Potential energy landscape description with Gamma distribution for supercooled liquids and glasses

TL;DR

This paper introduces a Gamma distribution-based model for the potential energy landscape of supercooled liquids and glasses, capturing asymmetry and fragile-to-strong transition phenomena more effectively than Gaussian models.

Contribution

It proposes using the Gamma distribution to better describe the potential energy landscape and configurational entropy, addressing limitations of Gaussian models and incorporating a singular term in the equation of state.

Findings

Gamma distribution effectively models asymmetry in Eis and Sc.

Captures fragile to strong transition via shifts in Eis distribution.

Provides an equation of state with a diverging term at the glass transition.

Abstract

The potential energy landscape, PEL, theory stands as one of the most successful frameworks for understanding supercooled liquids and glassy systems. A central element of this theory is the configurational entropy, Sc, which is traditionally represented by a symmetric Gaussian distribution. However, the asymmetric nature of the potential energy of inherent structures, Eis, poses a challenge to such a representation across wide regions of configurational space. In addition, the Gaussian distribution fails to represent fragile to strong transition, FST, observed in various fluids. In this work, we demonstrate that an asymmetric distribution, specifically the Gamma distribution, provides effective description of both Sc and Eis over broad ranges of density and temperature, T. The FST is interpreted through shifts of the Eis distribution and the curvature change of the Eis vs 1/T relation. In terms of energy changes, the FST is comparable to a liquid-liquid phase transition. Moreover, the revised PEL framework yields an equation of state that incorporates a singular term diverging at a glassy or jammed state, an important feature for accurately describing the pressure behavior of these systems.