Rethinking Balance Sheets: A Poisson-Nernst-Planck Based Approach for Modeling Concentration and Flux Profiles Inside an Electrochemical Cell

TL;DR

This paper compares the traditional balance sheet method with the Poisson-Nernst-Planck equations for modeling ion transport in electrochemical cells, demonstrating the latter's greater physical accuracy and broader applicability.

Contribution

It introduces a first-principles PNP-based approach to analyze ion transport, improving upon the limited scenarios where the balance sheet method is valid.

Findings

PNP equations offer a more physical and accurate analysis.

Balance sheet approach is valid only in limited cases.

PNP approach can be adopted for broader electrochemical modeling.

Abstract

Electrochemical cells serve as a building block for producing and storing electrical energy from chemical reactions. The analysis of ion transport in these systems forms the foundation for understanding more complex electrochemical systems that are becoming increasingly present in the broader societal energy infrastructure. From a pedagogical perspective, the ``balance sheets" introduced in Chapter 4 of Electrochemical Methods: Fundamentals and Applications by Alan J. Bard, Larry R. Faulkner and Henry S. White (hereafter referred to as BFW) provides a first-pass approach to analyze ion transport in electrochemical cells. However, the balance sheet approach lacks first-principles justifications from the underlying equations that describe the transport processes in electrochemical cells. In this work, we compare a first-principles approach via the Poisson-Nernst-Planck equations to describe ion transport in electrochemical cells to that of the balance sheet approach. By re-working the examples presented in BFW, we illustrate that the balance sheet approach is only valid in limited scenarios. Furthermore, we show that the PNP equations provide a more physical route to analyze ion transport in electrochemical systems. We hope the approach outlined here will be adopted by electrochemical engineering researchers and instructors.