Predictive Statistical Mechanics for Glass Forming Systems

Abstract

Using two extremely different models of glass formers in two and three dimensions we demonstrate how to encode the subtle changes in the geometric rearrangement of particles during the scenario of the glass transition. We construct a statistical mechanical description that is able to explain and predict the geometric rearrangement, the temperature dependent thermodynamic functions and the $\alpha$-relaxation time within the measured temperature range and beyond. The theory is based on an up-scaling to proper variables (quasi-species) which is validated using a simple criterion. Once constructed, the theory provides an accurate predictive tool for quantities like the specific heat or the entropy at temperatures that cannot be reached by measurements. In addition, the theory identifies a rapidly increasing typical length scale $\xi$ as the temperature decreases. This growing spatial length scale determines the $\alpha$-relaxation time as ${\tau }_{\alpha }\sim \exp (\mu \xi /T)$ where $\mu$ is a typical chemical potential per unit length.

10 pages, 16 figures, 2 tables

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• Pressure-energy correlations in liquids. I. Results from computer simulations
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Cited by in corpus (5)

• The role of local structure in dynamical arrest
• Dynamical coexistence in moderately polydisperse hard-sphere glasses
• The Effective Temperature in Elasto-Plasticity of Amorphous Solids
• From Liquid Structure to Configurational Entropy: Introducing Structural Covariance
• Statistical Mechanics of Glass Formation in Molecular Liquids with OTP as an Example