Explaining the T,V-Dependent Dynamics of Glass Forming Liquids: The Cooperative Free Volume Model Tested Against New Simulation Results

We present a rate model, the "cooperative free volume model" (CFV), to describe segmental relaxation times as a function of a system's free volume, V_free, and its temperature, T. Our most important result is an analytic expression that provides a full pressure dependent description in the Arrhenius to non-Arrhenius crossover region and at all higher T. We demonstrate agreement with extensive simulation results for both simple Lennard-Jones fluids and 20-mer polymers. In the CFV model, free volume dictates the number of cooperating particles and thus the overall free energy of activation. This underlies the volume contribution to dynamics, and has been successfully applied to all systems tested. The CFV model predicts the non-Arrhenius behavior on isobars, with an energetic contribution from changing T and, simultaneously, a contribution from changing V_free; the implication is a change in the number of cooperating particles. Furthermore, as the Arrhenius regime is approached, we show that the entropy of activation, and a significant contribution from the gas kinetic T-dependence, cannot be ignored.