## 3 Results and Discussion  
### Impedance Spectroscopy Results  
The addition of conductive fillers in a highly dielectric epoxy matrix can contribute to electrical impedance decrease of the system via a conductive network formation. A fundamental condition to the creation of the conductive network is the concentration of the filler to exceed a critical value, the percolation threshold. IS is a technique capable of monitoring the electric profile of the material under investigation with high sensitivity. The formation of the conductive network is indicated by a steep drop of the magnitude of the impedance by several orders of magnitude. Furthermore, the transition from the Ohmic (linear) to the non-Ohmic (non-linear) behavior of the material, inside the alternative electric field, shifts to higher frequencies. Figure 2a depicts the dielectric measurements of the whole range of binary and ternary systems after 1 h of the dispersion process. Within the first binary group, the CNTs0.1-I exhibited a frequency-dependent magnitude of impedance, which is a typical dielectric behavior, within the  
Figure 1: Experimental setup for the impedance spectroscopy measurements. experimental spectral range. As should be noted, \(|\)Z\(|\) values above 10\({}^{10}\) Ohm, at low frequencies, were at the detection limits of the employed setup, hence they presented noise fluctuations. The CNTs0.3-I and the CNTs0.5-I presented a major drop of \(|\)Z\(|\) after the first hour of the dispersion process (Figure 2a). More specifically, the CNTs0.3-I exhibited a drop by almost 4 orders of magnitude compared to CNTs0.1-I, while the CNTs0.5-I exhibited an even more notable decrease in \(|\)Z\(|\) by 6 orders of magnitude compared to CNTs0.1-I. This was a clear indicator of the formation of a 3D conductive network. The CNTs0.3-I protocol was sufficient to create a partial network which was fully accomplished at dispersion CNTs0.5-I, defining concentrations between 0.3 wt. % and 0.5 wt. % CNTs as the percolation threshold. Additionally, the transition from the Ohmic (linear) to non-Ohmic (non-linear) behavior shifted from below 10\({}^{-2}\) Hz for CNTs0.1-I to 10\({}^{1}\) Hz for CNTs0.3-I, and finally to 10\({}^{3}\) Hz for the CNTs0.5-I, verifying the conversion of the dielectric character of the nanocomposite to a more conductive one, due to the formation of the conductive network. The second binary group, consisted of the systems CB0.5-I, CB1-I and CB2-I, which after 1 h of dispersion process, did not present any changes due to the increase of the CB concentration, as the filler content did not exceed the percolation threshold (Figure 2a). The transition from the Ohmic to the non-Ohmic behavior occurred outside the experimental frequency range, below 10\({}^{-2}\) Hz. These results are in agreement with the literature, which suggests a much higher volume fraction for the formation of a conductive network in CB/resin systems [39]. It should be noted that additional experiments up to 9 wt. % CB did not alter the electrical behavior of the system. Finally, the ternary group exhibited the optimal electrical properties compared to aforementioned binary systems (Figure 2a). The CNTs0.5_CB2-I protocol presented a slightly more conductive profile from the CNTs0.5_CB1-I, due to the increase of the concentration of CB from 1 wt. % to 2 wt. % and  
Figure 2: Bode plots of binary and ternary systems for (**a**) 1, (**b**) 2, (**c**) 3 and (**d**) 4 h of dispersion process. the synergy with the 0.5 wt. % CNTs. Moreover, the ternary group showed the highest Ohmic to non-Ohmic transition frequency, indicating the worse dielectric profile among all specimens. Concerning the duration of the dispersion process, among the binary groups, the CNTs0.1-I, the CB0.5-I, the CB1-I and the CB2-I exhibited a stable highly dielectric behavior regarding dispersion time (Figure 2). CNTs0.3-I presented a slight decrease of the impedance indicating the continuous de-agglomeration of the CNTs aggregates during the dispersion process.