Shear-Transformation-Zone Theory of Linear Glassy Dynamics

TL;DR

This paper develops a linearized shear-transformation-zone (STZ) theory to describe glassy dynamics, capturing broad relaxation spectra and strain recovery behaviors, with implications for understanding aging and structural relaxation in glasses and soft materials.

Contribution

It introduces a novel linearized STZ model incorporating a broad distribution of activation barriers to explain glassy relaxation phenomena and strain recovery.

Findings

Frequency-dependent loss modulus shows an alpha peak near viscous relaxation.

Strain recovery involves initial barrier-disorder and subsequent structural aging.

The theory aligns with experimental data on soft glassy materials.

Abstract

We present a linearized shear-transformation-zone (STZ) theory of glassy dynamics in which the internal STZ transition rates are characterized by a broad distribution of activation barriers. For slowly aging or fully aged systems, the main features of the barrier-height distribution are determined by the effective temperature and other near-equilibrium properties of the configurational degrees of freedom. Our theory accounts for the wide range of relaxation rates observed in both structural glasses and soft glassy materials such as colloidal suspensions. We find that the frequency dependent loss modulus is not just a superposition of Maxwell modes. Rather, it exhibits an $\alpha$ peak that rises near the viscous relaxation rate and, for nearly jammed, glassy systems, extends to much higher frequencies in accord with experimental observations. We also use this theory to compute strain recovery following a period of large, persistent deformation and then abrupt unloading. We find that strain recovery is determined in part by the initial barrier-height distribution, but that true structural aging also occurs during this process and determines the system's response to subsequent perturbations. In particular, we find by comparison with experimental data that the initial deformation produces a highly disordered state with a large population of low activation barriers, and that this state relaxes quickly toward one in which the distribution is dominated by the high barriers predicted by the near-equilibrium analysis. The nonequilibrium dynamics of the barrier-height distribution is the most important of the issues raised and left unresolved in this paper.