## 2 Materials and Methods
### Measurements and Aging Tests  
As an initial process, all test cells were fully charged via constant-current-constant-voltage charging (5I\({}_{20}\), 2.6 V) for 30 h at 25 \({}^{\circ}\)C. After a pause of 4 h, the test cells were discharged with \(-\)4I\({}_{20}\) until the voltage reached 1.8 V to determine a capacity value. The test cells were recharged afterward for 24 h with the same charging strategy followed by a second pause of 24 h. Subsequently, the SoC was set to 80% with \(-\)2I\({}_{20}\). After a 5 h rest period, impedance spectra were measured with superimposed DC currents of \(\pm\)4.5I\({}_{20}\), \(\pm\)1.5I\({}_{20}\), \(\pm\)8I\({}_{20}\), \(\pm\)3I\({}_{20}\), \(\pm\)1I\({}_{20}\), \(\pm\)6I\({}_{20}\), and again \(\pm\)4.5I\({}_{20}\) at the end. The test cells were alternately discharged and charged with the denoted current rates by 5% of the nominal capacity. For every current rate, this cycle was performed twice. The _EIS_ started after \(\pm\)1% was charged or discharged. This method is described as a mini-cycle technique by [PERSON] et al. [13] and was optimized by [PERSON] et al. [17]. Impedance spectra were recorded with 8 frequencies per decade. The measurement started with the maximum frequency of 6 kHz and ended with the minimum frequency of 3 Hz for \(\pm\)8I\({}_{20}\) and 6 mHz for \(\pm\)1I\({}_{20}\). The measurement duration and therefore the number of frequencies were limited by the maximum SoC change of 5%. The measurement of impedance spectra was repeated for 40% and 0% SoC. The initial process is shown in Figure 2.  
Two cycling tests were performed on the test cells. The first cycling aging test, named here _hard AK3.4_, is based on the cycling test _AK3.4_, which is a standard aging test for starter-batteries for micro-hybrid applications [18]. It produces hard sulfation on the negative electrode, which is the reason for the capacity decay. A minimum SoC of 50 % was set for the cycling with \(-\)5I\({}_{20}\). One cycle started with 40 min charging with \(+\)7I\({}_{20}\) and a voltage limit of 2.4 V and ended with 30 min discharging with \(-\)7I\({}_{20}\). In total, 85 cycles were performed, which involved 15 charge and discharge cycles of full nominal capacity (full cycles equivalent (FCE)). After cycling, the residual capacity was discharged with \(-\)4I\({}_{20}\) until 1.8 V was reached. This residual capacity \(C_{res}\) was recharged again with a constant-current-constant-voltage charging (5I\({}_{20}\), 2.6 V). Subsequently, the cycling starts again. During the test no full charge of 24 h is performed to speed up the aging process, as a full charge would dissolve the sulfate crystals. Five hours after cycling and 5 h after recharging, _EIS_ was performed in the same way as that of the initial process. With these _EIS_ measurements recorded after different pre-histories (after cycling and after recharging), the dependency of impedance on the treatment of the cell could be analyzed. No defined SoC was set for the measurement of the impedance, as a full recharge would therefore be required. Figure 1: On the left side, the lead-acid test cell in a PVC box is equipped with a reference electrode and a temperature sensor. Air is pumped into the left side compartment and the ascending air bubbles mix the acid. The electrodes are connected in a 4-point measurement configuration for _EIS_. On the right side, a schematic representation of connections with the testing apparatus is shown. Due to the fact that other research groups working with lead-acid batteries obtain impedance spectra without a superimposed DC-current [6; 8; 9; 19], impedance spectra without a superimposed DC-current were additionally obtained for comparison. These spectra were recorded at the end of the 5 h rest periods after cycling and after charging. The spectra are difficult to interpret, so the results and the reason for the issue of not being interpretable are presented in Appendix A. The spectra without a superimposed DC-current are not considered further in the discussion.