The formula for peak current density of cyclic voltammogram on spherical electrodes with maximum occupation sites

Cyclic Voltammetry (CV) is essential for elucidating electron and ion transfer kinetics as well as diffusion properties at electrode interfaces. The peak currents in CV, measured at various scan rates, are influenced by ion transport rates, necessitating theoretical formulations for interpretation. Classical models assume simultaneous diffusion of oxidized and reduced species at equal rates within the electrolyte, which limits their applicability to ion-battery systems. In batteries, ion diffusion in electrodes is the slowest kinetic step, and electrode sites are limited, significantly impacting CV peak currents. This study introduces a novel framework to derive the formula for CV peak currents in battery electrodes, considering the finite number of occupation sites. The derived formula markedly differs from classical models and demonstrates robust agreement with finite difference solutions of relevant partial differential equations, enabling precise determination of ion kinetics in spherical electrodes within ion-battery systems.