MODELING ELECTRODE HETEROGENEITY IN LITHIUM-ION BATTERIES: UNIMODAL AND BIMODAL PARTICLE-SIZE DISTRIBUTIONS

In mathematical models of lithium-ion batteries, the highly heterogeneous porous electrodes are frequently approximated as comprising spherical particles of uniform size, leading to the commonly used single-particle model (SPM) when transport in the electrolyte is assumed to be fast. Here electrode heterogeneity is modeled by extending this to a distribution of particle sizes. Unimodal and bimodal particle-size distributions (PSD) are considered. For a unimodal PSD, the effect of the spread of the distribution on the cell dynamics is investigated, and choice of effective particle radius when approximating by an SPM assessed. Asymptotic techniques are used to derive a correction to the SPM valid for narrow, but realistic, PSDs. In addition, it is shown that the heterogeneous internal states of all particles (relevant when modeling degradation, for example) can be efficiently computed after the fact. For a bimodal PSD, the results are well approximated by a double-particle model (DPM), with one size representing each mode. Results for lithium iron phosphate with a bimodal PSD show that the DPM captures an experimentally observed double plateau in the discharge curve, suggesting it is entirely due to bimodality.

Automated summary

In this study, mathematical models were used to simulate the heterogeneous porous electrodes in lithium-ion batteries by considering the particle size distribution. The results showed that the single-particle model (SPM) could approximate the cell dynamics for a unimodal distribution, while a double-particle model (DPM) was needed for a bimodal distribution. Additionally, the study demonstrated an efficient method for computing the internal states of the electrode particles after simulation.