## 3 Results and Discussion
### Dynamic Mechanical Analysis (DMA)  
Figure 6 shows the storage modulus (\(E\)) curves for the VNR/MWCNT nanocomposite samples as a function of temperature. In this study, the dynamic mechanical properties of the VNR-based nanocomposites with different MWCNT particle concentrations for a given temperature range were investigated using this technique. In all the VNR/MWCNT nanocomposite samples, a plateau was observed between \(-100\)\({}^{\circ}\)C and \(-45\)\({}^{\circ}\)C corresponding to the glassy state. A plateau can be observed in the \(E^{\prime}\) modulus curve due to the mechanical energy stored in the glassy region due to the restriction of the movement of the VNR molecular chains. VNR/MWCNT nanocomposites exhibit elastic moduli values approaching 2500 MPa at the plateau corresponding to the glassy region. For all the specimens studied, the \(E^{\prime}\) modulus value decreases sharply as the temperature increases; i.e., between \(-65\)\({}^{\circ}\)C and \(-20\)\({}^{\circ}\)C is the temperature region where the glassy-to-rubbery transition occurs in the VNR-based specimens. All nanocomposites exhibit an abrupt drop in \(E^{\prime}\) modulus in this temperature range, which is referred to as the glassy transition region. This glassy-to-rubbery transition is attributed to the increase in the degrees of freedom of the polymer chains, that is, the increase in mobility of the VNR chains relative to each other, as well as the dissipation of mechanical energy during the cyclic deformation and heating cycle of the specimens. As the VNR/MWCNT nanocomposites reached \(-20\)\({}^{\circ}\)C, due to the relaxation and greater mobility of the VNR chains, their consistency changed from rigid to soft and malleable, indicating rubbery properties. The \(E^{\prime}\) modulus of all the VNR/MWCNT nanocomposites in this region is greater than the \(E^{\prime}\) modulus of neat VNR, demonstrating the reinforcing effect of MWCNTs on VNR. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Specimens** & \(\sigma_{100\%}\) & \(\sigma_{300\%}\) & \(\sigma_{500\%}\) & \(\sigma_{\text{at break}}\) & \(\epsilon_{\text{at break}}\) \\  & **(MPa)** & **(MPa)** & **(MPa)** & **(MPa)** & **(\%)** \\ \hline VNR & 0.72 \(\pm\) 0.04 & 1.73 \(\pm\) 0.10 & 3.19 \(\pm\) 0.24 & 8.84 \(\pm\) 2.48 & 780 \(\pm\) 34 \\ VNR/MWCNT1 & 0.84 \(\pm\) 0.03 & 2.08 \(\pm\) 0.05 & 4.02 \(\pm\) 0.06 & 9.48 \(\pm\) 2.03 & 731 \(\pm\) 43 \\ VNR/MWCNT2 & 0.94 \(\pm\) 0.06 & 2.42 \(\pm\) 0.18 & 4.80 \(\pm\) 0.40 & 10.45 \(\pm\) 0.62 & 708 \(\pm\) 29 \\ VNR/MWCNT3 & 1.09 \(\pm\) 0.07 & 2.87 \(\pm\) 0.22 & 5.84 \(\pm\) 0.34 & 9.65 \(\pm\) 2.16 & 640 \(\pm\) 38 \\ VNR/MWCNT4 & 1.28 \(\pm\) 0.09 & 3.31 \(\pm\) 0.17 & 6.81 \(\pm\) 0.40 & 10.62 \(\pm\) 2.09 & 617 \(\pm\) 43 \\ VNR/MWCNT5 & 1.47 \(\pm\) 0.05 & 3.94 \(\pm\) 0.19 & 8.03 \(\pm\) 0.40 & 9.67 \(\pm\) 1.60 & 553 \(\pm\) 53 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Mechanical parameters of the stress–strain curves: tensile strength at 100% (\(\sigma_{100\%}\)), 300% (\(\sigma_{300\%}\)), and 500% (\(\sigma_{500\%}\)) stress; tensile strength at break (\(\sigma_{\text{at break}}\)); and the elongation at break (\(\epsilon_{\text{at break}}\)) of neat VNR and VNR/MWCNT nanocomposites with different MWCNT fillers. This glass-to-rubber transition region is best seen as a strong peak in the _tan_\(\delta\) versus temperature curves shown in Figure 7. According to Figure 7, the strong peak observed in the graph of _tan_\(\delta\) versus temperature is related to the glass transition temperature (\(T_{g}\)). In general, the mechanical loss factor or _tan_\(\delta\) is considered to be an indicator of the damping properties of polymeric materials. As a result, it can serve as a means of identifying an equilibrium between elastic and viscous characteristics [12; 66]. The value of _tan_\(\delta\) of a composite may be influenced by a number of factors, including the type of filler and its distribution, as well as the interaction between the phases [12; 67].