On dynamic heterogeneity in supercooled liquids.

A simplified molecular theory for the dynamics of liquids near the glass transition temperature T(g) is developed and compared with experimental viscosity and diffusion behavior. Its basis is the spatial fluctuations of local density, a property that depends on isothermal compressibility and thus occurs naturally in all liquids at equilibrium. Instantaneous liquid structure is approximated by randomly distributed arrays of two domains having either higher or lower density than the average. The time dependence of fluctuations is represented by a sequence of such structures, each having a lifetime that varies with the macroscopic density. The dynamic environment of a molecule within a domain (slow or fast) depends on the density of its domain (high or low). Translational diffusion and orientational relaxation depend on different averages of the slow and fast domain contributions and lead, on approaching T(g), to a progressive departure from the Stoke-Einstein relationship. Predictions are made using macroscopic viscosity-density relationships within the individual domains. They depend only on the choice of domain size, which, according to this formulation, is insensitive to temperature. The data for three well-studied nonpolymeric liquids were found to be in reasonable accord with NMR assessments of domain size.