(Carl Wagner Memorial Award of the Electrochemical Society) Mathematical Modeling of Electrochemical Systems

Abstract

In order to understand and accurately predict the behavior of electrochemical materials, devices, and systems, it is necessary to develop sophisticated mathematical models that consider, for example, transport processes, electrochemical phenomena, thermal and mechanical stresses, and structural changes during operation. This insight aids in the design and operation of electrochemical systems for a particular application. This talk will review some of the mathematical models that we have developed to predict the behavior of electrochemically active materials, fuel cells, electrolyzers, and batteries. In particularly, I will discuss the mathematical models we have developed to better understand the effect of volume change on the behavior of batteries. There are many models in the literature that can predict the electrochemical performance of batteries (e.g., voltage versus time) under a variety of operating (e.g., current) and design (e.g., electrode thickness) conditions. However, existing models do not consider how stresses can build up in the system as the expanding porous electrode is being constrained by the battery casing. Here I show predictions of the dimensional and porosity changes in a porous electrode caused by volume changes in the active material during intercalation (e.g., lithium into carbon or silicon). Porosity and dimensional changes in an electrode significantly affect the resistance of the battery during cycling. In addition, volume changes generate stresses in the electrode, which can lead to premature failure of the battery. Material conservation equations are coupled with the mechanical properties of the porous electrode to derive governing relations that link dimensional and porosity changes to stresses that occur during the intercalation process. The stress-strain relationships used in this model, which are needed to predict porosity and dimensional changes, have been established by examining the similarities between thermal rock expansion (e.g., the exchange of thermal energy with the rock) and electrode expansion due to intercalation.