## 3 Results and Discussions
### Synergistic Mechanism  
Figure 1 demonstrates the formation of bridging structure between linear flexible MWCNT and thin platelet EGP in hybrid fillers, and Figure 3b shows synergistic effect when EGP content was more than 4.54 wt %. In order to reveal the synergistic mechanism, microscopic morphologies of SSPCM filled with 9.09 wt % EGP, 9.09 wt % MWCNT, and 9.09 wt % hybrid fillers, i.e., EGPsMWCNT\({}_{2}\), EGP\({}_{5}\)MWCNT\({}_{5}\), and EGP\({}_{3}\)MWCNT\({}_{7}\), were compared in Figures 6-8. For clarity, paraffin on sectional surface was removed by alcohol before observation. In PCM-10 EGP, EGPs were embedded in the SSPCM matrix. Some EGPs contacted each other to form thermally-conductive channels (shown in Figure 6b, red lines show the EGP edges, and EGPs are partly stacked), which helped to improve the thermal conductivity of SSPCM. However, there were still some aggregated EGPs, which were separated by SSPCM and would not contribute to thermal conductivity enhancement (shown in Figure 6a). In PCM-10 MWCNT, a large amount of MWCNT aggregated and was separated by the SSPCM matrix (Figure 7). Thermally-conductive channels or network were not constructed, that is why 9.09 wt % MWCNT did not improve the thermal conductivity of SSPCM greatly.  
(in Figure 8(a1,a2)). This morphology favored the formation of heat flow network and benefit thermal transport through the whole sample. Many MWCNTs were adhered to the surface or edge of EGPs (in Figure 8(a3)), bridging EGPs and the SSFCM matrix. This complex nanostructure enhanced the EGP-SSPCM interaction. Thus, phonons transported across the EGP-SSPCM interface easily, which decreased the interface thermal resistance. When the content of EGP was decreased (especially with EGP/MWCNT less than 5:5), it was so low that the distance between EGPs were too far for phonons to transport between two EGPs across the SSFCM matrix. At the same time, relatively high MWCNT content led to aggregation in the SSFCM matrix (Figure 8(b2,c2)), and fewer MWCNTs adhered to the surface or edge of EPGs (Figure 8(b3,c3)). As a result, the thermal conductive network could not be constructed, and the interface thermal resistance was increased (Figure 8(b1,c1)). Therefore, the synergistic effect between EGPs and MWCNT disappeared. The composites exhibited an additional property of two separated fillers. Thus, when the EGP/MWCNT ratio was 8:2, the composite exhibited the best thermal conductivity enhancement of SSFCM.  
The synergistic mechanism of the thermal conductivity enhancement of SSFCM by hybrid EGP\({}_{\text{x}}\)-MWCNT\({}_{10-\text{x}}\) filler is schematically illustrated in Figure 9. At appropriate EGP/MWCNT ratios, 7:3-9:1 in this paper, both EGPs and MWCNTs were dispersed well in the SSFCM matrix. Good dispersion of relatively high content EGPs created a high volume concentration of EGPs and a short distance between EGPs. At the same time, good dispersion of long and flexible MWCNTs made them more likely to connect EGPs and construct bridging structures (red lines in Figure 9). Now, the highly thermally-conductive network was constructed, and it is possible for phonons to transport along the highly-conductive backbone and bypass the low conductive matrix [38]. Furthermore, strong interaction between EGPs and MWCNTs decreased the interface thermal resistance. Therefore, the synergistic effect was observed. In contrast, at lower EGP/MWCNT ratios, EGPs were dispersed well, while the relatively high content of MWCNTs were easy to aggregate. The low content of EGPs made them separate farther apart. In this case, it is difficult for MWCNTs to connect to them. The aggregation of MWCNTs worsened in the situation. Therefore, only local heat transfer channels were formed, as show in Figure 9b, and the thermal conductivity of the hybrid-filled SSPCM was the same as the addition of the two individual fillers.