## 2 Materials and Methods
### THz Time-Domain Spectroscopy Technique  
The THz-TDS system, which is used to measure the THz-range transmission spectra of both the neat copolymers and graphene nanocomposite samples, is schematically presented in Figure 4. THz radiation was generated and detected using a commercial, low-temperature-grown GaAs (LT-GaAs) photo-conductive antenna emitter and detector from TeraVil Ltd., Vilnius, Lithuania [30]. The emitter and detector were excited and probed, respectively, by 100-fs-wide pulses, with 800-nm wavelength and 76-MHz repetition rate, generated by a femtosecond Ti:Sapphire laser. The spectral range of the spectrometer was \(\sim\)4 THz, with a maximum amplitude of \(\sim\)0.5 THz. The sample was placed directly between the emitter and detector, as shown in Figure 4, and measurements were taken at room temperature. To reduce the influence of water absorption, the THz emitter, detector, and sample holder were placed inside a Plexiglas(r) box that was purged with dry nitrogen, ensuring that the humidity during the measurement was below 5%. Figure 4: Schematic diagram of a THz-TDS setup. L1, L2: optical lenses; M1–M6: dielectric mirrors; BS: beam splitter, and OC: optical chopper. Figure 3: **(a)** Background-subtracted Raman spectrum from a FGL nanoflake embedded in PET-DLA 4060 copolymer matrix. The three prominent features are the D peak at \(\sim\)1340 cm\({}^{-1}\), the G peak at \(\sim\)1580 cm\({}^{-1}\), and the 2D peak at 2680 cm\({}^{-1}\). The inset presents a scanning fluorescence image of the region from which the spectrum was taken, with the studied nanoflake circled. For the images, the excitation wavelength was 632.8 nm and the laser power was 600 \(\mu\)W. **(b)** Background-subtracted Raman spectrum of graphene nanoflakes obtained by subtraction of the spectrum of neat PET-DLA 4060 copolymer, used as the graphene nanocomposite matrix. The latter two spectra are both shown in the inset in **(b)**, with arrows pointing to the characteristic features of the nanocomposite. The positions of the main peaks in the main panel are the D peak at \(\sim\)1311 cm\({}^{-1}\), the G peak at \(\sim\)1586 cm\({}^{-1}\), and the 2D peak at 2661 cm\({}^{-1}\). For each sample, we first performed a reference run with no sample inside the spectrometer to confirm the performance of the system. Next, we took two measurements; one of a graphene nanocomposite and the other of a corresponding neat co-polymer specimen. To get better results and reduce noise, each set of measurements consisted of at least ten averages. Our measurements were focused on two different sample types: A nominal 0.3-mm-thick, elastic PET-DLA 4060 copolymer and a nominal 0.9-mm-thick, stiff PET-DLA 6040 copolymer. For both sample types, the nanofiller content was the same, i.e., 1 wt%. Since our further analysis crucially depends on the sample thickness, all measurements were repeated several times. At different spots of the test sample, the corresponding local thicknesses were measured, and, subsequently, the results were averaged. Therefore, from now on, we will refer to a nominal 0.3-mm PET-DLA 4060 soft copolymer sample as a \"thin sample,\" and a nominal 0.9-mm PET-DLA 6040 stiff copolymer sample as a \"thick sample.\"  
Figure 5a presents the time-domain signals transmitted through dry nitrogen (the reference measurement), the thin and thick neat copolymers, and the corresponding thin and thick, 1-wt% graphene-polymer nanocomposite samples, respectively (see the legend for detailed color/line coding). As expected, the transient corresponding to the thick sample with graphene exhibits the smallest amplitude and the longest arrival time to the detector. The differences in time delays, with respect to the nitrogen signal observed in the signals corresponding to different samples, are caused by their different indexes of refraction, as will be discussed later in connection with Figure 6a. In Figure 5b, we present the corresponding (see the legend) power spectra of our time-domain signals obtained by means of fast Fourier transformation (FFT).