## 3 Results and Discussion
### Characterization of Dynamics
The addition of the resin, although lowering the efficiency of vulcanization, as it was observed when comparing the crosslink density of vSBR and vSBR_k (Table 2), yielded a slowdown of segmental dynamics, paralleled by an increase in \(T_{\rm g}\). Similar trends in \(\tau_{\rm s}\) upon resin addition to rubber matrices were found in investigations of \(\alpha\)-relaxation by broadband dielectric spectroscopy [13; 14; 15]  
For all samples, \(\tau_{\rm s}\) values show, as expected, decreasing trends by increasing the temperature (Figure 4a). However, quantitative analyses of these trends in terms of the commonly used Vogel\(-\)Fulcher\(-\)Tammann (VFT) function to obtain information on polymer fragility is hampered by the limited temperature range investigated. On the other hand, hints on the variation of fragility upon vulcanization or resin addition can be achieved by plotting Log\(\tau_{\rm s}\) as a function of \((T/T_{\rm g}-1)\) according to Equation (4):  
\[Log\Big{(}\frac{\tau_{\rm s}(T)}{\tau_{0}}\Big{)}=\frac{Log^{2}\bigg{(}\frac{ \tau_{\rm s}(T_{\rm g})}{\tau_{0}}\bigg{)}}{m\Big{(}\frac{T}{T_{\rm g}}-1 \Big{)}+Log\bigg{(}\frac{\tau_{\rm s}(T_{\rm g})}{\tau_{0}}\bigg{)}} \tag{4}\]  
Equation (4) is obtained by recasting the VFT equation [57]. In Equation (4), \(m\) is the fragility index, \(\tau_{0}\) is the pre-exponential factor of the VFT equation and the value of \(\tau_{\rm s}\) at the glass transition (\(\tau_{\rm s}(T_{\rm g})\)) is, by definition, a constant (100 s) [58]. If \(\tau_{0}\) and \(m\) do not change significantly, all samples are expected to exhibit the same behavior. Indeed, in our case, using \(T_{\rm g}\) values determined by DSC in \((T/T_{\rm g}-1)\), a good superposition was observed for the Log\(\tau_{\rm s}\) curves of all the samples (Figure 4b). These results indicate that both crosslinking by vulcanization and resin addition do not significantly affect the polymer fragility index, which yields a measurement of the rapidity with which segmental dynamics slow down upon approaching the glass transition by decreasing the temperature. Unchanged polymer fragility upon vulcanization was also reported for rubbers with low crosslinking degrees [52]. On the other hand, the addition of resin was previously found to increase the fragility index at high resin concentrations [13], suggesting that in our case the amount of resin was too low to show such an effect. For the vulcanized samples, the dynamics at low frequency was further investigated by analyzing \({}^{1}\)H spin-lattice relaxation in the rotating frame (\(T_{1\rho}\)). Although an estimate of \({}^{1}\)H \(T_{1\rho}\) was already obtained by analyzing the CP dynamics, \({}^{1}\)H \(T_{1\rho}\) data were more accurately measured at a spinlock field (\(\omega_{1}/2\pi\)) of 46 kHz by means of a dedicated experiment with direct \({}^{1}\)H detection. At all the investigated temperatures (from 303 to 343 K), the relaxation curves can be well reproduced by the combination of two exponential functions \(I(t)=I(0)\bigg{(}W_{a}e^{-\frac{t}{1\rho_{a}}}+W_{b}e^{-\frac{t}{1\rho_{b}}} \bigg{)}\), with \(W_{a}\cong\) 40-90%, \(T_{1\rho,a}\cong\) 0.6-2.3 ms, \(W_{b}\cong\) 10-60% and \(T_{1\rho,b}\cong\) 5-11 ms, which is very similar for vSBR and vSBR_k, as shown in Table S2. The effect of spin diffusion, which tends to average out differences between intrinsic relaxation times, makes a physical interpretation of the individual \(T_{1\rho}\) components very difficult. Nevertheless, dynamic information could be obtained by looking at the population weighted rate average \(R_{1\rho}^{PWRA}=\frac{W_{a}}{1\rho_{a}}+\frac{W_{b}}{T_{1\rho_{b}}}\), which is not affected by spin diffusion [29] (Table S3). As shown in Figure 5, \({}^{1}\)H \(R_{1\rho}^{PWRA}\) decreases by increasing the temperature for both vSBR and vSBR_k, indicating the presence of dynamic processes in the fast motion regime.