## 4 Conclusions  
In this study, the commercially available nZVZ was characterized by means of XRD and XPS. Comparison between the experimental and prediction values obtained by the RSM and the BP-ANN  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(\mathbf{K}\) & \(\mathbf{\Delta G^{0}\) (KJ/mol)}\) & \(\mathbf{\Delta S^{0}\) (kJ/mol/K)}\) & \(\mathbf{\Delta H^{0}\) (kJ/mol)}\) \\ \hline
293 & \(-1.2512\) & & \\
298 & \(-2.8320\) & & \\
303 & \(-4.1823\) & & \\
308 & \(-5.7419\) & & \\ \hline \hline \end{tabular}
\end{table}
Table 10: The thermodynamic parameters for adsorption of MG onto nZVZ.  
Figure 19: Plot of ln\(Kc\) vs. \(1/T\) for initial pH of 5, contact time of 120 min and initial concentration of 700.00 mg/L.  
models showed that the BP-ANN model was more accurate based on the value of \(R^{2}\) (0.9999). The maximum removal efficiency of MG under the optimum conditions was obtained with the aid of the RSM, ANN-PSO and ANN-GA models. The mean absolute errors between confirmatory and predicted results for the RSM, ANN-PSO, and ANN-GA models are 12.13%, 7.68% and 3.40%, respectively, which demonstrate that the ANN-GA model manifest a better agreement in predicting the removal efficiency of MG than the other two models. Additionally, both the ANOVA and sensitivity analysis demonstrate that the important process parameter is contact time. The equilibrium data of MG uptake by nZVZ were fitted to Langmuir, Freundlich and Temkin isotherms. The Langmuir model was found to fit the adsorption data well with maximum adsorption capacity of 1000.00 mg/g. The experimental data were well described by the pseudo-second order model (\(R^{2}\) = 0.9463) with higher correlation coefficients than the pseudo-second order model (\(R^{2}\) = 0.9302). From the thermodynamic study, it is concluded that the adsorption of spontaneous nature occurred in the range of temperature studied (293 K-308 K) due to the negative value of \(\Delta G^{0}\). The positive value of \(\Delta H^{0}\) indicated the endothermic nature of the adsorption interaction. This is in agreement with the results where the MG dye adsorption increases with an increase in temperature. The positive value of \(\Delta S^{0}\) reflects the affinity of the adsorbate for the adsorbent and the increased randomness at the solid-solution interface during the adsorption process. In conclusion, nZVZ can be a promising adsorbent for the removal of MG from aqueous solutions. Further studies should investigate the regeneration efficiency of the nZVZ for the removal of MG or other dyes (e.g., Methyl orange, Methylene Blue) as well as the removal efficiency of dyes via the permeable reactive barrier in the laboratory.  
This work was supported by the National Natural Science Foundation of China under Grant No. 21367009, the National 111 Project of China under Grand No. D17016 and the Postgraduate Educational Innovation Project of Guizhou Province under project No. GZS [2016] 04.  
[PERSON], [PERSON], [PERSON] and [PERSON] conceived and designed the experiments, performed the experiments and wrote the paper; [PERSON], [PERSON] and [PERSON] analyzed the data.  
The authors declare no conflict of interest.