Theory of collective charge transport and the inverse Haven ratio in polymerized ionic liquids and glasses

We have constructed a microscopic statistical mechanical theory of collective effects on the conductivity of polymerized ionic liquids (PILs) based on coupling of charge and density dynamical correlations. The complex activated single ion hopping process that determines the self-diffusion constant cancels out to leading order in the inverse Haven ratio. The essential physics arises from strong collective microstructural correlations on the Coulomb cage scale that couple the spatial and temporal correlations of forces between mobile ions. The dominant force correlation pathway arises from cation–anion attractions and the Coulomb cage order parameter. Excluded volume effects become important for large ions but are minor small ions. Consequently, collective effects increasingly suppress conductivity (and reduce the inverse Haven ratio) upon cooling and as ion size increases. The predicted trends are consistent with experimental measurements for various polymer chemistries and ion ranging from small (Li, Na, K) to large (TFSI). Intriguingly, if attractive Coulomb attractions are neglected and only repulsive dynamical force correlations considered, small ion PILs are predicted to exhibit inverse Haven ratios above unity similar to superionic ceramics.