Nearly-logarithmic decay in the colloidal hard-sphere system

TL;DR

This paper investigates nearly-logarithmic decay in colloidal hard-sphere systems near the liquid-glass transition, explaining it through mode-coupling theory and deriving a Cole-Cole formula that fits experimental data over three decades.

Contribution

It provides a microscopic explanation for nearly-logarithmic decay using mode-coupling theory and derives a Cole-Cole formula that accurately describes experimental data.

Findings

Mode-coupling theory fits experimental data well.

Nearly-logarithmic decay is linked to critical relaxation phenomena.

Derived Cole-Cole formula matches data over three decades.

Abstract

Nearly-logarithmic decay is identified in the data for the mean-squared displacement of the colloidal hard-sphere system at the liquid-glass transition [v. Megen et. al, Phys. Rev. E 58, 6073(1998)]. The solutions of mode-coupling theory for the microscopic equations of motion fit the experimental data well. Based on these equations, the nearly-logarithmic decay is explained as the equivalent of a beta-peak phenomenon, a manifestation of the critical relaxation when the coupling between of the probe variable and the density fluctuations is strong. In an asymptotic expansion, a Cole-Cole formula including corrections is derived from the microscopic equations of motion, which describes the experimental data for three decades in time.