Localized fluctuations of electrochemical properties in porous electrodes of lithium-ion batteries: Beyond porous electrode theory

Kurzfassung

Porous media with complex microstructures are often used as electrodes in lithium-ion batteries (LIBs) and in the other (electro-)chemical systems with heterogeneous reactions. In the battery context, important aspects of their behavior during charge and discharge can be described by homogenized models based on porous electrode theory (like a widely used DFN model). These models use a number of intuitive assumptions that allow neglecting a detailed microstructure description; these assumptions have been partially confirmed using rigorous mathematical homogenization procedures. Microstructure-resolving simulation results have been published recently that hint to the existence of spatially localized fluctuations of overpotential and concentration in porous electrodes that cannot be seen in DFN. Proper account of such fluctuations may be important for the phenomena strongly affected by the concentrations and potentials locally (like various aging processes). Here, we present the results of a new mathematical framework utilizing perturbation theory with small parameters that allow accurate standard homogenization of LIBs, but also introduces extensions beyond the standard theory. It will be shown theoretically how the fluctuations in question occur, how to estimate them based on cell characteristics, and to demonstrate the existence of well-defined trends and laws. Numerical simulation results are presented that agree with the main theoretical findings. Current, non-spherical particle shape, particle contacts and OCV slope appear to be the main factors affecting the scale of the local fluctuations. Based on the theory, no physically meaningful homogenization limit exists that sets these fluctuations to zero, which explains why they can be clearly seen in microstructure resolving simulations but not in DFN. The findings presented in this paper are decisive for the development of models extending DFN, preserving its computational robustness and yet fully utilizing all the necessary information about microstructure to capture structure induced local fluctuations.