## 3 Results and Discussion
### Adsorption Studies
#### 3.5.3 Adsorption Kinetics
This is in accordance with the findings from Mossbauer and XRD techniques and in line with the findings [16]. The saturation of the adsorption capacity of Fe\({}_{3}\)O\({}_{4}\) particles may occur and thus, the dye adsorption capacity onto Fe sample is low, when the time of reaction passed. The composites might be able to capture azo dye due to its diffusion through carbon matrix porosity; this occurs due to the following factors: (i) electrostatic interactions between -SO\({}_{3}\)\({}^{-}\) group as contained on the dye and Fe\({}^{3+}\)/Fe\({}^{2+}\) species phase over Fe/FeC and FeC composites; (ii) the \(\pi\)-\(\pi\) interaction between the azo dye aromatic structure (or even -N=N- groups) and OH groups as shown in Fe\({}_{3}\)O\({}_{4}\), since this hydroxyl groups appear on FTIR results spectroscopic signals and (iii) a possible electrostatic attraction between the azo dye structure and positive charges over composites surface; the later being confirmed by the positive charges found by zeta potential techniques. At this point, the structural, textural and morphological properties of the Fe composites undermine their high adsorption capability towards the Acid Red 66 dye. In summary, the adsorption data reflects better capacity of Fe-carbon composites, when comparing with Fe sample. Pseudo-First and Second Order Models  
The efficiency of adsorption can be described in terms of kinetic models via Lagergren pseudo-first-order and pseudo-second-order equations. The first-order kinetic model is extensively applied for the adsorption of dyes by using Equation (8), as described in the literature [46; 54]:  
\[q_{t}=q_{c}\big{(}1-e^{-k_{1}t}\big{)} \tag{9}\]  
Figure 10: UV-Vis absorption spectra for Acid Red 66 at different time intervals under visible light irradiation for FeC composite. The included Figure is the picture of the dye solution before (0 min) and after (120 min) adsorption processes. where, \(q_{e}\) and \(q_{t}\) are the adsorption capacity at the equilibrium and the individual capacity at various time, respectively. \(k_{1}\) (min\({}^{-1}\)) is the rate constant of the pseudo-first-order model of adsorption process and \(t\) is the time in minutes. In the case of the pseudo-second-order model, the chemisorption is the rate-limiting step while adsorption may take place on the sites where no interactions among the adsorbates occur. The equation is expressed as:  
\[q_{t}=\frac{t}{\frac{1}{k_{2}q_{e}^{2}}+\frac{t}{q_{e}}} \tag{10}\]  
where \(k_{2}\) (g\(\cdot\)mg\({}^{-1}\cdot\)min\({}^{-1}\)) is the rate constant of pseudo-second-order adsorption. According to Figure 9b, the initiation of decolorization in the solution occurs faster during the first 10 min. with 60% of the dye being removed from the solution, when Fe sample was tested; the decolorization is close to 80% for Fe-carbon based composites. However, a maximum adsorption capacity is reached with 95% of the dye removal at 20 min of reaction. For easy understanding the kinetic parameters of the pseudo-first-order and pseudo-second-order models, the data are shown in Table 6. The parameters calculated from the pseudo-first-order model have R\({}^{2}\) < 0.968 and _SD_ in the range of 0.045-0.067. This suggests that the pseudo-first-order model is less accurate, which is in agreement with previous studies of pseudo1 st order model as applied to dye adsorption process data [49]. Conversely, R\({}^{2}\) values of second-order kinetic model are above 0.987 with the _SD_ in the range of 0.022-0.043. Thus, best results are achieved by using pseudo-second-order model, as found for anionic dyes [45; 55; 56; 57; 58]. Furthermore, the rate constant of adsorption (\(k_{2}\)) is superior to 0.0133 g\(\cdot\)mg\({}^{-1}\cdot\)min\({}^{-1}\) with Fe/FeC holding the highest \(k_{2}\) values due to the rapid dye adsorption and removal.