Overlimiting Ion Transport and Reaction Limitations in Charged Porous Media

Abstract

Electrochemical reaction rates are controlled by both interfacial charge-transfer kinetics and reactive-ion transport. In charged porous media, fixed charges enrich reactive counterions near pore walls, enabling transport beyond the classical diffusion limit via surface conduction (SC). Under overlimiting conditions, classical Butler-Volmer kinetics predict indefinitely increasing current with overpotential, contrasting with microscopic electron-transfer theories, which impose a finite reaction-limited current. Here, we couple the one-dimensional leaky membrane model to coupled ion-electron transfer (CIET) kinetics to examine the interplay between transport and reaction limitations. The limiting behavior is governed by the scaled surface charge $(\tilde{\rho}_s)$ and a Damk\"ohler number $(Da)$ comparing reaction-limited and diffusion-limited currents. We derive analytical limiting-current expressions for neutral, positive, and negatively charged porous media, mapping underlimiting-to-overlimiting transitions in the $(Da,\tilde{\rho}_s)$ plane. By preventing reactive-ion depletion, SC restores polarization-curve sensitivity to charge-transfer kinetics that would otherwise be obscured by diffusion limitation. Fitting to published Cu electrodeposition data in charged AAO membranes yields $Da\approx24$. CIET parameters fitted to AAO($-$) also describe AAO($+$) and predict a finite AAO($-$) reaction limit beyond the applied voltage range. These results provide a framework for distinguishing transport-limited and reaction-limited responses in electrochemical systems and establish charged porous media as platforms to reveal electrochemical reaction-kinetic descriptors.