Excitation lines and the breakdown of Stokes-Einstein relations in supercooled liquids

TL;DR

This paper investigates the breakdown of the Stokes-Einstein relation in supercooled liquids by analyzing excitation lines through dynamical facilitation, revealing how dimensionality influences transport decoupling in strong and fragile glass formers.

Contribution

It introduces a dynamical facilitation-based approach to understand the origin of Stokes-Einstein violation in supercooled liquids across different models and dimensions.

Findings

Violation of the Stokes-Einstein relation at low temperatures.

Dimensionality affects the degree of violation in strong glass formers.

Weak dimensionality dependence observed in fragile glass formers, aligning with experimental data.

Abstract

By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation, we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former, and the other in a fragile glass former. At low temperatures, both models exhibit violation of the Stokes-Einstein relation, $D\sim\tau^{-1}$, where $D$ is the self diffusion constant and $\tau$ is the structural relaxation time. In the strong case, the violation is sensitive to dimensionality $d$, going as $D\sim\tau^{-2/3}$ for $d=1$, and as $D\sim \tau^{-0.95}$ for $d=3$. In the fragile case, however, we argue that dimensionality dependence is weak, and show that for $d=1$, $D \sim \tau^{-0.73}$. This scaling for the fragile case compares favorably with the results of a recent experimental study for a three-dimensional fragile glass former.