## 3 Results and Discussion
### Characterization by Equilibrium Swelling, MDR, and DSC
The values of \(T_{\text{g}}\) of the crosslinked IR and NR samples are higher than those of the corresponding uncured rubbers. In particular, for samples cured at the same temperature, a linear increase in \(T_{\text{g}}\) by increasing the crosslink density can be observed. A linear relationship between the \(T_{\text{g}}\) and crosslink density at a low degree of crosslinking is predicted by theoretical models [18; 67] and has been experimentally demonstrated for several crosslinked polymers [9; 10; 18; 42; 68]. The increase  
Figure 1: (a) Maximum torque (\(M_{\text{h}}\)) values from MDR measurements and (b) crosslink density values from equilibrium swelling experiments (\(v_{\text{c,sw}}\)) vs. sulfur content (S) in phr. (c) Molar ratio (\(mol_{\text{CL}}/mol_{\text{S}}\)) values between the total number of crosslinks and the initial amount of sulfur S\({}_{\text{g}}\) plotted vs. the initial molar amount of S\({}_{\text{g}}\) per gram of rubber (S, \(10^{-5}\) mol/g). Values of \(mol_{\text{CL}}/mol_{\text{S}}<1\) indicate the presence of unreacted sulfur or the occurrence of side reactions, which do not lead to the formation of elastically active crosslinks. Figure 2: (a) Percentage of mono- and disulfide bridges obtained by thiol-amine analysis vs. sulfur content (S). Crosslink density values from equilibrium swelling experiments and types of crosslinks formed in the (b) IR and (c) NR samples vulcanized at the indicated temperatures and sulfur contents. in \(T_{\rm g}\) upon increasing crosslinking can be explained by considering that the formation of covalent bonds between polymer chains results in a more compact polymer network, whereby the segmental motions of the chains are significantly hindered and require a higher amount of thermal energy to be activated. Interestingly, samples cured at 170 \({}^{\circ}\)C are characterized by higher values of \(T_{\rm g}\) and by a steeper slope of the linear dependence of \(T_{\rm g}\) vs. \(v_{\rm c,sw}\) compared to samples cured at 140 and 150 \({}^{\circ}\)C. In particular, the obtained slopes are 1.16, 1.22, and 1.64 K/(10\({}^{-5}\) mol/g) for the IR_140, IR_150, and IR_170 series, respectively; and 0.81, 0.91, and 1.10 K/(10\({}^{-5}\) mol/g) for the NR_140, NR_150, and NR_170 series, respectively. This result could be related to the presence of chemical modifications of the polymer chain, which as discussed above occur in larger amounts at high vulcanization temperatures. Indeed, such modifications, for instance the attachment of cyclic sulfide structures and bulky sulfur or accelerator pendant groups, restrict the mobility of the polymer chains, further contributing to the increase in \(T_{\rm g}\) (the so-called \"copolymer\" effect) along with the formation of crosslinks. Similar linear dependences on crosslink density for samples cured at 140 and 150 \({}^{\circ}\)C suggest that the decrease in crosslinking efficiency observed at 150 \({}^{\circ}\)C (Figure 1b,c) must be mainly ascribed to the presence of unreacted curatives or to the formation of zinc sulfide rather than to the occurrence of chemical chain modifications.