# Time Domain NMR in Polymer Science: From the Laboratory to the Industry
## 1 Introduction  
Nowadays, polymers are of major practical importance, since they have low cost and show unique physical properties, such as viscoelasticity, toughness, and ability to form either glasses, semi-crystalline or elastic materials, that scale easily with minimal variation of either chemistry, and molecular weight [1]. They are found in many applications, from packaging to automotive and healthcare [2]. It is fundamental to understand the materials' behavior, correlating their microscopic properties with their macroscopic performances in real applications and vice versa, in order to improve the final products, acting on either the polymer chemistry or the manufacturing parameters. Therefore, tools are needed to monitor the \"state of the art\" of the current materials and processes. NMR (nuclear magnetic resonance) has always been one of the main characterization techniques for solid polymeric materials, since its first applications in the 1970s. Particularly, solid-state NMR allows to study polymers at a molecular level in almost all their states and with minimal sample preparation procedure, in a non-destructive manner [3; 4; 5]. The use of high field instruments gives insights into the chemical and structural composition of polymers, but these instruments are expensive and require great maintenance limiting their application in industrial contexts. A powerful alternative can come from low-field benchtop devices, operating in time domain. They are easy to use, even for relatively unspecialized personnel, therefore they allow to conduct measurements fast and without any special sample preparation. With appropriate calibration procedure, quantitative information isobtainable. In addition to that, their small size makes them easily implementable in every laboratory, and their footprint is low since they operate through permanent magnets, which do not require cryogenic gases. Low-field instruments are both in closed geometry and in open geometry, such as the NMR-MOUSE [6]. The former are valuable tools to characterize bulk properties, while the latter possesses highly inhomogeneous fields, which, through hampering FID (free induction decay) detection, enables to gain space-dependent information, varying the position of the instrument on the material and its distance to the surface, thus selecting a slice along the material's thickness. The most industrially relevant topic is by far the NMR of proton (\({}^{1}\)H) atoms, ubiquitous in organic compounds, polymers, and natural materials. Though \({}^{1}\)H LF-TD-NMR does not provide chemical information, since after Fourier transform chemical shift dispersion is extremely limited and basically all the protons contribute to a single resonance, it has been proved to be useful to study the dynamical properties of polymer chains. This information can be drawn from the relaxation of \({}^{1}\)H spins. The restoration of a spin thermal equilibrium state with the lattice in an external static magnetic field, following a perturbation through sequences of electromagnetic pulses, is characterized by two relaxation times: a spin-spin (T\({}_{2}\)) and a spin-lattice (T\({}_{1}\)) relaxation time. Their magnitude is dependent upon how the interaction between spins and with the environment (the so-called lattice) is modulated by the molecular mobility.