Metastable Dynamics of the Hard-Sphere System

TL;DR

This paper extends mode-coupling theory to include metastability, showing that the glass transition in hard-sphere systems is gradual over a range of densities, affecting relaxation dynamics and aligning with colloidal experiment observations.

Contribution

It introduces a metastability-inclusive reformulation of MCT, revealing a non-sharp glass transition and variable relaxation exponents in hard-sphere systems.

Findings

Glass transition occurs over a density range, not at a sharp point.

Relaxation exponents depend on packing fraction and metastable potential scale.

Model aligns with recent colloidal system experiments.

Abstract

The reformulation of the mode-coupling theory (MCT) of the liquid-glass transition which incorporates the element of metastability is applied to the hard-sphere system. It is shown that the glass transition in this system is not a sharp one at the special value of the density or the packing fraction, which is in contrast to the prediction by the conventional MCT. Instead we find that the slowing down of the dynamics occurs over a range of values of the packing fraction. Consequently, the exponents governing the sequence of time relaxations in the intermediate time regime are given as functions of packing fraction with one additional parameter which describes the overall scale of the metastable potential energy for defects in the hard-sphere system. Implications of the present model on the recent experiments on colloidal systems are also discussed.