Impact of Concentration-Dependent Transport Properties on Concentration Gradients

The growing demand for improved batteries underscores the importance of measuring and un- derstanding ion transport within electrolytes. Concentration gradient visualisation approaches have been proposed to characterise electrolyte transport properties by fitting experimentally measured ion concentration gradients with Newman’s ion transport model to extract diffusion coefficient and cation transference number. 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 all con- centration visualisation methods is the assumption that transport properties remain invariant across the measured concentration gradient. In this study, we address this limitation by em- ploying perturbation theory to derive a hierarchical asymptotic solution of ion transport model during polarisation, for the first time accounting for concentration dependence. Our results show that deviations due to concentration dependence are negligible for small input charges. Exper- imental validation using ORGA with a model electrolyte further confirms that these deviations are 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.