## 3 Results and Discussion
### Analysis of the Statistical Design of Experiments
#### 3.6.2 Graphical Analysis
Indeed, based on Figure S2b, it can be concluded that an increase in the concentration of polyphenols leads to a lower efficiency of the dye removal process throughout the entire working range, as indicated by the steep negative slope of the corresponding line. On the other hand, the concentrations of Fe(II), Fe(III), and hydrogen peroxide appear to have a positive effect on the elimination of methylene blue. It is noteworthy that in the case of Fe(II) concentration, a maximum is reached beyond which a further increase in concentration has a negative impact on dye removal. For the concentrations of Fe(III) and H\({}_{2}\)O\({}_{2}\), although the positive influence gradually diminishes, no maximum is observed. This is particularly important considering the well-known regeneration reaction of H\({}_{2}\)O\({}_{2}\) from -OH radicals, as shown in Equation (7), or the deactivation of such radicals through reactions with excess hydrogen peroxide, as shown in Equation (13). However, similar to the case of chrysoidine, a sufficient concentration of hydrogen peroxide has not been achieved for these scavenging reactions to play a predominant role. The interaction plot, Figure S2c, suggests that the only pair of variables that clearly do not exhibit an interaction with one another are the concentration of Fe(II), denoted as A, and the concentration of Fe(III), denoted as B. In this case, the lines are parallel, indicating no interaction between these variables. In the remaining cases, although the lines do not intersect (or at least not within the graphically represented interval), marked differences in the slopes of the \"+\" and \"-\" lines can be observed. This is indicative of the presence of interactions between the variables. This interaction is particularly evident in the case of polyphenols (D) with Fe(III) (B), and especially, as expected based on previous discussions, with hydrogen peroxide (C). Indeed, since the addition of polyphenols removes the catalyst from the system (Fe\({}^{2+}\) and Fe\({}^{3+}\) ions), the role of H\({}_{2}\)O\({}_{2}\) as a generator of hydroxyl radicals is noticeably affected. Figure S2d shows the response surface plot corresponding to the removal of methylene blue. In this case, both iron ion concentrations have been fixed at their optimal values (see Table 2), while the concentrations of hydrogen peroxide and polyphenols were varied, and the change in the efficiency of methylene blue elimination was represented accordingly. It is striking how strongly the concentration of hydrogen peroxide influences the elimination efficiency, especially at low (\(-1\) and close to \(-1\)) polyphenol concentrations. Similarly, in the absence of hydrogen peroxide, polyphenols have a significant effect on the response variable. This is evident from the steep slope of the response surface curve at both extremes. In contrast, at coded values below \(-0.5\) for polyphenol concentration and above \(0.5\) for H\({}_{2}\)O\({}_{2}\) concentration, the response surface is nearly flat, and elimination efficiencies close to \(100\%\) are achieved (intense red color zone). From all of this, it can be inferred that by carefully selecting a working interval or optimal experimental conditions, the proposed method combining iron nanoparticle adsorption and radical oxidation through the Fenton (and/or \"Fenton-like\") process is capable of effectively removing methylene blue from aqueous solutions, achieving elimination efficiencies close to \(100\%\).