The overall fitting residue is lower for PDM-3D model, particularly at the lower frequencies. Current fitting tool provides information of Akaike information criterion (AIC) , which suggests that PDM-3D, with a lower AIC values, perform slightly better than PDM model (AIC = -1021 for PDM-3D and AIC = -900 for PDM). However, the uncertainties of the diffusion-related parameters (Table ) has increased likely due to the extra fitting parameter, D3 and θ 2 , are introduced. In conclusion, the original PDW model with two diffusion coefficients is the most practical option. The application of PDM-3D could lead to improved fitting results but with an increasing risk of overfitting and the cost of interpretability. Alternatively, it will be interesting to introduce a probability density function (PDF) of the diffusion coefficient in the PDW to have a better description of the parallel diffusion impedance. This is the same approach as used in the previous work , where a log-normal distribution of the diffusion lengths was introduced in the diffusion model. However, this brings a significant challenge being the determination of the PDF of the diffusion coefficient, which might be achieved through more extensive atomistic simulations. We will explore this topic in our future work. In addition to the fitted result of 4.65 V, all other fitted results can be found in Table . Although they generally show acceptable fitting qualities, the relative error (in brackets) increases with decreasing electrode potentials. This can be attributed to the sluggish kinetics at lower electrode potentials, which deviate from the basic assumptions of PDW. In Figure (a), the charge transfer resistance R ct significantly increases with lower electrode potentials. The application of PDW should avoid SOC regions with sluggish kinetics, occurring often in low SOC or very high SOC regions . In these regions, the assumption related to the solely diffusion-controlled process might be violated. The double layer capacitance C dl shows reasonable values that are in line with the theoretical expectations (10 to 40 µF/cm 2 ). C dl exhibits a steep increase from 4.4 V to 4.6 V, indicating drastic changes in surface conditions of LNMO. It could be related to the major phase transition of LNMO electrodes starting at the same potential window, as shown in the CV, Supplementary Materials (Figure ).