Transference Number of Electrolytes at Infinite Dilution

Understanding ion transport in the limit of infinite dilution is necessary for predicting the performance of electrochemical devices. While transport properties like ionic conductivity and diffusion coefficient can be readily extrapolated to zero concentration, establishing a reliable approach for determining the cation transference number with respect to the solvent velocity, t+0, remains a challenge. To address this challenge, we introduce an approach based on Newman's concentrated solution theory and fundamental dilute-limit constraints. We validate the approach using experimental data for a poly(ethylene oxide) (PEO)/ sodium bis(trifluoromethanesulfonyl)imide (NaTFSI) electrolyte and derive a simple quadratic equation relating t+0 to readily measurable transport properties. Our approach has the potential to provide more accurate models of concentration gradients and limiting current in electrochemical systems, thereby improving their use in design and optimization.