A model free energy for glasses

TL;DR

This paper introduces a model free energy framework for glasses, linking thermodynamic and dynamic properties to a first order phase transition and fluctuations, providing insights into the glass transition and related phenomena.

Contribution

It develops a novel free energy model based on graph expansions without loops, connecting glass transition features to phase transition proximity and fluctuations.

Findings

Density and heat capacity depend on temperature as derived from the model.

The alpha-relaxation time scale is characterized within the framework.

Fluctuation amplitudes increase near the phase boundary, supporting the phase transition hypothesis.

Abstract

We develop a model free energy from an expansion that basically includes graphs without loops. From this calculation, we derive the temperature dependence of the density (or specific volume), the typical time scale of the $\alpha$-relaxation, and the heat capacity. From this, we argue that the glass transition is dominated by the vicinity of a first order phase transition. The fluctuations, observable in principle as scattering, would support the findings and would increase in terms of amplitude close to the phase boundary (while the size stays constant). This amplitude is connected to the cluster size, also introduced in the cooperativity argument. Minor arguments about corrections from loops are discussed where we also might have found an argument for the "Boson Peak". The whole concept then bases on equilibrium arguments that are inhibited by -- to our view -- the fluctuations (high susceptibility) plus the high density that results in the strong growing of the cluster size.