Theoretically quantifying the effect of pre-lithiation on energy density of li-ion batteries

Pre-lithiation plays an increasingly significant role for high-energy Li-ion batteries (LIBs) since it can improve the energy density by compensating the Li loss during the initial cycle. The pre-lithiation related research so far has been focused on the development of materials and methods of pre-lithiation but has lacked theoretical and mathematical descriptions to illustrate the relationship between pre-lithiation and energy density. In this contribution, a series of mathematical formulas are derived to describe the gravimetric and volumetric energy densities of LIBs with pre-lithiation, by which the effects of the important parameters, e.g. the Coulombic efficiencies (CEs) of anode, the capacities of Li sources, etc., on the energy densities are well demonstrated. Then, the developed theory and mathematical formulas are applied to practical LIB systems, i.e. the cell using Li nickel manganese cobalt oxide (NMC) as a cathode and silicon-carbon (Si-C) composite as an anode, to identify possible energy density improvement after pre-lithiation. These systematic formulas with great universality have the potential to give significant guidelines for future studies on the pre-lithiation methods and be useful tools for the design of high energy LIBs with imperfect CEs from fundamental and practical perspectives.