Abstract
The diffusion of small molecules or ions within polymeric materials is critical for their applications, such as polymer electrolytes. Cross-linking has been one of the common strategies to modulate solute diffusivity and a polymer's mechanical properties. However, various studies have shown different effects of cross-linking on altering the solute transports. Here, we utilized coarse-grained molecular dynamics simulation to systematically analyze the effects of cross-linking and polymer rigidity of solute diffusive behaviors. Above the glass transition temperature Tg, the solute diffusion followed the Vogel-Tammann-Fulcher (VTF) equation, D = D0 e-Ea/R(T-T0). Other than the conventional compensation relation between the activation energy Ea and the pre-exponential factor D0, we also identified a correlation between Ea and Vogel temperature T0. We further characterized an empirical relation between T0 and cross-linking density. Integrating the newly identified correlations among the VTF parameters, we formulated a relation between solute diffusion and the cross-linking density. The combined results proposed the criteria for the optimal solute diffusivity in cross-linked polymers, providing generic guidance for novel polymer electrolyte design.