Impact of Concentration-Dependent Transport Properties on Concentration Gradients

The growing demand for improved batteries underscores the importance of measuring and understanding ion transport within electrolytes. Concentration gradient visualisation approaches have been proposed to characterize electrolyte transport properties by fitting experimentally measured ion concentration gradients with Newman’s ion transport model to extract diffusion coefficient D and cation transference number t + 0 . We have recently introduced the operando Raman gradient analysis (ORGA) technique, which follows a similar approach combining operando Raman microspectroscopy with electrochemical measurements to visualise the formation of concentration gradients in the electrolytes. However, a theoretical limitation shared by ORGA and most concentration visualisation methods, is the assumption that transport properties remain invariant across the measured concentration gradient. In this study, we address this limitation by applying perturbation theory to derive a hierarchical asymptotic solution to the ion transport model under polarization, thereby accounting for concentration dependence while avoiding the complexity of numerically solving the full Newman model. Our results show that deviations due to concentration dependence are negligible for small input charges and significantly smaller than typical experimental errors. This solution provides robust mathematical support for concentration visualisation methods and enables the direct determination of the concentration dependence of transport properties from a single gradient measurement.