## 3 Results and Discussion
### Adsorption Isotherm Studies  
The MB adsorption isotherm data were evaluated by three adsorption isotherm equations, e.g., Langmuir, Freundlich and Sips models [53; 54; 55]. Langmuir model is related to a homogeneous monolayer adsorption process, while Freundlich model is widely used for heterogeneous multilayer adsorption. Overall, Sips model is a combination of both Langmuir and Freundlich equations. Langmuir, Freundlich and Sips models can be expressed as follows (Equations (7)-(9), respectively):  
\[\mathrm{q_{e}}=\frac{\mathrm{q_{m}}\ \mathrm{K_{L}C_{e}}}{1+\mathrm{K_{L}C_{e}}} \tag{7}\]  
\[\mathrm{q_{e}}=\mathrm{K_{F}C_{e}^{1/n}} \tag{8}\]  
\[\mathrm{q_{e}}=\frac{\mathrm{q_{m}}\ \mathrm{(b_{s}C_{e}^{1/s})}}{1+\mathrm{(b_{s }C_{e}^{1/s})}} \tag{9}\]  
where, \(\mathrm{q_{e}}\) (mg g\({}^{-1}\)) is the equilibrium adsorption capacity and \(\mathrm{C_{e}}\) (mg L\({}^{-1}\)) is the equilibrium MB concentration in solution; \(\mathrm{q_{m}}\) (mg g\({}^{-1}\)) is the maximum monolayer capacity and \(\mathrm{K_{L}}\) (L mg\({}^{-1}\)) is the Langmuir constant, indicative of the affinity of the adsorbent towards the pollutant. Likewise, \(\mathrm{K_{F}}\) (L g\({}^{-1}\)) and 1/n are parameters of Freundlich equation; the value of 1/n is representative of the adsorption intensity. Finally, \(\mathrm{b_{s}}\) (L mg\({}^{-1}\)) is a constant of Sips equation, which depends on the temperature, and 1/s is another parameter related to the adsorption energy. Experimental and theoretical MB adsorption data are shown in Figure 8 and the calculated adsorption equilibrium parameters are collected in Table 2. According to the obtained low RMSE and high R\({}^{2}\) values, it could be affirmed that Sips model described very satisfactorily the experimental MB equilibrium adsorption data. Thus, the maximum adsorption capacity calculated from the model (320.5 mg g\({}^{-1}\)) was found very close to the experimental value (307.0 mg g\({}^{-1}\)), suggesting the homogenous surface of the adsorbent and the formation of a monolayer of MB molecules on its surface  
Figure 7: Experimental and theoretical kinetic curve of MB adsorption onto A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT beads. in the studied range of MB concentration (5-270 mg L\({}^{-1}\)). In this study, 1/n value resulted in 0.47, lower than 1.0, indicative of a favorable adsorption process. The maximum MB adsorption capacity values on several adsorbents reported in the literature are collected in Table 3. The significant adsorption capacity of A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT revealed that this composite is an excellent adsorbent for the removal of MB contaminant from wastewater. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Model** & **Parameter** & **Value** \\ \hline \multirow{4}{*}{**Langmuir**} & K\({}_{\text{L}}\) (L mg\({}^{-1}\)) & 0.03 \\  & q\({}_{\text{max}}\) (mg g\({}^{-1}\)) & 396.7 \\  & R\({}^{2}\) & 0.977 \\  & RMSE & 17.4 \\ \hline \multirow{4}{*}{**Freundlich**} & K\({}_{\text{F}}\) (L g\({}^{-1}\)) & 31.6 \\  & 1/n & 0.5 \\  & R\({}^{2}\) & 0.907 \\  & RMSE & 35.5 \\ \hline \multirow{4}{*}{**Sips**} & q\({}_{\text{max}}\) (mg g\({}^{-1}\)) & 320.5 \\  & K\({}_{\text{s}}\) (L mg\({}^{-1}\)) \(\times 10^{3}\) & 6.4 \\ \cline{1-1}  & n\({}_{\text{s}}\) & 0.6 \\ \cline{1-1}  & R\({}^{2}\) & 0.999 \\ \cline{1-1}  & RMSE & 4.1 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: MB adsorption isotherm parameters onto A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT beads at room temperature. Figure 8: Experimental and theoretical MB adsorption isotherms onto A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT beads.