Statistical Mechanics and Dynamics of a 3-Dimensional Glass-Forming System

TL;DR

This paper develops a statistical mechanical theory for the glass transition in a 3D glass-forming system, linking relaxation times to a growing length scale and enabling predictions beyond simulation capabilities.

Contribution

It introduces a criterion for selecting quasi-species to construct a finite-state theory of glass formation and relates the relaxation time to a rapidly increasing length scale.

Findings

The length scale $\xi$ increases rapidly as temperature decreases.

Relaxation time $ au_eta$ follows an exponential relation with $\xi$, $ au_eta o au_eta imes ext{exp}(rac{ ext{const} imes \xi}{T})$.

The theory predicts relaxation times at temperatures inaccessible to simulations.

Abstract

In the context of a classical example of glass-formation in 3-dimensions we exemplify how to construct a statistical mechanical theory of the glass transition. At the heart of the approach is a simple criterion for verifying a proper choice of up-scaled quasi-species that allow the construction of a theory with a finite number of 'states'. Once constructed, the theory identifies a typical scale $\xi$ that increases rapidly with lowering the temperature and which determines the $\alpha$-relaxation time $\tau_\alpha$ as $\tau_\alpha \sim \exp(\mu\xi/T)$ with $\mu$ a typical chemical potential. The theory can predict relaxation times at temperatures that are inaccessible to numerical simulations.