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

The diffusion behavior of small molecules and ions within polymer material is the key property of polymeric materials, such as polymer electrolytes, gas separation membranes, and separators, etc. Cross-linking is a common strategy to modulate solute diffusion and the mechanical properties of polymer hosts. However, the reported effects of cross-linking on the ion transport or solute diffusivity within polymer networks are divergent. Here, we utilized coarse-grained molecular dynamics simulation to investigate the effect of cross-linking density and polymer rigidity on solute diffusive behavior within polymer network. Above the glass transition temperature T_g, the diffusion of solute follows Vogel-Tammann-Fulcher equation, D=D₀exp(-E_a/R(T-T₀)). Our simulation results revealed that the pre-exponential factor D₀ and the pseudo activation energy E_a exhibit the conventional compensation correlation. Furthermore, we identified an additional correlation between E_a and Vogel temperature T₀ and an empirical relation between T₀ and cross-linking density. Integrating these newly determined correlations with the VTF equation, we derived a relation linking the solute diffusivity and the cross-linking density to identify the criteria for the optimal diffusivity. The combined results provide valuable guidance for the optimization of polymeric materials for various applications, particularly novel polymer electrolytes for energy devices.