Theory of local fluctuations of ion concentration and potential in porous electrodes

Abstract

Newman and coworkers have developed an electrochemical model of battery with porous electrodes that allows to predict many characteristics of charge-discharge cycle (voltage, potentials in different phases, etc.) quite accurately. The model is computationally effective because it generally neglects the spatial microstructure details, substituting them with averaged or representative features instead. Newman’s model can be derived through application of averaging procedure to the microscopic transport equations that govern the processes in the electrode phases. The applicability of the averaging can be justified within the mathematical framework of homogenization theory or with numerical experiments, in which one compares running averages with the predictions of Newman’s model. There are, however, processes (degradation, including SEI formation, lithium plating, heat generation, etc.) whose proper description requires tracing the local fluctuations of physical quantities on the microscopic level. These fluctuations are averaged out in Newman’s model. One can extract the relevant information from a microscopic numerical simulation, but it is much more computationally demanding. A systematic theoretical understanding of the connection between the fluctuations and the microstructure geometry is missing as well. To bridge this gap in the theory, we are developing an extension of Newman's model that predicts the local fluctuations of ion concentration and potential by combining insights from numerical simulations with mathematical analysis. We will present results on the dependence of the overpotential fluctuations on the shape of active material particles. Our ultimate goal is to produce a model that treats the fluctuations in a statistical manner and requires less computational recourses than the exact microscale model