Self-consistent generalized Langevin equation for colloid dynamics.

Abstract

We present a general self-consistent theory of colloid dynamics which, for a system without hydrodynamic interactions, allows us to calculate F(k,t), and its self-diffusion counterpart F(S)(k,t), given the effective interaction pair potential u(r) between colloidal particles, and the corresponding equilibrium static structural properties. This theory is build upon the exact results for F(k,t) and F(S)(k,t) in terms of a hierarchy of memory functions, derived from the application of the generalized Langevin equation formalism, plus the proposal of Vineyard-like connections between F(k,t) and F(S)(k,t) through their respective memory functions, and a closure relation between these memory functions and the time-dependent friction function Delta zeta(t). As an illustrative application, we present and analyze a selection of numerical results of this theory in the short- and intermediate-time regimes, as applied to a two-dimensional repulsive Yukawa Brownian fluid. For this system, we find that our theory accurately describes the dynamic properties contained in F(k,t) in a wide range of conditions, including strongly correlated systems, at the longest times available from our computer simulations.