Solute Diffusivity and Local Free Volume in Cross-Linked Polymer Network: Implication of Optimizing the Conductivity of Polymer Electrolyte

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 T_g, 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 E_a and the pre-exponential factor D₀, we also identified a correlation between E_a 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.