## 3 Selected Methods and Experimental Approaches for Analysis of HS Structure
### Solid State Investigations
#### 3.2.2 Nuclear Magnetic Resonance Techniques  
Nuclear magnetic resonance (NMR) is a locution referring to an ensemble of different techniques all based on the same principles and used to unveil chemical-physical characteristics in solid, liquid, and semi-solid phases [104, 105, 106, 107, 108]. The general theory about NMR technique is reported elsewhere [109]. Here we intend to give only a brief overview about the NMR principles. In details, nuclei with an odd number of protons and/or neutrons have a nuclear spin associated with a magnetic moment that orients when immersed in an external magnetic field (B\({}_{0}\)). At equilibrium, the orientation of the nuclear magnetic moments is distributed over different energy levels, characterized by having a slightly accessing population on the lowest energy level. This distribution of population can be perturbed by irradiating the sample with pulses of radiofrequency waves with an oscillating magnetic field (B\({}_{1}\)). After this excitation, the distribution of the orientations of the nuclear magnetic moments returns to the equilibrium configuration through two relaxation mechanisms. The first, defined as longitudinal relaxation, is linked to the recovery of the magnetization vector towards its equilibrium value, oriented along the direction of B\({}_{0}\) with consequent loss of energy. The second, called transversal relaxation, is responsible for the loss of phase coherence and the decay of the magnetization vector in the plane perpendicular to B\({}_{0}\). Both mechanisms act simultaneously, although they are characterized by different relaxation times defined as longitudinal or spin-lattice relaxation time, (T\({}_{1}\)) and transverse or spin-spin relaxation time (T\({}_{2}\)). The signals acquired by NMR technique can be analyzed in many different ways. As an example, in the NMR spectroscopy, the application of the Fourier transform provides plots (also referred to as spectra) where resonance signals are reported versus frequency. In order to make signal position independent of the strength of the applied magnetic field, the resonant frequency is expressed as chemical shift measured in part-per-millions (ppm). According to the number of the frequency axes, it is possible to differentiate among mono- (1D), bi- (2D) and three-dimensional (3D) NMR spectroscopy [110, 111]. While signal intensity is directly related to the number of nuclei which are excited by the applied pulse, signal position is dependent on the nuclear chemical environment. This is why NMR spectroscopy can be used both to investigate the structure and 3D conformation of complex organic molecules, and to determine the number of nuclei affected by the same chemical environment. However, the quantitative analysis performed on complex mixtures can be limited by the type of sample phase, the pulse sequence used for the NMR investigation and by hardware constraints [104, 112, 113]. A number of parameters affect the time scale of the relaxation processes such as, e.g., the molecular size, temperature, presence of paramagnetic metals and other factors linked to physical state of the system under study. In particular, when experiments are designed to measure relaxation times T\({}_{1}\) or T\({}_{2}\), the time decays of the NMR signal can be analyzed by using the inverse Laplace transform which allows to obtain the distribution of relaxation times [114; 115; 116; 117; 118]. This method, called time-domain (TD) NMR, is used to acquire information on molecular dynamics for both simple systems and complex mixtures [119]. In the last few decades, the new technique called Fast Field Cycling (FFC) NMR relaxometry is appearing on the scene of different scientific fields [119]. It is based on the rapid changes of the proton Larmor frequencies (\(\
u_{\rm L}\)) by modulating the current intensity passing through a coil printed on a silver support [120].