Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids

TL;DR

This paper presents a theoretical framework linking dynamical heterogeneities and avalanches in glass-forming liquids, explaining how local rearrangements and elasticity lead to critical behavior and Stokes-Einstein violation, supported by numerical simulations.

Contribution

It introduces a zero-temperature fixed point theory connecting dynamical heterogeneities, avalanches, and relaxation in glass-forming liquids, validated by simulations.

Findings

Growth of correlation length and volume controlled by zero-temperature fixed point

Distribution of local energy barriers relates to heterogeneity evolution

Decoupling of diffusion and relaxation time confirmed by simulations

Abstract

We provide a theoretical description of dynamical heterogeneities in glass-forming liquids, based on the premise that relaxation occurs via local rearrangements coupled by elasticity. In our framework, the growth of the dynamical correlation length $\xi$ and of the correlation volume $\chi_4$ are controlled by a zero-temperature fixed point. We connect this critical behavior to the properties of the distribution of local energy barriers at zero temperature. Our description makes a direct connection between dynamical heterogeneities and avalanche-type relaxation associated to dynamic facilitation, allowing us to relate the size distribution of heterogeneities to their time evolution. Within an avalanche, a local region relaxes multiple times, the more the larger is the avalanche. This property, related to the nature of the zero-temperature fixed point, directly leads to decoupling of particle diffusion and relaxation time (the so-called Stokes-Einstein violation). Our most salient predictions are tested and confirmed by numerical simulations of scalar and tensorial thermal elasto-plastic models.