Colloidal Glass Transition: Beyond Mode-Coupling Theory

Abstract

A new theory for dynamics of concentrated colloidal suspensions and the colloidal glass transition is proposed. The starting point is the memory function representation of the density correlation function. The memory function can be expressed in terms of a time-dependent pair-density correlation function. An exact, formal equation of motion for this function is derived and a factorization approximation is applied to its evolution operator. In this way a closed set of equations for the density correlation function and the memory function is obtained. The theory predicts an ergodicity breaking transition similar to that predicted by the mode-coupling theory, but at a higher density.PACS numbers: 82.70. Dd, 64.70.Pf, 61.20.Lc There has been a lot of interest in recent years in the theoretical description of dynamics of concentrated suspensions and the colloidal glass transition [1]. It has been stimulated by ingenious experiments which provide detailed information about microscopic dynamics of colloidal particles [2]. Due to the abundance of experimental data the colloidal glass transition has emerged as a favorite, model glass transition to be studied [3].One of the conclusions of these studies is the acceptance of the mode-coupling theory (MCT) as the theory for dynamics of concentrated suspensions and their glass transition [4]. Historically, this is somewhat surprising since MCT was first formulated for simple fluids with Newtonian dynamics [5] and only afterwards was adapted to colloidal systems with stochastic (Brownian) dynamics [6]. On the other hand, basic approximations of MCT are less severe for Brownian systems [7].MCT is a theory for correlation functions of slow variables, i.e. variables satisfying local conservation laws. For Brownian systems there is only one such variable: local density. MCT's starting point is the memory function representation of the density correlation function [8,9]. The memory function is expressed in terms of a timedependent pair-density (i.e. four-particle) correlation function evolving with so-called projected dynamics. For Brownian systems this step is exact [10]. The central approximation of MCT is the factorization approximation in which the pair-density correlation function is replaced by a product of two time-dependent density correlation functions. As a result one obtains a closed, nonlinear equation of motion for the density correlation function. This equation predicts an ergodicity breaking transition that is identified with the colloidal glass transition. MCT has also been used to describe, e.g., linear viscoelasticity [11], dynamics of sheared suspensions [12], and colloidal gelation [13]. By and large, its predictions agree with experimental and simulational results [4,14].In spite of these successes, MCT's problems are well known [4]. The most important, fundamental problem is that once the factorization approximation is made there is no obvious way to extended and/or improve the theory. This is most acute for Brownian systems because there the density is the...

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