## 2 Materials and Methods
### Graphene Nanocomite Preparation and Characterization
Since the starting nanofiller from Graphene Supermarket consisted of graphite nanoplatelets, HRTEM imaging confirmed that the subsequent process of dispersing this nanofiller in the monomers, followed by in-situ polymerization, had exfoliated the nanoplatelets as expected. The insets showed the individual layers with interlayer distances (calculated based on ten layers) equal to 0.355 nm and 0.362 nm for the top and bottom panels, respectively. In both cases, these values are close to the thickness of a single graphene sheet. We must stress, however, that it is difficult to precisely measure the thicknessof the graphene layers in our nanocomposite samples because flakes embedded within the polymer matrix are randomly oriented and their edges are often folded, making proper orientation of the sample during the TEM study difficult. Therefore, although our TEM images and measurements of the thickness of carbon planes in our nanoflakes are consistent with those of graphene monolayers, we cannot completely exclude the probability of having graphite nanoplatelets in our samples. The above-mentioned ambiguity was resolved by performing scanning fluorescence measurements and Raman spectroscopy. A beam from a helium-neon laser (632.8-nm wavelength) was focused on the sample, and the fluorescence was sent through a 635-nm pass filter (to block the laser line) and was collected by an avalanche photodiode. By scanning the sample using a movable nano-positioning stage, a spatial fluorescence image was created (see inset in Figure 3a). After the scan, the emission was redirected to a spectrometer equipped with a charge-coupled-device (CCD) camera to obtain the Raman spectrum (Figure 3a, main panel). A grating with 600 lines/mm was used to disperse the signal onto the CCD array. The nanoflake under investigation, from which the spectrum was taken, is circled in the inset. The three prominent features visible in the nano-Raman spectrum are the D peak at \(\sim\)1340 cm\({}^{-1}\), the G peak at \(\sim\)1580 cm\({}^{-1}\), and the 2D peak at 2680 cm\({}^{-1}\). These features correspond to a few-layer graphene (FLG) sample [29]. We have also performed Raman measurements of an entire 1-wt% graphene-polymer nanocomposite sample, as well as the reference neat PET-DLA 4060 copolymer specimen. Figure 3b shows a spectrum that our graphene nanofiller obtained by numerical subtraction of the neat polymer spectrum from that of the nanocomposite (both shown in the inset in Figure 3b). We note that the positions of the D, G, and 2D peaks very close to that of the nano-Raman study of a single flake. The only difference is the height of the D peak in Figure 3b, which is a defect peak. The discrepancy can be attributed to spectra being collected simultaneously from nanofiller flake edges as well as from within the flake. The edges will increase the observed D band in our spectra. Overall the observed Raman spectra corroborated the fact that, indeed, our nanofiller consisted predominantly of FLG nanoflakes. Figure 2: (**a**) Low-resolution (10 \(\times\) 10-μm2 area), representative TEM image of 1-wt% graphene PET-DLA 4060 nanocomposite. Twelve (most visible in the view) flakes are identified and the sizes of several flakes are listed. (**b**) HRTEM of the 7-nm \(\times\) 130-nm nanoflake. Insets show images of graphene planes and interplanar distances from two different sections of the nanoflake (marked as squares).