No 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 σ(r, r ′ ; t) ≡ δn(r, t)δn(r ′ , t) of its fluctuations δn(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 ′ ) ≡ δn(r, t)δn(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 σ 0 (r, r ′ ) towards its equilibrium state characterized by the equilibrium local concentration profile n eq (r) and equilibrium covariance σ 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.

One of the main elements of the self-consistent generalized Langevin equation (SCGLE) theory of colloid dynamics [Phys. Rev. E 62, 3382 (2000); 72, 031107 (2005)] is the introduction of exact short-time moment conditions in its formulation. The need to previously calculate these exact short-time properties constitutes a practical barrier for its application. In this Brief Report, we report that a simplified version of this theory, in which this short-time information is eliminated, leads to the same results in the intermediate and long-time regimes. Deviations are only observed at short times, and are not qualitatively or quantitatively important. This is illustrated by comparing the two versions of the theory for representative model systems.