The Distribution Function of Differential Capacity as a new tool for analyzing the capacitive properties of Lithium-Ion batteries

The Distribution Function of Differential Capacity (DDC) is introduced as a supportive method for analyzing the capacitive tail in impedance spectra, which is related to the solid state diffusion of species into/out of battery electrodes. The DDC provides insight into the individual time-dependent utilization of differential capacity, as charging/discharging occurs in different electrode compositions, structures, particle sizes or blends thereof with different time constants. The aggregate differential capacity of an electrochemical system is decomposed by (i) measuring the electrode's impedance spectrum, (ii) computing the complex capacity spectrum, and, (iii) computing its distribution function DDC. This paper presents the mathematical derivation of the DDC and shows, using a simplified electrode model, how individual capacity contributions and associated time constants become accessible.