## 2 Results and Discussion
### Methyl-\(\beta\)-Cyclodextrin/AEDTA Complex Characterization  
The interaction between methyl-\(\beta\)-cyclodextrinrin and AEDTA was investigated by FTIR, XRD, and NMR spectroscopy, well-established techniques for studying cyclodextrin inclusion complexes [12]. The methyl-\(\beta\)-cyclodextrinrin/AEDTA complex with a 1:1 molar ratio was extensively analyzed. To further confirm the interaction between the host and guest molecules, a physical mixture with the same molar ratio was also prepared. It has been vastly reported that the variation of the shape, shift, and intensity of the FTIR absorption bands of the guest or host molecule can provide information concerning the formation of complexes [20; 21]. Figure 2 illustrates the infrared spectra of methyl-\(\beta\)-cyclodextrinrin, AEDTA, and of the binary systems (complex and physical mixture). The characteristic AEDTA absorption peak at 1636 cm\({}^{-1}\), attributed to the scissoring vibration of the amino group [20; 22], shifted and changed in shape in the spectrum of the complex. The broadening of the same peak suggested an amorphization of AEDTA, a reasonable consequence of its complexation, while the shift toward lower wavenumbers reflected a change in the vibration energy of the amino group. These changes in the characteristic absorption band of the corrosion inhibitor highlighted the occurring of an interaction and opened two potential scenarios: the formation of an inclusion or non-inclusion complex. Conversely, the spectrum of the physical mixture perfectly overlapped with the spectra of the individual components, and the peak at 1636 cm\({}^{-1}\) remained sharp and centred at the same wavenumber of the AEDTA reference, indicating no significant interaction between the two components. The successful complexation of AEDTA and methyl-\(\beta\)-cyclodextrinrin was confirmed by XRD, a useful technique for the detection of cyclodextrin complexation in a powder or microcrystalline state [23; 24]. The XRD diffractograms are reported in Figure 3: the diffraction pattern of AEDTA exhibited several sharp peaks, indicating its crystalline structure, while the diffractogram of cyclodextrin was characteristic of an amorphous material. As expected, the XRD pattern of the physical mixture was a direct superimposition of those of the individual components, whereas the methyl-\(\beta\)-cyclodextrinrin/AEDTA complex showed two broad halos in the diffraction similar to those of methyl-\(\beta\)-cyclodextrinrin, indicating its amorphous state. This loss of crystallinity suggested that AEDTA and methyl-\(\beta\)-cyclodextrinrin were mixed at a molecular level, providing further evidence of complexation [25]. Figure 3: XRD diffractograms of AEDTA, methyl-\(\beta\)-cyclodextrintrin, their complex, and their physical mixture. Figure 2: ATR-FTIR spectra of AEDTA, Me–\(\beta\)-CD, their complex, and physical mixture. The box shows the spectral region with the characteristic absorption band of AEDTA and its shift due to complexation. The nature of the interaction between AEDTA and methyl-\(\beta\)-cyclodextrintrim was also explored using \({}^{1}\)H NMR spectroscopy, a powerful method for analyzing supramolecular assemblies in solution. Significant chemical shift changes in specific host or guest nuclei between the free and bound states can confirm the formation of inclusion complexes in solution [7]. Figure 4 presents the NMR spectra of AEDTA, methyl-\(\beta\)-cyclodextrintrim, and the methyl-\(\beta\)-cyclodextrintrim/AEDTA complex (1:1 molar ratio), with the chemical shifts (\(\delta\)) and displacements (\(\Delta\delta\)) detailed in Table 1[26]. The inclusion of AEDTA in the methyl-\(\beta\)-cyclodextrintrim cavity was indicated by the chemical shift variations in the host protons H\({}_{3}\) and H\({}_{5}\), compared to their positions in free CD molecules (Figure 5). Both cyclodextrin protons were shielded, signifying the inclusion of an electron-rich group, likely the -NH\({}_{2}\) group of AEDTA.