Deformed Butler–Volmer Models for Convex Semilogarithmic Current-Overpotential Profiles of Li-ion Batteries

The Butler–Volmer (BV) equation links the current flux crossing an electrochemical interface to electric potential drop across it with assumption of Arrhenius kinetics and Boltzmann factor. Applying semilogarithmic Tafel analysis in which logarithm is plotted vs overpotential, one expects straight lines from fundamental reaction rate kinetic process can be computed. However, some Li-ion battery data, focus here, show nonlinear convex profiles that cannot adequately fitted standard BV model. We propose instead two deformed models for such types behaviors constructed superposition cells exhibiting only local equilibrium thus giving rise power-law q-exponential κ-exponential functions. Non-Boltzmann distributions have been successfully employed modeling a wide spectrum physical systems nonequilibrium situations, but not yet batteries. verify validity on experimental data obtained LiFePO4 Li–O2