## 3 Results and Discussion
### Characterization of Dynamics
In Figure S3, the corresponding \(\chi^{\prime\prime}(\omega)\) curves are also shown. For all samples, at low temperatures, \(R_{1}\) shows a power law dependence on Larmor frequency with \(\gamma\cong 1\), suggesting that \(R_{1}\) relaxation is dominated by segmental dynamics (Regime 0). Correspondingly, the \(\chi^{\prime\prime}(\omega)\) curves display a maximum associated with the  
Figure 3: (**a**) \({}^{1}\)H NMRD curves for the investigated samples at the indicated temperatures. (**b**) Susceptibility master curves of the indicated samples; the black line represents the contribution of the segmental dynamics to the \(\chi^{\prime\prime}(\omega\tau_{\rm s})\) master curve of SBR_k. condition \(\omega\tau_{\rm s}\cong 1\), which shifts towards lower frequencies passing from uncured to vulcanized samples. Moreover, SBR_k and vSBR_k show \(\chi^{\prime\prime}(\omega)\) maxima at lower frequencies than the corresponding samples without Kristalex(tm) 5140. These results indicate a slowdown of segmental dynamics as a consequence of both crosslinking and resin addition, in agreement with the higher \(T_{\rm g}\) values measured by DSC (Table 2). At T \(\geq\) 323 K, the NMRD curves show two regions with different power law dependences. A region with \(\gamma\) values in the range 0.7-0.8, with \(\gamma\) decreasing by increasing the temperature, was detected at higher frequencies, ascribable to the overlap of Regime 0 with the Rouse regime (Regime I of the tube-reptation model). At lower frequencies, a region with \(\gamma\) of 0.25-0.28 was observed, which is attributable to the Rouse regime. For all samples, \(R_{1}\) increases with increasing temperature at high frequencies, while it decreases at lower frequencies, with a shift in the crossover point between Regime 0 and Regime I toward lower frequencies, due to the corresponding increase in \(\tau_{\rm s}\). For each sample, the NMR susceptibility \(\chi^{\prime\prime}(\omega)\) curves obtained at different temperatures were combined together to build \(\chi^{\prime\prime}(\omega\tau_{\rm s})\) master curves, under the assumption that the FTS principle holds true, to obtain \(\tau_{\rm s}\) values. \(\chi^{\prime\prime}(\omega)\) curves at 303 K were fitted to Equation (2) in order to obtain \(\tau_{\rm s}\). \(\beta_{CD}\) was found to be 0.12, in agreement with the value determined for SBR samples in a previous work [52]. At the remaining temperatures, \(\tau_{\rm s}\) values were determined as the frequency scaling factors used to build the master curves. The \(\chi^{\prime\prime}(\omega\tau_{\rm s})\) master curves obtained for all samples are shown in Figure 3b, while the values of \(\tau_{\rm s}\) as a function of 1000/\(T\) are reported in Figure 4a. The obtained \(\chi^{\prime\prime}(\omega\tau_{\rm s})\) master curves cover a frequency range of six decades and display characteristic shapes that well reflect the different dynamic regimes described above: at a high frequency, the contribution of segmental dynamics is dominant, while polymer dynamics assumes a significant importance for \(\omega\tau_{\rm s}<0.1\). Figure 4: (a) Correlation times for segmental dynamics, \(\tau_{\rm s}\), vs. 1000/\(T\) and (b) Log\(\tau_{\rm s}\) vs. (\(T/T_{\rm g}-1\)) for the indicated samples. \(T_{\rm g}\) values were determined by DSC measurements (Table 2). Errors on \(\tau_{\rm s}\) are lower than 5%. As expected from the trend of the maxima of the \(\chi^{*}(\omega)\) curves, \(\tau_{\rm s}\) values are longer in the vulcanized samples (vSBR, vSBR_k) with respect to the uncured ones (SBR, SBR_k), and in samples containing the resin (SBR_k, vSBR_k) with respect to those without it (SBR, vSBR). The increase in \(\tau_{\rm s}\) upon vulcanization is ascribable to the formation of crosslinks, which restrict segmental dynamics, also resulting in increased \(T_{\rm g}\) (Table 2).