## 3 Results
### Heterogeneous Photocatalysis
#### 3.3.2 Goethite
This enhancement is attributed to the greater generation of sulfate radicals, as previously discussed [36]. Figure 10: **(A)** Photocatalytic degradation of Nile Blue and **(B)** % degradation achieved in 60 min, in the presence of Goethite catalyst and different concentrations of S\({}_{2}\)O\({}_{8}\)\({}^{2-}\) (C\({}_{0}\) = 15 mg L\({}^{-1}\), C\({}_{\text{cataly}}\) = 100 mg L\({}^{-1}\), C\({}_{\text{oxidant}}\) = 100, 200, 300, 500 mg L\({}^{-1}\)). A comparison between Figures 2 and 10A shows that the rate of dye degradation is not different from that found in the presence of the oxidant alone. Therefore, the catalyst does not further enhance the formation of active radicals, and the decomposition of the dye is primarily due to the action of the oxidant. This can be confirmed by the following equation:  
\[\frac{\text{\%\emph{e}removal by Goethite}/\text{S}_{2}\text{Q}_{8}^{2-}}{\text{ \%\emph{e}removal by Goethite}+\text{\%\emph{e}removal by S}_{2}\text{Q}_{8}^{2-}}= \frac{76.69}{11.38+70.85}\%=0.93<1\]  
The above underscores that goethite does not contribute to enhancing the production of active radicals compared to that produced by the exclusive use of the S\({}_{2}\)O\({}_{8}^{2-}\) oxidant. Thus, there is no synergistic effect between goethite and persulfate ions. Therefore, the following experiments were carried out using only hydrogen peroxide as an oxidant. Consequently, goethite exhibits limited photocatalytic activity alone due to rapid electron-hole recombination, linked to its conduction band position. In the presence of H\({}_{2}\)O\({}_{2}\), it catalyzes hydroxyl radical generation via both leached iron ions (homogeneous Fenton-like reactions) and surface-mediated redox processes, leading to enhanced dye degradation and a clear synergistic effect. Conversely, with persulfate, goethite shows no synergistic interaction, indicating a minimal catalytic contribution beyond direct oxidant activation. A small amount of iron leaching is detected during the reaction, with concentrations remaining below 0.2 mg L\({}^{-1}\). While this minor leaching may contribute slightly to homogeneous Fenton processes, it does not alter the predominantly heterogeneous nature of the photocatalytic system. Thus, goethite acts primarily as a heterogeneous photo-Fenton catalyst when combined with hydrogen peroxide. Effect of Goethite Concentration  
Given the high efficiency of the system comprising goethite and hydrogen peroxide in degrading the target dye, it was subjected to further investigation. Consequently, experiments were carried out at four different goethite concentrations (100, 200, 300, and 500 mg L\({}^{-1}\)) (Figure 11). In Figure 11, we observe that as the catalyst concentration increases up to 200 mg L\({}^{-1}\), the degradation rate of the dye increases. This may be attributed to the increase in the  
Figure 9.0 (**A**) Photocatalytic degradation of Nile Blue and (**B**) % degradation achieved in 60 min, in the presence of H\({}_{2}\)O\({}_{2}\) and different concentrations of Goethite (C\({}_{0}\) = 15 mg L\({}^{-1}\), C\({}_{\text{oxidant}}\) = 200 mg L\({}^{-1}\), C\({}_{\text{cataly}}\) = 100, 200, 300, 500 mg L\({}^{-1}\)). specific surface area of the catalyst. Consequently, more active sites on the mineral's surface are now available for the oxidant and the dye, increasing the reaction rate. However, at higher catalyst concentrations, a decrease in the degradation rate is observed due to possible agglomeration of the goethite, which results in a reduction in the specific surface area available for the reaction in the treated solution. Furthermore, as the concentration of the catalyst increases, hydrogen peroxide tends to undergo excessive reaction with goethite, resulting in an unproductive consumption of the oxidant. This undesirable side reaction, characteristic of the heterogeneous Fenton process, significantly accelerates the depletion of H\({}_{2}\)O\({}_{2}\) and diminishes the overall efficiency of the system [41].