## 3 Results and Discussion
### Evaluation of the Degree of Vulcanization of NR Composites  
One typical method to evaluate the degree of vulcanization in elastomers is the determination of the average molecular weight of the rubber segments between neighboring cross-links, \(\overline{M_{c}}\), [31; 35]; a lower value of \(\overline{M_{c}}\) implies higher vulcanization and improvement in the mechanical properties. In that sense, the \(\overline{M_{c}}\) values for the NR composites vulcanized with different cross-linking agents and adding CB or SWCNTs were calculated and included in Table 6. As observed, the \(\overline{M_{c}}\) values obtained for the NR composites vulcanized with organic peroxides are higher than those of the NR-S composites; such behavior can be attributed to dissimilarities in the type and number of bonds formed during the cross-linking process. Specifically, the addition of SWCNTs to NR formulated with T29 and DCP leads to an important reduction in the \(\overline{M_{c}}\) values in comparison with those of the neat NR formulations and the NR-CB composites; this is indicative of a major degree of cross-linking derived from the existence of multiple interactions between SWCNTs and free radicals generated during the vulcanization process. Based on the above, it is possible to confirm that the use of SWCNT at contents <1 phr can increase the degree of vulcanization of NR mainly when organic peroxides are used as cross-linking agents, thus leading to the enhancement of mechanical properties of the developed NR composites, as previously discussed. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multirow{2}{*}{**Sample ID**} & **Tear Strength** & **Hardness** & \(\overline{M_{c}}\) \\  & **(N m\({}^{-1}\))** & & **g (g mol)\({}^{-1}\)** \\ \hline NR-S & 68.6 & 30.4 & 7353 \\ NR-S-CB & 61.2 & 31.6 & 7353 \\ NR-S-SWCNTs & 71.4 & 33.6 & 9434 \\ \hline NR-T29 & 6.3 & 17.2 & 64.831 \\ NR-T29-CB & 7.7 & 16.5 & 101,555 \\ NR-T29-SWCNTs & 8.0 & 18.2 & 17,752 \\ \hline NR-DCP & 51.5 & 35.4 & 8571 \\ NR-DCP-CB & 38.2 & 37.6 & 108,042 \\ NR-DCP-SWCNTs & 55.1 & 37.4 & 7353 \\ \hline NR-T145 & 36.2 & 23.3 & 19,584 \\ NR-T145-CB & 15.3 & 21.2 & 48,723 \\ NR-T145-SWCNTs & 23.4 & 24 & 29,215 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Values of tear strength, hardness, and \(\overline{M_{c}}\) obtained for NR composites. It is interesting to consider that the type of bonds formed during the cross-linking process depends on the curing agents. In the case of sulfur, mono- (C-S-C), di- (C-S\({}_{2}\)-C), and polysulfide (C-S\({}_{\text{x}}\)-C) bonds can be formed [4; 36; 37]. It is well known that the longer the bond that links the rubber molecules, then higher will be the mobility between polymeric chains, and thus, the final rubber compound will be more flexible. In contrast, organic peroxides generate exclusively C-C bonds less flexible than C-S\({}_{\text{x}}\)-C chemical bonds. As a result, one expects that the tensile failure strain will be higher in materials with C-S\({}_{\text{x}}\)-C bonds and lower in materials vulcanized with exclusive C-C bonds. This can explain the lower values of tensile strength obtained in the NR composites vulcanized with organic peroxides. Furthermore, it is well accepted that the interactions between nanotubes and rubber molecules occur through entanglements and classical nonbonded interactions [38]; however, the reduction observed in the vulcanization time of the NR-SWCNTs composites in conjunction with the increments in moduli, tensile strength, and reduction in the strain at breakage (Table 5) lead us to suppose that an interaction between the NR and the SWCNTs certainly occurred. A key condition for such an interaction to occur is an efficient dispersion of SWCNTs in the rubber matrix, which was accomplished by the previous SWCNTs dispersion in the masterbatch and the subsequent milling process with the components of the formulation. In that sense, we suggest a grafting reaction between the rubber macroradicals generated during the vulcanization process with the surface of SWCNTs.