## 6 Results and Analysis
### Post-Fitting Parameter Analysis  
The results of the post-fitting of the proposed equivalent circuit are shown in Figure 9. The double-layer capacitance and charge-transfer resistance, as well as SEI, are most influenced by aging. Here R\({}_{\text{ct}}\) increases, while R\({}_{\text{SEI}}\) slightly decreases as a function of the number of cycles for all the battery cells. The parameters of the IS show a systematic behavior but are pretty different from one cell to another, even if the cells are of the same type. Figure 9: _Cont._  
this dependence is non-linear. Furthermore, its influence dominates at low frequencies, which are affected by systematical deviations. This deviation heavily influences other parameters, namely the alpha-coefficient of the double-layer CPE, the capacitance and alpha-coefficient of the diffusion CPE. On the other hand, the SEI capacitance and its corresponding alpha-coefficient show less dependency on SoH, as shown in Figure 10b. In fact, the diffusion capacitance (CPE_diff), which exponentially increases due to the film layer forming, is analogous to the increase of the Warburg element depicted in [4]. As more electrons deposit on the SEI layer, the capacitance of the SEI layer also increases (CPE_SEI). On the other hand, the alpha coefficients of SEI (\(\alpha_{\text{CPE\_SEI}}\)) and of the diffusion (\(\alpha_{\text{CPE\_diff}}\)) are quasi-constant around 0.5. Due to the model which encapsulates both electrodes into one modified [PERSON] circuit, the alpha-coefficient of the double layer (\(\alpha_{\text{CPE\_diff}}\)) is higher than 1. As more electrons are deposited on the pores of the electrodes, the porosity is shrinking during cycling, which explains the decreasing value of the alpha-coefficient. Therefore, the consideration of individual model parameters is not sufficient. From all parameters, charge transfer and double layer capacitance show the highest sensitivity to aging. As the resistance values mainly influence the impedance spectrum, they are less prone to model mismatch and tuning problems: They tend to have more linear behavior than the CPE element's capacitance and alpha-coefficient. However, the SoH estimation from the resistances alone cannot be generalized: The parameters are mainly dependent on the batteries shaped during the first cycles of the batteries, making different offsets in \(\text{R}_{\text{ct}}\) vs. the number of cycles in figure. Furthermore, the aging coefficient seems to be also dependent on the cells, which makes the slope of \(\text{R}_{\text{ct}}\) vs. the number of cycles also different, as shown in Figure 9.  
To quantify the contributions of electrons in SEI and charge transfer, Equation (4) is applied. Figure 11 shows that the ratio of charge-transfer electrons \(\text{R}_{\text{ct}}\) to total charge-transfer electrons and SEI concentration (\(\text{R}_{\text{ct}}+\text{R}_{\text{SEI}}\)) increases with the number of cycles. This is due to the growth of the SEI layer over the cycles. Simultaneously, the ratio of REI to (\(\text{R}_{\text{ct}}+\text{R}_{\text{SEI}}\)) decreases from 99.52% to 80.17% by the 400 th cycle, at an average rate of 0.02% per cycle, for cell 1. By checking the four cells' behavior, the same pattern of the electrons' contribution in charge transfer, corresponding to the contribution of \(\text{R}_{\text{SEI}}\) to the total resistances in the charge transfer and SEI layer, can be seen in cells 1 and 4, as shown in Figure 12. Cell 2 and 3 exhibit similar behavior while still decreasing, is still different from cells 1 and 4. This is due to the fingerprint to each cell, with cells 1 and 4, respectively cell 2 and 3, sharing a similar cell voltage profile behavior as shown in Figure 6. However, it is also shown that  
Figure 11: Contribution of REI, respectively \(\text{R}_{\text{ct}}\) to \(\text{R}_{\text{ct}}\)+\(\text{R}_{\text{SEI}}\) for cell one as a function of the number of cycles. this method can only work starting from the 50 th cycle, to which the battery's internal chemical architecture is shaped.