Theory of activated molecular transport in crosslinked polymer networks

Activated transport of molecular penetrants in polymer melts and dry crosslinked networks is a fundamental physics problem relevant to selective transport for membrane separations and other diverse applications. A force-level statistical mechanical theory has been developed built on our recent advances for structural relaxation in the rubbery, supercooled, and glass regimes where segment hopping is coupled to longer range collective elasticity in a chemistry, crosslink density, and thermodynamic state dependent manner. A theory for penetrant hopping is formulated at the stochastic trajectory level based on the dynamic free energy concept which quantifies kinetic constraints from knowledge of microscopic structural correlations. The barrier crossing event is mechanistically coupled in a temporally self-consistent manner to facilitating thermally activated localized segment dynamical fluctuations. The penetrant activation barrier, and the degree of decoupling of its hopping time from the polymer alpha time, is predicted to be a rich function of molecular size relative to the Kuhn length, penetrant shape, specific polymer-molecule attraction, and thermodynamic state. In contrast to nanoparticles, strong crosslink-induced slowing down of structural relaxation is more important than geometric mesh confinement even for relatively large penetrants. Detailed comparisons with complementary experiments and simulations support the theory. The approach can be generalized to address activated charge transport and vitrification in polymerized ionic liquids, and coupled structural and bond exchange relaxation in vitrimers with dynamic bonds. This work was performed in collaboration with Baicheng Mei, Tsai-Wei Lin, Grant Sheridan, Chris Evans and Charles Sing.