## 3 Result and Discussion
### Results of the RSM Model  
In this section, statistical methods are applied to find the optimal synthesis parameters leading to a TiO\({}_{2}\) photocatalyst with the highest performance regarding DCF decay and mineralization. Using the optimal custom design model Version 13.0.5.0, the synthesis temperature and the calcination temperature were used as input variables (A) and (B), respectively. Four different models were applied, but only the quadratic model fit the pseudo-first-order DCF degradation rate and TOC removal, as shown in Tables S1 and S2, respectively. Statistic parameters obtained from data fitting for the quadratic model are summarized in Table 3. For the pseudo-first-order DCF degradation rate, the predicted \(R^{2}\) (0.440) is relatively low compared to the adjusted \(R^{2}\) of 0.877, i.e., the difference is greater than 0.2. Such a difference might result from large block effects [37]. The \(A_{deq}\) precision value (10.101), which measures the signal to noise ratio, is higher than 4, indicating an adequate signal [37]. For TOC removal, the predicted \(R^{2}\) of 0.831 is still in reasonable agreement with the adjusted \(R^{2}\) of 0.955, i.e., the difference is less than 0.2, the \(A_{deq}\) precision value (the signal to noise ratio) is 14.846, indicating an adequate signal for this parameter as well. The statistic parameters indicate that the quadratic model can predict both parameters inside the chosen region.  
\begin{table}
\begin{tabular}{l c c} \hline \hline
**Statistic Parameters** & **Kapp** & **TOC Removal** \\ \hline R\({}^{2}\) & 0.954 & 0.983 \\ Adjusted R\({}^{2}\) & 0.877 & 0.955 \\ Predicted R\({}^{2}\) & 0.440 & 0.831 \\ Adeq Precision & 10.101 & 14.846 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Statistical quadratic model data fitting for DCF decay rate and TOC removal.  
Figure 9: (**A**) Results of the reusability test for DFC degradation and (**B**) the proposed mechanism for DCF degradation using TiO\({}_{2}\) under irradiation with simulated sunlight.  
Figure 11 shows 3D surface plots which include the calcination and synthesis temperature interactions with the rate of DCF degradation and degree of TOC removal. Synthesis temperatures greater than 70 \({}^{\circ}\)C and calcination temperatures between 400 \({}^{\circ}\)C and 500 \({}^{\circ}\)C are necessary to prepare anatase TiO\({}_{2}\) which is photocatalytically active under solar irradiation. Contour plots showing the synthesis parameters leading to a highly active anatase photocatalyst are presented in Figures S4 and S5.  
Finally, the model was used to predict an optimal synthesis temperature and calcination temperature to form a catalyst with an anatase phase showing the highest DFC degradation rate and mineralization efficiency. An optimal synthesis temperature of 71 \({}^{\circ}\)C and an optimal calcination temperature of 440 \({}^{\circ}\)C were suggested by the model, leading to a DCF decay rate of 0.055 min\({}^{-1}\) and a mineralization rate of 100%. A new catalyst was synthesized with these parameters and tested in the DFC degradation process. The DFC degradation rate obtained with this new catalyst was slightly faster (0.063 min\({}^{-1}\)) than predicted and the TOC removal rate was 97%, slightly lower than the predicted value.