Two-Gaussian excitations model for the glass transition

TL;DR

This paper introduces a modified two-Gaussian excitations model that better captures the thermodynamics of glass-forming liquids, reproducing experimental and simulation results and predicting a phase transition in fragile liquids.

Contribution

The model extends existing two-state models by incorporating Gaussian widths for site energies, bridging simple models and the random energy model, and explaining thermodynamic behaviors across different glassformers.

Findings

Reproduces sharp heat capacity peaks observed in simulations.

Predicts a first-order phase transition in fragile liquids.

Shows the ideal glass has a narrow, system-invariant Gaussian distribution.

Abstract

We develop a modified "two-state" model with Gaussian widths for the site energies of both ground and excited states, consistent with expectations for a disordered system. The thermodynamic properties of the system are analyzed in configuration space and found to bridge the gap between simple two state models ("logarithmic" model in configuration space) and the random energy model ("Gaussian" model in configuration space). The Kauzmann singularity given by the random energy model remains for very fragile liquids but is suppressed or eliminated for stronger liquids. The sharp form of constant volume heat capacity found by recent simulations for binary mixed Lennard Jones and soft sphere systems is reproduced by the model, as is the excess entropy and heat capacity of a variety of laboratory systems, strong and fragile. The ideal glass in all cases has a narrow Gaussian, almost invariant among molecular and atomic glassformers, while the excited state Gaussian depends on the system and its width plays a role in the thermodynamic fragility. The model predicts the existence of first-order phase transition for fragile liquids.