# Time Domain NMR in Polymer Science: From the Laboratory to the Industry
## 3 Applications
### Polymer Physics
The curves around the minimum were fitted with the modified version of BPP equation and structural parameters,  
Figure 13: Crosslinking density (**a**) and relative distribution width of the average \(\mathrm{D_{res}}\) value (**b**) of various concentrations of DPTT (dipentamethylenethiuram tetrasulfide) and peroxide in natural rubber in three states: pre-vulcanization in latex state, dried film and post-vulcanization of the film itself (Reprinted with permission from reference [71]. Copyright 2012 American Chemical Society). as activation energy and distribution width parameter, were determined, showing a correlation with the crosslinking degree in the material [76]. Another interesting topic is the understanding of the reinforcement effect due to filler-rubber interactions [77]. MSE measurements showed that a gradient of polymer mobility exists around the filler particles, that can be separated in at least three components: a glassy, an intermediate and the network fraction. The fraction of immobilized component increases with increasing filler specific surface, but it is reduced with a similar trend with increasing temperature or solvent content. MQ was used to determine the existence of a highly crosslinked portion in case of covalent filler graffers with an optimal dispersion [78]. Furthermore, the effect of filler morphology was investigated with a similar method. Rod-like silica nanoparticles immobilize a higher amount of rubber respect to spherical ones due to the formation of domains of aligned rods where the glassy layers pertinent to different particles overlap (Figure 14). These observations correlated with higher reinforcing capabilities [79]. Processing conditions for in-situ generated silica have implications also for the amount of bound rubber. HE and SE were combined to reconstruct the FID, which was fitted using the three components described above. Both the expected silica yield and the sol-gel reaction time determines the amount of bound rubber, probably due to different dispersion level obtained inside the rubber matrix [80]. To highlight the direct interaction of the polymer matrix with the filler, combined analysis of \({}^{1}\)H MQ NMR and equilibrium swelling data have been adopted. The deviation of the crosslink density of rubbers in filled compounds from the masterline (1/M\({}_{\text{c,NMR}}\) vs. 1/M\({}_{\text{c,swelling}}\)) has been attributed to the effect of interaction with the filler. The stronger is the interaction, the more restricted is the degree of swelling, because of the topological restrictions imposed at the filler interface, while there is no significant change in the crosslink density measured through low-field NMR and consequently the deviation from the masterline is higher. It has been shown in reference [81] that the interaction becomes stronger with the introduction of organo-modified particles or nanosized fillers, such as graphene sheets, that also provide improved mechanical properties. Combined analysis of MSE data for rigid fractions determination, T\({}_{2}\) and DQ build-up curves can help in understanding morphology changes in thermoplastic elastomers. SEBS (styrene-b-ethylene-co-butylene-b-styrene) was investigated regarding the origin of a broad endothermic transition during heating at low butylene content (LB1 sample). MSE-FID measurements for rigid fraction confirmed that this transition is not a crystallization. T\({}_{2}\) variation with temperature highlighted the complexity  
Figure 14: Rubber rigid fraction at 313 K as a function of filler volume fraction for three vulcanized samples of SBR (styrene-butadiene rubber): loaded with silica (SiO\({}_{2}\)) particles with aspect ratio one (diamonds), loaded with SiO\({}_{2}\) particles with aspect ratio two (squares) and loaded with SiO\({}_{2}\) particles with aspect ratio five (circles) (Reprinted with permission from reference [79]. Copyright 2015 Royal Society of Chemistry).