Self-diffusion in colloidal suspensions. Intermediate times

Abstract

A theoretical approach to the study of self-diffusion properties of interacting colloidal particles in suspensions is developed. It is based on the assumption of a model for the memory function Ms(q,t), whose parameters are calculated by using exact short-time conditions for the self-diffusion propagator. Expressions, in terms of microscopic quantities of the system, for the time-dependent self-diffusion coefficient D(t) are derived from three different functional forms for Ms(q,t): a single-exponential function (already introduced in previous communications [J. L. Arauz-Lara and M. Medina-Noyola, J. Phys. A 19, L117 (1986); G. Nägele, M. Medina-Noyola, R. Klein, and J. L. Arauz-Lara, Physica A 149, 123 (1988)], an algebraic function, and a combination of the two. The latter one involves an adjustable parameter (the relative weight of the two modes) which can be determined by fitting the calculated values of D(t) to experimental data at long times. Explicit calculations of D(t) were carried out for systems of hard spheres interacting via a Derjaguin–Landau–Verwey–Overbeek type pair potential. Comparison of our results with Brownian dynamics data [K. J. Gaylor, I. K. Snook, W. van Megen, and R. O. Watts, J. Chem. Soc. Faraday Trans. 2 76, 1067 (1980)] shows that the bimodal model reproduces quite accurately the computer simulation data for D(t) with just one adjustable parameter, suggesting in this way that the actual functional form of the memory function may consist of a fast and a slow decaying mode.