Modelling Li Ion Battery Electrode Properties

In recent years, interest in using lithium-ion (Li-ion) batteries as power sources for a wide range of devices (particularly portable devices) has grown significantly. There is thus a real need to understand at a fundamental level a wide range of battery performance criteria (energy density, power density, safety, durability, cost). Our working group considered how to model the fundamental electrochemistry and transport of a simple Li-ion battery to obtain several basic mathematical results. We considered both a dilute-ion model for the electrolyte, as well as a model which assumes that Li ions are present in abundance (in excess). Both models assume Butler-Volmer interface reaction kinetics between the electrolyte and the solid electrodes (anode or cathode), and both are homogenized to obtain macroscale results. We also carried out a Monte Carlo simulation for transport in the solid electrode assuming that the electrolyte is a prefect conductor. This report is divided into six sections: The next section presents a first-principles derivation of a mathematical model for ion transport and reaction kinetics in a simple porous-electrode battery (cf. Figure 1). Ion transport is by advection and diffusion, and the assumptions are appropriate for dilute ion concentrations. The standard charge-neutrality assumption is made in the electrolyte except in a narrow Debye layer near the solid electrode. The Debye layer is accounted for by a Butler-Volmer interface (boundary) condition. The model system is next non-dimensionalized, simplified and averaged to obtain integrals for the total current produced by the cell. Details of this averaging are presented in an appendix.