Anal. Chem. 1993, 65, 55R-66R
Particle Size Analysis Howard G. Barth* DuPont Company, Central Research and Development, Experimental Station, P.O.Box 80228, Wilmington, Delaware 19880-0228
Shao-Tang Sun Hercules Incorporated, Research Center, Wilmington, Delaware 19894 Review Contents Introduction General Books and Reviews Scattering Techniques Books and Reviews Photon Correlation Spectroscopy Classical Light Scattering Turbidimetrylsmall-Angle Light Scattering Diffraction Optical Particle Counters Velocimetry Neutron/X-ray Scattering Size Exclusion/Hydrodynamic Chromatography Field-Flow Fractionation Electrozone Sensing Sedimentation/Centrifugation Disk Centrifuge Photosedimentometry Photosedimentometry Ultracentrifugation Sieving Other Techniques Intercomparison of Techniques Particle Shape Particle Size Standards Miscellaneous
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INTRODUCTION Preparing a review on particle size analysis is a difficult task because of the enormous breadth of technique and application areas. Furthermore, the definition of a particle becomes hazy when dealing with angstrom-size structures. This being the fifth review (see refs Al-A4), we have continued to streamline our coverage to make it as useful as possible for our colleagues. Apart from a few exceptions,we have omitted aerosol measurementdevices,such as air classifiers, impactors, cyclones, condensation particle counters, and differential mobility analyzers, and microscopy/image analysis, which are themselvesspecialized areas and are beyond the scope of this article. Areas that are included are listed in the table of contents. As in previous reviews, methodologies based on light scattering measurements continue to dominate particle size instrumentation. Photon correlation spectroscopy is now a well-establishedtechnique for particle size analysis in dilute solution. For concentrated solutions, diffusion wave spectroscopy appears to be the method of choice. During the past two years, there has been little activity regarding hydrodynamicand size exclusion chromatography for particle size analysis. The use of sedimentation field-flow fractionation (FFF) has shown steady growth for this review period. We are also beginning to see more activity in characterizing particles in terms of their adsorption properties and composition, in addition to particle size distributions. Literature searcheswere based on Chemical Abstracts from 1990, Vol. 113 (24), to 1993, Vol. 118 (lo), for scattering techniques, and to 1992, Vol. 117 (20), for all other methodologies. All relevant papers dealingwith new developments 0003-2700/93/0365-0055R$12.00/0
Howard G. Barth is a member of the research staff of the Corporate Center for Analytical Sciences at the DuPont Experimental Station, Wilmington, DE. Before joining the DuPont Company in 1988, he was a research scientist and group leader at Hercules Research Center. He received his B.A. (1969) and Ph.D. (1973) in analytical chemistry from Northeastern University. His specialties include polymer characterization, size exclusion chromatography, and high-performance liquid chromatography. He has published over 50 papers in these and related areas. Barth has also edited the book Modern Methods of Particle Size Analysis (Wiley, 1984) and coedited Modern Mefhodsof PolymerCharacferizafion(Wiley,199 1). He has also edited five symposium volumes on polymer characterization published in the Journalof AppliedPolymer Science. Barth was on the Instrumentation Advisory Panel of Analyfical Chemistry and was Associate Editor of the Journalof AppliedPolymer Science. He is cofounder and Chairman of the International Symposium on Polymer Analysis and Characterization. Barth is past Chairman of the Delaware Section of the American Chemical Society where he presently serves as councilor. Dr. Barth is a member of the American Chemical Society divisions of Analytical Chemistry, Polymer Chemistry, and Polymeric Materials Science and Engineering, Society of Plastics Engineers, and the Delaware Valley Chromatography Forum. He is also a Fellow of the American Institute of Chemists and a member of Sigma Xi. Shao-Tang Sun is a manager with the Aerospace Division of Hercules Research Center in Wilmington, DE. He is also project manager of the photonics program. Dr. Sun received his B.S. (1972) in physics from Tunghai University, Taiwan, and Ph.D. (1978) in physics from the State University of New York at Buffalo. Before joining Hercules Incorporated in 1983, he was a postdoctoral research associate at the Center for Materials Science and Engineering, Massachusetts Institute of T e c h nology. Dr. Sun is involved with applying physics concepts and methods to the understanding of polymeric and biological systems and also is responsible for the developmentof optical materials for information management. He is the author of more than 30 publications in photonics, light scattering, phase transition, polymer physics, and biophysics and is a coinventor on five patents. Dr. Sun is a member of the American Physical Society and the Optical Society of America.
in particle size analysis and applications of general interest were covered. Although our focus is on particles, pertinent references dealing with macromoleculesand micelles are given, especially in the light scattering and FFF sections. Suggestions for expanding coverage in specific areas of particle size analysis are welcome. Also, please contact the authors if we have missed significant papers, which we will include in the next review. We gratefully acknowledge the assistance of Ruth Curtiss (HerculesResearch Center) and Carol Perrotto (DuPont Co.), who have worked closely with us over the years in developing and improving literature search strategies for these reviews. We are also grateful to Rebecca R. Pennington for her excellent typing skills and her patience. 0 1993 American Chemical Society
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GENERAL BOOKS AND REVIEWS Three general books on particle characterization have been published during this review period (A5-A7). Books related to particle analysis in oceanography have been issued (A8, A9). Provder (AIO) edited the proceedings of an American Chemical Society symposium on particle analysis which consists of recent advances and research-related papers. Mittal ( A l l , A12) edited two volumes dealing with the detection, characterization, and control of particles in gases and liquids. Two related volumes on the detection, adhesion, and removal of particles on surfaces were edited also by Mittal (A13,A14). The ASTM subcommittee on liquid particle measurement issued a volume on this subject (A15). Alderliesten (A16)reviewed the nomenclature for describing mean particle diameters and distributions. A brief review on high-resolution particle size methods was given by McFadyen and Fairhurst (A17). Several articles on selecting particle size instrumentation have appeared (A18-AZO). Reviews dealing with the use of microscopy for particle size analysis were written (A21-A23). Other application reviews covered particle size analysis of ceramic materials (A24,A25), high-purity gases (A26), and contaminants found in the pulping of waste paper (A27)and in clinical medicine ( A B ) . Snow and Terry (A29)discussed the performance of particle size classifiers, while Kubier and Schubert (A30) reviewed their experiences using an air classifier. Methodologies of preparing samples for particle size analysis, with emphasis on dispersions, were covered by Polke et al. (A31). Borho et al. (A32)reviewed the effects of particle size distribution and interfacial forces on product properties in the manufacture of solids. A two-day short course entitled “Modern Methods of Particle Size Distribution: Assessment and Characterization” sponsored by the American Chemical Society was held recently (A33). This course, which is given on a regular basis, is a comprehensive review of theory, instrumentation, particle size methodologies, data analysis and interpretation, and applications taught by a group of scientists active in particle size analysis.
SCATTERING TECHNIQUES Light, neutron, and X-ray scattering techniques have been used extensively to study the structure and dynamics of particles and macromolecules in multicomponent systems. A wide range of size (angstrom to microns) can be determined. In a typical experiment, an incident beam with a given wavelength probes the medium of interest and the scattered radiation is analyzed with a suitable spectrometer. The momentum and energy differences between the scattered and the incident radiation are used to characterize the structure and dynamics of the medium. Scattering techniques are often noninvasive and nonperturbative to the medium investigated and thus useful for kinetics studies and the monitoring of events in situ. Books and Reviews A number of review articles were published during the past two years. Cotton ( B l )reviewed light, neutron, and X-ray scattering by disperse systems in homogeneous media. Hofer (B2),Mitchell (B3),Nicoli (B4),Wiese (B5-B7), andEstelrich and Pons (B8) covered various aspects of light scattering techniques. Kourti and MacGregor (B9)gave a comprehensive review of turbidimetry. Felton (B10) discussed the Fraunhofer diffraction particle sizing technique. Chandler ( B I I )and Knollenberg and Veal (B12)reviewed the hardware of optical particle counters. Ottewill (B13, B14) examined the use of small-angle neutron scattering to characterize colloidal dispersions. Photon Correlation Spectroscopy Photon correlation spectroscopy (PCS),also referred to as quasi-elastic or dynamic light scattering (QELS or DLS), is routinely used to obtain particle size or size distribution information from the time-dependent fluctuations of scattered light intensity caused by concentration fluctuations (Brownian motion) of particles. The diffusion coefficient of the Brownian particles is determined from the intensity autocorrelation function measured experimentally with a digital correlator. 58R
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The hydrodynamic radius is then calculated from the diffusion coefficient by using the Stokes-Einstein relation, assuming a spherical shape. In recent years, a new technique called diffusion wave spectroscopy (DWS)was developed to study concentrated or optically opaque systems. The method addresses dynamic light scattering in the multiple scattering limit and offers a new way to derive particle size information without sample dilution. Horne (C1) characterized the particle size of polystyrene latexes and concentration-dependent casein mobility in skim and concentrated milk using the DWS method. He demonstrated the ability of DWS to monitor particle size directly during online processing where sample dilution is not desirable. Another approach for concentrated sample solutions was described by Schaetzel et al. (C2). A dual-color crosscorrelation technique was used to separate singly scattered light from multiply scattered light. The dynamic structure factor was determined and was unaffected by multiple scattering. Trainer et al. (C3)reported the use of a direct-immersion waveguide device with the Microtrac ultrafine-particle analyzer. The inherent short optical path of the device allowed the investigation of particle size in high-concentration systems with minimal errors due to multiple scattering. Thomas (C4) deviced a fiber optic dynamic light scattering method to measure particle size in concentrated dispersions. Potential applications for online particle size determination were presented. An online particle size determination approach based on an automated sample acquisition and dilution system in combination with the PCS technique was described by Kourti et al. ( C 5 ) . The system was used to monitor online particle growth during the emulsion polymerization of vinyl acetate latexes in a pilot-plant reactor. Brown et al. (C6)reported the design, construction, and testing of a miniature, all-solidstate laser light scattering instrument for the determination of paticle sizes and size distributions. In a series of publications, the use of PCS for particle sizing application was reexamined and critically reviewed (C7-C9). The authors studied the effect of particle concentration and scattering angle on the size measurement of well-characterized polystyrene latexes. The average values of the diameters and the diffusion coefficients were discussed for different ranges of average particle size. It was concluded that the information obtained from the PCS measurements agrees essentially with the results from electron microscopy and static light scattering. Ruf et al. ( C I O ) described a method to eliminate the occurrence of spurious peaks in the size distribution analysis with results from errors in the correlation function baseline determination. The trade-off of this data analysis approach is the larger uncertainties introduced in the width of the size distribution. Different data analysis software packages were examined and compared using experimental as well as simulated PCS data (C11, C12). It was found that the average size values obtained by different software methods were not comparable. Overall, the CONTIN method seemed to yield the most reliable size distributions. DeLong and Russo (C13) demonstrated the application of zero-angle depolarized dynamic light scattering to article size and size distribution determinations with colloi&l TiOl dispersions and poly(tetrafluoroethy1ene) latex suspensions. Pendle and Swinyard ( C I 4 ) applied the PCS technique to measure the size distributions of natural latex. A bimodal distribution pattern was derived. The kinetics of latex particle growth in a continuous pilot scale reactor was followed with PCS and turbidity methods (C15). A new design involving the use of a remote sensor and fiber optics was described. Midmore (C16) investigated the moment of the aggregating latexes size distribution using PCS. The reaction rates in the dilute and high electrolyte concentration systems were determined. Okubo et al. (CI 7) studied the stepwise heterocoagulation process of small cationic polymer paticles onto large anionic polymer particles. The particle size distribution in each step was characterized using PCS. Lamy-Freund et al. ((218) measured the size and aggregation process of amphotericin &deoxycholate as a function of concentration.
PARTICLE SIZE ANALYSIS
Bottero et al. (C19) used PCS and small-an le X-ray scattering to understand the kinetics of partial hy rolysis of ferric nitrate salt. The structural differences between ferric nitrate salts and ferric chloride salts were discussed. Trott et al. (C20) reported the in situ measurement of particle formation in heated jet fuels usi PCS. The real-time studies indicate that the mean p a r t i 3 diameter increases with increased exposure time a t a fixed temperature. A number of interesting applications of PCS were published. The size and shape of particles of magnetic iron oxide in sus ensionsof ethylene glycol monoethyl ether/surfactants wereletermined (C21). Cotta and Pekala (C22)characterized the primary particle size in the initial reaction of formaldehyde with resorcinol and its dependence on the monomer ratio, gelation kinetics, and gel modulus. Bruenger and Schollmeyer (C23) measured the time and temperature effects on the article size distributions 0f.C. I. Disperse Red 60 and C. I. bisperse Orange 13 suspensions. Rawi et al. (C24) derived the thickness of po!ymer steric stabilizer on polypyrrole colloids in aqueous acidic media. An upper limit pol er layer thickness of 25 nm was calculated. De Smidt and g m m e l i n (C25) used model latex spheres to robe the viscosity of aqueous polymer solutions of cargoxymethylcelluloseand poly(vinylpyrro1idone). The stability of colloid dispersions was assessed usin multian le Dop ler electrophoretic light scattering and PC (C26). hcNeil-&ratson and Parker (C27) compared sveral methods for high-resolution submicron sizing. Delgado and Matijevic (C28) used PCS, classical light s.catteTing,.and electron microscopy to characterne the particle size distributions of inorganic colloidal dispersions. Critical issues relating to sample treatment were discussed. Devoisselle et al. (C29) analyzed small unilamellar liposomes containing fluorinated steroids with PCS and fluorine-19 nuclear magnetic resonance spectroscopy. The authors suggestedthe use of this combined spectroscopicapproach to evaluate liposomal formulation and control quality. Van der Put et al. ((230) determined the average degree of particle aggregation in ultrafine silicon nitride powders by PCS and sedimentation field-flow fractionation. Caceci and Billon (C31)investigated the lar e organic scatterers (50-200 nm in diameter) in a number o soil, lake, and groundwater humic acid samples using PCS and electrophoresis. The function of these negatively charged organic particles was discussed. Denkovand Petaev (C32)presented a perturbation approach to examine dynamic processes in suspensions of strongly charged particles at low volume fractions.
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Classical Light Scattering The well-develo ed technique of time-average light scattering is common y applied to determine weight-average molecular weight, z-average mean-square radius of gyration, particle shapes, and interaction of particles with size ran e from submicrons to tens of microns. Dobbins and Megari8s ( 0 1 )investigated the absorption, scattering, and differential cross sections for polydisperseaggregatesof prescribed fractal dimension and uniform primary particle size. Special attention was made for fractal-like aggregates that are formed by cluster/cluster aggregation. Kotlyar et al. ( 0 2 )derived an explicit form of the particle size distribution function for the case of coherent radiation scattering by disperse particles. Finsy et al. ( 0 3 , 0 4 ) discussed two types of data analysis of light scattering for particle size distribution determination. The maximum entropy method and a constrained regularization (CONTIN) method were used for data inversion. Experimental and simulated data were generated to validate the methods. Results were compared with PCS and electron develmicroscopy analyses. Schnablegger and Glatter (D5) oped an optimizedregularization technique for li ht scattering data inversion. The technique was applied to o!tain particle size information in the range of 10 nm up to several microns. A ray-tracing method was used to calculate the light scattering function for lar e irreguarly shaped particles ( 9 6 ) . Mroczka (07) described &e method of moments of particle size distribution analysis and the connection with angular light scatterin information. Minsk (08) to determine %e mean-volume radius taking into account the optical thickness
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et al. ( 0 9 )reported their study of light scatterin of spherical particles. The theory and their experimen setup were discussed. Online methods to determine particle sizes for particulate process streams were examined by Hobbel et al. (010).A forward scattering laser scattering device yielded highly reproducible results when used with a well-designeddilutor. The scanning backscatter instrument offered reproducibility of 2 4 % . Schoofs (011) presented particle size analysis of dry dispersed samples using a laser light scatteringtechnique. The development of measuring cells was reviewed. Kaye et al. (012) described a laser light scattering instrument for the classification of airborne particles on the basis of size, shape, and count frequency. A three-dimensional plot of size vs asymmetry factor vs count frequency was obtained to examine characteristic signature of aerosols. Nomizu et al. (013) developed a s stem to measure simultaneously the elemental content an size of airborne articles. The instrument consista of an inductively couple#-plasma emission spectrometer and laser light scattering apparatus. Benayahu et al. (014) used an inversion method to determine the size distribution of aerosols. The authors derived a perturbation formalism to solve the doublescatterin inversion problem. Chang and Biswas (015) studied tfie evolution of size distribution of nonabsorbing aerosols in a controlled methane/air flame. A light scatterin system was used to measure the dissymmetry of scattere light from Si02 particles. An in situ light scattering method was applied to characterize soot aggregates in flames (016). The particle radius, the number of monomers per cluster, and the fractal dimension were obtained for a premixed methane/oxygen flame. Bonczyk and Hall (017)formulated an approach to determine the structural parameters of soot clusters from extinction and multiangle scattering measurements. The fractal properties of soot particles in an ethylene/air slot burner were evaluated. Rodriguez and Kaler (018) studied the equilibrium structure of concentrated bin mixtures of monodisperse latex dispersions usin static l z t scattering. The scattered light intensity depenfed strongly on the particle size, total volume fraction, and volume ratio of large to small particles. The results were compared to calculations with the hard-sphere model. Vavra and Antalik (019) considered a transversal light scattering method to determine the average particle size and particle size distribution of polystyrene latexes. The angular light scattering pattern near 90' was used to derive the size of the scattering droplet (020). A simple relation between the droplet size and intensity fringe density was presented. Ando and Noguchi (021) measured the size distribution of paint particles in the atomizin air stream. Several coating conditions were examined. %lantz (022) describedthe use of surfactantsfor the preparation of particles in water-based coatings. Higashitani et al. (023) considered the effect of particle size on the coagulation rate of ultrafine colloidal particles. The rate decreased abruptly with smaller particle size, e.g., ) the kinetics 90 nm in diameter. Witkowski et al. (024studied of crystallization. The growth and the nucleation arameters were obtained with solute concentration data anlfrom light scattering measurements. Reardon et al. (025) compared the use of different techniques to determine the particle size of thermal spray powders. The techniques discussed were li ht scattering, sieve analysis, and elutriation. Xia et al. $26) followed the adhesion kinetics of phosphatidylcholine liposomeson uartz surface with an evanescent-wavelight scatteringmetho%.The authors found that no adhesion took place if the liposomes were smaller than 80 nm in diameter. The effect of monoand divalent salta was also explored. Watson and Jennings (027) calculated the scattering functions for dispersions of disk, rectangular-, s uare-, triangular-, and hexagonal-shaped particles. The res ts can be used to characterize colloidal particles for surface pigment ) and emulsion coating. Matsumura and Seki (028computed light scattering from isotropic ellipsoidal particles with the Fredholm integral method. Hu et al. (029)devised a light scattering system to measure the size distribution in a two-phase medium, such as in lowpressure stages of wet steam turbine. The apparatus has the
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capability to measure a wide range of particle size (5-200 pm). The range of measurement can be extended to 0.021000 pm by using lenses of different focal length. Klingen and Roth ( 0 3 0 ) evaluated the particle size of diesel-engine exhaust gas under different load and speed conditions. It was concluded that the principal particle agglomeration process was finished before the particles left the diesel-engine combustion chamber. Hsu et al. ( 0 3 1 )studied in situ Na2C03fume particle size and number density from a synthetic smelt. Processing parameters that control the fume particle formation were discussed. Antonietti et al. (032) described the controlled synthesis of m-diisopropenylbenzenecross-linked polystyrene latexes with particle size 10-60 nm in emulsion polymerization. Light scattering, neutron scattering, and electron microscopy techniques were used to characterized the process. Li (033) reported the study of size histories of boron particles in the ignition and combustion stages. Angulardependent light scattering method was used to determine the particle size. The data were used to calculate the cleansurface boron particle combustion. Turbidimetry/Small-Angle Light Scattering
Koo and Kneer (F6)examined the effects of multimodal and out-of-range particles to the Fraunhofer diffraction size determination. Two data inversion schemes were compared and analyzed. Harfield (F7)described the use of polarization intensity differential scattering method to enhance the laser diffraction analyzer. The method was shown to be useful for quality control in the manufacturing and dispersion of fine materials. Kenney and Hirleman (F8)analyzed the calibration factors for laser diffraction ring detectors. Zhang and Xu (F9) reviewed the effect of particle refractive index on size measurement. Hess and Gatzemeier (F10) compared diffraction spectrometers for particle size analysis. Strazisar ( F I 1 ) discussed particle size analyses using dry powder and wet techniques with laser diffraction instruments. Malghan and Lum (F12)reported factors affecting particle size distribution of hydraulic cements. Different dispersion solvents were evaluated. Fan et al. (F13)studied the particle concentration and particle size distribution in particle-laden turbulent jets of silica gel powder. The effect of jet velocity on particle size was presented.
In nonabsorbing systems, the turbidity is a measure of the reduction of transmitted light intensity caused by scattering from the medium. Kourti and co-workers ( E l )investigated the capability of turbidimetry to estimate particle size distribution in suspensions. The applicability of turbidimetry depends on two parameters, the ratio of the refractive index of the suspended particles to that of the medium and the ratio of the particle diameter to the wavelength of light in the medium. Brandolin et al. (E2) proposed a mathematical inversion method to determine the latex particle size distribution with turbidimetry. Khlebtsov et al. (E3, E4) presented a general analysis of polydisperse systems using turbidity. The formalism took into account the s ectral dependence of the refractive index of the particle anfmedium. Elicabe and Garcia-Rubio (E5) described a regularization technique to derive the particle size distribution of latex from turbidity data. Brandolin and Garcia-Rubio (E6)discussed the use of online turbidimetry to measure the particle size distribution in the latex reactor. Pekhovskaya et al. (E7) reported the use of spectroturbidimetry to analyze fatty emulsions. Surova et al. (E81 characterized the particle size of PVC emulsions and poly(2ethylhexyl acrylate) latexes. Sukop (E9) determined the particle size of acrylic binders used in leather finishing. Chen and Tsin (E10)established an empirical relation between the required flocculant amount and the initial parameters of treated water. The data were used for automated treatment of flocculantsin the purification of highly turbid natural water. Schaub and co-workers ( E l l )presented a theoretical model to calculate the size of aerosols for either transparent or absorbing particles. Comparisons between theory and experiment were made. Makoed and Sorokina (E12) characterized the particle size distribution in BaTiOB and Pd powders with low-angle light scattering. Vavra and Antalik (E131 disussed the use of low-angle spectrodissymmetry to determine the particle size distribution parameters for polydisperse spherical particles.
Sommer ( G I ) compared the theory and instrumentation of optical particle counters. The author combined li ht scattering theory and sample flow-laser beam theory to prefict the performance of optical particle counters. Plantz (G2) described the unique features of the Microtrac ultrafine particle analyzer. Particle size measurement of pigment, dye, and colorants was discussed. Liley (G3)proposed a procedure to analyze the size distribution function from optical particle counter data. The calibration of the optical particle counter was examined both theoretically and experimentally by Sachweh et al. (G4). Gebhart (G5)looked into the response of sin le-particle optical counters to particles of irregular shape. Tleoretical approximations were derived for particles with diameters either much less or much greater than the wavelength of light. The calculations were compared with experimental results generated using six different optical particle counters. Sloane et al. (G6) determined the aerosol particle size using optical particle counting and nephelometry simultaneously. Improved accuracy and precision of particle size distribution were obtained. Karg et al. (G7) compared the performance of low-pressure impactors with optical particle counters using NaHS03 as the model compound. Kondo et al. (G8)developed a flow-cell-type portable laser particle counter for in situ counting of process-induced particles. The apparatus was used to study the coagulation of small particles caused by the reaction between SiH4 and moisture/oxygen. Liebhaber et al. (G9) described the construction of a virtual impactor to be used with an optical particle counter. The impactor improves the sensitivity of optical particle counters for larger particles. Rudolph and Peter (GIO) developed an optical particle counter to characterize aerosols. The instrument was tested with different aerosol generators. Hering and McMurry ( G I I ) determined the optical counter response to monodisperse fractions of ambient Los Angeles aerosols. The result was compared to that for polystyrene latex spheres and to oleic acid particles of the same geometric diameters. Schumann and Heimgartner ((31.2)explored the use of a Climet CI-8060 optical partical counter for fog and droplet size determinations. The instrument was applied successfully in a field test of in-cloud scavenging of air pollutants. Adachi et al. (G13) constructed an automatic measuring system to simultaneously determine particle size and charge distributions in a clean room. The system includes an electrostatic condenser and optical particle counter. The data analysis method was validated with experiments. Livingston (G14)used two liquid particle counters to define the effective filtering operation for ultrapure water. Ichijo et al. (G15) discussed the use of a new flow-cell-type particle counter to detect particles in semiconductor processing gas. The minimum detectable particle diameter was 0.17 pm. Schurmann ((216)presented a new approach to test air filters. The laser particle counter and the Aerodynamic Particle Sizer T M system were used.
Diffraction Huzarewicz et al. ( F I )used the singular value decomposition method to solve the inverse Fraunhofer diffraction problem. Both numerical simulations and experimental data were presented. Sharma and Somerford (F2)described an approximate method to characterize particles of coated spheres. The method was applied to the study of cohesive sediments. Kusters and co-workers (F3) addressed the diffraction case where the ratio of refractive index between solute and solution is close to 1. A suspension of ice crystals in sucrose was examined by laser diffraction and optical microscopy. Wang et al. (F4)designed and built a Fraunhofer diffraction and Mie scattering laser particle sizer. The apparatus extended the measurement to smaller size ranges. Bott and Hart (F5)developed a diffraction system to cover a wide size measuring range. Two sets of Fourier collection optics were employed. The instrument can determine particle size from 0.1 to 1000 um. 58R
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Optical Particle Counters
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Broide and Cohen (G17)investigated the temporal evolution of cluster size distribution during salt-induced ag egation of polystyrene micros heres of 258 nm in radius. ‘f%e results were analyzed using t i e Smoluchoweki rate e uation. Steinkamp et al. (G18)described an im roved m&ilaser/ multi arameter flow cytometer for the anJysis and separation of bioyogical cells. Velocimet r y Edwards and Manr (HI) discussed the proper use of Poisson statistics in the size and volume flux measurements with phase-Doppler anemometry technique. The conditions for valid determinations of size distribution and rate of flow were defined. Sankar et al. (H2) presented a theoretical model to calculate measurement uncertainties of the Aerometrics phase-Doppler particle analyzer. Size resolutions of the order of h0.3 pm were found possible when the instrument was used to measure small spherical particles (
