Modeling a porous intercalation electrode with two characteristic particle sizes

A mathematical model of a complete cell containing a porous intercalation electrode with two characteristic particle sizes is presented. Galvanostatic cycling and relaxation phenomena on open-circuit are compared to a cell with a single particle size. Electrodes with a particle-size distribution show modestly inferior capacity-rate behavior in all cases considered in this work. The cycling results exhibit a mismatch in the states-of-charge of the surfaces of the different particle sizes located at the same position in the electrode. The magnitude of this mismatch correlates with the slope of the open-circuit potential vs. state-of-charge curve of the intercalation material. The relaxation on open circuit is substantially faster when the particles are uniformly sized. Asymptotic solutions were developed to aid in the description of the open-circuit behavior in the cases with nonuniform particle sizes. The particle-size distribution has a more pronounced influence on the open-circuit results than on the galvanostatic results.