Overall Semi-Empirical Rate-Law Formulation of a Lithium-Based Cell or Battery

The concept of the overall activation energy barrier to the occurrence of catalyzed chemical reactions involving the chemical species mass transport and intrinsic chemical reaction kinetics has been employed to develop the formulation presented in this paper. In an electrochemical cell, for example, Li_(s)/electrolyte/Li_xCuPc_(s), the overall cell activation energy barrier to the cell performance at a given temperature is expressed in terms of the difference between the cell open-circuit voltage and actual voltage as a function of the cell cathode active material lithium content, x, defined as g-atoms of lithium per g-mole of cell cathode active material. This voltage difference is assumed to account for the resultant sum of the energy barriers associated with the electrochemical reaction polarization at the cell electrode-electrolyte interfaces, lithium ion transport through the cell electrolyte, and lithium transport in the interstitial channels in a cell lithium-intercalating cathode active material, for example; solid copper phthalocyanine, CuPc_(s).

                To observe the trends of the cell current during the cell discharge and charge, computations were performed using the assumed values of some parameters involved in the presented formulation. The computed data are shown in the form of dimensionless quantities representing the cell discharge and/or charge currents as a function of lithium content in a cell, such as: Li_(s)/electrolyte/Li_xCuPc_(s) for some assumed parametric values. However, it is strongly recommended for the determination of various parameters involved in the formulation through a carefully designed experimental program for obtaining a practical cell performance model.