## 4 Discussion  
EIS measurements on a test cell with homogeneous and stratified electrolyte have shown a distinct influence of stratification on the impedance, as it was already observed by [PERSON] et al. [7]. Here the influence was analyzed in more details, as the stratification levels were adjusted and impedance spectra with various superimposed DC-currents were performed. The results from fitting the measured spectra to an EEC have shown a decreased ohmic resistance during stratification in comparison to the reference measurements before and after. With stratification the ionic conductivity of the electrolyte in the top of the test cell was larger than in the bottom. The resistance for the current was already smaller in the top with homogeneous electrolyte, and with stratification this resistance further decreased. Hence, the ohmic resistance of the cell was reduced with stratified electrolyte. This assumption based on the simulation results. With the implemented dependency of \(R_{i,AM}\) on the electrolyte density this decrease of \(R_{oblmic}\) could be reproduced for the first EIS measurements in the EIS set of _Strat. 1_. To the end of this simulated EIS set \(R_{oblmic}\) increased above the values simulated with homogeneous electrolyte during _Ref. 1_. In the simulation a huge difference between the local SoC arose and produced a further increased resistance in the bottom due to the SoC-dependency of \(R_{i,AM}\). This increased resistance dominated the resistance of the cell. It is also an explanation for the larger \(R_{oblmic}\) simulated during _Ref. 2_. In the measurements only the \(R_{oblmic}\) values measured at the end of _Strat. 2_ were bigger, than during the reference measurements. Here an improvement of the model is required. The measured increase of \(R_{ct,neg}\) from _Ref. 1_ to _Strat. 1_ could be reproduced with the concentration dependency of the exchange current \(I_{0}\) in srEEC. Also the increasing difference between _Ref. 1_ and _Strat. 1_ towards charging currents could be simulated, but not in the same quantity as observed in the measurements. The continues increase of \(R_{ct,neg}\) in the measurements with every EIS set, except _Ref. 4_, could not be reproduced in the simulations. [PERSON] et al. have determined the sulfation rate in the active mass of electrodes after cycling in stratified electrolyte with the result that the bottom part of the electrodes were sulfated, while the top part was almost free of sulfate crystals [10]. The simulated low SoC in the bottom and 100% SoC in the top after simulating _Strat. 1_ corresponds to these observations. The accumulated crystals in the bottom generate a higher resistance for the current path and the charge-transfer process, which is considered in the srEEC as well. Over time the accumulated crystals reduce their volume to surface area ratio, as this is energetically more convenient [26]. Because of this grow the dissolution rate of Pb\({}^{2+}\)-ions during charging decreases, so that the charge-transfer resistance in charging direction increased with time. This behavior can be a reason for the measured increase of \(R_{ct,neg}\) and was not simulated in srEEC. The progressing sulfation during the test procedure can be additionally an explanation for the increased \(R_{oblmic}\) at the end of EIS set _Strat. 2_. The beneficial effect of the stratification on the conductivity of the electrolyte is rescinded by the increasing sulfation. The decrease of \(\zeta\) at the end of the test procedure denotes an stronger inhomogeneity in the cell generated by the sulfation, because \(\zeta\) decreases with increasing inhomogeneity [16]. The measured results of _Ref. 4_ provide a further confirmation of the previous sulfation process. All resistance values decreased after the full-charge to values similar to them in _Ref. 1_, because the full-charge dissolved the sulfate crystals and cleared up the surface area for the charge-discharge reaction. The characteristic change of impedance could be also observed during cyclic aging tests [17].