## 3 Results and Discussion
### Optimization for the Removal of the FD&C Red 40 Dye in an Aqueous Solution
#### 3.2.4 Interaction Effects on Response and Process Optimization  
The mathematical model's 3D surface response plot and 2D contour plot for the pH and dye concentration interaction (Figure 2A,B) show that decreasing the pH of the solution from 10 to 1 causes an increase in the percentage removal of FD&C Red 40 dye from 0 to 100%. The contour diagram shows that the optimum pH has a value of 1.73, and the optimal amount of TiO\({}_{2}\) was 279.77 mg.  
As the concentration and pH levels decrease, the removal efficiency of the dye increases since the number of active adsorption sites will be more significant. Additionally, these molecules will have a net negative charge at the optimum pH (since the sulfonate groups of the FD&C Red 40 dye molecules are dissociated at this value [30], a result that coincides with the main effects analysis.  
On the other hand, the mathematical model predicts that the optimal initial concentration of the dye is 55.23 mg L\({}^{-1}\) at low pH levels, with the removal of 151.69% (which corresponds to a complete removal under experimental conditions) observed in the contour plot. This result highlights the more significant impact of the solution's initial pH than its initial concentration on the percentage of dye removal. The removal was almost zero at the same concentration level in a highly alkaline medium (pH \(>\) 10).  
3.2.5 Effect of the Addition and Dose of Graphene Oxide on the Removal Efficiency of FD&C Red 40 Dye  
Despite the optimal value of TiO\({}_{2}\) (279.77 mg) in the CCD, we used 300 mg of TiO\({}_{2}\) for the CS-GO-TiO\({}_{2}\)-GLA beads to replicate the same experimental conditions of runs 6, 13, and 15 of the CCD and to study the effect of GO on the dye removal efficiency.  
Table 5 shows the pH solution effect and the initial dye concentration when comparing the results obtained between experimental runs 6 and 13 of the CCD (whose pH values are equal) for the beads with 1 wt.% of GO, where an increase in the removal efficiency from 83.5% to 98.5% due to the decrease in the initial concentration of the dye from 45 mg L\({}^{-1}\) to 15 mg L\({}^{-1}\). In addition, an improvement in removal from 83.5% to 100.0% is observed between samples 6 and 15, where the pH value drops from 7 to 3. On the other hand, it can be observed that the addition of a more significant amount of GO does not have a greater influence on the removal of the dye. However, removal results show that beads with 3 wt.% of GO (96.7%) were more efficient than 1 wt.%. For that reason, we selected this percentage for subsequent experiments.  
Table 6 compares the removal efficiency of FD&C Red 40 dye between CS-TiO\({}_{2}\)-GLA and CS-GO-TiO\({}_{2}\)-GLA beads (with 3 wt.% GO). Adding GO to CS-TiO\({}_{2}\)-GLA beads can efficiently enhance FD&C Red 40 Dye removal, independent of pH and initial dye concentration. The modification of GO with CS is possible due to the existence of oxygenated groups through the nanosheet, which can interact with the polymeric matrix through supramolecular interactions [33]. In this way, the GO aligns itself between the CS chains, where it establishes an interlocking interaction that clings to the CS chains by hydrogen bonds. [34]. The improvement in adsorption capacity is due to GO's own characteristics (large surface area, good chemical stability, and a flat basal structure) and its role in the dye adsorption mechanism [35]. GO molecules play a role within the synthesized beads as new adsorption active sites where three possible types of interactions with the dye can occur (electrostatic, hydrogen bonds, and \(\pi\)-\(\pi\) interactions) [36]. The system's adsorption mechanism is discussed in more detail in the adsorption kinetics section.  
Figure 2: Three-dimensional response surface plot (**A**) and contour plot (**B**) of the removal efficiency of FD&C Red 40 dye.