Shear-Transformation-Zone Theory of Glassy Diffusion, Stretched Exponentials, and the Stokes-Einstein Relation

TL;DR

This paper links shear-transformation-zone (STZ) theory to glassy diffusion, stretched-exponentials, and Stokes-Einstein violations, showing how internal heterogeneities and correlated events explain complex glassy dynamics.

Contribution

It introduces a unified STZ-based framework that explains diffusion, relaxation, and viscosity behavior in glass-forming materials from first principles.

Findings

STZs are identified as dynamic heterogeneities in glasses.

Correlated cascades of events are necessary for Fickian diffusion near Tg.

STZ-induced viscosity enhancement explains Stokes-Einstein ratio temperature dependence.

Abstract

The success of the shear-transformation-zone (STZ) theory in accounting for broadly peaked, frequency-dependent, glassy viscoelastic response functions is based on the theory's first-principles prediction of a wide range of internal STZ transition rates. Here, I propose that the STZ's are the dynamic heterogeneities frequently invoked to explain Stokes-Einstein violations and stretched-exponential relaxation in glass-forming materials. I find that, to be consistent with observations of Fickian diffusion near $T_g$, an STZ-based diffusion theory must include cascades of correlated events, but that the temperature dependence of the Stokes-Einstein ratio is determined by an STZ-induced enhancement of the viscosity. Stretched-exponential relaxation of density fluctuations emerges from the same distribution of STZ transition rates that predicts the viscoelastic behavior.