Approach for Particle Sizing in Dense Polydisperse Colloidal

Direct particle sizing of colloidal suspensions at high solid concentrations is difficult due to confounding effects of multiple scattering and partic...
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Approach for Particle Sizing in Dense Polydisperse Colloidal Suspension Using Multiple Scattered Light Zhigang Sun,†,‡ Clint D. Tomlin,† and Eva M. Sevick-Muraca*,† Department of Chemical Engineering, Texas A&M University, College Station, Texas 77843-3122, and School of Chemical Engineering, Purdue University, West Lafayette, Indiana 47907-1283 Received May 16, 2001. In Final Form: July 23, 2001 Direct particle sizing of colloidal suspensions at high solid concentrations is difficult due to confounding effects of multiple scattering and particle interactions. In this work, the frequency domain photon migration (FDPM) technique, based upon multiple light scattering, is extended for particle sizing of colloidal suspensions at high volume fractions by combining an appropriate model to account for particle interactions. FDPM measurements of isotropic scattering coefficients were conducted to assess the effect of particle interactions of polydisperse polystyrene samples at high volume fractions ranging from 1% to 40%. The isotropic scattering coefficients were then compared with the theoretical predictions which include the full polydisperse hard sphere Percus-Yevick (HSPY) model as well as the decoupling approximation and the local monodisperse approximation models to account for excluded volume effects. Results show that the polydisperse HSPY model is suitable for accounting for particle interactions which predominately arise from volume exclusion effects and which influence light scattering. Upon use of the polydisperse HSPY model to predict static structure factors, the particle size distribution (PSD) of polydisperse polystyrene suspensions was recovered at high volume fractions up to 40% at two different wavelengths. Our inversion results agree well with PSD measured by dynamic light scattering at a diluted sample of the same suspensions (∼0.01% volume of solids).

Introduction Particle size, particle size distribution (PSD), and volume fraction are but one set of parameters that impact the behavior of colloidal suspensions. However, there are few techniques to characterize these parameters in dense colloidal suspensions. Most available optical particle sizing methods are based on single particle scattering, such as turbidity, angular static light scattering, and dynamic light scattering (DLS), and require considerable sample dilution to about 0.01-0.1% volume of solids. Otherwise, measurement calibration at the sample in which the particle characterization is to be accomplished is required to account for the confounding effects owing to multiple scattering and particle interactions. Dilution itself can cause changes in the PSD and can render the measurement less representative of the dense suspension. Although some modifications of existing methods, such as fiber optic dynamic light scattering (FODLS)1 and modified static light scattering,2 have been proposed to suppress of the influence of multiple scattering, these methods are not well suited for particle sizing on multiple scattering, dense colloidal suspensions. Other optical characterization approaches, such as diffusing wave spectroscopy3 and diffuse reflectance and/ or transmittance spectroscopy,4,5 have been promoted for characterizing dense colloidal suspensions. Both methods are based on multiple scattering, where the light propa* To whom correspondence should be addressed. Phone: 979458-3206. Fax: 979-845-6446. E-mail: [email protected]. † Texas A&M University. ‡ Purdue University. (1) Thomas, J. C.; Tjin, S. C. J. Colloid Interface Sci. 1989, 129, 15. (2) Lehner, D.; Kellner, G.; Schnablegger, H.; Glatter, O. J. Colloid Interface Sci. 1998, 201, 34. (3) Horne, D. S.; Davidson, C. M. Colloids Surf., A 1993, 77, 1. (4) Jiang, H. B. AIChE J. 1998, 44, 1740. (5) Kaplan, P. D.; Dinsmore, A. D.; Yodh, A. G.; Pine, D. J. Phys. Rev. E 1994, 50, 4827.

gation can be modeled as a photon diffusion process. However, unless particle interactions are otherwise accounted for, these methods will fail to provide accurate sizing information. Typically, the influence of particle interactions becomes significant when the solid volume fractions are greater than 5% or, alternatively, when the average interparticle spacing becomes comparable to or smaller than the wavelength of light. As an alternative to optical sizing methods, acoustic spectroscopy6 and electroacoustic spectroscopy7 have been developed for the characterization of suspensions and emulsions, where the interaction of sound waves with dispersed particles provides useful information of particle size and PSD. Similarly to light scattering methods, the acoustic theory for the dilute dispersed system is complete,8,9 whereas theory for the polydisperse concentrated system is far from completed.10 While several models based on first principles have been proposed to incorporate particle interactions into the acoustic theory (e.g., Ohshima-Dukhin-Shilov cell model11), few of them have been successfully used in practical applications, and most of these methods require empirical calibration to account for particle interactions at high volume fractions in order to provide accurate sizing information. Compared with light scattering, acoustic scattering may be strongly influenced by mechanical and thermal coupling effects between the continuous and disperse phases, which increases the complexity of modeling the sound propagation in concentrated systems. In addition, acoustic and electroacoustic spectroscopies require knowledge of the (6) McClements, D. J. Adv. Colloid Interface Sci. 1991, 37, 33. (7) Dukhin, A. S.; Ohshima, H.; Shilov, V. N.; Goetz, P. J. Langmuir 1999, 15, 3445. (8) Epstein, P. S.; Carhart, R. R. J. Acoust. Soc. Am. 1953, 25, 553. (9) Allegra, J. R.; Hawley, S. A. J. Acoust. Soc. Am. 1972, 51, 1545. (10) Dukhin, A. S.; Goetz, P. J. Langmuir 1996, 12, 4336. (11) Dukhin, A. S.; Ohshima, H.; Shilov, V. N.; Goetz, P. J. Langmuir 1999, 15, 6692.

10.1021/la010726o CCC: $20.00 © 2001 American Chemical Society Published on Web 09/08/2001

Approach for Particle Sizing

thermophysical properties of each phase, such as density, specific heat capacity, thermal conductivity, thermal expansion, and shear viscosity. Consequently, accurate values of these material properties and their variation with temperature are critical for recovery of accurate particle size and PSD from acoustic methods. Herein, we discuss the frequency domain photon migration (FDPM) technique, which is also based on multiple light scattering but provides new opportunities for characterization in dense polydisperse colloids that are not afforded by other optical and acoustic approaches. Since FDPM measures time-dependent propagation characteristics of light rather than the amount of light detected, it is self-calibrating and no external calibration is required. In addition, FDPM allows determination of both absorption and scattering properties independently and with high accuracy and precision.12 While FDPM has been successfully used to recover PSD and volume fraction in opaque, multiple scattering suspensions of polystyrene and titanium dioxide,13-15 corrections for the influence of particle interactions are necessary at high volume fractions (e.g., larger than 5%).16,17 Recently, we assessed particle interactions of monodisperse suspensions at high volume fractions using the FDPM method and successfully recovered particle sizes at high volume fractions by combining the monodisperse hard sphere Percus-Yevick (HSPY) model to account for predominate particle interactions.18 In this work, we seek to extend FDPM technique to recover PSD of polydisperse suspensions at high volume fractions by combining an appropriate model to account for the influence of excluded volume force as a predominate particle interaction. FDPM measurements of the isotropic scattering coefficient were conducted in polydisperse surfactant-stabilized latex samples at high volume fractions ranging from 1% to 40% and were then compared with predictions from Mie theory with three different models to account for the volume exclusion influence: (i) the full polydisperse Percus-Yevick model as well as the (ii) decoupling approximation and (iii) local monodisperse approximation to the Percus-Yevick model. Using the full polydisperse HSPY model, we then show recovery of PSD of latex samples from FDPM measurements at high volume fractions as well as at two independent wavelengths. Theory Light Scattering in Dense Suspensions. In a dense colloidal suspension, the average distance among particles is mediated by particle interactions in general and specifically by predominant volume exclusion effects. Since the interference of light due to closely spaced particles becomes significant, the scattering efficiency of a single particle in the ensemble is substantially reduced when compared to a particle within a dilute suspension. The static structure factor S(q,φ) accounts for the hindered scattering and must be incorporated into the expression (12) Sun, Z. G.; Huang, Y. Q.; Sevick-Muraca, E. M. Rev. Sci. Instrum., submitted. (13) Sevick-Muraca, E. M.; Pierce, J.; Jiang, H. B.; Kao, J. AIChE J. 1997, 43, 655. (14) Richter, S. M.; Shinde, R. R.; Balgi, G. V.; Sevick-Muraca, E. M. Part. Part. Syst. Charact. 1998, 15, 9. (15) Sun, Z. G.; Sevick-Muraca, E. M. AIChE J. 2001, 47, 1487. (16) Shinde, R.; Balgi, G.; Richter, S.; Banerjee, S.; Reynolds, J.; Pierce, J.; Sevick-Muraca, E. Appl. Opt. 1999, 38, 197. (17) Richter, S. M.; Sevick-Muraca, E. M. Colloids Surf., A 2000, 172, 163. (18) Sun, Z. G.; Clint, C. D.; Sevick-Muraca, E. M. J. Colloid Interface Sci., submitted.

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of isotropic scattering coefficient µ′s for a polydisperse, interacting colloidal suspension:

µ′s(λ) )

∫0∞

12φf(x) 2 3

kx

∫0π F(n,x,λ,θ) S(q,φ) ×

[

sin θ(1 - cos θ) dθ] dx (1)

where F(n,x,λ,θ) is the form factor for a particle of diameter x with relative refractive index of particle to medium n at wavelength λ, and θ is the scattering angle. The term φ represents the volume fraction of particles in the suspension and f(x) represents particle size distribution; k is given by 2πm/λ, where m is the refractive index of the medium; q is the magnitude of the wave vector, q ) 2k sin(θ/2). In eq 1, the form factor, F(n,x,λ,θ), can be calculated by classical Mie scattering theory of single particle scattering.19,20 The structure factor, S(q,φ), is a direct measure of the local ordering of colloidal particles, and the value of S(q,φ) is equal to unity in the absence of particle interactions (e.g., in a dilute suspension). For polydisperse systems, since particle interactions occur between colloids not only with same particle size but also with different particle sizes, the partial structure factor, Si,j, must be considered, where i and j represent particles with different sizes xi and xj, respectively. Equation 1 becomes

µ′s(λ) )

∫0π 12φ ∫∞ k2 0

f(xi)

∫0∞

f(xj)

Fi,j(n,xi,xj,λ,θ) × xi xj3 Si,j(n,xi,xj,λ,θ) sin θ(1 - cos θ) dxj dxi dθ (2) 3

where Fi,j is the binary form factor between the particles with different sizes xi and xj. If particle sizes are the same (i.e., i ) j), the form factor is simply calculated as a monodisperse system: / / Fi,i ) (f1,if1,i + f2,if2,i )

(3)

where f1,i and f2,i are the scattering amplitudes into two orthogonal polarization states arising from a particle with size xi, which can be calculated by Mie scattering theory. / / f 1,i and f 2,i are conjugates of f1,i and f2,i, respectively. However, if particle sizes are different (i.e., i * j), the binary form factor with different particle sizes is calculated by / / + f2,if2,j ) Fi,j ) Re(f1,if1,j

(4)

The calculation of the binary form factor with different particle sizes using Mie theory of light scattering (i.e., eq 4) is not the same as that for X-ray or neutron scattering. For X-ray or neutron scattering, the scattering amplitudes are real due to using the Rayleigh-Gans-Debye (RGD) approximation of Mie scattering theory so that Fi,j ) xFi,iFj,j. This is because the wavelengths of neutrons and X-rays are much longer than the effective sizes of the nuclei and electrons they scatter from, which makes the RGD approximation appropriate. However, the Mie scattering theory should be employed in this study due to the fact that the wavelengths used for our experiments are comparable to the particle sizes of colloids. Since the scattering amplitudes are complex for Mie scattering (19) Van de Hulst, H. C. Light Scattering by Small Particles; Chapman & Hall: London, 1957. (20) Bohren, C.; Huffman, D. Absorption and Scattering of light by small particles; John Wiley & Sons: New York, 1983.

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theory, eq 4 must be used to calculate the binary form factor with different particle sizes. Models for Static Structure Factor in Polydisperse Suspensions. In modern liquid state theory, the radial distribution function and the pair correlation function characterize the spatial correlation in position and the fluctuation in local density. The Fourier transform of the pair correlation function provides the static structure factor, S(q), which is a direct measurement of the local microstructure of particles. From a theoretical point of view, the static structure factor of colloidal suspensions is studied by means of the integral equation theory of liquids, which is based on the Ornstein-Zernike (OZ) equation with appropriate closure relations (e.g., PercusYevick (PY), the hypernetted chain (HNC), and the Rogers-Young (RY) relations) and pair potentials (e.g., hard sphere, electrostatic, van der Waals, etc.).21 The modeling of the structure factor in polydisperse colloidal suspensions using the above methods has been recently reviewed by Salgi and Rajagopalan22 and D’Aguanno and Klein.23 The accuracy of the theoretical results was assessed by Monte Carlo (MC) simulation or small-angle scattering experiments of light, X-rays, and neutrons. For a surfactant-stabilized, dense colloidal suspension, there are different particle interactions that contribute to the local microstructure and structure factor of suspensions. Since hard sphere excluded volume interactions predominately impact structure factor when compared to electrostatic forces, van der Waals forces, and depletion forces, particle interactions can be modeled to a first-order approximation as an effective excluded volume effect. In previous studies, we found that the monodisperse HSPY model is suitable for accounting for particle interactions in monodisperse suspensions at high volume fractions.18 For polydisperse systems, Virj24 and Blum and Stell25 independently derived analytical solutions of the partial structure factor Si,j for a polydisperse system by using the polydisperse HSPY approximation. In this work, the polydisperse HSPY model of Si,j developed by Blum and Stell is compared against measurement of isotropic scattering using multiple scattering light. Due to the complexity of the polydisperse HSPY model, approximations for the effective structure factor are often used for analysis of small-angle scattering data. Kotlarchyk and Chen proposed the decoupling approximation (DA),26 where the interference effects are described by an effective structure factor calculated by the monodisperse HSPY model for the average size of particles. The assumption of this approach is that the positions of the particles are independent of their sizes. Another approximation, proposed by Pedersen as the local monodisperse approximation (LMA),27 assumes that the positions of particles are completely correlated with their sizes so that each particle is surrounded by particles with the same size. The total scattering is then calculated as the sum of the scattering of monodisperse subsystems weighted with the size distribution of the system. In this work, the DA and LMA models are also compared against measurements of isotropic scattering using multiple scattered light. (21) Hansen, J. P.; McDonald, I. R. The Theory of Simple Liquids; Academic: London, 1986. (22) Salgi, P.; Rajagopalan, R. Adv. Colloid Interface Sci. 1993, 43, 169. (23) D’Aguanno, B.; Klein, R. J. Chem. Soc., Faraday Trans. 1991, 87, 379. (24) Virj, A. J. Chem. Phys. 1979, 71, 3267. (25) Blum, L.; Stell, G. J. Chem. Phys. 1979, 71, 42. (26) Kotlarchyk, M.; Chen, S. H. J. Chem. Phys. 1983, 79, 2461. (27) Pedersen, J. S. J. Appl. Crystallogr. 1994, 27, 595.

Sun et al. Table 1. Particle Size Information of Latex Samples Measured by the DLS Method in Dilute Suspensions sample

mean (nm)

deviation (nm)

polydispersity (%)

DLS results

143.5 ( 0.5

24.0 ( 1.2

16.7 ( 0.8

Experimental Section Materials. A polydisperse sample of concentrated, surfactantstabilized polystyrene suspension provided by Dow Chemical, Midland, MI, was used as received. The mean particle size, deviation, and polydispersity of the polystyrene sample were measured by using the dynamic light scattering method (Zetasizer 3000, Malvern Instruments, U.K.) at diluted concentration (∼0.01%), and the results are shown in Table 1. The stock solutions were then diluted at various particle concentrations ranging from 1% to 40% of solid volume with deionized ultrafiltered (DUF) water, where the exact volume fractions of samples were determined by evaporation measurements.14 FDPM Measurement. The FDPM measurements were performed on samples as a function of volume fraction at two different wavelengths, 687 and 828 nm. Briefly, the measurements consisted of measuring the phase shift (PS) and attenuation of average of intensity (DC) and amplitude (AC) at 12 different source-detector distances ranging from 7 to 11 mm in response to the source modulation at three different frequencies (30, 60, and 90 MHz). Measurements were conducted on samples of approximately 100 mL. The FDPM instrumentation and theory are described elsewhere.12,18 The optical parameters and their uncertainties were then calculated using AC and PS data as a function of source-detector position and averaged across all modulation frequencies, as outlined in ref 12. The isotropic scattering coefficients were then obtained as a function of volume fraction. Strategy for Recovery of PSD in Polydisperse Dense Suspensions. Once an appropriate model of Si,j is found to account for the influence of particle interactions on scattering intensity, the FDPM measurements were then used to recover particle size distribution, f(x), by solving the inverse scattering problem, described by eq 2. The algorithm to solve this inverse problem involves the minimization of a merit function, χ2: M

χ2 )

∑ [(µ′ )

O s j

- (µ′s)Cj ]2

(5)

j)1

where (µ′s)O j is the experimentally observed scattering coefficient and (µ′s)Cj is the value calculated from eq 2, based on the current guess for size distribution f(x). Other known quantities are the refractive index, m and n, as well as the volume fractions experimentally determined. In this work, we assume that the particle size distribution is a normal Gaussian distribution, which is characterized by two parameters (mean size and deviation). A simplex method provided by MATLAB (The Mathworks, Inc., Natick, MA) is used to determine the parameters of size distribution by minimizing eq 5.

Results and Discussion FDPM-Measured Isotropic Scattering Coefficient. Figure 1 illustrates the isotropic scattering coefficient as a function of volume fraction φ for latex samples at two different wavelengths of 687 and 828 nm. It shows that the isotropic scattering coefficients at each wavelength increase with increasing volume fractions up to a point (∼20% volume fraction) and then decrease. Comparably, at each volume fraction, the lower the wavelength, the greater the isotropic scattering coefficients. The error analysis of FDPM measurements shows that the precision of FDPM-measured isotropic scattering coefficients is less than 0.4% at both wavelengths so that the error bars of measurements overlap with the symbols in Figure 1. For comparison, the predicted values neglecting the effects of particle interactions (i.e., using Mie theory alone and structure factor equals unity in eq 1) were also

Approach for Particle Sizing

Figure 1. The isotropic scattering coefficient as a function of volume fraction at two different wavelengths. The solid and dashed lines represent predicted values by Mie theory without accounting for particle interaction at wavelengths of 687 and 828 nm, respectively. The square and triangle points represent FDPM measurement data at wavelengths of 687 and 828 nm, respectively. Error bars overlap with the symbols.

included in Figure 1. It clearly shows that Mie theory alone is unable to predict the nonlinear change of isotropic scattering coefficients with increasing volume fractions, and the effect of particle interaction should be considered by including the appropriate structure factor model. Comparison of Polydisperse Structure Factor Models. To find an appropriate structure factor model, the isotropic scattering coefficients predicted from Mie theory with three different structure factor models (i.e., HSPY, DA, and LMA models) were compared with the experimental data as a function of volume fraction. Figures 2 and 3 illustrate the comparisons for wavelengths of 687 and 828 nm, respectively. Each of the structure factor models predicts the nonlinear change of isotropic scattering coefficient with increasing volume fractions. When volume fraction is less than 7%, the predicted values from all models match the experimental data. However, when volume fraction is greater than 10%, there are differences among the isotropic scattering coefficients predicted by different structure factor models. The polydisperse HSPY model gives the closest estimates of FDPM-measured isotropic scattering coefficient when compared to the DA and LMA models. The LMA model may be a better predictor than the DA model and gives comparable predictions to the HSPY model at moderately concentrated suspensions (i.e., ∼15-20% of volume fractions). Similar results are also showed by Pedersen,24 where small-angle neutron scattering was used to study the interaction of a metallic alloy. We interpret these results as a validation of the polydisperse HSPY model for predicting the scattering properties of dense colloidal suspensions. Sensitivity of Measurements on Polydispersity. With the polydisperse HSPY model validated, we next sought to recover particle size information from experimental data. To accurately recover PSD from FDPM measurements, the model sensitivity of polydispersity on the isotropic scattering coefficient must be much larger

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Figure 2. Comparison of different structure factor models at a wavelength of 687 nm. The lines represent the predicted values using the polydisperse HSPY model (solid line), the LMA model (dashed line), and the DA model (dotted line). The points represent the FDPM measurement data, and the error bar are within the symbols.

Figure 3. Comparison of different structure factor models at a wavelength of 828 nm. The lines represent the predicted values using the polydisperse HSPY model (solid line), the LMA model (dashed line), and the DA model (dotted line). The points represent the FDPM measurement data, and the error bars are within the symbols.

than measurement error. To demonstrate model sensitivity to polydispersity, values of isotropic scattering coefficients were predicted using Mie theory with the poly-

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Figure 4. The isotropic scattering coefficient as a function of volume fraction at a wavelength of 687 nm predicted at differing polydispersity levels. The points represent FDPM measurements of the latex sample with error bars overlapping the symbols. The lines represent predicted values by the HSPY model using the same mean diameter as the sample but with differing polydispersity.

disperse HSPY model for suspensions of mean particle size (143.5 nm) but with differing polydispersity levels. The predicted and experimental results are shown for comparison in Figures 4 and 5 at 687 and 828 nm, respectively. The figures show that the differences in isotropic scattering coefficient arising from different polydispersity levels are small at low volume fractions. These differences increase with increasing volume fraction, which provides a greater opportunity to recover accurate PSD at high volume fractions than that at low volume fractions. At low polydispersities (10%) and large volume fractions (>15%), the accurate PSD can be recovered owing to the high sensitivity of polydispersity and high precision of FDPM measurements (∼0.4%) as shown in Figure 1. Recovery of PSD at High Volume Fractions. Since the polydisperse HSPY model is a good approximation for modeling particle interactions and since the precision of FDPM isotropic scattering measurement allows for sensitive detection of changing polydispersity, we sought to incorporate the polydisperse HSPY model with Mie theory (i.e., eq 2) to recover unknown particle size distributions from experimental data. In this work, we recovered the PSD of latex samples by fitting FDPM-measured µ′s at various volume fractions ranging from 1% to 40% at a single wavelength using nonlinear regression (i.e., eq 5). Figure 6 illustrates the measured (symbols) isotropic scattering coefficients and the fit (lines) using the Mie theory with the polydisperse HSPY model as a function of volume fraction at wavelengths of 687 and 828 nm. Figure 7 shows the PSD recovered from the FDPM data at 687 and 828 nm with that recovered from DLS measurement in diluted samples. The recovered mean

Sun et al.

Figure 5. The isotropic scattering coefficient as a function of volume fraction at a wavelength of 828 nm predicted at differing polydispersity levels. The points represent FDPM measurements of the latex sample with error bars overlapping the symbols. The lines represent predicted values by the HSPY model using the same mean diameter as the sample but with differing polydispersity.

Figure 6. The isotropic scattering coefficient as a function of volume fraction at 687 and 828 nm wavelengths. The solid and dashed lines represent the regressed fit using the polydisperse HSPY model, and the square and triangle points represent FDPM measurement data at wavelengths of 687 and 828 nm, respectively. The error bars of the measurements overlap with the symbols.

sizes and deviations from FDPM measurements at wavelengths of 687 and 828 nm are listed in Table 2. The

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volume exclusion may be successfully used for recovery of particle size distribution of interacting colloidal suspensions. Future work involves using FDPM measurements of a single suspension at one fixed volume fraction but measured at several different wavelengths in order to recover the PSD and volume fraction simultaneously. Conclusions

Figure 7. Comparison of recovered PSD by DLS measurement in a diluted sample (solid line) with that by FDPM measurement at a wavelength of 687 nm (dotted line) and at a wavelength of 828 nm (dashed line) in concentrated suspensions. Table 2. Recovered Particle Size Distribution from FDPM Measurements at Two Different Wavelengths wavelength (nm)

mean (nm)

deviation (nm)

polydispersity (%)

687 828

142.23 143.14

25.46 21.84

17.9 15.3

inversion results from FDPM measurement at concentrated suspensions agree well with the DLS results measured at diluted concentrations (∼0.01% volume fraction). Although our PSD recovery was based on the FDPM data at a single wavelength but different volume fractions, the PSD recovered from independent data sets at two different wavelengths are in close agreement. These inversion results demonstrate that the precise FDPM measurement along with the polydisperse HSPY structure factor model to predict dominant particle interactions from

The ability to recover particle size distribution of colloidal suspensions at high volume fractions depends largely upon whether an appropriate model exists for considering the influence of particle interactions. Most of the available particle sizing methods require empirical calibration when sizing at high volume fractions due to the lack of models to account for particle interactions. In this study, we have demonstrated that particle interactions significantly impact the measured scattering properties of polydisperse colloidal suspensions at high volume fractions and that the FDPM technique is a useful tool for choosing an appropriate model to account for particle interactions in dense polydisperse colloidal suspensions. By comparing FDPM measurements with theoretical predictions using different structure factor models (HSPY, DA, and LMA), we found that the polydisperse HSPY model is most suitable for accounting for the effect of particle interactions and local microstructure of colloidal suspensions at high volume fractions. By incorporating the polydisperse HSPY model to account for particle interactions, we successfully recovered particle size distribution from FDPM measurements at high volume fractions (1-40%). Our inversion results at high volume fractions agree well with DLS measurement at low volume fractions (∼0.01%). While our previous work has demonstrated that the FDPM technique can be used for particle sizing of polydisperse noninteracting colloidal suspensions (