## 3 Results and Discussion
### Characterization by \({}^{1}\)H TD-NMR
#### 3.2.3 1H Longitudinal Relaxation by FC NMR  
1H longitudinal relaxation is driven by the fluctuations of magnetic dipole-dipole interactions between 1H-1H spin pairs under the effect of molecular motions. 1H FC relaxometry has proven to be particularly useful for the study of dynamics of uncured and crosslinked elastomers, since \(R_{1}\) depends on different power laws of the Larmor frequency in the different dynamic regimes governing relaxation [71; 72]. It has been previously shown that the NMRD curves are dominated by glassy dynamics, and that on the basis of the FTS principle, it is possible to determine \(\tau_{\text{s}}\) values from NMRD curves acquired at different temperatures [42].  
In this work, in order to explore the possibility to derive from \(R_{1}\) measurements a parameter to be correlated with the crosslink density through a fast procedure, we tested the values of 1H \(R_{1}\) measured at single temperature and Larmor frequency. In Figure 6a, \(R_{1}\) values measured at 0.19 MHz and 30 \({}^{\circ}\)C are reported as a function of \(\
u_{\text{c,sw}}\). For samples vulcanized at the same \(T_{\text{v,ulc}}\), \(R_{1}\) progressively increases by increasing \(\
u_{\text{c,sw}}\), with a steeper increase at the highest curing temperature of 170 \({}^{\circ}\)C. This trend, similar to that observed for \(T_{\text{g}}\), is ascribed to the fact that both parameters are affected by glassy dynamics, which is influenced not only by crosslinking but also by chemical modifications of the polymer chains.  
In order to investigate the effect of the vulcanization conditions on 1H \(R_{1}\) in more detail, it is useful to look at the whole NMR susceptibility (\(\chi^{\prime\prime}\)) curves (Figure 6b,c) obtained from NMRD curves, as described in Section 2.6. A shift of the \(\chi^{\prime\prime}\) curves towards lower frequencies is observed, passing from the uncured to the crosslinked samples and by increasing the sulfur content, which is ascribable to the slowdown of glassy dynamics upon crosslinking [42]. 1H \(\chi^{\prime\prime}\) master curves of IR samples are shown as examples in Figure 7a, while those of NR samples are reported in Figure S2. As can be seen, after the application of the shift factor \(k\) along the frequency axis, the \(\chi^{\prime\prime}\) curves of the crosslinked samples perfectly overlap with that of the uncured one, indicating that neither crosslinking nor chemical modifications of the polymer chains affect the spectrum of motions, in agreement with the literature [39; 40; 41; 42; 73]. Different shift factors \(k\) are found for the different samples (Figure 7b); for each \(T_{\text{vulc}}\) the values of \(k\) progressively increase with the crosslink density, due to the  
Figure 6: (a) 1H \(R_{1}\) values measured at the Larmor frequency of 0.19 MHz and 30 \({}^{\circ}\)C vs. \(\
u_{\text{c,sw}}\). NMR susceptibility (\(\chi^{\prime\prime}\)) curves obtained from the 1H NMRD curves of the (b) IR and (c) NR samples.  
slowdown of glassy dynamics induced by the formation of permanent constraints. In particular, the dependences of Log\(k\) on \(\
u_{\rm c,sw}\) and \(T_{\rm vulc}\) reflect those observed for \(R_{1}\).  
Under the assumption of a VFT dependence of \(\tau_{\rm s}\) on temperature (Equations (4) and (5)), the values of Log\(k\) are plotted vs. the reduced variable \(T/T_{\rm g}-1\) (Figure 7c). As we can see, the curves for all samples from the same polymer overlap well, indicating that if \(\tau_{0}\) and the fragility index \(m\) remain the same, the observed variations of \(\tau_{\rm s}\) should be mainly ascribed to changes of \(T_{\rm g}\).