Bridging the Gap Between the Mode Coupling and the Random First Order Transition Theories of Structural Relaxation in Liquids

TL;DR

This paper develops a unified theory combining mode coupling and random first order transition theories to better describe structural relaxation in deeply supercooled liquids, accounting for activated events and their impact on dynamics.

Contribution

It introduces a modified mode coupling theory incorporating activated events from RFOT, providing a more comprehensive model of glassy liquid relaxation.

Findings

The combined model accurately describes the decay of the dynamic structure factor.

Activated events slow down near the glass transition, leading to structural arrest.

The theory explains hopping-dominated decay in supercooled liquids.

Abstract

A unified treatment of structural relaxation in a deeply supercooled glassy liquid is developed which extends the existing mode coupling theory (MCT) by incorporating the effects of activated events by using the concepts from the random first order transition (RFOT) theory. We show how the decay of the dynamic structure factor is modified by localized activated events (called instantons) which lead to the spatial reorganization of molecules in the region where the instanton pops up. The instanton vertex added to the usual MCT depicts the probability and consequences of such an event which can be derived from the random first order transition theory. The vertex is proportional to $exp(-A/s_{c})$ where $s_{c}$ is the configurational entropy. Close to the glass transition temperature, $T_{g}$, since $s_{c}$ is diminishing, the activated process slows beyond the time window and this eventually leads to an arrest of the structural relaxation as expected for glasses. The combined treatment describes the dynamic structure factor in deeply supercooled liquid fairly well, with a hopping dominated decay following the MCT plateau.