Theory of the molecular factors that control activated ion transport and decoupling in polymerized ionic liquids

We recently developed microscopic statistical mechanical theories of the structure, activated ion hopping rate, and segmental relaxation and glass transition temperature T_g of polymerized ionic liquids (PILs). These advances are combined to address families of experimental PILs aimed at understanding how polymer stiffness, T_g, anion-cation attraction strength, temperature-dependent dielectric constant, and ion size determine the ion relaxation time in liquids and glasses. The coarse grained polymer model is trained for Li-PILs to reproduce the experimental T_g and ion relaxation time at T_g, and then predictions are made for the full temperature dependence which are compared to experiment. Extending the analysis to larger ions (Na, K, Cs) reveals the competing effects of increasing Coulomb cage coordination number slowing down hopping, but reduction of anion-cation association energy speeds up hopping. A two regime master curve is discovered that organizes all ion relaxation time calculations in terms of an effective Coulomb attraction coupling constant, which suggests design rules for achieving superionic conductivity. Decoupling of ion and polymer segmental relaxation times and Walden plots are also analyzed. This work was done in collaboration with the FacT EFRC team at ORNL.