If electrode kinetics ape fast and concentration gradients can be ignored, the reaction in a battery electrode is confined to a narrow zone, which moves through the electrode as the battery is discharged. During this process, the ohmic resistance increases, and the cutoff potential may signal the end of the discharge. It is desirable to have a matching of the capacity of the electrode (and hence its thickness) with the time t(d) of discharge. Assuming that there is d certain specified separator thickness and that the electrolyte of the separator is the same as that permeating the positive electrode, it is possible to obtain the optimum porosity as a compromise between the desire to have active material present and the necessity to have a conduction path through the pores of the electrode. For a system with a foil negative electrode and an open-circuit potential which is independent of state of charge, this optimum value depends on one principal parameter T = U kappa(s)t(d)/q(+)L(s)(2), one which involves the time of discharge, the open-circuit potential U, the conductivity kappa(s), and thickness L(s) of the separator, and the capacity q(+) per unit volume of solids in the positive electrode. There is one other parameter: the ratio of the cutoff potential to the open-circuit potential. Other parameters are introduced to account for a more complex structure of the battery
Optimization of Porosity and Thickness of A Battery Electrode by Means of A Reaction-Zone Model
Newman, J. (1995). Optimization of Porosity and Thickness of A Battery Electrode by Means of A Reaction-Zone Model. Journal of the Electrochemical Society, 142(1), 97-101.