Model Formulation and Simulation of a Solid-State Lithium-Based Cell

The analytical formulation presented here is an attempt to predict the performance of a lithium anode/lithium-insertion cathode cell.  Specifically, the transient dimensionless lithium-ion concentration profiles, to observe the lithium-ion penetration into a cathode active material particle, can be computed for a cell whose performance is controlled by the lithium ion diffusion in the cathode active material during the cell discharge period.  The voltage loss associated with the lithium-ion diffusion can be analytically determined.  The formulation also provides analytical expressions for the calculation of the reversible cell voltage, voltage loss associated with the lithium-ion transport in the electrolyte, electron transport in the carbon conductor of the cathode composed of an active material, carbon and electrolyte, and the voltage loss due to the lithium-ion transport in the electrolyte separating the cell electrodes.  The cathode activation polarization (voltage loss), and the actual cell voltage and electric power can be predicted.  To provide examples of the application of the developed formulation, some generated numerical data are also shown in the form of plots.