Microscopic theory of the effects of penetrant shape on activated dynamics and selectivity in polymer melts and crosslinked networks

We generalize the force level self-consistent cooperative hopping theory for the activated relaxation and diffusion of dilute spherical penetrants in polymer melts and crosslinked networks to explicitly address the role of non-spherical molecular shape at fixed space filling volume (1d rod-like, 2d planar-like, 3d globular-like). A rich dependence of penetrant dynamics and degree of decoupling of the penetrant hopping rate from the polymer alpha relaxation on temperature and crosslinking is predicted in the deeply supercooled regime for relatively large penetrants due to the importance of emergent collective elasticity which becomes significantly stronger as penetrant shape anisotropy grows. In contrast, for smaller penetrants or at high/medium temperatures, penetrant hopping is a local process and the effect of penetrant shape at fixed space filling volume is relatively weak. An aspect ratio variable is proposed that organizes well our results. Quantitative comparison with recent diffusion experiments on chemically complex aromatic penetrants in crosslinked poly-(n-butyl acrylate) networks reveals good agreement, and testable new predictions are made. Our results provide new insights for achieving selective transport and separations in membrane applications.