Dynamics and Thermodynamics of the Glass Transition

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.

arXiv comment20 pages, no figures, some further revisions

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• Cooperative Strings and Glassy Interfaces
• Reversible plasticity in amorphous materials
• Steady-state, effective-temperature dynamics in a glassy material
• Excitation Chains at the Glass Transition
• Heterogeneous freezing in a geometrically frustrated spin model without disorder: spontaneous generation of two time-scales
• Anomalous diffusion and stretched exponentials in heterogeneous glass-forming liquids: Low-temperature behavior
• Glass Dynamics at High Strain Rates
• What are the interactions in quantum glasses?
• Anomalous diffusion in heterogeneous glass-forming liquids: Temperature-dependent behavior
• Quantitative Theory of a Relaxation Function in a Glass-Forming System
• Theory of Relaxation Dynamics in Glass-Forming Hydrogen-Bonded Liquids