Diffusion and rheology in a model of glassy materials

We study self-diffusion within a simple hopping model for glassy materials. (The model is Bouchaud's model of glasses (J.-P. Bouchaud, J. Phys. I Fran ce 2, 1705 (1992)), as extended to describe rheological properties (P. Soll ich, F. Lequeux, P. Hebraud, M.E. Cates, Phys. Rev. Lett. 78, 2020 (1997)). ) We investigate the breakdown, near the glass transition, of the (generali zed) Stokes-Einstein relation between self-diffusion of a tracer particle a nd the (frequency-dependent) viscosity of the system as a whole. This stern s from the presence of a broad distribution of relaxation times of which di fferent moments control diffusion and rheology. We also investigate the eff ect of how (oscillatory sheer) 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 rh eological response. The relevance of these findings to soft glassy material s (foams, emulsions etc.) as well as to conventional glass-forming liquids is discussed.