The development of next-generation electrolytes for energy storage is contingent on a rigorous understanding of transport phenomena in these systems. Here we present a theory for electrolyte transport integrating continuum mechanics, nonequilibrium thermodynamics, and electromagnetism. The theory gives rise to Onsager transport coefficients, which quantify ion correlations in an electrolyte. These transport coefficients can be calculated from molecular simulations using Green-Kubo relations, derived from nonequilibrium statistical mechanics using the Onsager regression hypothesis, and can be directly mapped to the more familiar Stefan-Maxwell transport coefficients.

We demonstrate the application of this theory to polyelectrolyte solutions, which have recently been under investigation as potential high cation transference number (t₊) electrolytes for Li-ion batteries. We compute the Onsager transport coefficients using coarse-grained molecular dynamics, observing strong anion-anion and cation-anion correlations which yield monotonically decreasing t₊  as a function of polyanion chain length. We further observe negative transference numbers in some systems. This analysis suggests that polyelectrolytes may not have favorable transport properties for batteries.