Theory of ion-mediated changes of structural relaxation and vitrification in polymerized ionic liquids

We combine PRISM theory of packing correlations with the Elastically Collective Nonlinear Langevin theory of activated hopping (coupled cage and longer range collective elasticity) to explore structural relaxation in dry polymerized ionic liquids (PILs). The model is charged semiflexible chains and spherical ions of highly variable size (mimicking Li,Na,Cs,Br,PF6,TFSI) which interact via screened Coulomb potentials. Given ion diffusion is much faster (decoupling) than structural relaxation in the supercooled regime, the ions are treated as dynamically ergodic. The theory predicts the laboratory timescale kinetic glass transition packing fraction or inverse Tg strongly shifts to higher values with increasing ion size. The physical mechanism involves ion-mediated changes of local polymer packing and dynamic plasticization which is different than for neutral polymer-solvent mixtures. Variation of the electrostatic interaction strength and backbone rigidity have quantitative, but not qualitative, effects. Overall, how ions change segmental relaxation, including the fragility, fall into two categories defined primarily by ion size. The theoretical results provide a basis for understanding the experimentally observed large variation of Tg with ion size in dry PolyILs.