Microscopic theory for the activated dynamics of molecules in polymer melts and crosslink networks

We construct a microscopic force level theory for the activated dynamics of dilute molecules of variable shape in dense polymer melts and crosslinked networks. Based on the elastically cooperative nonlinear Langevin equation theory of structural relaxation, the polymer matrix glass transition temperature (dynamic fragility) increases with (is largely independent of) crosslink density, trends which strongly impact penetrant motion. At fixed temperature with increasing crosslink density, the penetrant mean hopping time (or inverse diffusion constant) grows exponentially, and the degree of molecule and polymer alpha time decoupling varies in a nonmonotonic manner. These trends are robust to changing molecular shape and size, albeit with important quantitative differences. Predictions of the theory for the diffusion of an elongated aromatic penetrant in tightly crosslinked networks as a function of degree of crosslinking and temperature are in good agreement with recent experiments and simulations. Overall, the theoretical results as a function of penetrant size and shape, temperature, and degree of crosslinking provide insights concerning how to optimize the absolute and relative (selectivity) diffusion rates relevant to polymer-based membrane separations.