## 3 Results and Discussion
### Electrical Characterization
the density, it was possible to calculate the volume fraction of the reinforcement according to the rule of mixture for composites [61], described by Equation (9):  
\[\rho_{C}=\rho/\varphi_{f}+\left|\rho_{m}\left(1-\varphi_{f}\right),\right. \tag{9}\]  
where \(\rho_{C}\) is the density of the composite, considered equal to \(\rho_{b}\), measured for the evaluation of the flowability characteristics (see Section 2.1); \(\rho_{f}\) is the density of the filler; and \(\rho_{m}\) is the density of the PA12 matrix, the latter two given by the technical data sheets provided by the suppliers (see Table 1). In this way, the weight percentages of 4%, 6%, 8%, and 10% correspond to 0.092, 0.146, 0.195, and 0.241 volume fractions. Focusing attention on the results obtained for a compressive load of 1 kN, shown in blue in Figure 8, the percolation threshold was estimated as 0.091, corresponding to a weight percentage of xGNPs of around 3.9%; the electrical conductivity of the filler as 0.0143 S/cm; and the critical exponent as 1.971. Percolation is induced when the dispersed filler establishes a conductive pathway within the insulating matrix, promoting exponential growth of the conductivity [32]. The value of the percolation threshold obtained in this study is in line with the pertinent literature [62], which highlights a variation between 2.5% and 7.5%, typically given for exfoliated graphite nanoplatelets with a large lateral size compared to their thickness and which are therefore expected to form a more extensive and uniformly connected network throughout the matrix. Also, the percolation coefficient lies between 1.65 and 2 [13], while the electrical conductivity of the filler is around three orders of magnitude lower than the expected one, which theoretically should approach the electrical resistivity of the conductive nanofiller, i.e., between 10 S/cm and 10\({}^{3}\) S/cm [63]. This can be attributed to two main synergistic factors which lead to the formation of an imperfect pathway among the nanofillers: (i) a thin layer of polymeric matrix surrounds the nanoplatelets, offering resistance at the junctions of the network, and/or (ii) the clustering of the particles [64]. This effect is more evident with a low filler content and a low applied compressive load, as can be seen from the black and red lines in Figure 8, e.g., for 0.1 kN of applied load, the percolation coefficient reduced to 1.841, while the conductivity of the fillers was 0.0022 S/cm. This may be due to a lack of physical or direct contact between particles allowing the formation of conductive paths, as Figure 9 suggests. These results, although promising, highlight the need to further investigate the optimal xGNP content to properly tailor electrical conductivity depending on the final application, e.g., for electrostatic discharge applications, a value between 10\({}^{-2}\) S/cm and 10 S/cm is usually required, and for signal transmission applications, a value of 10 S/cm or more is needed [65]. Moreover, it is worth noting that, beyond a certain threshold, the geometry and continuity of the filler network may govern performance more than the filler content alone [66]. In fact, factors like filler type, concentration, and matrix material play crucial roles in achieving the desired quality. Figure 9: SEM images of cross-sections of samples with (**a**) 4% and (**b**) 10% contents of xGNPs.