## 2 Results and Discussion
Thus, we calculated the average \(SE_{T}\) as  
\[SE=SE_{T}\triangleq 10\ log_{10}\bigg{(}\frac{P_{inc}}{P_{trn}}\bigg{)}=10\ log_{1 0}\bigg{(}\frac{1}{T}\bigg{)}=SE_{R}+SE_{A} \tag{2}\]  
where  
\[SE_{R}=10\ log_{10}\bigg{(}\frac{1}{1-R}\bigg{)} \tag{3}\]  
\[SE_{A}=10\ log_{10}\bigg{(}\frac{1-R}{T}\bigg{)} \tag{4}\]  
\(SE_{R}\), \(SE_{A}\) refer to the reflection and absorption \(SE\), respectively. The higher the \(SE\) the better the shielding. The \(SE\) (also denoted as \(SE_{T}\), with \(A\), \(T\), \(R\) indicating the absorption, transmission and reflection, respectively) is usually quantified in terms of the logarithm of the incident power \(P_{inc}\) over the transmitted power \(P_{trn}\)[41; 42] and thus expressed in decibels (dB). Figure 8 depicts the S\({}_{21}\) (transmission; Figure 8a) and the S\({}_{11}\) parameters (reflection; Figure 8b) of the AC samples (AC, AC/OD, AC/CNTs/OD), in the frequency range 3.2-7.0 GHz. Figure 9 depicts the absorption (Figure 9a) and the total shielding efficiency (\(SE_{T}\)) (Figure 9b) spectra of the AC samples (AC, AC/OD, AC/CNTs/OD), in the frequency range 3.2-7.0 GHz. Figure 8: Transmission S\({}_{21}\) (**a**) and reflection S\({}_{11}\) (**b**) coefficients from 3.2 to 7.0 GHz (C-band) for AC samples. Figure 9: Absorption (**a**) and \(SE_{A}\) (**b**) from 3.2 to 7.0 GHz (C-band) for AC samples. Figure 10 depicts the S\({}_{21}\) (transmission; Figure 10a) and the S\({}_{11}\) parameters (reflection; Figure 10b) of the EG samples (EG, EG/OD, EG/CNTs/OD), in the frequency range 3.2-7.0 GHz. Figures 7 and 9 clearly illustrate that the reflection of AC and EG samples is almost zero. As a result, the EMI shielding effect due to reflection (\(SE_{R}\)) is also negligible and in all cases; the total SE is simply \(SE_{T}=SE_{A}\) (see Equation (4)), which is in agreement with the literature on carbon-based composite materials [43]. Figure 11 depicts the absorption (Figure 11a) and the total shielding efficiency (\(SE_{T}\)) (Figure 11b) spectra of the EG samples (EG, EG/OD, EG/CNTs/OD), in the frequency range 3.2-7.0 GHz. As one can see, in all cases, the dominant shielding mechanism is absorption, which is also supported by the increasing absorption levels when MWCNTs are incorporated. As expected, and observed in Figures 8 and 10, the composites' electrical resistivity decreased with the addition of MWCNTs, and the composites' EMI \(SE\) increased with the addition of MWCNTs. The decrease in electrical resistivity is due to an increase in the number of electrically conductive networks (due to MWCNTs), and the increase in EMI \(SE\) can be ascribed to the decrease in the composites' electrical resistivity and the increase in absorption filler volume fraction [44]. On the other hand, as one can see from Figures 8 and 10, all AC samples exhibit higher EMI \(SE\) levels compared to the corresponding EG samples. As already stated, the AC samples, a porous form of graphite with a complex and imperfect structure, have a higher surface reactivity and adsorption capacity [35] compared to EG ones. Indeed, pore size has a significant impact on electrical conductivity, as it affects the movement of charge carriers within the material. Expanded graphite primarily features larger pores, typically in the mesoporous, while activated carbon is known for its highly developed microporous structure, though it also contains mesopores and macropores. The presence of different pore sizes (microporous, mesoporous, macroporous) can create a complex network that enhances connectivity between conductive pathways, allowing for better transport pathways for charge carriers [45]. This is actually the reason that the AC samples exhibit better EMI \(SE\) properties compared to the EG ones. Figure 11: Absorption (**a**) and \(SE_{A}\) (**b**) from 3.2 to 7.0 GHz (C-band) for EG samples. Figure 6:0 Transmission S\({}_{21}\) (**a**) and reflection S\({}_{11}\) (**b**) coefficients from 3.2 to 7.0 GHz (C-band) for EG samples.