Universal scaling, dynamic fragility, segmental relaxation, and vitrification in polymer melts.

Our theory of dynamic barriers, slow relaxation, and the glass transition of polymers melts is numerically applied using parameters relevant to real materials. The numerical results are found to be in qualitative agreement with all the approximate analytic expressions previously derived with quantitative differences on the order of approximately 20-30% or much less. The analytic prediction of a universal temperature dependence of the alpha relaxation time, and its intimate connection with the idea of a nearly universal crossover time, is established. Inter-relations between the breadth of the deeply supercooled regime, two definitions of the dynamic fragility, and the magnitude of the fast local Arrhenius process at the glass transition temperature are demonstrated and system-specific limitations identified. A quantitative application to segmental relaxation over 16 orders of magnitude in a polyvinylacetate melt yields encouraging results regarding the accuracy of the theory. The theoretical relaxation time results are well fit by multiple empirical forms (generally containing an assumed singular aspect) using parameters consistent with experimental studies. No physical significance is ascribed to this finding, but it does provide additional support for the temperature dependence of the alpha relaxation process predicted by the theory.