## 3 Results and Discussion
### Thermal-Mechanical Properties
The dispersion of boron nitride particles did not show a significant increase of k, compared to pristine silicon crosslinked matrix, especially at low volume percentage. A clear variation of k can be noticed only for the formulation containing the highest tested content of the filler (6.6% in volume), showing an increase of k of about 43%. The lower thermal conductivity enhancement could be attributed to the lack of percolation threshold because of particles shape. The effect of boron nitride filler at a low percentage is discussed in many studies [6; 20; 34]. The samples containing CNTs showed lower enhancement of thermal conductivity; however, it is important to mention that the maximum load of CNT was fixed at 0.6 vol%, a much lower value compared to the maximum concentration achieved for metal particles (15 vol%). This is due to the detrimental effect of the CNT filler on workability. The composite with the lowest amount of CNT shows a k increase of 9% with respect to the matrix, whereas by further increasing the CNT content up to 0.3 vol% or 0.6 vol% it was not achieved any further significant increase. This could be attributed to the fact that it was not reached the percolation threshold which could allow to have a good heat conductivity within the polymeric matrix. Nevertheless, it is evident the higher thermal conductivity enhancement with respect to BN at a much lower volume fraction. This could be attributed both to the higher k value of CNT (CNT 2000-6000 W/mK) with respect to BN (250-300 W/mK) [34], as well as to the higher surface area of the CNTs with respect to the BN particles. In fact, the filler-matrix interface plays an important role in thermal conductivity: fillers with a higher surface/volume ratio are more efficient in improving thermal conductivity [34]. This was already demonstrated by comparing spheroidal and dendritic copper filler at the same volume content and showing the higher efficiency of the dendritic particles, which shows higher S/V ratio. The qualitative analysis considering spheroidal shape (lower S/V ratio) and dendritic shape (higher S/V ratio) was confirmed also in this study as the k value demonstrate. The best thermal behavior of composite elastomers can be achieved by selecting the proper combination in terms of filler type, shape, dimension, and surface/volume ratio. The thermal diffusivity values (\(\alpha\)) are directly connected to thermal conductivity (k), and the data for all investigated composites are collected in Figure 9. It is evident a thermal diffusivity enhancement for all the investigated fillers, and in agreement with the results of thermal conductivity, the size and shape of the fillers can strongly influence heat dispersion throughout the composite. The thermal conductive properties evaluation of the composites, measured by means of Hot Disk, were compared with the measurements through a thermal imaging camera, where the variation of temperature as a function of time indicates the thermal diffusivity; the collected data are in agreement with the Hot Disk results. All the measurements are reported in the Supplementary Material (Figures S12-S18).