Statistical Mechanics of Topological Fluctuations in Glass-Forming Liquids

TL;DR

This paper develops a statistical mechanics framework to model topological fluctuations in glass-forming liquids, linking microscopic disorder to macroscopic properties and accounting for composition and temperature effects.

Contribution

It introduces a novel approach that incorporates localized topological fluctuations into the calculation of degrees of freedom, extending traditional mean-value analyses.

Findings

Full distribution of properties can be calculated as a function of composition, temperature, and history.

The approach captures the impact of localized fluctuations on macroscopic behavior.

Provides a generalized model linking structure fluctuations to thermodynamic variables.

Abstract

All liquids are topologically disordered materials; however, the degree of disorder can vary as a result of internal fluctuations in structure and topology. These fluctuations depend on both the composition and temperature of the system. Most prior work has considered the mean values of liquid or glass properties, such as the average number of topological degrees of freedom per atom; however, the localized fluctuations in properties also play a key role in governing the macroscopic characteristics of any glass-forming system. This paper proposes a generalized approach for modeling topological fluctuations in glass-forming liquids by linking the statistical mechanics of the disordered structure to topological constraint theory. In doing so we introduce the contributions of localized fluctuations into the calculation of the topological degrees of freedoms in the network. With this approach the full distribution of properties in the disordered network can be calculated as an arbitrary function of composition, temperature, and thermal history (for the nonequilibrium glassy state). The scope of this current investigation focuses on describing topological fluctuations in liquids, concentrating on composition and temperature effects.