Universality Class of Ion-Intercalation Models

A dominant model of intercalation kinetics, the Butler-Volmer relation, predicts polarization curves reasonably well for moderate overpotentials (below 0.3 V). It assumes that the diabatic potential energy surfaces (dPESs) are linear, even though ab initio constrained density functional theory (DFT) calculations show strong deviations from linearity within this voltage range. We prove that the Butler-Volmer kinetics does not require the linearity of dPES; instead, it indicates membership in a universal class of kinetic models satisfying two fairly weak assumptions. A subset of this universality class conceptualizes both intercalation and adsorption at a heterogeneous interface as a spherical object traversing two uniform continua. The assumptions enforce an approximate symmetry, which is used to reduce the number of DFT calculations required to model the potential energy surfaces by half or more. If a specific model in this universality class is empirically fixed, a total of three DFT calculations are required to model the potential energy surfaces of intercalation or adsorption, whereas the corresponding DFT computation reported in the literature requires twenty two.