Multi-Species, Multi-Reaction Model for Porous Intercalation Electrodes: Part I. Model Formulation and a Perturbation Solution for Low-Scan-Rate, Linear-Sweep Voltammetry of a Spinel Lithium Manganese Oxide Electrode

We formulate and implement a porous electrode model that includes multiple lithium-insertion species and associated electrochemical and homogenous reactions. This multi-species, multi-reaction (MSMR) model can account for the multiple current peaks observed in voltammetry data at slow scan rates and is also consistent with X-ray diffraction analysis of several different electrode materials. The MSMR model is used to simulate linear-sweep voltammetry data of a porous electrode of spinel lithium manganese oxide at different scan rates, and an analytic solution to these equations at very slow scan rates is given, based on a perturbation analysis. The greatest sensitivity at these slow scan rates is to the thermodynamic parameters, because the electrode is close to a state of dynamic equilibrium. The poor sensitivity to transport parameters means that it is not possible to distinguish between transport effects and a small amount of hysteresis that could be present in the slow-scan voltage measurements. These facts are illustrated using both the analytic solution and its comparison to numerical calculations. In Part 2, the analytic solution will be combined with numerical simulations at higher scan rates to complete the fitting process of transport, kinetic and thermodynamic parameters, along with a small amount of hysteresis.