## 3 Results and Discussion
### Adsorption Studies
#### Thermodynamic Studies  
The thermodynamic parameters such as adsorption enthalpy (\(\Delta H\)), entropy (\(\Delta S\)) and Gibbs Energy (\(\Delta G\)) are estimated to provide the information of the bond strengths between the adsorbent surfaces and Acid Red 66 molecule. The estimation of \(\Delta H\), \(\Delta S\) and \(\Delta G\) in single-component system is achieved by the following equations:  
\[C_{s}=C_{0}-C_{w} \tag{5}\]  
\[K_{ad}=(C_{0}-C_{w})/C_{w} \tag{6}\]  
\[\Delta G^{o}=-RT(lnK_{ad}) \tag{7}\]  
\[ln(K_{ad})=-\frac{\Delta H^{o}}{RT}+\frac{\Delta S^{o}}{R} \tag{8}\]  
where \(K_{ad}\) is the adsorption coefficient represented by the equilibrium concentration of the adsorbate on the solid (\(C_{s}\), mg\(\cdot\)L\({}^{-1}\)), \(C_{0}\) is the initial concentration and the equilibrium concentration of the adsorbate in solution (\(C_{w}\), mg\(\cdot\)L\({}^{-1}\)), \(R\) is the gas universal constant (8.314 \(\cdot\)mol\({}^{-1}\cdot\)K\({}^{-1}\)) and \(T\) is the absolute temperature (K). The \(\Delta G\) values at distinct temperatures of 25 \({}^{\circ}\)C, 50 Thermo C e 70 \({}^{\circ}\)C are obtained from \(K_{ad}\) parameter from Equation (6) while \(\Delta H\) e \(\Delta S\) values are predicted from the ln \(K_{ad}\) versus 1/\(T\) plot (Figure 8). The ln \(K_{ad}\) versus 1/\(T\) plots for Langmuir and Freundlich isotherms follows a linearity. The thermodynamic parameters are summarized in Table 5.  
The calculated adsorption heat obtained are \(-\)28.1, \(-\)38.5, and \(-\)74.3 kJ\(\cdot\)mol\({}^{-1}\) for the Acid Red 66 adsorption of Fe, FeC and Fe/FeC, respectively. These negative values confirm the feasibility and exothermicity of adsorption. This also illustrates a high preference for Acid Red 66 dye to adsorbb chemisorption on the FeC and Fe/FeC composites. The negative values for \(\Delta G\) confirm the spontaneity of the adsorption of Acid Red 66 over FeC and Fe/FeC composites, in good agreement with the literature reports that shows the physisorption occurrence over \(\Delta\)G values in the range of 0 to \(-\)20 kJ\(\cdot\)mol\({}^{-1}\)[51; 52]. This also illustrates a preference for Acid Red 66 dye to adsorb by either chemisorption or physisorption processes on the composites. In agreement, the findings states that the mean free energy of sorption in the E \(<\) 8.0 kJ\(\cdot\)mol\({}^{-1}\) range represents the physisorption process while 8.0 \(\leq\) E \(\leq\) 16.0 kJ\(\cdot\)mol\({}^{-1}\) indicates the ionic exchange and the E \(>\) 16.0 kJ\(\cdot\)mol\({}^{-1}\) suggests the chemisorption occurrence during the adsorption of Acid Orange 7 (AO7) over chitosan-based magnetic adsorbents [52]. Interestingly, \(\Delta G\) values decrease with the increase of adsorption temperature with Fe sample at 70 \({}^{\circ}\)C being an exception. Comparable results are obtained for the adsorption of Acid Red 66 onto carbon nanotubes [53]. Another observation is the fact that the solution is at the isoelectric point with pH = 6.8 and thus, the hydroxyl groups and sulfonic groups from the dye are weakly interacting with the surface of the Fe sample causing repulsions, in some extension (\(\zeta\) = \(-\)5.56 mV, Table 2). In contrast, the surface of the Fe-based composites has positive charges (\(\zeta\) = \(+\)10.8 mV for FeC and \(\zeta\) = \(+\)24.9 mV for Fe/FeC at the same pH value. This may promote the interactions among the negative charge of the \(-\)SO\({}_{3}\)\({}^{-}\) and \(-\)N=N- groups of the azo dye and the composites. Therefore, the adsorption capacity follows the order Fe/FeC \(>\) FeC \(>\) Fe, according to the arranged chemical system for adsorption of Acid Red 66. Figure 8: Vant’ Hoff plots for Acid Red 66 adsorption on (a) Fe, (b) FeC and (c) Fe/FeC.