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This study investigates the interplay between ion transport and electrochemical reaction kinetics in charged porous media, revealing that surface conduction (SC) allows for transport beyond classical diffusion limits under overlimiting conditions. By coupling a one-dimensional leaky membrane model with coupled ion-electron transfer (CIET) kinetics, the authors derive analytical expressions that characterize the transition between underlimiting and overlimiting behaviors based on the scaled surface charge and Damköhler number. The findings highlight that SC can enhance sensitivity to charge-transfer kinetics, providing a new framework for understanding transport and reaction limitations in electrochemical systems, validated against experimental data from copper electrodeposition in charged anodic aluminum oxide membranes.
Surface conduction enables ion transport to exceed classical limits, fundamentally altering our understanding of electrochemical reaction kinetics in charged porous media.
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.