Electrochemical polarization around metallic particles — Part 1: The role of diffuse-layer and volume-diffusion relaxation

Abstract

We have developed an extension of the theory and mathematical description of the commonly used Wong model of electrode polarization. The full solution of the Poisson-Nernst-Planck system is provided, including three additional unknown coefficients, which describe the microscale polarization response at the surface of a perfectly conducting particle. The model involves two simultaneously acting polarization mechanisms. The first is related to the dynamic charging of diffuse layers induced over the poles of the particles, which relaxes on a time scale proportional to the particle radius and Debye length of the electrolyte solution. The second is a volume-diffusion mechanism, which is activated by reaction currents through the solid-liquid interface, i.e., faradaic currents due to charge-transfer reactions. The relaxation time of the resulting concentration polarization around the particle increases quadratically with the particle radius and the fraction of electroactive cations in the electrolyte. Although diffuse-layer polarization dominates the effective response for small particles and in the absence of reactive cations, volume-diffusion polarization only affects the macroscopic behavior if the particle size exceeds a critical value. From the closed-form analytic expressions for both relaxation times that we used, we derive a critical particle radius that depends on Debye length and reactive cation concentration. Based on the improved understanding of the underlying polarization processes, we also review some recent conceptual models of metallic polarization and correct several physical misconceptions inherent to these reinterpretations of the classic theory.