## 3 Results and Discussion
### Thermodynamic Adsorption  
The effect of the temperature on MB adsorption onto A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT composite beads was studied at four different values, i.e., 283, 293, 303 and 313 K. The results showed a positive correlation between MB adsorption and temperature, suggesting the endothermic nature of the process, which is in agreement with the results obtained from the monolayer model. The thermodynamic parameters, e.g., the enthalpy or heat of adsorption (\(\Delta H^{\circ}\)), the change in the standard Gibbs' energy (\(\Delta G^{\circ}\)) and entropy (\(\Delta S^{\circ}\)) were calculated using the following equations [27]:  
\[\Delta G^{\circ}=-R\cdot T\cdot In\,K_{c} \tag{12}\]  
\[K_{c}=\frac{q_{e}}{C_{e}} \tag{13}\]  
\[\log\!\left(\frac{q_{e}}{C_{e}}\right)=\frac{-\Delta H^{\circ}}{2.303\cdot R \cdot T}+\frac{\Delta S^{\circ}}{2.303\cdot R} \tag{14}\]  
where, \(q_{e}\) (mg g\({}^{-1}\)) is the equilibrium MB adsorption capacity, C\({}_{e}\) (mg L\({}^{-1}\)) is the equilibrium MB concentration, \(\Delta H^{\circ}\) (kJ mol\({}^{-1}\)) is the enthalpy variation, \(\Delta S^{\circ}\) (J mol\({}^{-1}\) K\({}^{-1}\)) is the entropy, \(\Delta G^{\circ}\) (kJ mol\({}^{-1}\)) is the change in the standard Gibbs' energy, K\({}_{c}\) is the equilibrium constant, T (K) is the temperature and R is the universal gas constant (8.314 J mol\({}^{-1}\) K\({}^{-1}\)). The enthalpy (\(\Delta H^{\circ}\)) and entropy (\(\Delta S^{\circ}\))parameters were evaluated by plotting log(q\({}_{\rm e}\)/C\({}_{\rm e}\)) versus 1/T, resulting in values of 36.9 kJ mol\({}^{-1}\) and 195.1 J mol\({}^{-1}\) K\({}^{-1}\), respectively. The obtained positive value of the enthalpy is indicative of an endothermic process. Thus, the enthalpy value resulted smaller than 40 kJ mol\({}^{-1}\), indicating that MB adsorption onto A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT composite beads can be considered as a physisorption process, governed by electrostatic interactions, mainly van der Waals forces. \(\Delta\)G\({}^{\circ}\) parameters at 283, 293, 303 and 313 K were of \(-\)18.3, \(-\)20.2, \(-\)22.2 and \(-\)24.1 kJ mol\({}^{-1}\), respectively. The negative \(\Delta\)G\({}^{\circ}\) values indicated the spontaneous and the physical nature of MB adsorption process onto the synthesized composites. The change in the adsorption entropy (\(\Delta\)S\({}^{\circ}\)) was positive, suggesting that the MB molecules increased their randomness at the solid/liquid interface during the adsorption. Proposed Adsorption Mechanism of MB onto A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT Composite Beads  
The adsorption mechanism was investigated by FTIR analysis. The FTIR spectra of MB and A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT composite before and after adsorption are depicted in Figure 9. The adsorption mechanism of methylene blue has been extensively reported in the literature. Thus, [PERSON] et al. [63] have previously found that MB molecules could be adsorbed on alginate and acidified MWCNTs beads, on one hand, by \(\pi\)-\(\pi\) dispersion interactions with the aromatic regions of MWCNTs, and, on the other hand, by electrostatic attractions with the carboxylate groups present in alginate and MWCNTs. So, different adsorption mechanisms can be proposed when the adsorbent is a composite formed by different materials. The interactions between MB molecule and A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNTs beads were verified by FTIR analysis (Figure 9). After adsorption, the FTIR spectrum of A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT clearly showed the MB signature, indicating its adsorption onto the composite beads. The bands appearing at 1394 and 1339 cm\({}^{-1}\) are referred to the aromatic rings of MB. The characteristic C=C band of the aromatic rings detected at 1179 cm\({}^{-1}\) in the MB spectrum appeared at 1175 cm\({}^{-1}\) in the FTIR of A/\(\gamma\)-Fe\({}_{2}\)O\({}_{3}\)/f-CNT after adsorption [64].