Collective diffusion of anisotropic hard-particle mixtures

Abstract

Predicting the dynamics of anisotropic mixtures of different species is a challenging theoretical task. We show that Dynamical Density Functional Theory (DDFT), a theory predicting time evolution of the one-particle-density through a free energy functional, can be simplified to a diffusion equation. To quantify the dynamical relaxation behavior, we deduce corrections to the regular long-time collective diffusion coefficients from the direct correlations between the interacting particles and determine these effective diffusion coefficients analytically for a number of hard-particle systems, including mixtures of hard spheres, as well as isotropic and nematic phases of uniaxial spherocylinders and biaxial spherotriangles. Finally, we discuss how to generalize our approach to systems with positional order and suggest a possible application to predicting relaxation times of orientational order parameters.