Diffusion and the Mesoscopic Hydrodynamics of Supercooled Liquids

The description of molecular motion by macroscopic hydrodynamics has a long and continuing history. The Stokes−Einstein relation between the diffusion coefficient of a solute and the solvent viscosity predicted using macroscopic continuum hydrodynamics is well satisfied for liquids under ordinary to high-temperature conditions, even for solutes as small as the solvent. Diffusion in supercooled liquids near their glass transition temperature has been found to deviate by as much as 3 orders of magnitude from that predicted by the Stokes−Einstein Relation [J. Chem. Phys. 1996, 104, 7210].1 On the basis of the random first-order transition theory [Phys. Rev. A 1987, 35, 3072, Phys. Rev. A 1989, 40, 1045, and Proc. Natl. Acad. Sci. U.S.A. 2000, 97, 2990],2-4 supercooled liquids possess a mosaic structure. The size- and temperature-dependence of the transport anomalies are quantitatively explained with an effective medium hydrodynamics model based on the microscopic theory of this mesoscale, mosaic structure.