Aspects of the dynamics of colloidal suspensions: Further results of the mode-coupling theory of structural relaxation

TL;DR

This paper presents extended results of the mode-coupling theory for colloidal suspensions, explaining structural relaxation dynamics, non-diffusive long-time behavior, and scaling laws, with implications for light scattering experiments and generalized Stokes-Einstein relations.

Contribution

It provides new insights into the wave vector dependence of relaxation times and amplitudes, and extends the theory to include non-zero frequency effects and short-time dynamics.

Findings

Structural relaxation becomes non-diffusive at long times.

Wave vector dependence explains observed scaling in experiments.

Generalized relations support previous theoretical reasoning.

Abstract

Results of the idealized mode-coupling theory for the structural relaxation in suspensions of hard-sphere colloidal particles are presented and discussed with regard to recent light scattering experiments. The structural relaxation becomes non-diffusive for long times, contrary to the expectation based on the de Gennes narrowing concept. A semi-quantitative connection of the wave vector dependences of the relaxation times and amplitudes of the final $\alpha$-relaxation explains the approximate scaling observed by Segr{\`e} and Pusey [Phys. Rev. Lett. {\bf 77}, 771 (1996)]. Asymptotic expansions lead to a qualitative understanding of density dependences in generalized Stokes-Einstein relations. This relation is also generalized to non-zero frequencies thereby yielding support for a reasoning by Mason and Weitz [Phys. Rev. Lett {\bf 74}, 1250 (1995)]. The dynamics transient to the structural relaxation is discussed with models incorporating short-time diffusion and hydrodynamic interactions for short times.