# Physical Hybrid of Nanographene/Carbon Nanotubes as Reinforcing Agents of NR-Based Rubber Foam
## 3 Results and Discussion
### Dynamical Mechanical Analysis (DMTA)  
DMTA is a technique used to analyze and characterize foam nanocomposite samples based on their response to an applied dynamical, mechanical, and thermal force. DMTA results are often expressed in terms of the storage modulus (E'), loss modulus (E\"), and loss factor (tan \(\delta\)), which describe the ability of the materials to lose energy as heat to mean damping and their ability to revert to their original shape and size from the deformation when the oscillating applied force is removed. The E' test data used to describe the stiffness of composite materials and their variation as a function of temperature is presented in Figure 9a for all foam nanocomposite samples. The observed increase in E' values above Tg with increased GNS/CNT content can be attributed to increasing GNS/CNT hybrid nanofiller concentration. It should be noted that this increase in E' is negligible at temperatures below the glass transition (Tg) due to  
Figure 8: Thermal degradation behavior of the NR/CNT/GNS foams with different hybrid nanofiller content: (**a**) TGA curve and (**b**) DTG curve. the rigidity of the nanomaterials. As the temperature rose from \(-100\)\({}^{\circ}\)C to \(-50\)\({}^{\circ}\)C, the E\({}^{\prime}\) values decreased for all samples. A substantial decrease in E\({}^{\prime}\) was seen in the temperature range between \(-60\)\({}^{\circ}\)C and \(-40\)\({}^{\circ}\)C of the curve related to the matrix's glass transition temperature. The observed increase in E\({}^{\prime}\) values above T\({}_{\rm g}\) can be attributed to the interaction between the polymer matrix (NR) and the CNT/GNS hybrid nanofillers that led to the reinforcement phenomenon. Strong interactions preserve the porous structure against temperature rise [37]. E\({}^{\prime}\) is a material's response by losing energy to the surroundings due to the applied external oscillating force. Figure 9b indicates the variation of E\({}^{\prime\prime}\) for NR/CNT/GNS nanocomposite foams as a function of temperatures. It was noted that the E\({}^{\prime\prime}\) curve of NR/CNT/GNS containing a higher amount of CNT/GNS hybrid nanofiller showed a slightly wider peak in the E\({}^{\prime\prime}\) curve, which suggests a broad relaxation time distribution of NR chains. It is well-known that the broadness of the peak in multicomponent polymeric systems is primarily controlled by heterogeneity: either the intrinsic differences among components' relaxation properties (dynamic heterogeneity) or their detailed state of local concentration fluctuations (local heterogeneity) [38]. The dispersion of rigid nanoparticles in polymeric matrices resulting in local and dynamic heterogeneity can lead to significant damping capability, which is mutually correlated with a broader peak of E\({}^{\prime\prime}\). Figure 9: _Cont._  
Tan \(\delta\), also called the loss factor, is calculated from the ratio of loss modulus to storage modulus (E\({}^{\prime\prime}\)/E\({}^{\prime}\)). The tan \(\delta\) curves are plotted as a function of temperature for all samples, as shown in Figure 9c, and the data are further tabulated in Table 3. Comparing the maximum T\({}_{\rm g}\) values of the samples provided in Table 4, the T\({}_{\rm g}\) increased from 42.14 \({}^{\circ}\)C to 52.29 \({}^{\circ}\)C. It is observed in Figure 9 and that Table 3 peak of this curve (tan \(\delta_{\rm max}\)) decreased with increasing CNT and GNS amount. The results show that the glass transition temperature of the S0 samples increased slowly from \(-\)45.77 \({}^{\circ}\)C for the S2 sample to \(-\)38.69 \({}^{\circ}\)C. This could be due to the physical interactions between the nanofillers and the rubber matrix. Figure 9c shows that the T\({}_{\rm g}\) of the nanocomposite had a slight transition to higher temperatures. This increase in T\({}_{\rm g}\) could be correlated to a restriction of the mobility of the segments in the matrix in the presence of carbon-based nanofillers [39; 40].