Modeling the performance of rechargeable lithium-based cells: design correlations for limiting cases

We use simplified models based on porous-electrode theory to describe the discharge of rechargeable lithium batteries and derive analytic expressions for the cell potential, specific energy, and average power in terms of the relevant system parameters. The resulting theoretical expressions are useful for design and optimization purposes and also can be used as a tool for the identification of system limitations from experimental data. The system treated is an ohmically-limited cell with no concentration gradients having an insertion reaction whose open-circuit potential depends linearly on state-of-charge. Although the slope of the open-circuit potential controls the reaction distribution in the porous electrode, we find that the cell potential is independent of this slope. The results are applied to a cell of the form Li|polymer|LiyMn2O4 in order to illustrate their utility.