# Time Domain NMR in Polymer Science: From the Laboratory to the Industry
## 3 Applications
### Polymer Physics
Indeed, they showed the linear, but shifted along the y axis, correlation of R\({}_{2}\) and R\({}_{\mathrm{DQ}}\) (rate of DQ build-up), on samples of EPM and EPDM crosslinked rubber (Figure 12). The non-zero intercept is attributed to the additional term of incoherent dephasing. Figure 11: Vulcanized polybutadiene and polyisoprene crosslink density measured by both equilibrium swelling and MQ TD-NMR (arrow indicates increasing cure time). The good correlation between the two methods is indicated by the linear fitting, creating the so-called masterline. The non-zero intercepts indicate the contribution of entanglements to the NMR signal (Reprinted with permission from reference [67]. Copyright 2015 Wiley). Figure 12: Correlation between effective relaxation rate R\({}_{2}\) and R\({}_{\mathrm{DQ}}\) for sulfur- and peroxide-cured EP(D)M samples (Reprinted with permission from reference [70]. Copyright 2011 American Chemical Society). Moreover, MQ possesses the added value to provide information on the actual structure of the network, through the study of \(\mathrm{D_{res}}\) distributions. For example, it was applied to differentiate the effect of sulfur and peroxide vulcanization, with the first giving a more homogeneous network [70]. That was observed also in the study of the evolution of network structure during the processing of natural rubber latex particles [71], that cannot be probed with other methods, such as rheology or swelling. \(\mathrm{D_{res}}\) and the associated distributions were used to define the crosslinking degree during three steps of the processing: pre-vulcanization in the latex state, film formation and post-vulcanization, whose variations are graphically represented in Figure 13a,b, respectively. MQ single-point measurements were chosen to obtain the pre-vulcanization kinetics in the latex state. The study pointed out that sulfur creates a homogeneous network, whereas peroxide promotes the formation of a core-shell structure, which develops into an inhomogeneous network once the film is formed [72]. That was believed to come from the different diffusion rate vs. reaction rate of the two vulcanizing agents. In the end, the difference reflects onto the strain-induced crystallization behavior of natural rubber, affecting, in turn, the stress-strain properties. The more homogeneous network created by sulfur is, in fact, able to enhance homogeneously the molecular orientation induced by crosslinks, while the clustering induced by peroxides reduces the degree of orientation [73]. The DQ-build up is represented by a variety of functions, commonly Gaussians or Abragam-like, which are used to fit the data and obtain information about the residual dipolar coupling values. For a deeper analysis, these functions are also implemented as kernel functions in the Tikhonov regularization procedure. Using a kernel function with angular dependence, the MQ analysis can also monitor the effect of uniaxial stretching in rubbers [74]. The results on natural rubber samples showed the inadequacy of established models for elasticity after deformation. However, Baum-Pines sequence is not applicable in highly crosslinked systems, such as resins, because it is too lengthy to record the signal from highly coupled portions. Some modified versions, with five, three or two pulses, have been proposed. Although the determination of \(\mathrm{D_{res}}\) was successful on a common resin, such as diglycylil ether of bisphenol A (DGBA) with diethylene triamine as curing agent [75], it is necessary to combine results from separate experiments with two-pulse and three-pulse to describe reliably the build-up curve. Another approach has been proposed, that is the use of \({}^{1}\)H \(\mathrm{T_{1}}\) according to the BPP theory (Equation (1)). The BPP equation was modified incorporating a distribution of correlation times related to the degree of couplings. \({}^{1}\)H \(\mathrm{T_{1}}\) measurements with INVREC sequence at different temperatures were conducted on fully cured resins of DGBA with hardners of different molecular weights.