Faradaic and capacitive charging of an electrolyte-filled pore in response to a small applied potential

Abstract

Electrochemical devices often charge both through Faradaic reactions and electric double layer formation. Here, we study these coupled processes in a model system of a long electrolyte-filled pore subject to a small suddenly applied potential, close to the equilibrium potential Ψeq at which there is no net Faradaic charge transfer. Specifically, we solve the coupled Poisson–Nernst–Planck and Frumkin–Butler–Volmer equations by asymptotic approximations, using the pore’s small inverse aspect ratio as the small parameter. In the early time limit, the reaction–diffusion equations yield an extended Faradaic transmission line model that includes a voltage source, Ψeq, biasing the Faradaic reactions, captured by the resistance RF. In the long-time limit, the pore exhibits a nontrivial potential of zero total charge, Ψpztc=Ψeq1−Ẑ(0)/RF, where Ẑ(0) is the experimentally accessible zero-frequency impedance of the system. This expression provides a new means to measure the Faradaic contribution to Ψpztc experimentally.