Diffusion and rheology in a model of glassy materials

TL;DR

This paper analyzes self-diffusion and rheology in a glassy material model, revealing the breakdown of the Stokes-Einstein relation near the glass transition and the effects of flow on diffusion.

Contribution

It extends Bouchaud's glass model to include rheological properties and investigates diffusion behavior under flow near the glass transition.

Findings

Breakdown of Stokes-Einstein relation near glass transition.

Flow induces finite diffusivity below the glass transition.

Diffusivity shows power-law frequency dependence at higher temperatures.

Abstract

We study self-diffusion within a simple hopping model for glassy materials. (The model is Bouchaud's model of glasses [J.-P. Bouchaud, J. Physique I 2, 1705 (1992)], as extended to describe rheological properties [P. Sollich, F. Lequeux, P. Hebraud and M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)].) We investigate the breakdown, near the glass transition, of the (generalized) Stokes-Einstein relation between self-diffusion of a tracer particle and the (frequency-dependent) viscosity of the system as a whole. This stems from the presence of a broad distribution of relaxation times of which different moments control diffusion and rheology. We also investigate the effect of flow (oscillatory shear) on self-diffusion and show that this causes a finite diffusivity in the temperature regime below the glass transition (where this was previously zero). At higher temperatures the diffusivity is enhanced by a power law frequency dependence that also characterises the rheological response. The relevance of these findings to soft glassy materials (foams, emulsions etc.) as well as to conventional glass-forming liquids is discussed.