## 2 Materials and Methods
### Parameterization  
For the parameterization of the srEEC the same EIS set as denoted in Section 2.1 was performed at 90%, 80%, 60%, 40%, 20%, 10% and 0% SoC. At the beginning the test cell was charged for 24 h with constant-current-constant-voltage charging (51\(\mathrm{I}_{20}\), 2.6 V) followed by a pause of 24 h. The single SoC levels were set by discharging with \(-2\) I\({}_{20}\) and a subsequent pause of 5 h. During the measurement the acid was mixed to avoid stratification. These parameterization measurements were performed in parallel to the stratification measurements on another test cell with the same configuration. All impedance spectra of the parameterization measurement were fitted to an equivalent electrical circuit with one resistance connected in series to one RC-element containing the charge-transfer resistance and the double-layer capacitance of the negative electrode. The fitting process is equally performed as described in [17]. The positive electrode parameters were not determined from the spectra, as in most impedance spectra the half-circle of the positive electrode was not adequately visible or affected by time-variant processes. The charge-transfer process and double-layer capacitance of the positive electrode were parameterized from the voltage response during the charging and discharging of 1% SoC before EIS. This voltage response was fitted to an RC-element in time-domain using the function _fit_ in Matlab with default settings. Before, the linear change of voltage (with slope \(m\)), generated by diffusion to the end of the pulse, was subtracted as well as the voltage drop over the ohmic resistance \(R_{ohmic}\) and the charge-transfer resistance of the negative electrode \(R_{ct,neg}\) (see Equation (16)). In Figure 4 this process is illustrated. The values for \(R_{ohmic}\) and \(R_{ct,neg}\) were determined for the present DC-current and SoC from the previous parameterization of these elements. The value for the slope \(m\) was determined by the fitting of a linear function to the last part of the pulse. \[V_{pulse,corrected}(t)=V_{pulse,measured}(t)-I_{DCH}*(R_{ct,neg}(I_{DCH}, SoC)+R_{ohmic}( SoC))-m\cdot t \tag{16}\]  
Because of the current dependency of the charge-transfer resistance this approach is not able to determine the double-layer capacitance correctly [3]. The voltage curve is nonlinear and cannot be described by a linear model. However, for the simulation of the current distribution the resistances are relevant and not the capacitances. This also means that the simulated impedance spectra will differ from the measured spectra in the part of positive electrode. The \(R_{ct}\) values at different DC-currents were used to determine \(I_{0}\) of Equation (3) for the positive and negative electrodes, while \(\alpha\) was set fix to 0.25 for the positive electrode and 0.407 for the negative electrode. The values for \(\alpha\) were determined from previous parameterization process of Butler-Volmer equation with variable \(I_{0}\) and \(\alpha\). However, the resulting \(\alpha\) values were not constant over the DC-currents, which should be the case. Therefore the average of the single \(\alpha\) values were used as fixed value. \(I_{0}\) for negative electrode is only valid for discharging, because the measured \(R_{ct,neg}\) in charging direction could not be described by the Butler-Volmer equation, as already described. The measured SoC and current dependency of \(R_{ct,neg}\) in charging direction is described with the surface polynomial function in Equation (17) with the local currents \(I_{x}\) and local SoC values \(SoC_{x}\).