## 3 Results and Discussion
### Modeling and Optimization by RSM  
In the present study, the normal plot of studentized residuals vs. predicted probability values indicates that the model is suitable owing to the data distributed homogeneously on either side of the straight line following the Gaussian distribution (Figure 8) [46]. A satisfactory correlation (\(R^{2}\) = 0.9813) between the experimental and predicted removal efficiency suggests that the model is reliable (Figure 9). Three dimensional response surface plots are shown in Figure 10, which represent the changes in removal efficiency depending on every two factors when the other factors are set to the fixed values [47]. Initial pH as an important independent variable does not only affect the aqueous chemistry of molecules but also the surface binding sites of the adsorbents. The zero point of charge (pHzpc) indicates a net surface charge equal to zero [48]. MG (pKa = 10.3) becomes more protonated in acidic solutions and deprotonated in basic solutions [49]. The surface of nZVZ is positive when the solution pH is above the pHzpc, whereas the surface of nZVZ is negative when the solution pH is below the pHzpc [50]. From Figure 10a, it can be observed that an increase in pH and temperature enhances the removal efficiency of MG. Furthermore, the final pH of the solution was higher than the initial pH of the solution. The initial pH of the solution was acidic while the final pH of the solution was found to be alkaline (Figure 11). At higher pH, the number of negatively charged sites increase so that the adsorption was favored between the adsorbent and the cationic MG molecules due to a strong electrostatic attraction [30]. According to the RSM-BBD experimental design, the corresponding quadratic polynomial regression model is expressed by Equation (11). Notably, the positive values of coefficients for A (initial pH), B (temperature), especially C (contact time) illustrate the synergistic effect on the response.  
\[\begin{split} Y&=63.12+10.44\;\text{A}+10.34\;\text{B }+12.71\;\text{C}-2.21\;\text{D}-4.50\;\text{AB}-8.53\;\text{AC}+6.22\;\text{AD}\\ &\quad+2.38\;\text{BC}+2.63\;\text{BD}+1.10\;\text{CD}+6.21\; \text{A}^{2}-3.12\;\text{B}^{2}-3.32\;\text{C}^{2}+1.97\;\text{D}^{2}\end{split} \tag{11}\]  
Figure 8: Normal plot of studentized residuals vs. normal % probability.  
Figure 10: _Cont._  
Figure 9: The plot of correlation between experimental and predicted removal efficiency.  
The results for the analysis of variance (ANOVA) are summarized in Table 2, which can be used for identifying the significant factors. The \(F\)-value for the model is 52.57 implying that the model is significant. Since the \(p\)-values are less than 0.050, all first-order terms (initial pH (A), temperature (B), contact time (C) and initial concentration (D)) exhibit a high significance on the removal efficiency of MG. The combined effects of initial pH and temperature (AB), initial pH and contact time (AC), initial pH and initial concentration (AD) and the square of the initial pH (A\({}^{2}\)) also show a significance on the removal efficiency of MG at the 95% confidence level. Based on the \(F\)-values of independent variables, the order for these parameters influencing the removal efficiency of MG is: contact time > initial pH > temperature > initial concentration.  
Figure 11: The difference between the initial and final pH of the solutions.  
Figure 10: Three dimensional response surface plots for the malachite green (MG) removal: (**a**) Initial pH—Temperature; (**b**) Initial pH—Contact time; (**c**) Initial pH—Initial concentration (**d**) Temperature—Contact time; (**e**) Temperature—Initial concentration; (**f**) Contact time—Initial concentration.