Activated dynamics, loss of ergodicity, and transport in supercooled liquids.

Abstract

The dynamics of the transition from supercooled liquid to glass is examined in terms of several probes: ergodic measures, self-diffusion coefficients, the Van Hove self-correlation functions, and the shear viscosity. Constant-pressure molecular-dynamics calculations at several temperatures are performed for a Lennard-Jones mixture and binary mixtures of soft spheres. The temperature dependence of the ergodicity diffusion parameters for both systems follow the Vogel-Fulcher law. On the other hand, the self-diffusion coefficients exhibit Arrhenius behavior for the soft-sphere system, but Vogel-Fulcher behavior for the Lennard-Jones system. These observations suggest that loss of effective ergodicity may be the universal feature of glass-forming substances. Various probes of the dynamics of the mixtures studied here suggest that the mechanism for mass transport dramatically changes from a simple diffusive process to one that involves activated transitions. The temperature at which this occurs is higher than the glass transition temperature ${\mathit{T}}_{\mathit{g}}$ and lies in the range 1.1T/${\mathit{T}}_{\mathit{g}}$1.3. In this temperature range the effective ergodic times also increase very rapidly and suggest that the relaxation process is dominated by the presence of barriers in configuration space. We also show that the Stokes-Einstein relation between the shear viscosity and the self-diffusion coefficients starts to break down in the temperature range where the ergodic convergence times increase dramatically.