# Time Domain NMR in Polymer Science: From the Laboratory to the Industry
## 1 Introduction
In fact, they show well-known dependence with the motional correlation time \(\tau_{\mathrm{c}}\) (Figure 1), described by the BPP equations (Bloembergen-Purcell-Pound) [7], in the hypothesis of two equal spins where the only relaxation channel is the dipolar interaction between them:  
\[\frac{1}{T_{1}}=\frac{3}{10}\frac{\gamma^{4}\hbar^{2}}{r^{6}}\tau_{c}\bigg{\{} \frac{1}{1+\omega_{0}{}^{2}\tau_{c}^{2}}+\frac{1}{1+4\omega_{0}{}^{2}\tau_{c} ^{2}}\bigg{\}}; \tag{1}\]  
\[\frac{1}{T_{2}}=\frac{3}{20}\frac{\gamma^{4}\hbar^{2}}{r^{6}}\tau_{c}\bigg{\{} 3+\frac{5}{1+\omega_{0}{}^{2}\tau_{c}^{2}}+\frac{2}{1+4\omega_{0}{}^{2}\tau_{ c}^{2}}\bigg{\}}. \tag{2}\]  
Therefore, their determination can be exploited to discriminate different dynamical regimes inside the material, depending on its structure and morphology. Motional correlation times affect, in turn, macroscopic dynamical behavior, related to viscoelasticity, mechanical response, and processing characteristics, which are, in the end, the main concerns for specific applications. Some methods require additional equipment, such as fast-field cycling (FFC) and pulse field gradient (PFG). Figure 1: Behavior of T\({}_{1}\) and T\({}_{2}\) as a function of correlation time (in double-log scale) for \(\frac{1}{2}\) spins. FFC allows to measure T1 as function of the variation of the magnetic field strength, spanning on a wide range of frequencies. This can be obtained either with a single instrument, capable of fast electrical switching of the field, or physically moving the sample in instruments with different magnetic fields [8]. Referring to Equation (1), the analysis of the dispersion curve of T1 vs. \(\omega_{0}\) (Larmor frequency, that is the frequency associated with the precession of the spin caused by the magnetic field) allows to distinguish different correlation times, which define different dynamics inside the polymeric material [9]. This can be useful to perform \"molecular rheology\" experiments. Instead, PFG is a technique to monitor the molecular diffusion and requires a tunable magnetic field gradient. The NMR signal attenuation after the pulsed gradient is dependent on the diffusion coefficient of the molecule [10]. It can be exploited to study the dynamics of polymers in solution or inside porous materials [11; 12]. Although interesting for polymer characterization, these two techniques will not be further addressed in this review, since we decided to deal with the basic equipment for LF-TD-NMR in the characterization of polymeric items. Although in principle all nuclear spins can be studied with LF-TD-NMR, only abundant \(\frac{1}{2}\) spins can be measured with reasonable signal-to-noise ratio, furthermore, only spins with high gyromagnetic have significant Larmor frequencies at low field, basically only two systems satisfy these two requirements at the same time: \({}^{1}\)H and \({}^{19}\)F. In this review, we focus just on \({}^{1}\)H, and we would like to highlight the main applications of pulse sequences that can be conducted on low-field NMR instruments and the relevant parameters that can be drawn out. Parameters that can help to understand polymeric materials in two different environments: at an academic level for the characterization of innovative polymeric materials or to highlight basic polymer physics, in the industry for R&D and quality control (QC). A special section has been dedicated to bioplastics. In fact, future perspectives are oriented towards the substitution of traditional plastics with raw materials coming from natural resources. Preliminary studies have been made to assess the physical properties of these new materials.