## 3 Results and Discussion
### Temperature Homogeneity in the Battery Pack  
Apart from the average (maximum) temperature of the pack, it is of high importance to keep the temperature differences between the individual cells low. Figure 4 shows the evolution of the maximum temperature difference of the cells in the use/charge cycle for the different investigated materials, as well as the temperature distribution in the cells shortly after the use phase.  
For all of the cooling materials and phases used, the cells are cooler at the corners than at the center (Figure 4a). Compared to the reference, all the solid cooling materials significantly reduce the maximum temperature difference in the cells. Shortly after the maximum temperature is reached, the temperature difference is the highest. The difference is 2.4 \({}^{\circ}\)C for heat-conductive polymer I, 2.6 \({}^{\circ}\)C for heat-conductive polymer II, 2.9 \({}^{\circ}\)C for the latent heat storage material (the maximum difference is reached shortly after the start of cool-down phase I for all three materials), and 5.2 \({}^{\circ}\)C for the reference (the maximum is reached in the middle of cool-down phase I). During charging, the maximum temperature difference is lower: 4.4 \({}^{\circ}\)C for the reference, 1.4 \({}^{\circ}\)C for heat-conductive polymer I, 2.0 \({}^{\circ}\)C for heat-conductive polymer II, and 2.3 \({}^{\circ}\)C for the latent heat storage material. As heat-conductive polymer I has the lowest temperature difference, high thermal conductivity and a low thermal mass are most likely beneficial for good temperature homogeneity in the cell pack. During the phase change of latent heat storage material, the temperature difference is significantly reduced, indicating the highly beneficial influence of the phase change on the temperature homogeneity.  
Figure 4: Temperature homogeneity in the cell pack. (**a**) Temperature difference of the cells in the center and the cells at the edges (average cell temperature) during the whole use/charging cycle. Cells at the edges are 0.5 to 5 \({}^{\circ}\)C (depending on cooling material and phase) cooler than the cells in the center. (**b**) Temperature distribution in the cells at the end of use phase (8 min, cell size: radius 21 mm, height 70 mm, cuboid indicates the position of the cooling materials).  
Figure 4b, which highlights the temperature distribution in the cells, clearly illustrates the cooling effect of the solid cooling materials, as the parts of the cells in contact with the cooling materials (the central part within the cube) are lower than the heads of the cells not in contact with the cooling materials. The cooling materials take up the heat produced in the cells, and therefore, the parts in contact with the materials are cooler than the parts not in contact, for which the cell surface temperature is set by the thermal mass of the cells and the conductive heat transfer is at the surface only. The temperature difference between the head with no contact and the central part of the cells indicates that it might be beneficial for the temperature homogeneity to design the pack in a way that the cooling material totally encapsulates the cells, leaving no free heads with no contact to the cooling materials.