## 4 Conclusions  
In this work, different TD-NMR methods--including measurements of \({}^{1}\)H transverse and longitudinal relaxation times and of residual dipolar couplings, \(D_{\rm res}\)--were applied to the study of IR and NR samples vulcanized in different conditions. In particular, the effects of curing temperature and sulfur content were explored, while keeping constant the accelerator amount. The comparison of NMR results with data from equilibrium swelling and DSC experiments provided information on structural and dynamic features of the formed polymer networks and on their effects on the investigated NMR observables. Chemical modifications of the polymer chains were found to occur at high curing temperatures, which hinder fast segmental motions, causing at the molecular level increased characteristic times of the glassy dynamics, \(\tau_{\rm s}\), as reflected by the longitudinal relaxation behavior investigated by \({}^{1}\)H FC NMR, and causing at the macroscopic level an increased glass transition temperature, as measured by DSC. On the other hand, both \({}^{1}\)H \(D_{\rm res}\) and effective transverse relaxation rates showed good linear relationships with the crosslink density measured by swelling experiments, indicating a strong correlation of these NMR parameters with the formation of the rubber network but a substantial independence from the chemical modifications of polymer chains. The slopes obtained for IR and NR were similar, and in the case of \(D_{\rm res}\) in agreement with those reported in the literature. The obtained results support the utility of the adopted TD-NMR methods for the characterization of the network structure of rubber materials at the molecular level. In particular, both \(D_{\rm res}\) and \(T_{2}\) measurements were confirmed to be valuable empirical approaches to estimate the crosslink density of the polymer network, either as a complementary or even alternative approach to more widely used macroscopic methods, such as equilibrium swelling and mechanical measurements. The following are available online at [[https://www.mdpi.com/article/10.3390/polym14040767/sl](https://www.mdpi.com/article/10.3390/polym14040767/sl)]([https://www.mdpi.com/article/10.3390/polym14040767/sl](https://www.mdpi.com/article/10.3390/polym14040767/sl)): Figure S1: Maximum torque (\(M_{\rm h}\)) determined by MDR measurements vs. \(\
u_{\rm c,sw}\). Table S1: Best fit parameters obtained from the analysis of the CPMG relaxation curves of the sulfur-cured IR samples. Table S2: Best fit parameters obtained from the analysis of the CPMG  
Figure 7: **(a) NMR susceptibility (\(\chi\)”) master curves of the IR samples obtained as described in Section 2.6. **(b)** Log\(k\) vs. \(\
u_{\rm c,sw}\) and **(c)** Log\(k\) vs. \(T/T_{\rm g}-1\). relaxation curves of the sulfur-cured NR samples. Figure S2: NMR susceptibility (\(\chi^{\prime}\)) master curves of the NR samples. Conceptualization, M.G., F.M. and L.C. ; methodology, F.M., F.N., E.C., M.C., L.G., M.A., S.B., L.C. and M.G. ; software, F.N., F.M. and E.C. ; validation, F.N. and F.M. ; formal analysis, F.N., L.C., M.C. and F.M. ; investigation, F.M., F.N., E.C. and L.C. ; resources, M.C., L.G., M.A., L.C., F.M., S.B. and M.G. ; data curation, F.N., F.M. and M.C. ; writing--original draft preparation, F.M., F.N., M.G., L.C. and M.C. ; writing--review and editing, M.C., L.G., M.A., F.N., F.M., S.B., L.C., E.C. and M.G. ; visualization, F.N. and F.M. ; supervision, M.C., M.A., L.G. and M.G. ; project administration, M.C., M.A., L.G. and M.G. ; funding acquisition, M.C., M.A., L.G., S.B., L.C., F.M. and M.G. All authors have read and agreed to the published version of the manuscript. The work was partially funded by Regione Toscana and Pirelli Tyre SpA (POR FSE 2014-2020 Asse A--\"NMR4 DES\" project). The data presented in this study are available on request from the corresponding authors. CISUP (Center for Instrument Sharing-University of Pisa) is acknowledged for the use of the Bruker Avance Neo 500 solid-state NMR spectrometer.