## 3 Results and Discussion
### Dielectric Constant  
Knowing the \(n(\omega)\) dependence, it is easy to calculate the spectra for the relative dielectric constant \(\varepsilon_{1}(\omega)\) for both the neat co-polymer and the graphene nanocomposite, for both the thin and thick samples, as shown in Figure 7a,b, respectively. The resulting \(\varepsilon_{1}(\omega)\) spectra are flat, as we observed earlier for the \(n(\omega)\) dependences presented in Figure 6a. The insertion of graphene nanoflakes increases the dielectric constant of the corresponding nanocomposite sample. Despite a very large frequency  
Figure 6: **(a)** Index of refraction and **(b)** absorption spectra for the tested neat copolymer and 1-wt% graphene nanocomposite samples. Note: The thin sample consisted of PET-DLA 4060 copolymer, while the thick one consisted of PET-DLA 6040. The data points were trimmed according to sample bandwidth (see Figure 5b).  
difference, our numerical values of \(\varepsilon_{1}(\omega)\) are close to those reported by [PERSON] et al. [21], measured at radio frequencies from 8 to 12 GHz.  
The \(\varepsilon_{1}(\omega)\) spectra presented in Figure 7 were subsequently used to estimate the dielectric constant of only graphene flakes embedded in the polymer. Our approach is based on the classical Clausius-Mossotti relation that describes the dielectric constant of a composite sample \(\varepsilon_{\mathrm{c}}\)[36] as  
\[\varepsilon_{c}(\omega)=\frac{3\varepsilon_{\mathrm{pl}}(\omega)+2N\alpha}{3 \varepsilon_{\mathrm{pl}}(\omega)-N\alpha}\varepsilon_{\mathrm{pl}}(\omega), \tag{9}\]  
where \(N\) represents the density of the graphene nanoflakes and \(\alpha\) in this case, is a so-called \"atomic polarizability\". We note here that the effective-medium theory of Bruggeman, most commonly used for the composite material analysis, are not applicable here since it requires that volume fraction of a filler material be at least 10% [37]. This condition is, obviously, not fulfilled in our case because we have only 1 wt% of graphene nanoflakes in the copolymer matrix. On the other hand, based on the TEM images (see Figure 2a), the graphene nanoflakes in our samples are well separated from each other. Consequently, we can assume that they act as independent and noninteracting particles in a host material and use the Clausius-Mossotti relation that is the exact solution of a dielectric constant of a medium having classically interacting dipoles embedded in an insulating matrix. Therefore, we simply treat each flake as a dipole and the dielectric constant of graphene nanoflakes \(\varepsilon_{gr}(\omega)\) should be proportional to \(N\alpha\) and given as  
\[\varepsilon_{\mathrm{gr}}(\omega)=N\alpha*\frac{1}{\delta}, \tag{10}\]  
where \(\delta\) is the volume ratio of graphene nanoflakes to the entire sample volume. Of course, the 1-wt% ratio does not reflect the volume ratio, so we used the TEM images of our samples (see Figure 2a) to estimate the volume percentage of the randomly distributed and orientated graphene nanoflakes inside our nanocomposite. The calculation results of \(\varepsilon_{gr}(\omega)\) are shown in Figure 7 as symbols. The error bars represent an uncertainty of \(\sim\)30% in our evaluation of \(\delta\). Comparing the results presented in Figure 7a,b, we see that ignoring the low-frequency section of \(\varepsilon_{gr}(\omega)\) for the thin sample (mentioned in earlier Fabry-Perot reflections), the \(\varepsilon_{gr}(\omega)\) values for both graphene nanocomposite samples are very close to each other and are \(\sim\)7 \(\pm\) 2.  
Figure 7: Real part of the complex dielectric function spectra (solid lines) for **(a)** thin and **(b)** thick polymer and 1-wt% graphene nanocomposite samples. Note: The thin samples consist of PET-DLA 4060 copolymer, while the thick one was PET-DLA 6040. The open circle and open square symbols present the effective graphene flake dielectric function based on the Clausius–Mossotti relation. The error bars are \(\sim\)30%.