Journal Article

Hopping and the Stokes–Einstein relation breakdown in simple glass formers

Charbonneau, Patrick, Zamponi, Francesco, Parisi, Giorgio, Jin, Yuliang

2014

Overview

Significance Like crystals, glasses are rigid because of the self-caging of their constituent particles. The key difference is that crystal formation is a sharp first-order phase transition at which cages form abruptly and remain stable, whereas glass formation entails the progressive emergence of cages. This loose caging complicates the description of the glass transition. In particular, an important transport mechanism in this regime, hopping, has thus far been difficult to characterize. Here we develop a completely microscopic description of hopping, which allows us to clearly assess its impact on transport anomalies, such as the breakdown of the Stokes–Einstein relation. One of the most actively debated issues in the study of the glass transition is whether a mean-field description is a reasonable starting point for understanding experimental glass formers. Although the mean-field theory of the glass transition—like that of other statistical systems—is exact when the spatial dimension [Formula], the evolution of systems properties with d may not be smooth. Finite-dimensional effects could dramatically change what happens in physical dimensions, [Formula]. For standard phase transitions finite-dimensional effects are typically captured by renormalization group methods, but for glasses the corrections are much more subtle and only partially understood. Here, we investigate hopping between localized cages formed by neighboring particles in a model that allows to cleanly isolate that effect. By bringing together results from replica theory, cavity reconstruction, void percolation, and molecular dynamics, we obtain insights into how hopping induces a breakdown of the Stokes–Einstein relation and modifies the mean-field scenario in experimental systems. Although hopping is found to supersede the dynamical glass transition, it nonetheless leaves a sizable part of the critical regime untouched. By providing a constructive framework for identifying and quantifying the role of hopping, we thus take an important step toward describing dynamic facilitation in the framework of the mean-field theory of glasses.

• Publisher: National Academy of Sciences
• Subject: cages / Cephalopelvic disproportion / Colloids / Crystals / Geometric lines / Glass / glass transition / Liquids / Modeling / Nucleation / Particle interactions / Phase transitions / Physical Sciences / Physics / Power laws