## 3 Results and Discussion
### Shielding Efficiency  
For the calculation of the total shielding efficiency (\(SE_{T}\)) in Equation (2), real and imaginary permittivity values are determined. The \(SE_{T}\) can be expressed as the logarithmic ratio of transmitted and incident wave powers. \(SE_{T}\) also can be determined as the sum of the contributions from the three primary shielding mechanisms, which are reflection (\(SE_{R}\)) in Equation (3), absorption (\(SE_{A}\)) in Equation (4), and multiple reflections (\(SE_{MR}\)). The significance of \(SE_{MR}\) in relation to \(SE_{T}\) is relatively minor compared to \(SE_{A}\) and \(SE_{R}\). If \(SE_{T}\geq 10\) dB, \(SE_{MR}\) is generally considered insignificant. The reflection shielding efficiency (\(SE_{R}\)) is contingent upon the impedance of the medium through which the wave is propagating \(\eta_{0}\) denotes the impedance of the medium through which the waveis propagating. \(\eta_{\rm s}\) represents the surface impedance. \(\sigma\) is the electrical conductivity. \(\mu^{\prime}\) and \(\mu^{\prime\prime}\) are permeability values. t is the thickness in m. Since neither the fillers nor the polymer materials used in the study exhibited any magnetic properties, permeability was not taken into account [25; 40]. For the calculation of absorption shielding, it was assumed that the thickness is 2 mm, as stated in the sample preparation title. According to Equation (3), thickness does not affect reflection shielding. Considering Equations (3) and (4), it is expected that the total shielding efficiency will increase as the AC conductivity increases. Additionally, as the frequency increases, the reflection tends to decrease, and the absorption tends to increase. The AC conductivity is calculated with Equation (1). \(\varepsilon_{0}\) is the permittivity of free space (8.854 \(\times\) 10\({}^{-12}\) Fm\({}^{-1}\)) [38], and f is the frequency in Hertz. \(\varepsilon^{\prime\prime}\) is the imaginary permittivity which is measured by VNA. Frequency-dependent AC conductivity of the presented compositions is illustrated in Figure 4.  
\[\sigma_{AC}=2\pi f\varepsilon_{0}\varepsilon^{\prime\prime} \tag{1}\]  
\[SE_{T}=10\text{log}\,\frac{P_{in}}{P_{out}}=SE_{A}+SE_{R}+SE_{MR} \tag{2}\]  
\[SE_{R}(dB)=-20\text{log}\,\frac{\eta_{0}}{4\eta_{\rm s}}=39.5+\frac{10\text{ log}\,\sigma}{2\pi f\mu} \tag{3}\]  
\[SE_{A}(dB)=8.7t\sqrt{\pi\sigma f\mu^{\prime}} \tag{4}\]  
Figure 3: Real (**a**,**b**) and imaginary (**c**,**d**) permittivity values depend on frequency and graphite/carbon black content. All samples were assumed to have negligible multiple reflection contributions, and this was not taken into account in the analysis. The decision to ignore multiple reflection contributions was based on the assumption that any re-reflected waves would be absorbed within the material, as the thickness of the material was greater than the critical thickness value known as the skin depth [41]. By increasing the amount of filler, both \(SE_{A}\) and \(SE_{R}\) values tend to increase significantly in the high-frequency region illustrated in Figures 5 and 6. This could be due to the creation of multiple conduction pathways within the bulk structure of the samples. \(SE_{R}\) values are quite high when compared to \(SE_{A}\) for all cases. Both graphite and carbon black filled samples show a lower absorption shielding effectiveness, for graphite filled in the range 0-1.5 dB in Figure 5a and for carbon black filled in the range 0-5 dB in Figure 5b. It is seen in Figure 6 reflection is the main mechanism of the shielding efficiency, which constitutes the majority of total efficiency for all types of samples. Reflection shielding efficiencies are in the range of 19-21 dB for graphite filled in Figure 6a and 8-17 dB for carbon black filled in Figure 6b. Considering graphite samples, \(SE_{R}\) remains almost unchanged in spite of the increasing frequency. On the contrary, \(SE_{A}\) shows an upward movement directly proportional to the frequency of the incident photon.