## 3 Results and Discussion  
### Structural Characterization and Degree of Mixing  
The presence of domains with different molecular mobility in the samples was investigated through the analysis of on-resonance \({}^{1}\)H FIDs acquired using the MSE pulse sequence [35]. Indeed, this analysis allowed protons in different dynamic environments to be distinguished on the basis of spin-spin relaxation times, \({}^{1}\)H \(T_{2}\), whose values monotonically increase as the degree of mobility increases [35; 36; 37; 38; 39; 40]. For all the analyzed samples, a small proton fraction associated to the Gaussian function was detected, with a very short \(T_{2}\) on the order of 20-30 us, ascribable to molecular fragments with highly restricted mobility, including polymer segments involved in physical and chemical constraints, such as entanglements and crosslinks, and in interactions with filler particles. The two exponential components are instead characterized by longer \(T_{2}\) values ranging from \(\sim\)100 to \(\sim\)800 us, and they account for most of the protons in the polymer chain segments and for protons in liquid-like components, including TDAE and dangling chains. By passing from the uncured to the vulcanized samples, an increase in \(W_{g}\) and a concomitant decrease in the \(T_{2}\) values of both exponential functions were observed. This effect can be ascribed to the formation of chemical crosslinks between the polymer chains, causing a reduction in molecular mobility. As the resin was added, an increase in the rigid fraction on the order of 5-8% was observed, accompanied by a decrease in both \(T_{2,\ell 1}\) and \(T_{2,\ell 2}\) values. Because the \({}^{1}\)H FID of pure resin can be nicely reproduced by a Gaussian function characterized by a \(T_{2}\) value of 20 us (Figure S1), the higher \(W_{g}\) values obtained for SBR_k and vSBR_k can reasonably be ascribed to a contribution of the resin protons to the Gaussian component. Indeed, it was estimated that the resin protons account for 10% of the total proton content in both samples. Furthermore, the decrease in \(T_{2,\ell 1}\) and \(T_{2,\ell 2}\) values reflects a slowdown of the dynamics of all the other components of the samples, mainly the polymer, induced by the presence of resin. In order to ascribe the regions at different mobilities to different sample components, \({}^{13}\)C high-resolution SSNMR experiments were carried out on vSBR and vSBR_k. In particular, \({}^{13}\)C DE/MAS spectra were recorded to obtain quantitative spectra, while \({}^{1}\)H-\({}^{13}\)C CP/MAS spectra selectively highlighted the more rigid components of the samples. In fact, the CP process relies on the magnetization transfer from abundant (\({}^{1}\)H) to rare (\({}^{13}\)C) nuclei mediated by the heteronuclear dipolar interaction, enhancing the detection of \({}^{13}\)C nuclei in close proximity to protons in rigid environments. Furthermore, the CP dynamics is strongly influenced by molecular motions, as they directly affect the extent of dipolar interaction, as well as \({}^{1}\)H \(T_{1p}\), and can be studied by analyzing CP spectra recorded at different contact times. The \({}^{13}\)C DE/MAS spectra acquired for vSBR and vSBR_k are reported in Figure 2a,b. Both spectra presents broad signals, mainly due to the distribution of chemical shifts typical of amorphous materials. Specifically, a group of signals at low chemical shifts (0-50 ppm) is present, ascribable to the aliphatic carbon nuclei of the polymer and TDAE, and to naphthalene carbons in TDAE. In the spectrum of vSBR_k, an additional contribution from CH\({}_{2}\) carbons of Kristalex(tm) 5140 can be observed between 30 and 50 ppm. At higher chemical shifts (100-160 ppm), signals from aromatic and alkene carbons were detected. In the spectrum of vSBR_k, it is also possible to observe low intensity signals at about 167 and 87 ppm due to the first-order spinning sidebands of the tertiary aromatic carbons of the resin.