## 2 Materials and Methods  
### Lead-Acid Test Cells and Measurement Equipment  
The lead-acid test cells consisted of one negative plate enclosed by two positive plates with separator bags. The plates and the separator bags were taken out of a commercial lead-acid starter-battery, wherein they were formatted by the manufacturer. Two lead wires (99% lead, 4 mm thickness) per plate were welded on the lug of the plates, one wire for the current flow and the other to measure the voltage. Shrink tubes around the wires prevented short circuits. With this 4-point measurement configuration, the measured impedance of the electrodes did not contain the impedance of the wires or the welding spot.  
PVC boxes were used as test cell housing and were filled with 1250 mL of sulfuric acid with a density of 1.28 g -cm\({}^{-3}\)\(\pm\) 0.02 g -cm\({}^{-3}\). The nominal capacity of the test cells was 10 Ah, which is the nominal capacity of the commercial battery (70 Ah) reduced by the ratio of plates in the test cell and the commercial battery (8 negative and 7 positive plates). All capacity-dependent values are related to the nominal capacity of 10 Ah here. The current rates are given here as a multiple of the I\({}_{20}\) rate, which is the current to discharge the nominal capacity within 20 h, here 0.5 A.  
To avoid stratification of the acid during the aging tests, the cells were equipped with a mixing system, illustrated in Figure 1. The PVC box has two small side compartments and the main compartment containing the plates. The walls separating the compartments are perforated. The holes at the top and the bottom of the walls are open, while the other holes are closed. Air is pumped over a PVC tube into the left compartment. The ascending air bubbles transport the higher concentrated acid from the bottom of the compartment to the top. This movement of the acid provokes the suction of the acid from the bottom of the main compartment to the left compartment and generates a circulation of the acid in the test cell. This system mixed the whole volume within 15 min.  
The test cells were equipped with a hydrogen reference electrode _HydroFlex_ from _Gaskatel_ for a pH range from \(-2\) to \(16\), which is suitable for temperatures from \(-30\,^{\circ}\) C to 200 \({}^{\circ}\) C. With the reference electrode, the impedance of the negative electrode was measured separately from the impedance of whole cell. The acid-resistant temperature sensor AD590 from _Digatron_ with a range of \(-30\,^{\circ}\) C to \(100\,^{\circ}\) C and an accuracy of \(\pm 1\,^{\circ}\) C measures the acid temperature in a side compartment. The test cells were connected to a _Digatron_ test rig (MCT 10-06-12 ME), which can set voltages between 0 and 6 V (\(\pm 0.2\%\) accuracy) and currents up to \(\pm 10\) A. For _EIS_, the _EISmeter_ of the company _Digatron_ was used. The _EISmeter_ has a measurement range from 0.3 to \(3000\,\Omega\) with an accuracy of \(\pm 1\%\) for the impedance amplitude and \(\pm 1^{\circ}\) for the impedance phase shift. It stimulates the cell with a sinusoidal current and measures the voltage response. The current amplitude is controlled by the voltage response amplitude such that the voltage amplitude does not exceed a maximum value, which is set to 1.5 mV.