## 1 Introduction  
Polymeric materials have been widely employed in electronic packaging, batteries, cable terminations, and power devices. Thermal loading in these applications has become a critical issue for the further development of electronic devices. Indeed, miniaturization, functionalization of electronic devices, and thermal dissipation are challenging problems. High thermal conductive composites need to be designed to dissipate and transfer the generated heat, especially for thermal interface materials (TIM) [1, 2]. PDMS are widely used in TIM applications [1, 3, 4, 5, 6, 7] due to their high flexibility and thermal stability. However, they possess low thermal conductivity (k) which may limit their application in devices. The value usually varies from 0.1 to 0.5 Wm\({}^{-1}\) K\({}^{-1}\) according to the different polymeric matrix [8, 9]. Low thermal conductivity of these materials is related to the presence of amorphous domains which localize the vibrational modes, limiting heat transfer [10]. An accessible route to improve k is to embed macro- micro- or nano-fillers in the polymeric matrix and to enhance the thermal properties of the material [11]. In particular, carbon-based, ceramic, and metal fillers have been added to polymeric matrices to improve their thermal properties [9, 10]. Heat transmission is the result of two different contributions: free electrons and phonon. Phonons are mainly responsible for thermal conduction in carbon and ceramic materials, on the other hand, thermal conductivity of metals can be completely attributed to free electrons motion, whereas phonons' role is negligible. Both the mechanisms can be used to enhance the k value of a PDMS based composite. The final value of k depends on the loading, distribution, shape, and size of the conductive fillers, as well as on the matrix-filler interface, composition, and nature of the components [10]. Carbon-based fillers include carbon black (CB) particles, carbon nanotubes (CNT), graphene, and graphite. The variety of allotropes cover a remarkable range of thermal properties with k varying from 0.01 W mK\({}^{-1}\) to above 3000 W mK\({}^{-1}\)[12; 13; 14]. [PERSON] et al. [15] reached an increase of 65% of k value by adding CNT in a silicon matrix. [PERSON] et al. [4] used multi-walled carbon nanotube (MWNT) in an epoxy matrix to increase thermal conductivity. The study compared MWNT with alumina nanoparticles and underlines the higher k value reached with MWNT due to high thermal conductivity and high aspect ratio of carbon-based filler. The MWNTs form ideal thermal conducting pathways leading to a marked increase of thermal conductivity of the composites. Thus, the minimal addition of filler (0.4 wt.%) leads to an increase of k of about 80% compared to the pristine polymer matrix [16]. [PERSON] et al. [7] prepared silicon composite adding expanded graphite (EG) by melt mixing and solution intercalation. The maximum thermal conductivity value of silicon/EG was 0.32 Wm\({}^{-1}\) K\({}^{-1}\) reached at a content of 9 phr and through solution intercalation, whereas 0.24 Wm\({}^{-1}\) K\({}^{-1}\) was achieved by the standard method of melt mixing. EG was also added into high-density polyethylene (HDPE) by [PERSON] et al. [17] to improve the thermal conductivity. Ternary composites were produced by combining CNT to the previous EG/HDPE composite to further increase the thermal dissipation. CNT create an internal network producing a conductive path for the heat. [PERSON] et al. [18] measured thermal conductivity of 1.08 Wm\({}^{-1}\) K\({}^{-1}\) of PDMS filled with multilayer graphene flakes (MGFs) and graphene foam (GF). Ceramic-based fillers, such as alumina, zinc oxide, boron nitride, have been also used to develop high thermally conductive TIMs. [PERSON] et al. [1] compared the effect of alumina (Al\({}_{2}\)O\({}_{3}\)) and zinc oxide (ZnO) in a silicon matrix. The thermal pads filled with ZnO reached higher k values compared to Al\({}_{2}\)O\({}_{3}\), when added at the same amounts.