection system was used at the end of the column (see
`Chapter 8). Small attempted to determine whether size fractionation could
`be obtained. based on van der Waals interaction between the packing
`surface and a '"solution· ' phase consisting of submicron particles in sus(cid:173)
`pension. It was rationalized that the larger particles should be retained
`longer than the smaller. thereby affecting a size-based separation. Initial
`experimentation demonstrated that separation occurred. but in the direc(cid:173)
`tion opposite to the prediction. This prompted a closer investigation of
`the phenomenon and led to the development of what is now a potentially
`useful and promising technique. The basic equipment consists of a chro(cid:173)
`matographic column packed with beads. An aqueous solution, the mobile
`phase. is pumped through the column at a known flow rate. The nature
`of both the column packing and the mobile phase are critical to the sep(cid:173)
`aration. A pulse of a colloidal suspension is injected into the column in
`just the same fashion as any other chromatographic separation technique.
`Mobile phase from the end of the column is passed through a suitable
`detection system, such as a flow-through spectrophotometer of the type
`used in liquid chromatography. and the detector response of the colloid
`is determined as a function of elution time (see Chapter 8).
`
`

`

`54
`
`PARTICLE CHARACTERIZATION OF DISPERSIONS AND EMULSIONS
`
`The rate of elution of a fraction from a column is expressed by a di(cid:173)
`mensionless parameter, the retention factor, Rf. This number is the ratio
`of the rate of migration of the particulate peak to the rate of the mobile
`phase flow through the interstitial volume of the column and is indepen(cid:173)
`dent of the flow rate or column dispersion. The interstitial flow rate can
`be determined by the use of suitable markers, such as sodium dichromate,
`injected into the column with the suspension.
`Experimentally, it was shown (20) that the Rf increased with increased
`particle diameter, and separation improved as the size of the packing
`material was decreased. The elution volume of a sample was not affected
`to any marked degree by the composition of the packing material itself.
`Addition of electrolytes to the mobile phase slowed the rate of elution
`to the point where the elution order of a mixture was reversed, larger
`particles eluting more slowly than the smaller. This was accounted for
`by suggesting that electrolytes suppressed the electrostatic repulsion ex(cid:173)
`isting between packing surface and particle. At low electrolyte concen(cid:173)
`trations, this repulsion was sufficient to cause the smaller particles to
`move into the higher velocity streamlines located in the center of the
`interstitial spaces.
`The Rf is always greater than unity, suggesting that the particles them(cid:173)
`selves are moving faster than the mobile phase. This is explained by a
`hydrodynamic effect. The particles are assumed to be rigid, so that they
`cannot approach the wall of the interstitial space any closer than the
`particle radius. Since the mobile phase velocity is higher in the center of
`the interstitial space, there is a tendency for particles to be forced toward
`the center. The resultant particle velocity is faster than the average mobile
`phase velocity. This hydrodynamic effect qualitatively explains why
`larger particles move faster than smaller ones, but is not entirely satis(cid:173)
`factory, since subsequent work has demonstrated the i