Dynamic Model of Super-Arrhenius Relaxation Rates in Glassy Materials

TL;DR

This paper introduces a dynamic model explaining super-Arrhenius relaxation rates in glassy materials through thermally nucleated molecular rearrangements facilitated by string-like fluctuations near shear transformation zones, predicting a crossover from Vogel-Fulcher to Arrhenius behavior.

Contribution

It presents a novel dynamic mechanism involving string-like fluctuations and domain interfaces to explain super-Arrhenius relaxation in glasses, extending existing models.

Findings

Modified Vogel-Fulcher formula at low temperatures

Crossover from super-Arrhenius to Arrhenius behavior

Agreement with experimental data in the crossover region

Abstract

We propose that the super-Arrhenius relaxation rates observed in glassy materials are determined by thermally nucleated rearrangements of increasing numbers of molecules at decreasing temperatures. In our model of this mechanism, string-like fluctuations in the neighborhood of shear transformation zones (STZ's) provide routes along which rearrangements can propagate, and the entropy associated with long enough strings allows the rearrangement energy to be distributed stably in the surrounding material. We further postulate that, at low enough temperatures, these fluctuations are localized on the interfaces between frustration-limited domains. Our result is a modified Vogel-Fulcher formula at low temperatures that crosses over to a simple Arrhenius law as the glass changes from being solid-like to liquid-like. To achieve agreement with experiment in the crossover region, we need to make what seem to us to be overly strong assumptions about the behavior of frustration-limited domains.