Diffusion and rheology in a model of glassy materials |
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Authors: | RML Evans ME Cates P Sollich |
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Institution: | (1) Department of Physics & Astronomy, The University of Edinburgh, JCMB King's Buildings, Mayfield Road, Edinburgh EH9 3JZ, UK, GB |
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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. Phys. I France 2, 1705 (1992)), as extended to describe rheological properties (P. Sollich, F. Lequeux, P. Hébraud, 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.
Received 31 August 1998 and Received in final form 25 January 1999 |
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Keywords: | PACS 64 70 Pf Glass transitions - 66 10 Cb Diffusion and thermal diffusion - 83 50 Fc Linear viscoelasticity |
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