where c is the concentration of the intercalated lithium in the solid, µ(c) is the chemical potential of the intercalated lithium, ϕ +/s represents the lithium-ion electrical potential in electrolyte or solid, a + is the activity of the lithium ions in electrolyte depending on its concentration c + , i denotes the intercalation current density, and R f is the film resistance from degradation. We adopt the general quantum-mechanical framework for intercalation reaction kinetics provided by coupled ion-electron transfer (CIET) theory , which has two simple limits. For fast electron transfer with slow ion transfer ("ion-coupled electron transfer", ICET), the theory predicts classical Butler-Volmer kinetics with quantum-mechanical parameters; in the opposite limit of rate-limiting electron transfer ("electron-coupled ion transfer", ECIT), the theory combines Marcus kinetics with corrections for nonequilibrium thermodynamics of ion transfer . The latter was first proposed as a mechanism for lithium intercalation in lithium iron phosphate , and recently validated by inverse learning from x-ray images , so we assume the ECIT limit of CIET theory for our modeling examples. The results hold generally for other types of CIET reactions, since the concentration dependence, which controls degradation and capacity loss at high filling fractions, does not vary much with different types of intercalation reactions . It is convenient that an accurate approximation of the ECIT rate is available , given by