## 2 Materials and Methods
### Measurement Methodology  
Mechanical properties of fabricated composite samples were studied using uniaxial tensile test, three-point bending (flexural) test, and dynamic mechanical analysis (DMA). Besides that, ultrasound speed in the samples was measured providing data on the corresponding elastic moduli. The experimental methodology is depicted schematically in Figure 2.  
Tensile tests were carried out in accordance with ASTM D-638 using an Instron 1122 universal testing machine (Instron, Norwood, MA, USA) at a tensile rate of 10 mm/min under normal conditions. The values of tensile strength \(\sigma_{b}\), relative strain at break \(\epsilon_{b}\), and tensile modulus \(E_{b}\) were determined from the obtained stress-strain curves. Three-point bending tests were carried out in accordance with ASTM D-790 also using the Instron1122 universal testing machine, with a distance between the supports of 30 mm and loading speed of 10 mm/min under normal conditions. The span length to thickness ratio equaled to 20. Based on the loading diagrams, the values of bending stress at a given deflection \(\sigma_{f}\), the deflection \(S\), a relative bending strain \(\epsilon_{f}\) and a flexural modulus \(E_{f}\) were determined. The measurement error was calculated with a 95% confidence level. Dynamic mechanical analysis was carried out in bending mode at the temperature of 23 \(\pm\) 2 \({}^{\circ}\)C using a DMA 242 C setup (Netzsch, Selb, Germany) at the frequencies of 0.1, 0.5, 1, 2, 10, 50 Hz and dynamic force of 2 N. Frequency dependencies of the dynamic elastic modulus \(E^{\prime}\), loss modulus \(E^{\prime\prime}\), and mechanical loss tangent \(\tan\delta=E^{\prime\prime}/E^{\prime}\) were obtained.  
Figure 1: Cryo-SEM images of composite samples filled with 5 wt% of carbon allotropes: fullerenes C60 (**a**,**d**), carbon nanotubes CNT (**b**,**e**), graphene (**c**,**f**) with different magnification.  
Figure 2: Flowchart of the experimental procedure.  
The dynamic elastic properties of composite samples were studied also by the analysis of variations of the Young's modulus obtained from measurements of ultrasonic wave velocities. The velocities of longitudinal and shear ultrasonic waves in the samples were measured using, respectively, piezoelectric transducers SC1812 (Amati Acoustics, St.Petersburg, Russia) and V154-RB (Olympus, Waltham, MA, USA). The ultrasonic waves were generated at the frequency of 2 MHz and were further modulated by a meander. Wave velocities in the samples were determined from the time delay of the signal on the receiving transducer. As known according to the acoustoelastic theory the velocities of longitudinal (\(V_{p}\)) and shear (\(V_{s}\)) ultrasonic waves in a sample are related with the Lame elastic moduli \(\lambda,\mu\) of the material as \(V_{p}=\sqrt{(\lambda+2\mu)/\rho}\); \(V_{s}=\sqrt{\mu/\rho}\), where \(\rho\) is the material density. The Young's modulus \(E_{c}\) was calculated from the obtained values of \(\lambda\) and \(\mu\) using the equation: \(E_{c}=\mu(3\lambda+2\mu)/(\lambda+\mu)\).  
Measurements by tensile and three-point bending tests and DMA analysis were performed on 3 to 5 samples of each composite. Measurements of ultrasound velocity were performed on single samples of each composite but were repeated thrice for each sample. The results obtained were averaged over the measurement sets.