Effective Measures of Thickness Evolution of the Solid Electrolyte Interphase of Graphite Anodes for Li-Ion Batteries

Upon forming, the intensity or thickness of the solid electrolyte interphase (SEI) in a Li-ion battery (LIB) evolves to various states depending on the cell materials and operation conditions. Despite a crucial role in comprehending the behaviors of an LIB, its quantitative measure is far from satisfactory mainly because of the undue complexity of the concentration profiles of the comprising chemical species. Here, we calculate the depth profiles of atomic mole fractions of C and F and their ratio as R_C/F = C/F of graphite anodes for LIBs in comparison to an X-ray photoelectron spectroscopy (XPS) experiment. To this end, we take a differential equation approach to dC/dt*, where t* is the reduced XPS etching time for depth. As a result, the respective analytical expression derived for C, F, and R_C/F(t*) is verified to accurately account for the experiment. Moreover, we show that R_C/F(t*) in the j state can be practically expressed in $$, where γ is a constant for a given anode. Based on this, we suggest ξ^* = (α + β - β)/α as a measure of the SEI thickness evolution from the i to j state in terms of the cycle number. As an intriguing finding, the SEI thickness evolves up to about 3 times that of its initial state, beyond which it does not appear to grow any more.