Onsager Transport Coefficients and Transference Numbers in Polyelectrolyte Solutions and Polymerized Ionic Liquids

Electrolytes featuring negatively charged polymers, such as nonaqueous polyelectrolyte solutions and polymerized ionic liquids, are currently under investigation as potential high cation transference number (t+) electrolytes for lithium-ion batteries. Herein, we use coarse-grained molecular dynamics simulations to characterize the Onsager transport coefficients of polyelectrolyte solutions as a function of chain length and concentration. For all the systems studied, we find that the rigorously computed transference number is substantially lower than that approximated by the ideal solution (Nernst–Einstein) equations typically used to characterize these systems due to the presence of strong anion–anion and cation–anion correlations. None of the polyelectrolyte solutions achieve t+ greater than that of the conventional binary salt electrolyte, with some solutions having negative t+. This work demonstrates that the Nernst–Einstein assumption does not provide a physically meaningful estimate of the transference number in these solutions and calls into question the expectation of polyelectrolytes to exhibit a high cation transference number.