Thermal Modeling of Porous Insertion Electrodes

Isothermal calorimetry was performed on Li|LiPF 6 in ethylene carbonate:dimethyl carbonate|LiAl 0.2 Mn 1.8 O 4-δ F 0.2 cells. The measured rate of heat generation varied substantially with time. To understand why, we investigated the entropy, irreversible resistance, and heats of mixing. Two methods for computing the heat of mixing, one computational and one analytic, are derived. We demonstrate how the energy balance of Rao and Newman accounts for heat of mixing across electrodes, but neglects heat of mixing within particles and in the electrolyte, which may be of equal magnitude. In general, the magnitude of the heat of mixing, which is the amount of heat released during relaxation after interruption of the current, will be small in materials with transport properties sufficiently high to provide acceptable battery performance, with the possible exception of heat of mixing within the insertion particles if the particle radius is large. Comparing simulations of heat generation to calorimetry measurements reseals that the entropic heat is significant and accounts for much of the variation of the rate of heat generation. The rate of irreversible heat generation is larger when the open-circuit potential varies steeply with lithium concentration, because of diffusion limitations within the solid.