## 4 Characterization of Nanomaterials  
The study of nanomaterials includes the characterization of their structure as well as their physicochemical, mechanical, optical, and electronic properties. One of the most robust techniques for studying nanostructures is X-ray diffraction (XRD), whose objective is to determine the lattice parameters and atomic arrangement, as well as obtain the orientation, size, and crystallinity, of the nanostructures, which in turn determines the structural arrangement. By using techniques such as transmission electron microscopy (TEM), scanning electron microscopy (SEM), and scanning transmission electron microscopy (STEM, which is a merger of TEM and SEM), a sample picture is generated using an electron beam, where the path of the electron is controlled by the use of electrostatic or electromagnetic lenses. When an input electron beam impacts the surfaces of a sample, atoms interact, resulting in the generation of secondary electrons, back-scattered electrons, diffracted electrons, and particular X-rays that vary greatly depending on the surface morphology, topography, and chemical composition. For the elemental surface analysis, energy dispersive X-ray spectroscopy (EDS) is used in conjunction with SEM and is based on the Bragg diffraction principle. This allows us to identify the chemical composition because it can detect almost all elements [29; 30]. Atomic force microscopy (AFM) generates a three-dimensional nanomaterial surface image, which allows us to collect quantitative and qualitative data on morphology, size, surface roughness, and texture. To calculate the dimensions of surface features, it measures the attraction and repulsion forces through the van der Waals interactions between a probe and a sample surface. In addition, AFM can be used to estimate mechanical properties, such as stiffness or adhesion strength, and electrical properties, such as conductivity or surface potential. A modified version of AFM is magnetic force microscopy (MFM), which detects the magnetic fields for imaging down to 100 nm in resolution and can be employed to characterize and manipulate 1D and 2D nanomaterials. The operational principle of MFM is based on the quantification of long-range magnetostatic force, which is situated over the sample surface at a constant height between the magnetic sample and magnetically coated probe [31]. Furthermore, nanomaterial three-dimensional visualization is possible with confocal scanning laser microscopy (CSLM), as well as by observation of the interaction or distribution of the wall material by using fluorochromes that bind to specific functional groups of the target molecule [32]. Dynamic mechanical analysis (DMA) allows us to characterize the interfacial interactions between the polymeric matrix and the filler particles. Commonly, it is used in films that add solid particles to enhance their properties. The material is subjected to oscillating force given by temperature and frequency. In terms of the functions of stress (\(\sigma\)) and strain (\(\gamma\)) forces applied, these determine the transition temperature (Tg), storage modulus (E'), loss modulus (E\"), and tan value (\(\delta\)), which then translate into the flexibility film and isotropic properties of the final coating [33]. The change in the properties of the nanomaterials as a function of temperature requires a differential thermal analysis (DTA). Currently, thermal stability is evaluated by thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), thermal analysis (DTA), and dynamic mechanical analysis (DMA). The first one measures the sample weight in the function of the temperature in a specific controlled atmosphere. The second determines the material transitions. It means the melting, crystallization, and glass transition of a nanomaterial. The third method measures the materials' melting points and decomposition in order to quantitatively assess and determine the chemical composition of nanomaterials by studying a substance's thermal performance when it is heated.