Ion Transport in an Electrochemical Cell: A Theoretical Framework to Couple Dynamics of Double Layers and Redox Reactions for Multicomponent Electrolyte Solutions

TL;DR

This paper develops an asymptotic theoretical model for ion transport in electrochemical cells that couples double-layer dynamics and redox reactions, enabling efficient and accurate simulations of multicomponent electrolytes.

Contribution

The authors derive a novel asymptotic model that integrates double-layer formation and redox reactions for multicomponent electrolytes, overcoming limitations of previous simplified approaches.

Findings

Model shows excellent agreement with numerical simulations.

Redox reactions influence double-layer charging at short times.

The framework is computationally efficient and stable for large potentials.

Abstract

Electrochemical devices often consist of multicomponent electrolyte solutions. Two processes influence the overall dynamics of these devices: the formation of electrical double layers and chemical conversion due to redox reactions. However, due to the presence of multiple length and time scales, it is challenging to simulate both processes directly from the Poisson-Nernst-Planck equations. Therefore, common modeling approaches ignore one of the processes, assume the two are independent, or extrapolate the results from reaction-free systems. To overcome these limitations, we formulate and derive an asymptotic model by solving the Poisson-Nernst-Planck equations for an arbitrary number of ions in the thin-double-layer limit. Our analysis reveals that there are two distinct timescales in the system: double-layer charging and bulk diffusion. Our model displays excellent quantitative agreement with direct numerical simulations. Further, our approach is computationally efficient and numerically stable, even for large potentials. We investigate the dynamics of charging for a binary electrolyte and three-ion system, and find that redox reactions impact the double-layer charging process at short times whereas they modify the double-layer capacitance at long times. Overall, the proposed theoretical framework advances our ability to simulate electrochemical devices that contain multiple ions and widens opportunities for future research in the field.