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The Butler-Volmer (BV) equation links the current flux crossing anelectrochemical interface to the electric potential drop across it with theassumption of Arrhenius kinetics and the Boltzmann factor. Applying thesemilogarithmic Tafel analysis in which the logarithm of current is plotted vs.the overpotential one expects straight lines from which the fundamentalreaction rate of the kinetic process can be computed. However, some Li-ionbattery data, which is the focus here, show nonlinear convex profiles thatcannot be adequately fitted with the standard BV model. We propose instead twodeformed BV models for the analysis of such types of behaviors constructed fromthe superposition of cells exhibiting only local equilibrium and thus givingrise to the power-law $q$-exponential and $\kappa$-exponential functions.Non-Boltzmann distributions have been successfully employed for the modeling ofa wide spectrum of physical systems in nonequilibrium situations, but not yetfor batteries. We verify the validity of the deformed BV models on experimentaldata obtained from \ce{LiFePO4} and \ce{Li}-\ce{O2} batteries.

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