Dynamics of fluids in quenched-random potential energy landscapes: a mode-coupling theory approach

Abstract

Motivated by a number of recent experimental and computational studies of the dynamics of fluids plunged in quenched-disordered external fields, we report on a theoretical investigation of this topic within the framework of the mode-coupling theory, based on the simple model of the hard-sphere fluid in a Gaussian random field. The possible dynamical arrest scenarios driven by an increase of the disorder strength and/or of the fluid density are mapped, and the corresponding evolutions of time-dependent quantities typically used for the characterization of anomalous self-diffusion are illustrated with detailed computations. Overall, a fairly reasonable picture of the dynamics of the system at hand is outlined, which in particular involves a non-monotonicity of the self-diffusion coefficient with fluid density at fixed disorder strength, in agreement with experiments. The disorder correlation length is shown to have a strong influence on the latter feature.

Dynamics of a noninteracting colloidal fluid in a quenched Gaussian random potential: a time-reversal-symmetry-preserving field-theoretic approach

“…This similarity can be traced back to the linearity of the kernels with the density correlation functions, which generically enforces continuous ergodicity-breaking transitions, if any [7,8]. Such a linearity is an expected generic feature of MCT-like approaches to fluids in random fields, which has been found in all previous studies, either strictly [11][12][13][14][15][16] or to leading order in the strong disorder regime [39][40][41][42]. There is however one important difference with regard to the behavior of the nonergodicity parameter.…”

“…The details of the critical dynamics near the threshold are illustrated by In most respects, this scenario is the same as the one found within the MCT [42]. This similarity can be traced back to the linearity of the kernels with the density correlation functions, which generically enforces continuous ergodicity-breaking transitions, if any [7,8].…”

“…(IX.1c) at t = 0, knowing that N 0 k (0) = λρ 0 D 0 q k · qΦ q = 0 by isotropy. This requires that This feature is at variance with the self-consistent MCT predictions [42].…”

“…This indeed appears as an interesting new window on the use of field theory and its relation with MCT, complementary to what has already been done. Note that, within MCT, the presence of interactions does not actually lead to any particular technical difficulty [39][40][41][42]. However, for more general considerations, it clearly seems advisable to first isolate the effects of disorder from those of interactions, hence the present restriction to noninteracting systems.…”

“…We now summarize the main results of our work. The first-order bare theory (FOBT) gives a dynamical equation for the density correlation function that can be put in the same form as that of the self-consistent MCT developed by one of us [39][40][41][42], albeit with a memory term written in terms of the bare correlation function [see Eqs. (IX.…”