# Enhanced Adsorption of Methyl Orange by Mongolian Montmorillonite after Aluminum Pillaring
## 3 Results
### Isotherms of MO Adsorption  
The relationships between the equilibrium concentrations of MO and the adsorption capacities of Mt, P-MMt, and P-MMt-C400 are shown in Table 10 and Figure 9. They show that the adsorption capacity of P-MMt-C400 is significantly different from those of MMt and P-MMt, which correspond identically to the results of adsorption kinetics. Therefore, three isotherm models (the Langmuir model, the Freundlich model, and the Redlich-Peterson model) were used to study the MO adsorption of P-MMt-C400.  
Three adsorption isotherm models (Langmuir, Freundlich, and Redlich-Peterson) were perfectly fitted by the MO adsorption data of P-MMt-C400, with high correlation coefficients (R\({}^{2}\) = 0.977, 0.994, and 0.998, respectively) (Figure 10).  
\begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Kinetic Model**} & \multicolumn{2}{c}{**Parameter**} \\ \cline{2-3}  & **q\({}_{\text{exp}}\) (mg/g) at 640 min** & **3.42 \(\pm\) 0.04** \\ \hline \multirow{4}{*}{Pseudo-first-order (PFO)} & \(q_{\text{c}}\) (mg/g) & 3.28 \(\pm\) 0.19 \\ \cline{2-3}  & \(k_{1}\) (min\({}^{-1}\)) & 0.0443 \(\pm\) 0.0100 \\ \cline{2-3}  & \(\text{R}^{2}\) & 0.921 \\ \hline \multirow{4}{*}{Pseudo-second-order (PSO)} & \(q_{\text{c}}\) (mg/g) & 3.53 \(\pm\) 0.20 \\ \cline{2-3}  & \(k_{2}\) (mg/g)/min & 0.0184 \(\pm\) 0.0056 \\ \cline{2-3}  & \(\text{R}^{2}\) & 0.941 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Parameters of the pseudo-first-order and pseudo-second-order kinetic models fitted by the MO adsorption data of P-MMt-C400.  
Figure 9: MO adsorption by MMt, P-MMt, and P-MMt-C400 in different equilibrium concentrations of MO; SD is added to each point as an error bar, n = 3.  
According to Table 5, the adsorption of MO by P-MMt-C400 was a better fitting for the Freundlich isotherm model (R\({}^{2}\) = 0.994) than for the Langmuir model (R\({}^{2}\) = 0.977). In the Freundlich isotherm, the value of 1/n is 0.30, approaching zero. Although the Langmuir model is inferior to the Freundlich model in the fitting of the MO adsorption isotherms, it still has a high correlation coefficient (0.977). Thus, the value of \(q_{m}\) obtained from the Langmuir model can be used to predict or represent the maximum adsorption capacity of P-MMt-C400, which is 6.23 mg/g. Compared to the maximum adsorption capacity (0.25 mg/g) of MMt calculated by Langmuir fitting in MO adsorption by MMt, the MO adsorption capacity of P-MMt-C400 was around 25 times larger than that of MMt. In this study, the Redlich-Peterson model was the best fit for MO adsorption by P-MMt-C400 with R\({}^{2}\) = 0.998, compared to the Langmuir and Freundlich models.  
\begin{table}
\begin{tabular}{c c c} \hline
**Isotherm Model** & **Parameter** & **P-MMt-C400** \\ \hline \multirow{3}{*}{[PERSON]} & \(q_{m}\) (mg/g) & 6.23 \(\pm\) 0.27 \\ \cline{2-3}  & \(K_{L}\) (L/mg) & 0.436 \(\pm\) 0.066 \\ \cline{2-3}  & R\({}^{2}\) & 0.977 \\ \hline \multirow{3}{*}{Freundlich} & \(K_{F}\) ((mg/g)/(mg/L)\({}^{\mathrm{nr}}\)) & 2.29 \(\pm\) 0.07 \\ \cline{2-3}  & \(1/n\) & 0.30 \(\pm\) 0.01 \\ \cline{2-3}  & R\({}^{2}\) & 0.994 \\ \hline \multirow{3}{*}{Redlich-Peterson} & \(K_{R}\) (L/g) & 9.87 \(\pm\) 2.81 \\ \cline{2-3}  & \(\alpha_{R}\) (L/mg) & 3.43 \(\pm\) 1.21 \\ \cline{2-3}  & \(\beta\) & 0.76 \(\pm\) 0.02 \\ \cline{2-3}  & R\({}^{2}\) & 0.998 \\ \hline \end{tabular}
\end{table}
Table 5: Parameters of the Langmuir, Freundlich, and Redlich–Peterson models fitted to the adsorption of MO onto P-MMt-C400.  
Figure 10: MO adsorption by P-MMt-C400 in different equilibrium concentrations, fitted by the Langmuir, Freundlich, and Redlich–Peterson isotherm models.