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

TL;DR

This paper models the coupled Faradaic and capacitive charging processes in an electrolyte-filled pore under a small applied potential, deriving analytical expressions for the potential of zero charge and proposing a new experimental measurement method.

Contribution

It introduces an asymptotic approximation-based model for coupled electrochemical processes in pores, revealing the potential of zero charge influenced by Faradaic reactions.

Findings

Derived an extended Faradaic transmission line model including a voltage source.

Provided an explicit expression for the potential of zero charge considering Faradaic effects.

Suggested a new experimental approach to measure Faradaic contributions to the potential of zero charge.

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 $\Psi^\text{eq}$ 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, $\Psi_\text{eq}$, biasing the Faradaic reactions, captured by the resistance $R_F$. In the long-time limit, the model exhibits a nontrivial potential of zero charge, $\Psi_\text{pzc} = \Psi_\text{eq}[1 - \hat{Z}(0)/R_F]$, where $\hat{Z}(0)$ is the experimentally accessible zero-frequency impedance of the system. This expression provides a new means to experimentally measure the Faradaic contribution to $\Psi_\text{pzc}$.