A mathematical model for intercalation electrode behavior I. Effect of particle-size distribution on discharge capacity

A mathematical model is presented to study the effect of the particle size distribution (PSD) on the galvanostatic discharge behavior of the lithium/separator/intercalation electrode system. A recently developed packing theory has been incorporated into a first-principles model of an intercalation electrode to provide a rational basis for including the effect of PSD on packing density. The model is used to investigate how binary mixtures of spherical particles affect electrode capacity. The electrode capacity of an insertion electrode is calculated for various parameters including applied current density, thickness of the electrode, and volume fraction, size, and size ratio of the particles. The model shows that an electrode comprised of two different sized particles can have a significantly higher capacity than an electrode consisting of single-sized particles. However, increasing the packing density increases the liquid-phase diffusion resistance. As a result of the trade-off between packing density and liquid-phase diffusion resistance, discharge capacity can be optimized by adjusting the particle size, volume fraction of large and small particles, and the size ratio. Pulse discharge of an intercalation electrode comprised of two different sized particles shows a marked difference in transient behavior from that of an electrode which has single-sized particles. Since there are many parameters which control the performance of the electrode, use of this model should aid greatly in making superior electrodes.