Obstruction model of the fractional Stokes-Einstein relation in glass-forming liquids

Diffusion of tracer molecules in glass-forming liquids is modeled in terms of diffusion in an obstructed space. The obstructions, which model heterogeneities in supercooled liquids, are taken to be spherical and frozen in position for simplicity. This idealized model leads to the widely observed "fractional Stokes-Einstein (FSE) equation" (D proportional to (eta/T)(-xi), 0 < xi less than or equal to 1) relating the tracer particle diffusion coefficient D and the fluid viscosity eta. The spherical obstruction model indicates the exponent value xi = 3/5, but xi is predicted to vary somewhat with obstruction shape. Experimental values of xi are summarized for comparison with our model. (C) 1998 Elsevier Science B.V. All rights reserved.