## 2 Experimental
### Long-Term Cycling
In this paper, this test is presented at room temperature. The evolution of the discharge capacity and the State-of-Health (SoH) of the cell 2 with the number of cycles is illustrated in Figure 1. The capacity loss observed in Figure 1 translates for the ageing of the cells caused by their cycling. The SoH evolution of the cells is based on the recording of their capacity at 25 \({}^{\circ}\)C every 100 FEC. At the level of the electrodes, the measured Equilibrium Potential of the uncycled and cycled NMC positive electrodes are shown in in Figure 2. The Equilibrium Potential of the electrodes dependent on the stoichiometry are in agreement with [22; 32; 33]. Stoichiometry is defined by the amount of \(Li^{+}\) intercalated in an electrode over the maximum amount of \(Li^{+}\) that can be stored that electrode. As in Figure 2, the stoichiometry varies between 0 and 1 representing the x in \(Li_{x}Ni_{0.4}Mn_{0.4}Ca_{0.2}\). The highest Equilibrium Potential value corresponds to the lowest stoichiometry (0) of the electrode. With increasing stoichiometry, the Equilibrium Potential of the uncycled and cycled electrodes are decreasing down to 3 V during the lithiation of the electrodes. Reversely, as the delithiation of the electrodes proceeds the Equilibrium Potential of the electrodes are increasing up to 4.15 V. After long-term cycling, both loss of active material and loss of cyclable lithium are affecting the stoichiometries in the battery cells electrodes [34]. NMC electrodes exhibit lower potential \begin{table}
\begin{tabular}{l l} \hline \hline
**Cells** & **Purpose** \\ \hline Cell 1 & Thermal characterisation at 100\% SoH \\ Cell 2 & Thermal characterisation at 95\% SoH \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Cells testings and purposes. near the maximum stoichiometry in the end of the lithiation process in accordance with [22; 32; 33]. This reflects for a faster lithiation process of cycled electrodes due to ageing. Reversely, higher potential near the minimum stoichiometry is observed for cycled electrodes due to their faster delithiation process. This behaviour leads to an increase in the hysteresis (difference between the Equilibrium Potential associated to the lithiation and the delithiation processes) of the cycled electrodes compared to uncycled electrodes. In Figure 3 (left), the measured discharge capacity of the uncycled and cycled NMC electrodes are illustrated. The cycled electrode exhibit a discharge capacity equal to 5.67 mAh when the initially uncycled electrode show a capacity equal to 5.87 mAh. Conformingly to what expected, the cycled NMC electrode is discharging faster, leading to a lower discharge capacity than prior long-term cycling. The analysis of the incremental discharge capacity (\(dQ/dV\)) of both electrodes in Figure 3 (right) confirms the impact of the long-term cycling on the performances of the initially uncycled electrodes. Indeed, a decrease in the intensity of the peak in the \(dQ/dV\) curve is observed for the cycled electrode as observed in [22; 32]. At the level of the negative electrodes, in Figure 4, the measured Equilibrium Potential of the uncycled and cycled Graphite electrodes are presented. As previously observed for the positive electrode and in agreement with the literature [33; 35; 36; 37; 38], the Equilibrium Potential of both uncycled and cycled electrodes are dependent on their stoichiometry. After long-term cycling, Graphite electrodes exhibit lower potential near the maximum stoichiometry in the end of the delithiation process. This reflects for a faster lithiation process of cycled electrodes due to ageing. Reversely, higher potential near the minimum stoichiometry is observed for cycled electrodes due to their faster delithiation process. These observations are in line with  
Figure 1: Evolution of the discharge capacity and the State-of-Health (SoH) of the cell 2 with the number of cycles. Figure 2: Uncycled and cycled Nickel Manganese Cobalt (NMC) equilibrium potential versus stoichiometry.