Mathematical modeling of interdigitated electrode arrays in finite electrochemical cells

TL;DR

This paper develops theoretical models for interdigitated electrode arrays in finite electrochemical cells, providing bounds, response times, and criteria for when finite and semi-infinite behaviors are similar, validated by simulations.

Contribution

It introduces new theoretical expressions and bounds for finite cells, extending existing semi-infinite models, and offers criteria to compare finite and semi-infinite cell behaviors.

Findings

Derived lower and upper bounds for diffusion-limited current in finite cells.

Provided expressions for transient and steady-state concentration profiles.

Validated theoretical results through simulations.

Abstract

Accurate theoretical results for interdigitated array of electrodes (IDAE) in semi-infinite cells can be found in the literature. However, these results are not always applicable when using finite cells. In this study, theoretical expressions for IDAE in a finite geometry cell are presented. At known current density, transient and steady state concentration profiles were obtained as well as the response time to a current step. Concerning the diffusion limited current, a lower bound was derived from the concentration profile and an upper bound was obtained from the limiting current of the semi-infinite case. The lower bound, which is valid when Kirchhoff's current law applies to the unit cell, can be useful to ensure a minimum current level during the design of the electrochemical cell. Finally, a criterion was developed defining when the behaviors of finite and semi-infinite cells are comparable. This allows to obtain higher current levels in finite cells, approaching that of the semi-infinite case. Examples with simulations were performed in order to illustrate and validate the theoretical results.