General Non-equilibrium Theory of Colloid Dynamics

TL;DR

This paper develops a non-equilibrium theoretical framework for colloid dynamics, extending Onsager's theory to describe the evolution of local concentration and fluctuations in colloidal liquids, including effects of external fields and dynamic arrest.

Contribution

It introduces a self-consistent non-equilibrium theory for colloid dynamics based on an extension of Onsager's fluctuation theory, incorporating local mobility and memory functions.

Findings

Describes evolution from initial to equilibrium states of colloidal liquids.

Provides a framework for understanding aging and dynamic arrest.

Accounts for spatial heterogeneities and external fields.

Abstract

A non-equilibrium extension of Onsager's canonical theory of thermal fluctuations is employed to derive a self-consistent theory for the description of the statistical properties of the instantaneous local concentration profile n(r,t) of a colloidal liquid in terms of the coupled time evolution equations of its mean value n(r,t) and of the covariance {\sigma}(r,r';t) \equiv <{\delta}n(r,t){\delta}n(r',t)> of its fluctuations {\delta}n(r, t) = n(r, t) - n(r, t). These two coarse-grained equations involve a local mobility function b(r, t) which, in its turn, is written in terms of the memory function of the two-time correlation function C(r, r' ; t, t') \equiv <{\delta}n(r, t){\delta}n(r',t')>. For given effective interactions between colloidal particles and applied external fields, the resulting self-consistent theory is aimed at describing the evolution of a strongly correlated colloidal liquid from an initial state with arbitrary mean and covariance n^0(r) and {\sigma}^0(r,r') towards its equilibrium state characterized by the equilibrium local concentration profile n^(eq)(r) and equilibrium covariance {\sigma}^(eq)(r,r'). This theory also provides a general theoretical framework to describe irreversible processes associated with dynamic arrest transitions, such as aging, and the effects of spatial heterogeneities.