Quantitative Theory of a Relaxation Function in a Glass-Forming System

TL;DR

This paper develops a quantitative model explaining the relaxation behavior in a glass-forming system by considering the interplay between long-lived clusters and the background, linking fragility to temperature-dependent local structures.

Contribution

It introduces a new theoretical framework that quantitatively describes relaxation functions in glass-formers considering cluster-background interactions.

Findings

Relaxation slowdown is due to competition between long-lived clusters and background.

Total relaxation function is a weighted sum over clusters and background.

Fragility is quantitatively linked to temperature-dependent local structures.

Abstract

We present a quantitative theory for a relaxation function in a simple glass-forming model (binary mixture of particles with different interaction parameters). It is shown that the slowing down is caused by the competition between locally favored regions (clusters) which are long lived but each of which relaxes as a simple function of time. Without the clusters the relaxation of the background is simply determined by one typical length which we deduce from an elementary statistical mechanical argument. The total relaxation function (which depends on time in a nontrivial manner) is quantitatively determined as a weighted sum over the clusters and the background. The `fragility' in this system can be understood quantitatively since it is determined by the temperature dependence of the number fractions of the locally favored regions.