Anal. Chem. 1087, 59, 142R-162R
Particle Size Analysis Howard G. Barth,* Shao-Tang Sun, and Robyn
M.Nickol
Hercules Incorporated, Research Center, Wilmington, Delaware 19894
INTRODUCTION This is the second biennial review on this subject to appear in Analytical Chemistry (IA). Because of the lar e number of techniques available for particle size analysis and the broad range of applications and particle size (A to mm), this is a rather difficult area to survey. We had prevously classified particle size techniques into a number of major categories which included sedimentation techniques, chromatography, electrozone sensing, microscopy, scattering techniques, and sieving/filtration (IA). Because of the diversity of topics in this review, the contents of this article are given in Table I to aid the reader. Selected applications using scattering techniques and other approaches are listed in Tables I1 and 111, respectively. The most active areas of particle-size analysis are photon correlation spectroscopy and single-particle counters coupled to image analyzers. In addition, there has been substantial growth and development of field-flow fractionation. Microscopy, of course, continues to be the mainstay of particle size analysis and usually serves as a referee method. Over the past two years, we have seen the introduction of number of new instruments employing laser-light sources and advanced data acquisition and processing systems, which play a key role in advancing the state-of-the-art of particle size analysis. Papers published from late 1984 to late 1986 (Chemical Abstracts 1984,101(21) though 1986,105(22)) were searched for relevant papers published in English, French, German, and Russian. With the exception of several techniques, polymers in solution were excluded even though they can be classified as particles; however, micelles were covered. Because of the enormous breadth of topics, in terms of sample type, technique, and particle size range, a number of different search strategies were used to include as many pertinent articles as possible. To this end, we gratefully acknowledge the work of Ruth Curtiss, Hercules Technical Information Division, for her excellent search routines.
GENERAL BOOKS AND REVIEWS Lowell and Shields (IOA) published a book on powder surface area and porosity measurements which discusses both theory and methodologies. A book entitled Physical and Chemical Characterization of Airborne Particles by Spurny (14A) recently appeared. A two-volume series, Particle Characterization in Technology, edited by Beddow (ZA, 3A) was recently published. Volume I deals with microanalysis of particles and particle size analysis applications. Chapters of interest include characterization of pharmaceutical materials (Chapter 4), fractal description of particles (Chapter 3, practical aspects of electrozone size analysis (Chapter 8), and particle characterization methods for liquid suspensions (Chapter 10). Volume I1 contains chapters concerned with morphological analysis of particles. The International Society of Optical Engineerin (4A) published a proceedings volume on particle sizing ancfspray analysis. A proceedings on fine particles and fibers was issued by the Ontario Research Foundation (11A) which includes chapters on fractal analyais of particles, image analysis, particle size data presentation, differential mobility analysis, and particle size analysis applications of flavors, seasonings, ceramics, and fillers. Leschonski (8A) discussed the present state and future trends of particle characterization including measurement of particle shape and on-line measurements. Leschonski (7A), Haley and Joyce (6A), and Raper (13A) presented brief reviews of particle size analysis techniques. Ohsawa and Asanoma (12A) discussed the use of laser techniques for the determination of particle size distribution in combustion products. Lieberman (9A) wrote a comprehensive overview 142 R
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Table 1. Review Contents
General Books and Reviews Scattering Techniques Photon Correlation Spectroscopy Classical Light Scattering Small-Angle Light Scattering Turbidimetry Fraunhofer Diffraction Velocimetry Neutron Scattering X-ray Scattering Technique Combinations Applications Chromatographic Techniques Hydrodynamic Chromatography Field-Flow Fractionation Single-ParticleCounters Light Blockage Electrozone Microscopy/ImageAnalysis Sieves/Classifiers Sedimentation Aerosol Measurement Devices Other Techniques Selected Applications Intercomparison of Techniques Data Analysis Particle Size Standards Comminution
of the characterization of particles in liquids. In this chapter he discusses the reasons why particles are analyzed, problems in sample handling, and methods and instrumentation that are used. Lastly, it is worth mentioning that Gilson Company (5A) has recently issued an informative particle size analysis equipment catalog covering sieves, classifiers, comminution devices, and a variety of other particle size instruments which are fully described.
SCAllERING 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. In a typical experiment an incident beam 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 radiations characterize the structure and dynamics of the medium. Two techniques that have attracted a great deal of recent attention for particle size determination are quasi-elastic light scattering (QELS) (also referred to as photon correlation spectroscopy (PCS), dynamic light scattering, or time-dependent light scattering), and small-angle neutron scattering (SANS). Active research using these two methods has increased because of the commercial availability of the instrumentation and the accessibility of neutron scattering facilities. In this section, the emphasis will be placed on the application of these two relatively new approaches to particle size analysis. In the case of classical light scattering, the radius of gyration of the particle is determined from the wave vector dependence or angular dependence of the time-averaged scattering intensity. However, with PCS, the size information is obtained from the time-deDendent fluctuations resulting from Brownian motion of partides. The diffusion coefficient of the Brownian particles is determined from the intensity autocorrelation function measured experimentally with a digital correlator. The hydrodynamic radius is then calculated from the diffusion coefficient by using Y
0 1987 American Chemical Society
PARTICLE SIZE ANALYSIS
ershy. Before joining HerCUieS. 1°C.. in 1974. he was a postdoctoral fellow in clinical Chemistry at Hahnemann Medical CoIlege in mliaddphb. He is a frequent bctUrer at s h a l cou~sess~onsoredby the Deb-
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Sha~-lsnpSun Is a reSBarch physicist with the Materials Science Division of Hercules Research Center in Wiiminglon. DE. He received his B.S. (1972) in physics hom Tunghal University. Taiwan. and Ph.0. (1978) m physics hom the State University 01 New Y a k at Buffalo. Belwe Pining Hercubs. Inc.. in 1983. he was a postdoctorat research associate at the Center lor MaterL ab Science and Engineering. MaSJaChUSetlS Institute 01 Technology. He is interested in applying physics concepts and methDdS to lhe understanding 01 polymeric and biologicai systems and Is 8150 interested in optical properties 01 materiais. He is lhe author 01 more than 20 publications in light scanering. phase transition. polymer physics. and biOphy5iCI. He is a member of the American Physical Society, Material~Research Society. and the Society 01 F'hotDOptiCal InStrUmentation Engineers. R e p M. Nlckol is a chemist with the AnaMica1 DMslon of Hercules Rewarch Center In Wilminaton. DE. She received her B.S. (1981) in :hemistry lrom the State Universh ty of New Y a k al Buffalo. Belwe iolning Hercules. Incapo~aled.In 1984. she was a research Chemist at Calgon Corporation. Pittsburgh. He7 s p e C l ~ l t l ~ Sinclude microscopy and partkb size analysis. Ms. Nickol is a member of the Division of Analytical Chemistry and Polymeric Materials and Engineering of the ACS.
the Stokes-Einstein relation. This method is used to probe particle sizes ranging from 1 0 . ' to em. The power of PCS lies in ita relative ease of use, rapid determination of diffusion coefficients with high precision ( 1 pm diameter particles. Steric FFF. In this subtechnique, used for large particle separation (>1 to 100 pm), particles do not form a diffuse layer, but remain fairly close to the wall. The larger particles sample larger velocity streamlines as compared to smaller particles which sample, on an average, smaller velocity streamlines. As a result, larger particles elute first. (This mechanism is similar to HDC.) Koch and Giddings (3IQ)examined the effects of flow rate and sedimentation force on particle resolution in steric FFF. Schure and co-workers (40Q)used this technique to separate coal fly ash. Thermal FFF. During the past two years, Giddings' group has been quite active in thermal FFF. The theory and practice of thermal FFF were reviewed including the application of the technique to 2 X lo7molecular weight polystyrene (11Q). Brimhall et al. ( I Q ) developed expressions for the thermal diffusion coefficient and the thermal diffusion factor for polystyrene in ethylbenzene as functions of molecular weight and temperature. With the use of an empirical equation, the molecular weight analysis of polystyrene can be accomplished without the need of calibration standards. Schimpf and Giddings (37Q) studied the effects of molecular weight, structure, and solvent composition on the thermal diffusion coefficient using thermal FFF. Gunderson and Giddings (22Q)demonstrated that retention in thermal FFF is a function of the concentration diffusion coefficient, which depends on molecular size, and a thermal diffusion coefficient, which depends only on polymer composition. They concluded that compositional variations can be evaluated by a combination of thermal FFF and SEC measurements. These authors also derived an expression for the velocity profile across the channel in thermal FFF (2IQ). A theoretical treatment of retention and nonequilibrium peak broadening was given for an exponential concentration profile combined with an asymmetrical velocity profile. Kirkland and Yau (298) used programmed temperature gradient thermal FFF to characterize polydisperse polyethylene and poly(methy1methacrylate). These authors (30Q) have also fractionated a number of water-soluble polymers using thermal FFF including poly(ethy1ene oxide), poly(ethylene glycol), sodium poly(styrene sulfonate), and poly(vinyl pyrrolidone). Martin and Hes (32Q)used a low-angle laser light scattering detector coupled to a thermal FFF apparatus for the analysis of poly(methy1methacrylate) dissolved in dimethylformamide. Martin and Reynaud (33Q) applied thermal FFF for the characterization of asphaltenes.
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SINGLE-PARTICLE COUNTERS Light Blockage
Bowen et al. (2R) developed an instrument to measure cluster size distributions in colloidal dispersions based on passage of individual clusters through an optical-flow channel partially illuminated by a laser beam. A multichannel pulse-height analyzer is used to give a cluster size distribution. Because measurements are made at low angles, pulse height is proportional to the square of the number of particles in a cluster and independent of cluster shape and orientation. These authors have applied this technique to study salt-induced aggregation of polystyrene latexes (3R). Copper and Clough (6R) used a single-particle analyzer (OAS, optical array spectrometer) to monitor particle size distribution in a fluidized bed. These authors (7R-9R) also derived an optimal filtering algorithm to rectify noise associated with measuring particle size distribution in a fluidized bed. Jonasz (IOR) described a method for determining the nonsphericity of marine suspended particles based on a relation between the size distribution obtained by using a volume-sensitive and a projected-area-sensitive particle counter.
Szymanski and Liu (11R,13R)studied the performance of a narrow-angle and wide-angle, forward-scattering laser aerosol spectrometer. The range of the instrument in the narrowangle mode was from 0.2 to 0.7 pm for transparent particles. Aerosols of polystyrene latex particles, dioctyl phthalate pdrticles, India ink, and methylene blue were analyzed. Van der Meulen et al. (14R)determined the size resolution of laser optical counters by taking into account the fact that monodisperse aerosols give a pulse-height spectrum whose trailing ed e falls off indefinitely. They also discussed errors introducej when aligning the optics using the observed pulse-height spectrum. Robinson and Lamb (12%) reported on the calibration of an optical particle counter in which the response to latex and water particles (0.3-15 pm) was calculated on the basis of Mie theory. Buettner (4R)discussed the use of an optical-particle counter to calibrate an impactor and cyclone. Conner and Knapp (5R)compared an in-stack optical-particle size monitor to an in-stack cascade impactor to monitor coal-fired fly ash. Both devices were able to detect praticles in the range of 0.2-20 pm. Aharonson et al. (IR)described a computerized system for determining particle size distributions based on a laser-beam moving past individual particles. Optical blockage is measured with a PIN photodiode which is related to particle size. An internal microscope is focused on the measuring zone for visual television display and shape analysis by a computer. Electrozone Sensing
An overview of the Coulter counter particle system was given by Kinsman (6s). In this method, particles are suspended in an electrolyte and pumped through an aperture that has an electrode on both sides. As each particle passes through the orifice, it displaces its volume in electrolyte causing resistance changes proportional to the volume of the particle. Karuhn and Berg (4s)commented on the selection and preparation of electrolytes, sample preparation, and data acquisition and processing. Karuhn (5s)also suggested that statistics such as skewness, mode, and geometric standard deviation of mass and population distribution curves must be calculated to achieve the most useful information from particle size analysis. The effectiveness of antibiotics on bacteria cells was related to the volume breakdown in cells. Schulz and co-workers (20s) measured volume distributions of Escherichia coli cultures by a Coulter counter channel analyzer. Biological studies were also conducted by Barnes and Talbert ( I S ) . The size of bacteria cells exposed to platinum was measured with the Coulter counter. Garti et al. (3s) studied the concentration effects of a Span 80/Tween 80 emulsifier svstem on water-oil-water emulsions. In'these emulsions, additkes such as electrolytes affected their stability. Because of osmotic gradients, water was transported across the oil phase in these emulsions. The Coulter counter was used to evaluate the size increase or decrease of the aqueous droplets. The Coulter counter was used by Nystroem et al. (8S, 9 s ) to determine the solubility and dissolution rates of two slightly soluble materials suspended in micellar solutions. Doutre and Guthrie (2s)were awarded a patent on a method for determining particulates in molten metals such as Al, Ga, Zn, and Pb. Molten metal was passed through a small orifice. A current was applied across the aperture; particulates of about 15 pm or greater were detected by a voltage pulse whose magnitude is dependent on particle size. Lenk ( 7 s ) received a patent for a device used for detecting particles in an electrolyte.
MICROSCOPY / IMAGE ANALYSIS Lenth et al. ( 1 5 0 described a high-speed, automated system for particle shape analysis. The unit consisted of a TV camera and monitor, microscope, analog-to-digital converter, computer, and digital color-image display device with memory. Snelling (272') described the use of an image analyzer for sizing sodium fire aerosols, reactor crude particles, and calcium--silver aerosol particles. Williams (31r ) used optical-imageanalysis to determine the apparent density and distribution of particle diameters in samples containing significant amounts of cavernous particles. The method was applied t o atomized ferANALYTICAL CHEMISTRY, VOL. 59, NO. 12, JUNE 15, 1987 * 149R
PARTICLE SIZE ANALYSIS
rosilicon powder. Automatic TEM image analysis was described by Ralph (217') to determine particle and grain size distributions. An automated optical microscopy technique was developed by McQuaker and Sanberg (187') to examine coal dust in airborne particulates. Shibaoka (257') reported on an incident-light microscopic method for characterizing unburned char particles in fly ash. Char particles ranged in volume size from 10 to >lo00 pm. Vleeskens (307') found the maximum size of char particles to be approximately 50 pm with an optical image-analysissystem. Coal fly ash particles were also examined with SEM and energy-dispersive X-ray analysis (EDXRA) by Lichtman and Mroczkowski (167'). Bayard (17') suggested using the light microscope for the initial screening of fine particles. He pointed out the usefulness in detecting sources of corrosion, filter failure, or contamination. Negative staining was once used only in biology for the examination of viruses, bacteria, and protein molecules by light and electron microscopy. Nowadays, this method has been used on a wider selection of materials. Scholsky and coworkers (237') viewed polystyrene latex particles as small as 0.02 pm under the TEM by negatively staining the particles with potassium phosphotungstate. The accuracy, high resolution, and easy preparation of this method were found to be superior compared to the platinum/carbon shadowing techstudied ) the effects of rubber nique. Jang and Chan (11!l' particle size on the mechanical properties of a high-impact polystyrene material. The rubber-phase morphology and particle distribution were characterized by Os04 staining, ultramicrotoming, TEM, and computerized image analysis. Gross and Webb (77') applied quantitative digital-video optical microscopy to measure the individual low-density lipoprotein particles, intensified with fluorescent iodide, on cell surfaces. Frank et al. (47') described aurothioglucose staining as an improved staining procedure over uranyl acetate staining for determining ribosomal subunit structure. Sanders (227') discussed the use of TEM for the examination of materials such as catalysts, including clusters of atoms, small crystalline particles, zeolites, and deposits of carbon which are formed on catalysts during reaction. He also applied image-processing techniques. Yacaman (327') commented on the important role particle shape plays in catalysis. TEM techniques including weak multibeam imaging, topographic refraction imaging, dark field, and microdiffraction were reviewed and used to characterize the shape, crystal structure, and size distribution of metal particles. Gai and co-workers (57') characterized small supported metal particles using high-resolution electron microscopy (HREM), probe diffraction, and image calculations. Smith (26T) discussed the usefulness of HREM in materials research. Instrumental limitations and applications were also reviewed. Jefferson et al. (127') resolved the atomic structure of goldsilicon catalyst particles with a 200-keV TEM. Tucker and co-workers (297') developed an ultramicrotomy technique to study the nucleation and growth phenomena of A1,0, particles. Iijima (107') also viewed single-crystal structures of individual -pA1203particles. Instead of thin sectioning, he used a HREM with a TV system under ultrahigh vacuum. Khan and Mitchell (147') studied the particle size of an alumina desiccant by electron microscopy. Jiang and co-workers (137') prepared Ni-Fe alloy particles on TiOz and A+03 supports by coimpregnation. Alloy particles were identified and sized with STEM, EDXRA, magnetic susceptibility, and Moessbauer spectroscopy. Davidson (37') reviewed particle analysis by electron microscopy, X-ray spectroscopy, X-ray diffraction, scanning Auger spectroscopy, and electron energy-loss spectroscopy. Yamada et al. (337') found that latex particles of 0.09-0.33 pm differed from +6 to -18% by electron microscopy vs. the manufacturer stated size. Hoehr (97') evaluated different types of fibers by TEM/EDXRA. Particles of similar chemical composition were analyzed further with selected-area electron diffraction. Popov et al. (207') used computer-aided (Fortran) electron microscopy to determine the degree of dispersion of perfluoro-containing emulsions used as blood substitutes. The method was shown to be simple and gave accurate results. Neuhaeuser and Gaertner (197') studied the electrophoretic mobility of disperse dye particles in aqueous suspensions with an automated Parmoquant-2 microscope. 150R
ANALYTICAL CHEMISTRY, VOL. 59, NO. 12, JUNE 15, 1987
Hartman (87') used the center-distance finding technique based on array sizing to determine the mean size and distribution of monosize microspheres by optical microscopy. A new electron microscope method was developed by Seidel and co-workers (247') to view distance distributions of particles in photographic layers. Cluster algorithms were used by Bezdek (27') to predict particle shape. Gray et al. (67') described the technique of stereopsis which involved taking two images of the same area at 0" and 10" tilts from the horizontal axis and piecing together the electron micrographs as one. This three-dimensional type image was shown to give a more accurate account of the number of single particles in an aggregate than by the traditional two-dimensional micrograph approach. Soot aerosols such as diesel were studied in this manner. McCrone (175") has devised a method, known as huffing, for performing microchemical testing on nanogram single particles. A new holographic interference electron microscope method was devised by Tonomura and co-workers (285")to determine the magnetization and thickness distributions of cobalt particles.
SIEVESKLASSIFIERS The accuracy of sieving depends on the loading on the sieve, sieving movement, and particle shape. Usually, sieves will allow particles to pass through based on cross-section diameter rather than length. Metal powders were used by Rajpal and co-workers ( 1 0 to study the effects of particle morphology on batch sieving behavior. Sieve cascadograph, a new technique, was developed by Meloy et al. (7U, 8U) to measure particle shape. This technique involved shaking a monosized powder through a stack of identical sized sieves and measuring the weight of the powder leaving the lowest sieve as a function of time. This was used to produce a signature representative of the particle-shape distribution. Kuga et al. (6U) used a screen mill to comminute sands with particle sizes of 500-710 pm. The particle projections were measured by a light microscope/digitizer system. They reduced 16 shape indices into four main shape factors which included elongation, global roughness, surface roughness, and angularity. Rogers and Brame (11U) evaluated the performance of a new technique, high-frequency vibrating screens, on fine limestone, ore, and coal slurries. Of the screen cloths tested, they found that the slurry feed rate had no significant effect on the size classification of the slurries. However, an increase in the volume-percent solids concentration of the slurry decreased the particle size. A wet-sieving method was developed by Jablonka and Munro (4U) for measuring the particle size distribution of casein curd in skim milk. The mean particle size was found to increase with increasing pH and temperature. Nakagawa et al. (9U) developed a particle-shape classifier to fractionate particles with respect to their sphericity. Dietzsch ( I U ) evaluated a Bahco classifier in terms of particle size distribution of
