4.2.2. Pulse Test Evaluation

Figure 8 shows the cell voltage course during the relaxation period and the DRT derived from the time domain data. Again, the values at 20% (upper graphs) and 80% SOC (lower graphs) are given and the same cell as in Section 4.2.1 is evaluated.

**Figure 8.** Measured voltage relaxation and derived DRTs over aging (**a**) At 20 % SOC; (**b**) At 80% SOC.

The voltage courses show a slowdown of the relaxation process as aging progresses. The DRT derived by the time domain data reveals changing parameters of processes with large time constants as the reason. A strong increase of polarization contributions can be observed for low frequencies. Compared to the DRT obtained from frequency domain data, not only a more pronounced increase can be observed. In addition, more processes with large time constants can be identified, since the DRT can also be specified for frequencies that are lower than 1 mHz.

According to Equation (10), the DRT only provides representative values for the frequencies ≤5 Hz. The DRT is cut off accordingly for frequencies above 5 Hz. The process with the smallest time constant shown in Figure 7 (assigned to the SEI) is therefore not visible.

The disappearance of a polarization contribution of a process at moderate frequencies and 20% SOC can be confirmed. The number of processes in the range of moderate frequencies between 0.1 and 5 Hz corresponds to the number determined on the basis of frequency domain data. However, the greater spread of the time constants and the polarization with no discernible trend shows that due to the lower sampling frequency the accuracy is too low to reliably quantize the parameters of the identified processes at moderate frequencies.

4.2.3. Comparison of DRT by Time and Frequency Domain Data

The results of the experimental studies can be summarized as follows:


4.2.4. Correlation of the Capacity and the Identified Process Parameters

Figure 9a shows the capacity course during the aging of a cell and the corresponding polarization contribution of the process with the largest time constant, which is determined by time domain data at 60% SOC. The polarization contribution is referred to below as *Rtaumax* . The results belong to the cell that has already been evaluated in the previous Sections 4.2.1 and 4.2.2.

**Figure 9.** (**a**) Capacity course and polarization contribution *Rtaumax* vs. cycles. (**b**) Correlation between capacity and *Rtaumax* .

For a better overview of the correlation between the two parameters, the development of *Rtaumax* is plotted over the capacity. A strong negative correlation can be found for ≥2250 cycles. During the first cycles, the increase in polarization in relation to the capacity fade is less pronounced. Regardless of which scenario, a significantly weaker increase in *Rtaumax* could be confirmed for all cells at the beginning of the aging tests. Thus, the average correlation coefficients *Ccoef f* for each scenario and for the cycles ≥2250 are given in Table 3.


**Table 3.** Different operating conditions.

Taking into account the measurement data only for cycles ≥2250, a Pearson correlation coefficient of ≥98% can be specified for scenarios *Sc*1 and *Sc*3, which indicates a high negative correlation between the two parameters. For scenario *Sc*2, the correlation is weaker, but still noticeable.

Figure 10 shows the capacity courses over the cycles for all cells examined.

**Figure 10.** Capacity course vs. cycles during the long-term cycling.

For scenario *Sc*2, a recovery of cell capacity can be seen. After 2250 cycles, the capacity remains relatively constant at around 48 A h. Because of the flat curve, the accurate correlation is more difficult to determine because of the corresponding small changes in polarization *Rtaumax* are difficult to detect. This could be one reason why the correlation coefficient is lower in scenario *Sc*2.

To further investigate the reasons for the lower correlation coefficient, the correlation between the capacity of the anode and the polarization *Rtaumax* was determined. The determination of the loss of active material at the anode (LAMAn) on the basis of the non-invasive measurements during the checkups was carried out in [27]. The correlation between the LAMAn and *Rtaumax* was ≥ 96% for each cell of scenario *Sc*1 from cycle 0 to 9050. Taking into account the uncertainties in the estimation of the LAMAn, 96% is a high value and it can be stated that the increase in *Rtaumax* is associated with the LAMAn. For all cells of scenario *Sc*1 the decrease in capacity at the anode was more pronounced compared to the cells of *Sc*2. Gantenbein et al. has already experimentally confirmed a higher LAMAn for cells that were cycled at SOC levels above 65%, while the LAMAn for cells that were cycled below 45% was neglible [31]. The lower LAMAn provides a further reason for the lower correlation in *Sc*2 and the lower capacity fade during aging. For the cells of *Sc*3, the LAMAn after 3850 cycles could not be determined due to a change in the electrode balance [27]. According to the results of [31] a comparatively high LAMAn is to be expected. This statement is supported by the correlation factor determined for scenario *Sc*3 (see Table 3).

In contrast to the correlation to the cell capacity (see Figure 9), the linear relationship between LAMAn and increase in *Rtaumax* is visible from the first few cycles of the longterm test. It is known from the literature that the cell capacity can be limited by different degradation mechanisms in different aging stages of a LIB (e.g., [35,36]). In a previous

publication, the loss of lithium inventory (LLI) was identified as the main aging mechanism during the first few cycles of the aging study described [27]. The LAMAn becomes the limiting factor for the capacity of the cells of scenarios *Sc*1 and *Sc*3 after 2250 cycles. Therefore, a correlation between the cell capacity and the *Rtaumax* only becomes visible after 2250 cycles. It is thus assumed that the correlation between the cell capacity and *Rtaumax* originates from the correlation of LAMAn and *Rtaumax* .
