(33d) 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.