Theory of Ion-Mediated\nSegmental Localization, Activated\nStructural Relaxation, and the Glass Transition in Polymerized Ionic\nLiquids

We combine polymer integral equation theory for structural\ncorrelations\nwith a force-level theory for activated segmental relaxation to construct\na microscopic theory for how ions modify the onset of segmental localization,\nthe polymer alpha relaxation time, and glass transition temperature, <i>T</i><sub>g</sub>, in dry polymerized ionic liquids (PolyILs).\nOur most important findings concerning the behavior of <i>T</i><sub>g</sub> are (i) a weak dependence on anion–cation Coulomb\nattraction strength due to strong decoupling of ion and segmental\ndynamics, (ii) strong reduction with increasing mobile ion size due\nto both plasticization effects and weakening of ion-modified monomer\ncaging, and (iii) increase with backbone rigidity and intrachain dynamic\ncooperativity. We quantitatively estimate <i>T</i><sub>g</sub> variations as ion size and polymer static and dynamic rigidity are\nwidely varied. The experimental data of 19 PolyILs are organized into\na specific pattern consistent with the theoretical predictions with\nglass transition temperatures varying over a very wide range (∼250\nK) as observed experimentally. Based on the theoretical results, suggestions\nare made concerning the search for high conductivity Li- or Na-based\nPolyILs based on further lowering of <i>T</i><sub>g</sub> via new polymer synthesis. Calculations of the alpha time as a function\nof packing fraction reveal the dynamic fragility increases for larger\nmobile ions, a more flexible backbone, and/or a smaller degree of\nintrachain dynamic cooperativity, as a consequence of the increasing\nimportance of collective elasticity in determining the activation\nbarrier. An analysis of transient segmental localization and a crossover\nto activated dynamics reveals similar, but not identical, trends as\npredicted at the laboratory vitrification timescale.