Mean-Field Theory, Mode-Coupling Theory, and the Onset Temperature in Supercooled Liquids

TL;DR

This paper explores the relationship between the onset temperature in supercooled liquids and the breakdown of mean-field theories, linking energy landscape changes, mode-coupling transitions, and finite-size effects.

Contribution

It demonstrates that the onset temperature corresponds to an ergodic-nonergodic transition in mode-coupling equations and relates landscape properties to packing and free volume rather than potential energy.

Findings

Mode-coupling equations undergo a transition near $T_{o}$

Inherent structure changes are governed by packing and free volume

Finite-size ROM shows corrections to mean-field behavior at $T_{o}$

Abstract

We consider the relationship between the temperature at which averaged energy landscape properties change sharply ($T_{o}$), and the breakdown of mean-field treatments of the dynamics of supercooled liquids. First, we show that the solution of the wavevector dependent mode-coupling equations undergoes an ergodic-nonergodic transition consistently close to $T_{o}$. Generalizing the landscape concept to include hard-sphere systems, we show that the property of inherent structures that changes near $T_{o}$ is governed more fundamentally by packing and free volume than potential energy. Lastly, we study the finite-size Random Orthogonal Model (ROM), and show that the onset of noticeable corrections to mean-field behavior occurs at $T_{o}$. These results highlight new connections between the energy landscape and mode-coupling approach to supercooled liquids, and identify what features of the relaxation of supercooled liquids are properly captured by mode-coupling theory.