## 2 Results and Discussion
### Study of the Methyl-\(\beta\)-Cyclodextrin/AEDTA Complex  
To gather information on the stoichiometry of the complex, thirteen complexes were synthetized employing different host/guest molar ratios (Table 2, Section 2.2).  
\({}^{1}\)H NMR spectra of pure components and methyl-\(\beta\)-cyclodextrintrim/AEDTA complexes are reported in Figure 6.  
The stoichiometry of the complex was determined using the continuous variation method, originally proposed by [PERSON] (1928) [27]: this method is based on induced chemical shift variation, \(\Delta\delta\), that is experimentally determined, and it is directly related to the concentration of the complex. \(\Delta\delta\) is defined as the difference between the chemical shifts of the free molecule and the bounded one.  
NMR spectra were recorded for a series of solutions in which the total concentration of the two species was kept constant at 3 mM and the concentration ratio of the single components (r = [AEDTA]/([AEDTA] + [Me-\(\beta\)-CD]) or r = [Me-\(\beta\)-CD]/([AEDTA] + [Me-\(\beta\)-CD]) was varied between 0 and 1.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Solution No.** & **AEDTA (mM)** & **Methyl-\(\beta\)-Cyclodextrin (mM)** \\ \hline
1 & 0.25 & 2.75 \\
2 & 0.50 & 2.50 \\
3 & 0.75 & 2.25 \\
4 & 1.00 & 2.00 \\
5 & 1.25 & 1.75 \\
6 & 1.50 & 1.50 \\
7 & 1.75 & 1.25 \\
8 & 2.00 & 1.00 \\
9 & 2.25 & 0.75 \\
10 & 2.50 & 0.50 \\
11 & 2.75 & 0.25 \\
12 & 0.00 & 3.00 \\
13 & 3.00 & 0.00 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Molar concentrations of the methyl-\(\beta\)-cyclodextrintrim /AEDTA complex solutions.  
Figure 5: Zoom in on NMR spectra of methyl-\(\beta\)-cyclodextrintrim and the complex.  
Under these conditions, if a physical quantity directly related to the concentration of the complex can be measured and plotted as a function of r, its maximum value will be reached at r = m/m + n, where m and n are AEDTA and methyl-\(\beta\)-cyclodextrintrin proportions in the complex, respectively. When signals are rapidly averaged by the exchange between free and bound states, the quantity \(\Delta\delta_{\text{obs}}\)[AEDTA] or \(\Delta\delta_{\text{obs}}\)[Me-\(\beta\)-CD] (where \(\Delta\delta_{\text{obs}}\) is the chemical shift difference between free AEDTA or Methyl-\(\beta\)-Cyclodextrin and the observed value for a given ratio r) will be proportional to the complex concentration. Therefore, \(\Delta\delta_{\text{obs}}\)[AEDTA] or \(\Delta\delta_{\text{obs}}\)[Me-\(\beta\)-CD] can be plotted against r [28; 29]. Figure 7 highlights the most significantly affected chemical shifts. The continuous variation plot of \(\Delta\delta_{\text{obs}}\)[Me-\(\beta\)-CD] against r of the internal protons H\({}_{3}\) and H\({}_{5}\) showed a maximum at r = 0.5, indicating a 1:1 complex stoichiometry.  
Figure 6: NMR spectra of AEDTA, methyl-\(\beta\)-cyclodextrintrin, and their complex.  
Figure 7: [PERSON]’s plot of H\({}_{3}\) and H\({}_{5}\) of Me-\(\beta\)-CD.  
A corresponding [PERSON]'s plot for the NH\({}_{2}\) protons could not be drawn, as no visible signal was observed in the spectra. However, it is reasonable to assume that the complex followed an equimolar host-guest ratio.