Diffusion of Charged Colloidal Particles at Low Volume Fraction: Theoretical Model and Light Scattering Experiments DIMITER N. PETSEV 1 AND NIKOLAI D. DENKOV Laboratory of Thermodynamics and Physico-chemical Hydrodynamics, Facultyof Chemistry, Universityof Sofia, 1126 Sofia, Bulgaria Received April 30, 1991; accepted August 21, 1991 An appropriate mean force potential was utilized in Felderhof's Theory to derive simple analytical expressions for the concentration dependence of the collective and short time self diffusion coefficients, as well as for the sedimentation velocity of charged spherical particles. It is demonstrated theoretically that the osmotic viriat and the Oseen hydrodynamic terms play a dominant role. To check the theoretical model, the dependence of the collective diffusion coefficient on the volume fraction of latex particles was experimentally studied. Dynamic light scattering was used at several different concentrations of electrolyte. It turns out that our experimental results, as well as the results of other authors, are in very good agreement with the proposed theoretical model. The results show that the increase of the electrolyte concentration leads to increase of the particle charge, but almost does not change the particle surface potential. A minimum in the dependence of the diffusion coefficient of a single particle on the ionic strength was also obtained. © 1992 Academic Press, Inc. 1. INTRODUCTION The first step in the quantitative treatment of the Brownian diffusion was made by Ein- stein ( 1 ). He expressed the diffusion coefficient of spherical particles through the well known Stokes-Einstein relation, KT DSE - 6~r~a ' [ 1.1 ] where DSE is the diffusion coefficient, KT is the thermal energy, n is the solvent shear vis- cosity, and a is the colloidal particle radius. This formula is valid for a single sphere, sub- jected to Brownian motion when no other spheres are present. The latter is a severe re- striction, especially when the suspension is not infinitely diluted and/or long range interpar- ticle forces are acting. Even the short range hard sphere interactions may affect the value of the diffusion coefficient, above a certain 1To whom correspondence should be addressed. Journal ~2f Colloid and lnterface Science, Vol. 149, No. 2, March 15, 1992 concentration of colloidal particles. Further- more, such situations lead to a distinction of two types of diffusion coefficients: (i) self-dif- fusion coefficient, given by (2) f0 ° 1 (V(0). V(t))dt, [1.21 Ds =3 where Ds is the self diffusion coefficient, V is the velocity of a single particle, and t is time; (ii) collective diffusion coefficient, which is the quantity that multiplies the concentration gradient in Fick's Law, j = -Dc grad C. [1.31 In Eq. [1.3], j is the particle flux, Dc is the collective diffusion coefficient, and C is the particle concentration. When the suspension is infinitely diluted, the two coefficients Ds and Dc coincide. However, they may differ in the ease of finite concentrations of Brownian par- ticles. For example, if hard sphere interactions are present, Ds decreases with the particle 329 0021-9797/92 $3.00 Copyright © 1992 by Academic Press, Inc. All rights of reproduction in any form reserved.