Diffusion of tracer molecules in glass-forming liquids is modeled in terms of diffusion in an obstructed space. For simplicity the obstructions are taken to be spherical and frozen in position. This idealized model of the long-lived dynamic heterogeneities in these viscous fluids leads to the widely observed fractional Stokes-Einstein relation (D = C([eta]/T)[zeta], 0 < [zeta][GE] 1) between the tracer particle diffusion coefficient D and the host fluid viscosity [eta]. The spherical obstruction model indicates [zeta] = 3/5 and some variation of the exponent is predicted to occur with the variation of the shape of the obstructions. Experimental values of [zeta] are summarized for comparison with our model.
Citation: Journal Non-Crystalline Solids
Pub Type: Journals
glass-forming liquids, obstruction model, Stoke-Einstein relation