Stokes-Einstein violation in glass-forming liquids

The Stokes-Einstein relation D=${\mathit{k}}_{\mathit{B}}$T/(C\ensuremath{\eta}a) (\ensuremath{\eta} is the shear viscosity; D is the diffusion constant; C=6\ensuremath{\pi} for no-slip and 4\ensuremath{\pi} for slip boundary conditions; a is the molecular diameter) holds over a wide temperature range in many liquids. However, in a variety of fragile glass-forming liquids, a, as defined by the above expression, becomes smaller with decreasing temperature as the glass transition is approached. In an attempt to explain this experimental result, we propose that special thermal fluctuations cause domains in the liquid to become temporarily more fluidized, so that a diffusing particle can move through fluidized regions, but is inhibited from moving in the unfluidized region. We introduce a mean-field picture of this fluctuating fluid, and solve two versions for their hydrodynamic flow fields. The resulting reduced drag force can account for the violation of the Stokes-Einstein relation seen in fragile glass-forming liquids, with plausible values for the size of the fluidized region and the mean-field reduction in viscosity.