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In mathematical models of lithium-ion batteries, the highly heterogeneousporous electrodes are frequently approximated as comprising spherical particlesof uniform size, leading to the commonly-used single-particle model (SPM) whentransport in the electrolyte is assumed to be fast. Here electrodeheterogeneity is modelled by extending this to a distribution of particlesizes. Unimodal and bimodal particle-size distributions (PSD) are considered.For a unimodal PSD, the effect of the spread of the distribution on the celldynamics is investigated, and choice of effective particle radius whenapproximating by an SPM assessed. Asymptotic techniques are used to derive acorrection to the SPM valid for narrow, but realistic, PSDs. In addition, it isshown that the heterogeneous internal states of all particles (relevant whenmodelling 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 phosphatewith a bimodal PSD show that the DPM captures an experimentally-observeddouble-plateau in the discharge curve, suggesting it is entirely due tobimodality.

Modelling electrode heterogeneity in lithium-ion batteries: unimodal and bimodal particle-size distributions