Ion Mobilities, Transference Numbers, and Inverse Haven Ratios of Polymeric Ionic Liquids

We probe the ion mobilities, transference numbers, and inverse Haven ratio of ionic liquids and polymerized ionic liquids as a function of their molecular weight using a combination of atomistic equilibrium and nonequilibrium molecular dynamics simulations. In contrast to expectations, we demonstrate that the inverse Haven ratio increases with increasing degree of polymerization (N) and then decreases at larger N. For a fixed center of mass reference frame, we demonstrate that such results arise as a consequence of the strong cation-cation correlated motions, which exceed (in magnitude) the self-diffusivity of cations. Together, our findings challenge the premise underlying the pursuit of pure polymeric ionic liquids as high transference number, single-ion conducting electrolytes.