Anal. Chem. 1991, 63,1 R-1OR
Particle Size Analysis Howard G. Barth* Du Pont 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
INTRODUCTION Preparin a review on article size analysis is a difficult task because of &e enormousgreadth of technique and application areas. Furthermore, the definition of a particle becomes hazy when dealing with angstrom-size structures. This being the fourth review (see refs Al-A3), we have continued to streamline our coverage to make it as useful as possible for our colleagues. We have omitted aerosol measurement devices and microscopy/image anal sis, which are themselves specialized areas and are beyonithe scope of this article. Areas that are included are listed in Table I. Methodologies based on light scattering measurements continue to dominate particle sue instrumentation. With this review, we re ort the introduction of a new dynamic light scattering tectnique-diffusion wave spectroscopy-which holds great promise for determining particle size measurements in concentrated or optically opaque systems (see Photon Correlation Spectroscopy). The use of acoustic spectroscopy also appears to be a promising approach, althou h relatively few reports have appeared thus far (see Other 4echniques). The ease of setting up a hydrodynamic chromatographic (HDC) system, except for software considerations, has been an attractive feature of HDC for determining particle size distributions, despite its limitations and present lack of commercial instrumentation. For field-flow fractionation (FFF),the number of papers appears to have remained almost constant, as compared to our last review. It is of interest to note that one group of researchers has been responsible for about one-third of these FFF ublications. Literature searches were base$ on Chemical Abstracts 1988, 109 (25), to 1990,113 (24),for all relevant papers dealing with new developments in article size analysis and applications of general interest. d t h some exce tions, references to obscure journals and a ers publishecfin Japanese or Chinese were not not i n c d e l . Although our focus is on articles, pertinent references dealing with macromoleculesanxmicelles are iven, especially in the HDC and FFF sections. d e atefully acknowledge the assistance of Ruth Curtiss ( H e r c x s Research Center) and Neil Feltham (Du Pont Co.) who have worked closely with us over the years in developing and improving literature search strategies for these reviews.
GENERAL BOOKS AND REVIEWS Books and conference roceedings on particle size analysis that have been publishecfdurin this review period are listed in refs A4-A6. (For books and reviews relating to specific techni ues, please consult the appropriate sections in this article7 General, comprehensive reviews on particle size methodolo 'es have been written by Barth and Sun (A3)and Miller and fines ( A n . Several reviews concerning particle size instrumentation for online ap lications have also appeared (A&AIO). Leschonski ( A l l )8scussed the present and future trends in particle size analysis. Pohl (A12)wrote on selecting particle size analyzers. In a chapter on the "Physical Properties of Particles and Polymer", McDonnell and Walsh (A13), Du Pont Contribution No. 5789. 0003-27Q0/91/0363-1R$09.5OlO
Table I. Review Contents General Books and Reviews
Scattering Techniques Books and Reviews Photon Correlation Spectroscopy Classical Light Scattering Turbidimetry/Small-Angle Light Scattering Diffraction Optical Particle Counters Velocimetry Neutron/X-ray Scattering Chromatographic Techniques Size Exclusion Chromatography Hydrodynamic Chromatography Field-Flow Fractionation Electrozone Sensing Centrifugation/Sedimentation
Disk Centrifuge Photosedimentometry Photosedimentometry Ultracentrifugation Other Techniques Intercomparison of Techniques Data Analysis/Particle Shape Particle Size Standards covered particle size analytical techniques. Other general reviews that have appeared include particle size analysis of emulsions (A14),suspensions (A15),aerosols (A16),and environmental pollutants (A17).
SCATTERING TECHNIQUES Light, neutron, and X-ray scattering techni ues have been used extensively to study the structure an! dynamics of particles and macromolecules in multicomponent systems. A wide range of size (angstrom-micrometer) can be determined. In a typical experiment, an incident beam with proper 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 comprehensive symposium on the theory and practive of optical particle sizing was held in Rouen, France, May 12-15,1987. The proceedings are available in a book entitled Optical Particle Sizing: Theory and Practice, edited by Gouesbet and Grehan (B1). All the important optical techniques for particle sizing were presented and reviewed. A summary of the state-of-the-art of key techniques was also given. Several books on light scattering principles and practices were published (B2-B5). Ap lications of neutron scattering for materials science were &cussed in a symposium pro0 1991 American Chemical Society
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ceedin (B6). A book entitled Neutron & X-Ra Scattering: Compgmentary Techniques has also been puclished (B7). Scarlett (B8)reviewed laser instruments for particle size measurement using online process control conditions. Yan and Clarke (B9)described application of scattering techniques for the in situ determination of particle size distribution in colloids. Bernard (BIO)reviewed particle sizing in combustion systems with laser light scattering methods. Photon Correlatlon Spectroscopy
Photon correlation spectroscopy (PCS), also referred to as quasi-elastic or dynamic light scattering (QELS or DLS), is routinely used to obtain article size or size distribution information from the time iependent fluctuations of scattered light intensity caused by concentration fluctuations (Brownian motion) of particles. The diffusion coefficient of the Brownian articles is determined from the intensity autocorrelation function measured ex erimentally with a digital correlator. The hydrod amic rad!us is then calculated from the diffusion coefficient using the Stokes-Einstein relation. One area of active research is the study of concentrated or optically opaque systems. Recently, the so-called diffusionwave s ctrosco y (DWS) a roach offers a new way to derive articpe size " inPormation. his method addresses dynamic Hght scatterin in the multiple scattering limit. Pine and collea ues ( C l j describe the theory of this new technique. Excelknt agreement between theory and experiment was shown, and the mean size of the particles was measured. Horne (C2)used the DWS method to study-thepolydisperse suspension of casein micelles in milk. Mixtures of monodisperse latexes were examined to derive an empirical weighting function for the analysis of the effect of polydispersity in particle size (C3). Fraden and Maret (C4) investigated the effects of short-range inte article correlations on the multiple scattering of light in co loidal suspensions. A theoretical model was developed by Yan and Clarke (C5) to intepret dynamic light scattering results from highly concentrated colloidal systems with a narrow distribution of particle sizes, where optical (i.e., refractive index) and size polydispersities were completely coupled. Concentrated water-in-oil microemulsions formed from water, Aerosol OT, and apolar solvent were characterized. .The AOT-stabilized water microemulsion droplets have a size polydispersity of about 6.5%,which is smaller then prevjously thought. Bertero et al. (C6)reviewed several methods of data analysis to extract polydispersity information from the measured correlation function. Resolution limits characterizing the reconstitution of the size distribution function were discussed. Hallett et al. (C7) presented a new approach to analyze number distributions. Comparison of results obtained from PCS and electron microscopy was made for unimodal, bimodal, and trimodal distributions. Ross and Nguyen (C8) addressed the issue of correlation function analysis and examined the spectral properties of the re ularized inversion of the Laplace transform. Duke et al. looked into factors that impacted on the accuracy and precision of PCS measurements. Techniques were developed to control the concentration, uniformity, and dispersion of the sample. A new photon correlation spectrometer was described by Nordmeier and Lechner (CIO).The instrument is capable of simultaneous recording frequency-inte rated and incoherent-elastic light scattering. Brown et af. (C11) constructed and tested several miniature light scatterin systems usin o tical fibers, semiconductor laser diodes, av&nche and PI4 pkotodiodes. It was illustrated that lpw-cost dynamic light scattering ap aratus is ossible for online process monitoring and control. kicoli et a f (C12)demonstrated instrumentation for fast, accurate, online determination of particle size distribution of submicrometer emulsions with good reproducibility. Sineva and colleagues (C13) studied the particle size distribution of microemulsions of octane-water-amyl alcoholsurfactant systems. Kinematic viscosity and octanelwater solubilization were discussed. Hwan et al. (C14) measured the emulsions of a water-Tween 40- enzene system. They also determined the particle radius and molecular wei ht of elatin micelles with sedimentation and PCS techniques fC15). bolotskii et al. (CI6)characterized the microemulsion system
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of Aerosol OT with the combination of sedimentation of QELS methods. Caldwell and Li (CI7) described the advantage of combining PCS and sedimentation field-flow-fractionation methods. The conditions that would reduce errors in the analysis of particle sizes were suggested. The authors applied the techniques to understand two emulsions, Liposyn and Hercon 85. Static and dynamic li ht scattering techniques were employed to characterize filute aqueous dispersions of polytetrafluoroethylene latex particles (C18). The anisotropy, size, and translational and rotational diffusion coefficients of the particles were determined. Bergqvist and Strand (C19)established the utility of PCS as a fast and reliable quality control tool for the sizing and stability test of radiolabeled colloids in pharmaceutical ap lications. Good agreement between PCS and the standarfsizing technique of microfiltration was found. Bruenger and Schollmeyer (C20, (721) proposed using latex suspensions as a model for dyes to understand the dyein of poly(ethy1ene terephthalate) fibers with disperse dyes. 'fhe latex suspensions were evaluated by PCS. Klyubin et al. (C22) investigated the particle size distnbution of polystyrene latex during coagulation as a function of KC1 concentration. Kourti et al. (C23) demonstrated online determination of particle size distribution in a latex reactor during emulsion polymerization of vinyl acetate. Sampling every 10-20 min was achieved. Thomas (C24) used fiber-optic dynamic light scattering to characterize the particle size of concentrated dispersions of a growing acrylonitril-tyrene copolymer latex. The coagulation kinetics of silica hydrosol of 4 different sizes (44.8,101,180, and 515 nm) were investigated by Ludwig and Peschel (C25, C26). The rate constants for rapid and slow coagulation were determined at various electrolyte concentrations. The smallest particles were found to be the most stable. Agrawal (C27)reviewed the application of PCS to characterize dilute suspensions of ceramic powders. The kinetics of flocculation of aluminum oxide particles was considered, and limitations of the method were discussed. Zachariah et al. (C28) compared the use of DLS and classical an ular dissymmetry method for the in situ measurements of shcon dioxide particles formed in a counterflow-diffusion-flame reactor. DLS were found to be less robust then the classical technique as a possible online diagnostic tool for process control. Madani and Kaler (C29)studied the aging and stability of vesicle dispersions that were formed by sonication of aqueous dispersions of synthetic surfactant sodium 4-(4'-heptylnony1)benzenesulfonate. Vesicle stability and size were stro functions of the sonication process, temperature, time, an electrolyte concentration. Ruf et al. ('230) described the theory, methodology, and application of DLS for determinmg the size distribution of vesicles. Ficarra et al. (C31) reported the use of PCS to determine particle size and weight distributions of pharmaceutical powders, e.g., sulfadiazine, caffeine, and phenobarbital. The authors concluded that PCS was su erior then the diffuse reflectance method for showing the fteterodispersit of the powders. Sattelle et al. (C32) determined the h drdynamic diameters of several toxin particles in distilledr water.
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Classical LIgM Scatterlng
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 range from submicrometers to tens of micrometers. Felde (DI) presented a method to obtain particle size distributions with light scattering. With this model, particle sizes from 1 to 50 hm could be measured, and particle size distributions with more than one modal value could be determined. Blum and Fissan ( 0 2 ) discussed the determination of particle size distribution parameters usin a laser li4ht scattering spectrometer. The method seemed to be limited to unimodal distributions described by two parameters. A semiempirical method was proposed by Licinio and Delaye (03) to calculate the scattering intensities for polydisperse colloids based on an effective hard-s here model. The model was applied to interpret dynamic lig t scattering data
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PARTICLE SIZE ANALYSIS Howard a. Barth k a member of the research staff of the Analytical DMsion of Central Research & Development at Du Pont Experimental Station, Wiimington, DE. Before joining the Du Pont 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 specialities include potymer characterization, viscometry, size exclusion chromatography, and high-performance IiquM chromatography. He has published over 50 papers in these and related areas. Barth has also edited the book, Modern Melhods of Particle Size Analysis (Wiiey), and coedited, Modern Mefhods of Polymer Characterlzatlan(Wiley). He has also edited three symposium volumes on pofymer characterization published in the Journal of Applied Polymer Scbnce Barth was on the Instrumentation Advisory Panel of Ana&tical Chemistry and was Associate Editor of the J m a l of ApplM Pdymer ScEence. He is cofounder and Chairman of the International Symposium on Polymer Analysis and Characterization. Barth is past Chairman of the Delaware Section of the ACS where he presently serves as councilor. Dr. Barth is a member of the ACS divisions of Analytical Chemistry, Polymer Chemistry, and Polymeric Materlais Science and Engineering, the AAAS, Society of Plastics Engineers. and the Delaware Valley Chromatography Forum. He is also a Fellow of the American Institute of Chemists.
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Shao-Tang Sun k a research supervisor with the Aerospace Division of Hercules Research Center in Wnmington, DE. He is also project manager of the photonics program. Dr. Sun received his B.S. (1972) in physics from funghai University, Taiwan, and Ph.D. (1978) In physics from the State University of New York at Buffalo. Before joining Hercules Inc. in 1983, he was a postdoctoral research associate at the Center for Materiais Science and Engineering, Massachusetts Institute of Technology. Dr. Sun is involved with applying physics concepts and methods to the understanding of polymeric and biological systems and also is interested in optical properties of materials. He is the author of more than 20 publicatkms in light scattering, phase transition, potymer physics, and biophysics and is a co-inventor on two patents. Dr. Sun is a member of the American Physical Society and the Optical Society of America.
generated with concentrated a-crystalline protein dispersions. Okuda et al. (04) derived an approximated equation to characterize rolate spheroidal aerosol particles. The equation was analyzeXnumericallyin terms of particle size and aspect ratios. Sample aerosols of barium sulfate were used to validate the calculation. Paramanov and Lopatin (05)described the angular dependence of light scattering by a suspension of soft spheroidal particles. Jones and Savaloni (06,07) were interested in the development of a light scattering instrument to detect fibers. The authors discussed several types of fibers and their respective theoretical treatments. With their instrument, fibers of diameter greater than 1.6 pm could be discriminated from spheres and irregular particles of similar size. The calculation implied that the fiber aspect ratio as low as two could be detected. Al-Chalabi et al. (08)suggested the use of the instrument to monitor asbestos contamination in a workshop atmosphere. The fiber diameter could be measured as low as 0.5 pm, but the smallest fiber size that could be discriminated was 1 pm. An inline particle size analyzer for use in the processing industry was described by Hoffman (09).The device measures the size distribution over a range of 1-lo00 pm. Zurlo and Chigier (DIO) presented a particle sizer based on the polarization ratio detection of scattered light. The application for diesel sprays was reported. Von Benken et al. (011) constructed an apparatus for real-time size and speed determination of blow-off particulates from pulsed irradiation experiments. Measurements of micrometer-size particles moving a t approximately 105 cm/s were demonstrated. Shimizu and Ishimaru (012) developed a differential Fourier transform inversion technique for determiningthe size distributions of randomly distributed scatterers. Their approach was demonstrated in practice with latex spheres and
bacteria. Curry (013)examined the constrained eigenfunction method for the inversion of remote sensing data. Hofer et al. (014)reported elastic light scattering data for the characterization of oil-water emulsions. The authors proposed to use the technique for pharmaceutical applications, such as detecting undesired large particles in fat emulsions for intravenous administration. It was concluded that elastic light scattering was more advantageous than QELS for providing both number distribution and intensity distribution. Attwood and Ktistis (015)carried out experiments on oilin-water microemulsions formed from isopropyl myristate, polysorbate 60, sorbitol, and water. Elbing and co-workers (016)investigated emulsion polymerization by using light scattering. Mechanism of latex particle formation from microemulsions of vinyl stearate was suggested. Knollenberg (017)compared several polystyrene latexes to the NBS standard reference material by using an open cavity laser aerosol spectrometer operating a t wavelengths of 633 and 1152 nm. It was shown that the measured diameters could differ from the nominal diameters by more than 20%. Jerkovic and Fissan (018)described an optical monitor for the detection of size distribution parameters and particle number concentration of product aerosols. White and Macias (D19) characterized the nature of aerosols at Spirit Mountain, NV, with light scattering. Leaitch et al. (020)presented airborne and lidar measurements of aerosol and cloud particles in the troposphere over Alert Canada. Kimbrell and Yeung (021)reported the use of light scattering for the determination of particle sizes in a laser-generated plume. Large carbon particles, on the order of 85 nm and larger, were observed in a plume generated from pyrolytic carbon. Bengtsson and Alden (022)investigated the soot particle sizes in premixed ethylene flames by using a pulsed Nd:YAG laser. Bockhorn and colleagues (023)measured soot particle sizes in flat premixed sooting flames of several hydrocarbons with oxygen. The optical results were compared with data obtained by electron micrographs. In the Rayleigh regime of scattering, the results from the two approaches agreed well. In the Mie regime, the agreement was not as good. ) particle sizing in combustion systems Bernard (024reviewed by using scattered laser light techniques. Stejskal et al. (025) characterized poly(methy1 methacrylate) particles prepared by the dispersion polymerization of methyl methacrylate in decane. Hara and Nakajima (026) studied the polyelectrolyte complexes composed of heparin and partially aminoacetalized poly(viny1 alcohol) in aqueous solution. Turbidimetry/Small-Angle Light Scattering
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 ) reviewed the application of turbidity in particle size determination. The technique was evaluated for online use. Elicabe and Garcia-Rubio (E2)studied the latex particle size distribution from turbidimetry. Using the inversion technqiue based on solutions to Fredholm integral equations, the authors demonstrated the validity of their method with model polystyrene latex mixtures. The selection of the regularization parameter in inverse problems was also discussed (E3). DeLong and Russo (E4)determined particle size distribution of titanium dioxide dispersed in polymer matrixes using zero-angle depolarized light scattering. The existence of large size particles was observed, contrary to the electron microscopy result. Desbordes et al. (E5)presented new experimental results on small-angle polarized and depolarized light scattering from almost isotropic, spherical polystyrene latexes. The data compared closely with calculations based on the exact Mie theory. Sedlacek (E6)discussed size estimation of nearly monodisperse spherical particles in the multivalued region. Polystyrene latex particles were characterized with the forwardangle dissymmetry techni ue, transmission electron microscopy, and the integral tugidity ratio method. Suetsugu et al. (E7) measured particle sizes and interparticle distances of stearic acid coated and uncoated calcium carbonate particles in polypropylene or polystyrene. The effects of the mixing variables on particle size were assessed. ANALYTICAL CHEMISTRY, VOL. 63, NO. 12, JUNE 15, 1991 3 R
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Dlffractlon
Biancaniello et al. (FI) examined the use of a nonintrusive particle sizing instrument based on the principle of laser Fraunhofer diffraction. The particle size distribution and mean size were determined in real-time for metal powder produced by inert gas atomization. Hirleman and Dellenback (F2)proposed a particle sizing instrument based on a reconfigurable online detector array that could be adapted to the measurement. The so-called ada tive Fraunhofer diffraction particle sizing instrument incluied a magneto-optic spatial light modulator as the feedback control component. Kaye and Trottier (F3) examined the issue of structural features on the analysis of diffraction data. In the case of respirable dusts, such as quartz, diesel exhausts, fly ash, and nuclear melt-down fumes, accurate size information depended on the proper deconvolution of diffraction data by taking into account of structural effects. Mroczka (F4)looked into ways that could im rove the overall performance of the integral transform of $iffraction data. Koo and Chaboki (F5)compared several published integral transform methods. Various sets of data obtained from gas-turbine and rocket- ropulsion industries were analyzed. Allen and Bakker (F6)$iscussed the article sizing of sprays using a diffractometer and addresseithe issue of nonhomogeneous s ray clouds. Roy and Tessier (3’7) considered the effect of Eght reflection and showed that a more accurate particle-size distribution could be obtained by taking into account geometrical optics during the analysis of diffraction data. Gulder (F8)deviced schemes to address multiple scattering in a dense spray and develo ed empirical ex ressions for engineeringapplications. Ulric! and Stepanski (&) developed a laser diffraction technique for online measurement of crystal growth rate. At high suspension density, proper correction was taken into account for particle size distribution analysis. Jager et al. (FIO)built an automatic dilution unit for online dilution of the process stream of dense slurries. The unit was integrated with a Malvern 26ooc article-sizeanalyzer for fast determination of particle size iistribution of the slurries. Bott and Hart (FII) described an approach to extend the useful sizing range for diffraction instruments. High resolution particle sizing of extremely wide dynamic range from 0.1 to 1000 pm was achieved. Couto et al. (FI2)constructed a particle size anal zer by using a small He-Ne laser. Von Bernuth (F13) evJuated an improved commercial particle size analyzer. Diamond (F14) discussed the use of a commercial laser diffraction instrument to characterize particle size distributions of fly ashes. The results compared well with classical sedimentary data. Laser diffraction method offered the potential for rapid and accurate determination that could be used for acceptance and quality assurance programs. Mueller and co-workers (F15)studied the effect of antiflacculants on suspension stability. The size distribution was obtained by using a laser diffractometer. Optical Particle Counters
Lieberman (GI) examined the parameters that controlled the counting efficienc and accuracy of o tical liquid-borne particle counters. Geghart (G2)reviewefthe use of o tical particle counters (OPC) for the characterization of airgorne particles. Specifications of the instrument for different applications were described. Wang et al. (G3) evaluated the performances of a hi h pressure particle counter (PMS HPGP-101) for particfe sampling from compressed gases. Copper and Grotzinger (G4)looked into the factors that influence the purchasing of a particle counter. The authors presented a method to compare various counters based on cost and the reproducibility of measurements. Baas and co-workers (G5)reported the evaluation of performance of three commercial surface particle counters: a Tencor Surfscan 4000, an Aeronca WIS 200, and an Inspex ES20/20. Coplen et al. (G6) described particle counting errors caused by air bubbles in liquid-borne optical particle counters. A single-particle optical sizing instrument was developed by Plessers et al. (G7, G8). The particle size and size distribution of both stable and a gregating colloidal dispersions could be determined. Coagufation of model latexes by salt was studied. Endoh et al. (G9)constructed a laser light 4R
ANALYTICAL CHEMISTRY, VOL. 63, NO. 12, JUNE 15, 1991
scattering particle counter to monitor contaminant in chemical vapor deposition processes. Bottlinger and Umhauer (GIO, G11) investi ated the particle shape and structure factors that contriiuted to light scattering intensity. Precise calibration curves were generated to eliminate the effect of shape and structure for the analysis of particle size distributions. Umhauer ((312)reviewed the particle size counting technique for in situ measurements of particles in gas-particle flows. Sachweh and Buettner (G13, G14)described an improved optical particle counter using a digital signal processing scheme instead of an analog processor. The digital system offered the advantage of lower size detection limit and hi her detectable number concentration (G15). Buettner (($16) was interested in characterizing flow separation and classifying the particle size distribution in the airborne state. Using an aerodynamic calibration technique, the author could measure size distribution of nonspherical particles. Karasikov and Krauss (G17)used a time-of-transition method to determine particle sizes over a wide range without errors induced by high or low refractive index. Particles with different absorbances could be accurately analyzed. Koseki and Takahasi (GI8) developed an online method for the determination of impurity level in deionized water with an airborne particle counter. Lehtimaki et al. (GI91presented a sedimentation method for the calibration of a particle counter. The particle size range of the method was >0.3 pm. Bulmer (G20)described a dispersion technique for the sample preparation of oil sand solids. A Microtrac 7995-11 counter was used to determined the particle size distribution that was used to assess the suitability of oil extraction. Lee et al. (G21)evaluated the accuracy of commercial liquid-borne optical counters. Monodisperse,nonabsorbing, and spherical polymer latexes were used. Better than 20% accuracy was shown. Dreiling and Jaenicke (G22)studied the size distribution of aerosols 111 the plume at Munich and along the Alps abroad an aircraft. The errors introduced by pressure variation and the aircraft were discussed. Velocimetry
Timnat (HI) compared two laser-based techniques, laser Droppler anemometry and phase Doppler anemometry, for simultaneous determination of particle size and velocity in two-phase flows. The proper use of each technique was discussed. Nakatani and colleagues (H2)reported a laser multifocus velocimeter for measuring the particle diameter, velocity, and refractive index simultaneously. The key component of the instrument was a phase diffraction grating with pulse width modulation capability. Bauckhage (H3) examined factors that were required for the analysis of phase Doppler measurements of particle size and velocity in a two-phase flow. The effect of o tical absorption and ro hness of the particles was discussex. Wriedt a miniaturized laser Doppler anemometer et al. (H4) by using semiconductor laser diode. The instrument was used to help analyze and design a spray process. Saffman (H5) described a phase Doppler anemometer for determining particle size, velocity, and concentration. evaluated the Whisker Particle Collector Crossway et al. (H6) and Laser Aerosol Spectrometer for sizing aerosol particles. Experiments were carried out with aluminum oxides aerosols to compare the performances of the two techniques. Kliafas studied the errors introduced by flow turbidity in et al. (H7) particle sizing with the laser Doppler anemometer. Data generated at two different depths of field, 5 and 10 cm, were collected and analyzed. McDonell et al. (H8) developed a phase Doppler interferometry technique to measure metal atomizer particle size and velocity. The instrument was applied t o establish a relationship between the atomizer o eration and the particles enerated. The technique was d o used by McDonell and iamuelsen (H9)to investigate particle size, velocity, and mass flux in two-phase flows. Examples of glass beads in a jet flow, two-phase flow in a spray field, and others were illustrated. Albrecht and co-workers (HIO) reported the development of a laser Doppler anemometer for particle sizing. Ebdon et al. (HII) used a phase/Doppler-shift laser spray analyzer to characterize the particle size distribution of aerosols in sample
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PARTICLE SIZE ANALYSIS
chambers for a inductively coupled lasma spectrometer. Parameters, such as the type of chamter and gas flow rate, were addressed. The { potential and electrophoretic mobility were simultaneously determined with a Codter Delsa 440 analyzer (Hl2). Size information was calculated from the diffusion coefficient. Yee and Ho (H13) obtained the aerodynamic particle size distributions with a two-spot He-Ne laser velocimeter. A neural computational network method was develo ed for the possible real-time air monitoring of environmend bacterial, and artificial aerosols for occupational health and air pollution studies.
Band broadening can also be severe, and suitable corrections may be needed. Since SEC and hydrod amic chromatoaphic techniques are not absolute met ods, column caliration using standards of known particle size is required. Lorenz and co-workers (J1,J2) com ared particle size distribution results of polymer latexes ottained by SEC to data from ultracentrifugation; SEC gave a more broadened distribution. The effect of mobile phase composition on elution behavior was also studied. During this review only several other SEC applications were noted: ca sulfide particles (J3, J4) and polymer latexes (J5).
NeutronlX-ray Scatterlng Rabiej and Wlochowicz (11)reviewed the use of small-angle
In h drodynamic chromatography (HDC), the separation can d e place in columns containing either porous or nonporous packings, as well as in open ca illary columns. In packed columns, velocity gradients proguced by the flow of the mobile hase through the interstices of the packed bed are responsitle for the separation. Smaller particles will tend to sample velocity streamlines near the packing surface and will travel at a lower average velocity than larger particles, resulting in the elution of larger particles first. With porous packings, the separation mechanism is more complex, involving both size exclusion and hydrodynamic processes. In capillary HDC, particles are subjected to radial hydrodynamic forces, causing particles to seek an equilibrium distance between the center and the wall of the capillary. Because this radial position is dependent on particle size, lar er particles elute first, as in packed-column HDC. Typicaf separation ranges are 0.03 to C1.5 pm for packed columns and from 0.7 to 50 bm for capillary HDC. Silebi and co-workers published a number of papers on capillary HDC. Included were studies on capillary diameter, mobile phase velocity, and composition (J6-J9), separation efficiency (J10),axial dispersion (JI1 ), separation mechanism (J12, &3), and com arison of HDC to other particle size analysis techniques 5 1 4 4 1 6 ) . In the latter studies, these authors claim that, at similar separation efficiency, the analysis time of sedimentation field-flow fractionation (see next section) is 3-8 times longer than for HDC (J14). Revillon et al. (Jl7) discussed the effects of mobile phase composition, flow rate, injection volumes, and column dimensions on cap HDC separation. In a subsequent paper (J18), this group so reported on HDC software for data acquisition and processing. Shir ami et al. (Jl9)studied the effect of flow rate on capillary I%C separation. This grou also applied HDC for determining particle (0.05-10 pm? contaminants in a bioreactor (520). An interesting application of capillary HDC was reported by Bos and co-workers (J21),who used this technique to study the temperature behavior of micelles of a isoprene-styrene diblock copolymer in decane. In the transition range, both the micellar and the molecular forms of the block co olymer were observed, and micelle size information was oEtained. Dieguez Bosch et al. (522) reported on a modified packed-column HDC procedure using controlled- ore glass and used this method to characterize and purify eposomes (523). Kraak and mworkers (J24,J25) packed columns with 2-pm nonporous silica particles for the separation of polystyrene macromolecules of molecular weight 10"107, as well as proteins and inorganic colloids. Hoagland and Prud'homme (J26) used packed-column HDC to study polymer dynamics. Von Wald and Langhorst (J27) investigated the suitability of using an online viscometer for HDC of particles and concluded that a highly sensitivity viscometer would be required to obtain particle-size information.
X-ray scatterin (SAXS)to determine the particle shape and size in colloidafsystems. Sasanuma et al. (12)analyzed the microporosity of carbon fibers with the SAXS method. The average article size of y-alumina was also characterized and corelate! to the heat-treatment conditions. Blau et al. (13) studied particle size distribution and agglomerate structures in several ceramic materials, such as y-alumina, a-alumina, kaolin, and silicon nitride. The sintering behavior was related to a size dependent structural parameter. The particle size distribution and particle interaction of colloidal silica dispersions were investi ated by Moonen et al. (14). SAXS,electron microscopy, and static and dynamic light scatterin techniques were used. The data were consistent with a Eard sphere model calculation. Kakugo et al. (15) measured the crystallite size of titanium trichloride catalysts dispersed in polypropylenes. Plavnik and Troshkin (16) discussed the mathematics of deriving particle size distribution from SAXS and small-angle neutron scattering (SANS) data and presented an interation approach. Far o et al. (17)examined the role of cosurfactant on the size any shape fluctuations of the decane-Aerosol OT-butanol-water microemulsion droplets. SANS was employed to determine the average size distribution. The neutron spin-echo techni ue was applied to obtain dynamic information of shape uctuations. Both SANS and SAXS techniques were used to c h c t e r i z e particle sizes and aggre ation in carbon black filled polyeth lene com mites by dtignall et al. (18).The voids on the carton artic es was inferred from the com arison of SAXS and SAhS data. The morpholo and s u r i c e pro erties of carbon particles were reported.%allner et al. (197 studied the c stalline size of the compacted palladium system with bothYANS and SAXS methods. The change of crystalline size and volume fraction during thermal annealing was monitored. Yang et al. (110) described the development of supermolecular structure in polystyrene latexes. A graduated core-shell model for the supermolecular structure was suggested from the SANS data. Jayasuri a and co-workers (111) used the SANS technique to assess tge size and effective surface charge of polystyrene latex articles in concentrated dispersions. Results were discusseain conjunction with data from electron microscopy and conductometric titration. SANS, SAXS,and turbidimetry measurements were made to understand the interfacial behavior of monodisperse silica sols (112). Calcium-induced coagulation of silica particles was analyzed. Bianchi and colleagues (113) evaluated the microstructure of a Udimet 720 nickel superalloy turbine blade with the SANS technique. Nondestructive analysis of the precipitation in the alloy was demonstrated. Solt et al. (114 characterized the defect particle size in an irradiated reactor pressure vessel steel specimen. Several irradiation and thermal treatments were investigated.
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CHROMATOGRAPHIC TECHNIQUES Slze Excluslon Chromatography
In size exclusion chromato aphy (SEC), the separation is based on the distribution ofgparticles between the mobile phase and the pores of the packing material. Although this is a relatively simple technique to use, physical entrapment of the sample within the packed bed or at the inlet and outlet frits of the column may occur, leading to low sample recovery.
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tf
Hydrodynamlc Chromatography
9
Field-Flow Fractlonatlon
Field-flow fractionation (FFF)is a se aration technique for both particles and macromolecules. field is ap lied perpendicular to the carrier stream flowing in a t k n , o en channel. This force causes particles (or macromolecules7to artition among velocity streamlines enerated by the parak l i c velocity profile in the carrier fluii. The velocity is close to zero near the walls of the channel and reaches a maximum at the center of the channel. When a cross-field is applied, particles are forced into different velocity streamlines de-
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ANALYTICAL CHEMISTRY, VOL. 63, NO. 12, JUNE 15, 1991 * 5 R
PARTICLE SIZE ANALYSIS
pendinq on their size. As a result, small particles, which can diffuse into higher velocity streamlines, elute first followed by larger articles that are found closer to the wall of the channel. $he particle size elution order is the reverse of SEC and HDC. A number of different cross-fields have been used or evaluated theoretically; however, the most commonly used cross-field for particles is sedimentation (centrifugation). General. Reviews on FFF have been published by Giddings and co-workers (K1-K5), Widmer and Lori (K6),and Levin (K7). Janca et al. (K8) reviewed the rinciples and experimental implementation of focusing {FF methods. Giddings (K9)described a multidimensional FFF ap roach. In one system, different separation stages are couple8 in the other, two independent displacements are carried out in a planar channel structure. Giddings (KIO)described a pinched-inlet system in which the channel thickness at the inlet end is reduced to hasten relaxation. Koch (K11) presented a desi n for a split-flow channel. Theories have been pro osed for %FFin an annular channel (K12),in an annular gap ktween coaxial tubes (K13), and in a rectangular cross-section channel (K14). U rozov (K15)derived equations for FFF. Semenov (K16, K 1 8 investigated the effect of force fields near the channel wall. Aleksandrov and Andreev (K18) reviewed developments of analytical instrumental at the USSR Academy of Sciences including FFF. Electrical FFF. Giddin s (K19)described the separation as well as capillary zone performance of electrical electrophoresis and isoelectric focusing. Factors affecting resolving power and separation speed are addressed, and capabilities of these techniques are com ared. Thormann et al. (K20) discussed the rinciples a n i instrumentation of electrical hyperlayer FFqand compared this technique with capillary isoelectricfocusing. Janca and mworkers (K21-K23) presented the principles and demonstrated several applications of isoelectric focusing FFF. Stevens (K24) presented a simulated study of the use of an alternating transverse electric field in FFF. Flow FFF. Giddings (K25) described a new concept for achieving hydrodynamic relaxation in which an injected sample is driven rapidly toward its equilibrium distribution by flow. This approach is based on the use of permeable wall elements (or frit elements). An auxiliary substream of carrier fluid, ermeating uniformly into the FFF channel near the inlet, gives the sample, entrained in its own substream, close to its equilibrium position. These frit elements can also be used to enrich the sample a t the outlet. Joensson and Carlshaf (K26) used a porous hollow fiber rather than a flat channel for flow FFF. With this technique, precise control of the cross-flow was obtained. A theory describing retention and band broadening was developed. In a subse uent paper (K27),gradient elution in the hollow-fiber flow FF% ap aratus was reported. A atent was also awarded to these aut ors for this approach k 2 8 ) . Wahlund and Litzen (K29)improved u on an asymmetrical flow FFF channel that enables the loaing of large sample volumes. The method was applied to the separation of proteins, plasmids, polysaccharides, and unicellular algae. The use of a thinner channel and flow programming was also reported by these authors for the separation of proteins, nucleic acids, and viruses (K30). Giddings (K31) used flow FFF in the normal, steric, and hyperlayer modes to fractionate polystyrene latexes in the range 0.01-50 pm. “his group also used flow FFF to determine the molecular we’ ht distribution of humic samples (K32) and flow/hyperlayer l%F to fractionate various 3- and 5 p m HPLC silica supports (K33)and ground coal and limestone samples (K34). Sedimentation FFF. Schure et al. (K35)applied Fourier and iterative deconvolution methods to account for nonequilibrium band broadening in sedimentation FFF. The fundamentals of sedimentation FFF (steric transition, relaxation, lift forces, and cyclic operation) were presented by Lee (K36). Jones and Giddings (K37) used a multidimensional sedimentation FFF procedure in which a narrow fraction of latex particles collected from one run is reinjected for a second run under different conditions. Lee et al. (K38) used a channel inlet splitter to obtain rapid hydrodynamic relaxation of the sample by using the stopless flow method. Takeuchi (K39)
SFF,
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was awarded a atent for using a countercurrent system in a sedimentationSFF mode. In essence, samples are separated by partitioning between two liquid phases. Particle-wall interactions durin sedimentation FFF caused by electrostatic and/or van der d a d s forces were studied by Giddings and colleagues (K40, K41), Karaiskakis and coworkers (K42,K43), and Mori et al. (K44,K45). Ex loitation of these interactions to enhance separations has l e t t o a new FFF subtechnique termed “potential barrier FFF”. Caldwell and Li (K46, K47) used a combination of sedimentation FFF and photon correlation spectroscopy to characterize emulsions and polyst ene latexes. Sedimentation FFF was used to determine the gnsity of st ene-butadiene (K48),vinyl acetate-acrylic copolymer (K48jrand poly(viny1 chloride) latexes (K49, K50). Application areas of sedimentation FFF include 1 (meth 1 methacrylate) (K51-K53) and polystyrene latex (&rparticfe aggregation studies, pigment quality control (K54),river water K56), metal hydrosols (K57), diesel soot particulates (K55, (K58), fused unilamellar vesicles (K59),and cartilage roteoglycans (K60). Finally, Merkus et al. (K61) reporte on the evaluation of a commercial sedimentation FFF instrument. Thermal. Reviews on thermal FFF have been published by Giddings (K62) and Schimpf (K63). The latter pa er discusses theor , experimental, and use of thermal F F P t o stud thermal iffusion of polymers solutions. Schimpf and Gidchfings (K64) used this technique to determine the thermal diffusion coefficients of a number of polymer-solvent combinations. The authors found that thermal diffusion was essentially independent of molecular weight but varied with the chemical composition of the polymer and solvent. Kirkland et al. (K65)studied retention effects in thermal FFF and noted that retention is a function of polymer and solvent composition and is proportional to solvent viscosity. An algorithm that corrects for system dispersion was presented by Schimpf et al. (K66). Using this deconvolution approach, the authors were able to determine the olydispersity of a ! and Chen (K67) narrow polystyrene standard to be 1.004.oaC used a reversed-flow method for determinin system dispersion from which polymer polydispersity coufd be estimated. Kirkland and Yau (K68) examined the effect of operating parameters (flow rate and the time-delay and decay-time constants) on the accuracy of molecular weight measurementa by time-delay, exponential-decay thermal FFF. This roup also described the use of an online viscometer couplei to a thermal FFF apparatus (K69, K70). Thermal/hyperlayer thermal FFF was used by Giddings (K71)for the separation of ultrahigh molecular weight polystyrenes.
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ELECTROZONE SENSING Goeransson ( L l ) reported on the use of a hydrodynamically focused aperture to improve the accuracy of a Coulter counter. The aperature also prevented articles from reentering the sensing zone. Markus et al. (L2Yalsofound that this aperture improved resolution and accuracy. The linearity and response of focused aperatures were studied by Cowan and Harfield (L3). Berg and co-workers (L4, 155) developed a “pressurereversal” technique in which the Coulter principle was used to study single-particled amics., When a particle enters the aperture, the resistive p z it produces is wed to activate two miniature valves which serve as pressure switches. When the particle exits from the pore, the reversed pressure drives the particle back into the pore, and the process is repeated. The authors have used this technique to study single-particle dissolution and flow dynamics.
CENTR I FUGATION/SEDI MENTATION General
General formulation of boundary conditions and sedimentation of low concentration suspensions was presented b Kharin and Ryazhskikh (MI). Ivanov (M2) studied the s e d imentation rate of suspensions of sand and pyrite in water. Sedimentation rates of concentrated suspensions of light and heavy particles in inclined channels were determined by MacTaggart et al. (M3).
PARTICLE SIZE ANALYSIS
Bernhardt (M4) reviewed methodologies for pre aring dispersions for sedimentation analysis. The author (A&) also discussed the problems and limits associated with sedimentation analysis. Hietala and Smith (M6) discussed the effect of porosity of used silica articles on gravitational settling. Chen et al. (M7) an A8TM centrfugal sedimentation method to determine particle size distribution of alumina and kaolin samples. Disk Centrifuge Photosedlmentometry Tscharnuter et al. (MB)discussed the importance of extinction efficiency corrections to obtain accurate particle size distributions in a disk centrifuge. Devon and co-workers (M9) claimed that reliable particle size information could be obtained without the use of explicit optical corrections. These also reported that the effect of slit width error authors (M10) in measuring latex particle size distributions was small. In derived an equation that relates addition, this group (M11) the diameter of swollen articles to ita sedimentation time in the disk centrifuge. #his approach was applied to voidcontaining acrylic polymer particles. Hansen (M12)used a density gradient within the disk to produce running conditions that were more stable than typical start techniques. Methods for calculating particle sizes in the density gradient were also given. A density gradient ap roach cells, was also used by Middelberg et al. (M13)for sizing E. protein inclusion bodies, and cell debris.
COE
Photosedlmentometry
Photosedimentometry was used to study the study effects of article interactions on size distribution measurements Particle interactions increased the width of the distribution, especially at low settling rates. Beckers and Veringa (M15) discussed several limitations pertaining to the Horiba CAPA-BOO instrument and arrived a t the following conclusions: 1. The low end of the distribution is underestimated, since the light attenuation coefficient is considered constant for all particle sizes. 2. Signal noise is countered as large particles. 3. The acceleration phase of the centrifuge, if neglected, causes a shift toward the high end of the distribution. An X-ray sedimentometer and a Ladal pipet centrifuge were used to determine particle sizes of talc, calcite, and lead oxide down to 0.04 pm (M16).Finally, the construction of an inexpensive photosedimentometer was described by Dalas and Koutsouka (M17).
(d4).
Ultracentrifugation
Mueller (MIB) re orted on an automated method for determining the particye size distribution of dispersions. With this instrument, base line resolution was possible between two particles differin differing in diameter by 10%. Maechtle (MI97 developed a procedure for determinin the particle size distribution of extremely broad distributecfdispersions (20-2000 nm). Torosyan (M20) also reported on a method of ultracentrifuging highly dispersed samples.
OTHERTECHNIQUES Pospech and Schneider ( N I ) used mercury intrusion measuremenb to obtain mean particle size. A method based on laser-induced breakdown acoustic emission was evaluated by Kitamori et al. (N2, N3). With this a proach, particles of
