(Norman Hackerman Young Author Award) Multiphase Porous Electrode Theory
Authors: Smith Raymond B. , Bazant Martin Z. 
Published: February 2020

As batteries become increasingly common and important in products we use in our daily lives, it becomes similarly important to be able to model their behavior at full cell length and time scales. This capability facilitates both their design and use. The diverse applications in which batteries are applied each require careful design optimization in order to provide the most cost-effective solution satisfying the product needs, and experimentally exploring the full design space in order to find the optimum is impractical. Cell models help drastically narrow the space, enabling cost-effective product development. With existing cells, the models can help provide estimates of difficult-to-measurable internal variables, which may inform usage constraints. In order for the models to provide the most value and ability to extrapolate beyond their training data, their underlying physics must be as representative as possible of the real electrochemical system. Porous electrode theory has been developed, validated, and extended for many battery chemistries for decades and serves as the basis for most physical models at full cell length scales. In this work, we continue in that tradition by exploring the incorporation of new models for both the active particles and the interfacial electron transfer reaction kinetics. In the active particles, we employ non-equilibrium thermodynamics, enabling us to consistently describe particles with internal phase separation within a Cahn-Hilliard-type phase field framework. Many practically relevant electrode materials exhibit phase separation during lithium insertion, and various approaches have been used to model these systems, many of which either neglect the details of the resulting concentration profiles or describe the phase interfaces using numerically inconvenient phase boundaries with no interfacial tension. In the phase field approach, phase boundaries appear and disappear spontaneously according to the governing free energy functional without specialized numerical methods for interface tracking, and they naturally structure themselves in energy-minimizing configurations according to their interfacial tension, system stresses, etc. Rather than being a fit input, the equilibrium voltage emerges as a result of the free energy functional and the highly non-uniform concentration profiles as the average system concentration varies. The lithium in the active materials is consistently coupled to the electrolyte phase by variationally defined reaction kinetics, represented either by a generalized Butler-Volmer expression or quantum-mechanical electron transfer theories such as Marcus-Hush-Chidsey kinetics extended for concentrated solutions. This generalization of porous electrode models reduces directly to the more familiar “Newman” model with concentrated solution theory in the electrolyte in the case of solid solution active materials. Here, we will explore the theoretical developments in the model and present relevant examples, with a focus on comparisons with previous models and some experimental evidence in support of the approach.