Wavenumber dependence of the structural relaxation time in the crossover regime of supercooled liquid dynamics

TL;DR

This paper presents a unified theory combining mode coupling and RFOT to explain the wavevector-dependent relaxation times in supercooled liquids, revealing a crossover from diffusive to activated dynamics.

Contribution

It introduces a novel unified theoretical framework that explains the wavenumber dependence of relaxation times in supercooled liquids, bridging diffusive and activated dynamics.

Findings

The theory predicts a smooth crossover in relaxation mechanisms.

It explains the near-linear q dependence of relaxation time.

The approach unifies experimental and simulation observations.

Abstract

As a liquid is progressively supercooled an intriguing weakening of the wavenumber ($q$) dependence of the structural relaxation time $\tau(q)$ in the large q limit is observed both in experiments and simulation studies. Neither the continuous Brownian diffusive dynamics nor the discontinuous activated events can alone explain the anomalous wavenumber dependence. Here we use our recently developed theory that unifies the mode coupling theory (MCT) for continuous dynamics and the random first order transition theory (RFOT) treatment of activated discontinuous motion as a nucleation (instanton) process, to understand the wavenumber dependence of density relaxation. The predicted smooth change in mechanism of relaxation from diffusive to activated, in the crossover regime, is wavevector dependent and is eventually responsible for sub-quadratic, almost linear, $q$ dependence of the relaxation time.