Ohm's law for ion conduction in lithium and beyond-lithium battery electrolytes

The viability of next generation lithium and beyond-lithium battery technologies hinges on the development of electrolytes with improved performance. Comparing electrolytes is not straightforward as multiple electrochemical parameters affect the performance of an electrolyte. Additional complications arise due to the formation of concentration gradients in response to dc potentials. We propose a modified version of Ohm's law to analyze current through binary electrolytes driven by a small dc potential. We show that the proportionality constant in Ohm's law is given by the product of the ionic conductivity, κ, and the ratio of currents in the presence (i_ss) and absence (i_Ω) of concentration gradients, ρ₊. The importance of ρ₊ was recognized by Evans et al. [Polymer 28, 2324 (1987)]. The product κρ₊ is used to rank order a collection of electrolytes. Ideally, both κ and ρ₊ should be maximized, but we observe a trade-off between these two parameters, resulting in an upper bound. This trade-off is analogous to the famous Robeson upper bound for permeability and selectivity in gas separation membranes. Designing polymer electrolytes that overcome this trade-off is an ambitious but worthwhile goal.