Metastable Dynamics above the Glass Transition

TL;DR

This paper extends the mode coupling theory of the liquid-glass transition by incorporating metastability through defect density variables, revealing how slow defect dynamics influence the glass transition without a specific critical temperature.

Contribution

It introduces defect density as a slow variable into MCT, providing a new framework to understand metastability and dynamic slowing down near the glass transition.

Findings

Metastability parameters vary smoothly with temperature.

Slowing down corresponds to a shallow metastable well.

Defect diffusion coefficient approaches a critical value.

Abstract

The element of metastability is incorporated in the fluctuating nonlinear hydrodynamic description of the mode coupling theory (MCT) of the liquid-glass transition. This is achieved through the introduction of the defect density variable $n$ into the set of slow variables with the mass density $\rho$ and the momentum density ${\bf g}$. As a first approximation, we consider the case where motions associated with $n$ are much slower than those associated with $\rho$. Self-consistently, assuming one is near a critical surface in the MCT sense, we find that the observed slowing down of the dynamics corresponds to a certain limit of a very shallow metastable well and a weak coupling between $\rho$ and $n$. The metastability parameters as well as the exponents describing the observed sequence of time relaxations are given as smooth functions of the temperature without any evidence for a special temperature. We then investigate the case where the defect dynamics is included. We find that the slowing down of the dynamics corresponds to the system arranging itself such that the kinetic coefficient $\gamma_v$ governing the diffusion of the defects approaches from above a small temperature-dependent value $\gamma^c_v$.