## 4 Discussion

Table 3: Rates on sulfur oxide (\(SO_{4}\)) of negative and positive electrodes at different positions in %. falsified impedance values at frequencies above 100 Hz. It is assumed that a distinct inhomogeneous sulfation of negative electrode continuously changed the current distribution before and during _EIS_. With the presence of lead-sulfate crystals, the probability is higher that newly generated lead-sulfate accumulates on these crystals than the probability of the generation of new small crystals during discharging. During charging, more small crystals are dissolved than large crystals due to the smaller ratio of the surface area and the volume of large crystals [26]. During the aging test, large crystals accumulate at the bottom, so fewer small crystals are generated at the bottom than at the top during discharging. Therefore, the few small crystals at the bottom are dissolved very fast, so the amount of \(Pb^{2+}\) ions decreases quickly at the bottom, while the amount is still sufficient at the top of the electrode. With a low number of \(Pb^{2+}\) ions, the resistance of the charge-transfer process increases. This process moves from the bottom of the electrode to the top. This could be a reason for the permanent change of the state from the beginning of _EIS_ to the end with consequently useless impedance spectra with charging DC-currents. For the discharge direction, the required \(SO_{4}^{-}\) in the acid is adequately available [27], so this effect is not present in the spectra with discharging DC-currents. Single impedance values of different test cells increased at the same rate and had similar impedance values during aging, provided that pre-history, frequency, and DC-current were equal; otherwise, the rates varied. The most critical dependency here is the pre-history, as this is the less controllable factor in the field. The rates of change (see Table 2) measured after cycling were all greater than after charging. This effect was more distinct for lower frequencies, where electro-chemical processes are present. An explanation for this observation is difficult to find considering only single impedance values. To which electro-chemical process the values correspond is unknown. The fitted parameters of the EEC, however, provide a better basis for finding an explanation, as they can be directly linked to an electro-chemical process. \(R_{ablmic}\) shows the same rate of increase for all pre-histories. Only at 80% SoC in the soft AK3.4 test is the increase slower. This is equal to the 1 kHz values. \(R_{ct,neg}\) is also always smaller at 80% SoC compared with after cycling during _soft AK3.4_. Assuming a beneficial effect of the 24 h charging phase in _soft AK3.4_ in the form that large sulfate crystals were partly dissolved, the reduced sulfation provokes reduced resistances for the current flow and the charge-transfer process. This effect seems to disappear during cycling, as the resistances were increased after cycling. Furthermore, the aging tests ended with the voltage drop below 1 V during the cycling phase. The time-constant values \(\tau_{neg}\) determined during _soft AK3.4_ confirms the theory. They decrease with a smaller rate than during _hard AK3.4_. This indicates a slower decrease of the double-layer capacitance and therefore a slower sulfation. Only at the end of the _soft AK3.4_ aging test on \(TC1\) does the time constant measured after cycling become equal to the values of _hard AK3.4_. The fitted values of the _hard AK3.4_ test show a more complex behavior. The time-constant values after charging were greater than after cycling because of the increased \(R_{ct,neg}\) values. They were also greater than during _soft AK3.4_, which indicates a larger double-layer capacitance. Maybe this is an effect of the shorter pause and missing discharge phase between the charging phase and _EIS_ in _hard AK3.4_.