Hopping induced continuous diffusive dynamics below the non-ergodic transition

TL;DR

This paper develops a theory showing how hopping induces continuous diffusion below the non-ergodic transition in supercooled liquids, explaining experimental observations and the interplay of different dynamical processes.

Contribution

It introduces a nonlinear interaction model between hopping and continuous diffusion, successfully predicting temperature dependence and relaxation behaviors in supercooled liquids.

Findings

Hopping induces continuous diffusion below the transition.

The theory predicts the temperature dependence of relaxation parameters.

It explains the variation of the stretching exponent with fragility.

Abstract

In low temperature supercooled liquid, below the ideal mode coupling theory transition temperature, hopping and continuous diffusion are seen to coexist. We present a theory which incorporates interaction between the two processes and shows that hopping can induce continuous diffusion in the otherwise frozen liquid. Several universal features arise from nonlinear interactions between the continuous diffusive dynamics (described here by the mode coupling theory (MCT)) and the activated hopping (described here by the random first order transition theory). We apply the theory to real systems (Salol) to show that the theory correctly predicts the temperature dependence of the non-exponential stretching parameter, $\beta$, and the primary $\alpha$ relaxation timescale, $\tau$. The study explains why, even below the ergodic to non-ergodic transition, the dynamics is well described by MCT. The non-linear coupling between the two dynamical processes modifies the relaxation behavior of the structural relaxation from what would be predicted by a theory with a complete static Gaussian barrier distribution in a manner that may be described as a facilitation effect. Furthermore, the theory explains the observed variation of the stretching exponent $\beta$ with the fragility parameter, $D$.