Dynamics and Thermodynamics of the Glass Transition

TL;DR

This paper proposes a theory that links the slow relaxation in glasses to activated molecular chains influenced by disorder, explaining the Vogel-Fulcher law and the entropy crisis near the glass transition.

Contribution

It introduces a disorder-corrected model of excitation chains that accounts for super-Arrhenius relaxation and diverging length scales at the glass transition.

Findings

The model recovers the Vogel-Fulcher law in three dimensions.

The length of excitation chains diverges at the Vogel-Fulcher temperature.

Partial ergodicity breaking explains entropy vanishing at the Kauzmann temperature.

Abstract

The principal theme of this paper is that anomalously slow, super-Arrhenius relaxations in glassy materials may be activated processes involving chains of molecular displacements. As pointed out in a preceding paper with A. Lemaitre, the entropy of critically long excitation chains can enable them to grow without bound, thus activating stable thermal fluctuations in the local density or molecular coordination of the material. I argue here that the intrinsic molecular-scale disorder in a glass plays an essential role in determining the activation rate for such chains, and show that a simple disorder-related correction to the earlier theory recovers the Vogel-Fulcher law in three dimensions. A key feature of this theory is that the spatial extent of critically long excitation chains diverges at the Vogel-Fulcher temperature. I speculate that this diverging length scale implies that, as the temperature decreases, increasingly large regions of the system become frozen and do not contribute to the configurational entropy, and thus ergodicity is partially broken in the super-Arrhenius region above the Kauzmann temperature $T_K$. This partially broken ergodicity seems to explain the vanishing entropy at $T_K$ and other observed relations between dynamics and thermodynamics at the glass transition.