# Time Domain NMR in Polymer Science: From the Laboratory to the Industry
## 3 Applications
### Polymer Physics  
Since relaxation times are directly connected to correlation times, molecular dynamics theories can be properly investigated. Molecular dynamics in well-entangled polymer liquids has to be delved into because it has important outcomes in the prediction of melts viscosity and processing conditions [56]. TD-NMR has been used to test the predictions of the reptation model [57], especially in the Doi-Edwards regimes II-IV [58] (constrained Rouse, reptation and free diffusion of chains), relating to the determination of the orientational autocorrelation function (OACF) \(C(t)\), which depends on the second Legendre polynomial P\({}_{2}\)(cos\(\theta\)), where \(\theta\) is the segmental orientation relative to a reference direction, which, in case of NMR experiments, is the external magnetic field direction [59]. \(C(t)\) describes the probability of the reptation tube survival, which is higher as the degree of anisotropy of segmental orientation fluctuations is higher, that is the average over time of P\({}_{2}\) differs from 0. MQ experiments are basically founded on the non-annulment of the integral upon all the P\({}_{2}\)(cos\(\theta\)) of every dipolar coupled spin pair, therefore an in-depth study of signal functions derived from this kind of experiments revealed to be highly effective in the reconstruction of \(C(t)\). MQ signals of polybutadiene (PB), polyisoprene (PI) and polydimethylsiloxane (PDMS) in a broad range of molecular weights had been recorded. Effects of both molecular weight and temperature on the MQ build-up were evaluated, together with the variation of the uncoupled fraction, to confirm the existence of possible additional relaxation processes, such as contour length fluctuations. Direct calculations of \(C(t)\) were carried out, applying improved analytical representation [60], under the approximation that C(\(\tau_{\text{DQ}}\)) is proportional, according to an initial rise approximation of the I\({}_{\text{nDQ}}\) curve, to I\({}_{\text{nDQ}}\)(\(\tau\))/\(\tau^{2}\) on the \(\tau_{\text{DQ}}\) time scale, at short times. This is especially valid for describing directly motion regime II (constrained Rouse), whereas to determine longer time results into the III and IV regimes, time-temperature superposition principle (TTS) was applied. I\({}_{\text{nDQ}}\) at several temperatures were fitted to estimate the D\({}_{\text{res}}\) values, used to calculate C(\(t\)) and each result was appropriately shifted accordingly to the entanglements correlation time, obtained from the literature. The so-obtained \(C(t)\) curve, presented in Figure 10, was then fitted to determine transition regime times and exponential trends. The observations confirmed that flexible homopolymers have very similar motional behavior, following the theoretical prediction of the tube model and its molecular weight dependence. However, higher mobility than predicted in the regime II was found, indicating a less static tube constraint [61]. Regime 0 and I are instead usually investigated with fast-field cycling experiment [62; 63; 64]. More recently, another approach was proposed to extract the analytical parameter of OACF directly from MQ signal functions. Briefly, MQ signals have been interpolated using an approximated function for \(C(t)\), namely constant at very short time and a power law at longer times, in a similar fashion to \(C(t)\) of elastomers. This allows the fitting over a larger data range, overcoming the high errors for the initial rise analysis and of TTS and allowing to study transition areas. The authors claim that this approach could help to study even phenomena where different dynamical processes coexist and TTS is not applicable [65]. Lately, a different method for characterizing intermediate to fast regime motion ( >kHz) was proposed by [PERSON] et al. [33] based on a dipolar filter, which suppresses the signal from rigid segments.