# Time Domain NMR in Polymer Science: From the Laboratory to the Industry
## 3 Applications
### Polymer Physics
Whenever some molecular segments become more mobile, the signal is no longer completely suppressed and can be refocused with an MSE block, creating an echo the more intense the higher the mobility. The onset temperatures of dynamic processes occurring in the material are therefore accessible, together with their activation energies, as seen for aPP (atactic polypropylene) and PIB (polyisobutylene). The variation of filter time at different temperatures for both polymers induces a displacement of the MSE echo intensity curves at longer times, because of increasing correlation time, and an increasing maximum intensity, correlated to narrowing distributions of correlation times, proved using a Tikhonov regularization procedure on the curves. The contribution of entanglements to elasticity in elastomers was also studied. Variation of DQ NMR build-up curves and consequent Dres as function of crosslinker functionality had been employed to test the validity of the most common elasticity models: the affine and phantom model. The found linearity between functionality and Dres is an indication of better accuracy of the phantom model, although it does not account properly for the contribution of defects. The existence of non-zero intercepts was an indication of contribution to anisotropy, i.e., to elasticity, of entanglements. Defects act as diluents, like solvent molecules, with no further contribution to elasticity [66]. Another study that demonstrates the better accuracy of the phantom model in describing the elastomer network was conducted by [PERSON] et al. [67], employing MQ NMR experiments. Samples of PB, PI and their blends at increasing cure times were analyzed. Linear correlation (Figure 11) between the crosslink density from swelling experiments, obtained with the modified Flory-Rehner equation for filled elastomers, based on the phantom model, and TD-NMR crosslink density, from Dres calculation, was found. The study also highlighted the sensitivity of TD-NMR to the minimal variation of crosslink density with cure time and its different mechanism according to chemically different rubbers, leading contingently to different network structures. The capability to distinguish different rubbers has always been a challenge because of elastomers' complex nature, due to the many different variables that can play a role, but MQ opened the possibility to potentially verify the effect of each of them. Figure 10: Constructed correlation function for polybutadiene (PB) with a molecular weight of 87 kDa. The analytical results obtained by the experimental InDQ had been shifted according to the time–temperature superposition principle (TTS) principles, converting \(\tau_{\text{DQ}}\) into \(t/\tau_{\text{e}}\) by division with the theoretical \(\tau_{\text{e}}\) from literature (Reprinted with permission from reference [60]. Copyright 2011 American Chemical Society). Furthermore, spin-spin relaxation time \({}^{1}\)H T\({}_{2}\) measured through Hahn echo decay, depends on the degree of motional anisotropy, i.e., to the constraints' density. The relationship is highlighted in the theory of [PERSON] [68], that provides a direct proportion between the number of statistical segments between two junctions and the \({}^{1}\)H T\({}_{2}\) at high temperature in the approximation of gaussian chains (Z=T\({}_{2}\)P/\(\alpha\)T\({}_{2}\)\({}^{\mathrm{rl}}\) where \(\alpha\) is a theoretical coefficient depending on the angle between the segment axis and the internuclear vector with the nearest spin on the chain and T\({}_{2}\)\({}^{\mathrm{rl}}\) is T\({}_{2}\) at temperature far below T\({}_{g}\)). A successful example of that is given by the evaluation of network structure in polyacrylate systems PEGDA-HA (polyethylene glycol-700-diacrylate-hexyl acrylate) [69]. However, some drawbacks to this approach can be individuated: the equation above is dependent on the assumption of Gaussian chains and R\({}_{2}\) (I/T\({}_{2}\)) contains a contribution from incoherent loss of transverse magnetization, as proposed in the paper of [PERSON] et al. [70].