Activated hopping, barrier fluctuations, and heterogeneity in glassy suspensions and liquids

Our entropic barrier hopping theory of glassy hard sphere colloidal suspensions is extended to include heterogeneity within a simple trap model framework. The origin of local domains, their size, and the corresponding static barrier fluctuations are attributed to mesoscopic density fluctuations of an amplitude controlled by the bulk compressibility. Based on typical values of the density fluctuation correlation length in dense liquids, the domain size on which correlated hopping occurs is estimated to be 3-4 particle or molecular diameters. Consequences of barrier fluctuations include an increased average relaxation time, faster diffusion, stretched exponential relaxation, diffusion-viscosity decoupling, and a fractional Stokes-Einstein relation. The common origin of the fluctuation effects is the heterogeneity-induced component of the barrier. For colloidal suspensions in the typically studied volume fraction regime the barrier fluctuations have modest consequences, but significantly larger effects are predicted in the putative glassy regime. A statistical dynamical analysis of domain lifetime suggests that for suspensions the relaxation time of mesoscopic collective density fluctuations is at least as long as the single particle hopping time. A general, model-independent analysis of the single molecule incoherent dynamic structure factor for suspensions and thermal liquids has also been performed in the long time and intermediate wavevector regime. The coupling of single particle density and longitudinal stress fluctuations results in a wavevector-dependent apparent diffusion constant and a dynamic correlation length scale which is strongly temperature dependent and directly related to the translation-rotation decoupling factor. This dynamic length is estimated to be 10 times larger than a molecular diameter for tris-naphthyl benzene near the glass transition temperature but shrinks to a molecular size above the crossover temperature that signals the emergence of collective barriers.