Investigation of the diffusion phenomena in lithium-ion batteries with distribution of relaxation times

The distribution of relaxation times method (DRT) has been widely used to quantify the numbers and characterize the properties of the physico-chemical processes inside the Li-ion battery (LIB). While most of the published works focused on the mid-high frequency range, the processes in the low frequency area, such as diffusion, have garnered less attention. The difficulties of applying the DRT to the diffusion processes include the more complicated mathematical treatment involved, the unknown influence of the porous electrode on the DRT spectra and the evaluation of the measured impedance with the developed theory. The galvanostatic intermittent titration technique (GITT) has been widely applied to determine the solid diffusion coefficient for the LIB. However, the GITT does not consider the geometry of the active material particles and cannot effectively separate the contribution of the solid diffusion from other processes, such as liquid diffusion. In the present work, a comprehensive theory is developed to investigate the DRT spectra of a LIB with a physics-based impedance model. Furthermore, an analytical expression is developed for the DRT spectra and analyzed in detail. The developed theory can help to determine the solid phase diffusion coefficient with a firm physico-chemical background. Based on the developed theory, the solid diffusion coefficients of the silicon graphite (SiC) and NMC811 are determined with a commercial cell. Besides, the galvanostatic intermittent titration technique (GITT) has been applied to the same cells and the measurement results are compared with that using the DRT method. The comparison indicates that GITT cannot exclude the influence of the liquid diffusion and the solid diffusion coefficients will be underestimated.