Shear-Transformation-Zone Theory of Viscosity, Diffusion, and Stretched Exponential Relaxation in Amorphous Solids

TL;DR

This paper extends the shear-transformation-zone (STZ) theory to explain viscosity, diffusion, and relaxation behaviors in amorphous solids near their glass transition, emphasizing the role of STZ transition rate distributions.

Contribution

It demonstrates that STZ rate-distributions account for temperature-dependent viscosity, stretched-exponential relaxation, and Stokes-Einstein violations in amorphous materials.

Findings

STZ rate-distribution causes strong temperature dependence of viscosity.

Stretched-exponential relaxation naturally arises from the same STZ distribution.

Temperature dependence of viscosity explains Stokes-Einstein violations near $T_g$.

Abstract

The shear-transformation-zone (STZ) theory has been remarkably successful in accounting for broadly peaked, frequency-dependent, viscoelastic responses of amorphous systems near their glass temperatures $T_g$. This success is based on the theory's first-principles prediction of a wide range of internal STZ transition rates. Here, I show that the STZ rate-distribution causes the Newtonian viscosity to be strongly temperature dependent; and I propose that it is this temperature dependence, rather than any heterogeneity-induced enhancement of diffusion, that is responsible for Stokes-Einstein violations near $T_g$. I also show that stretched-exponential relaxation of density fluctuations emerges naturally from the same distribution of STZ transition rates that predicts the viscoelastic behavior. To be consistent with observations of Fickian diffusion near $T_g$, however, an STZ-based diffusion theory somehow must include the cascades of correlated displacement events that are seen in low-temperature numerical simulations.