## Materials and Methods
### Experiments
#### 2.4.5 Equilibrium Adsorption Studies  
25 mL of CV at the \(3.34\times 10^{-5}\), \(1.67\times 10^{-5}\), \(8.34\times 10^{-6}\), \(3.34\times 10^{-6}\), \(1.67\times 10^{-6}\), and \(6.68\times 10^{-7}\) M concentrations were employed with 20 mg of adsorbent and 30 rpm for 60 min followed by settling for 60 min. Samples were then centrifuged at 1550 rpm for 15 min and passed through a 0.45 \(\mathrm{\SIUnitSymbolMicro m}\) filter before each absorbance reading. Tests were carried out at media pH (6.5-7.5) and room temperature (25 \({}^{\circ}\)C) in triplicate. The adsorption data were then adjusted to the Langmuir, Langmuir-like, Freundlich, Sips, Redlich-Peterson, and Evolich models. The amount of CV adsorbed was calculated from:  
\[\mathrm{A}\mathrm{d}\mathrm{s}\mathrm{s}\mathrm{r}\mathrm{p}\mathrm{t}\mathrm{p} \mathrm{t}\mathrm{p}\mathrm{t}\mathrm{p}\mathrm{t}\mathrm{p}\mathrm{t}\mathrm{p} \mathrm{t}\mathrm{p}\mathrm  
\[RL=\frac{1}{1+k_{1}*C_{0}} \tag{5}\]  
where, \(C_{e}\) corresponds to the equilibrium concentration of dye (mg/L); \(Q_{e}\) is the quantity of dye adsorbed onto the adsorbent at equilibrium (mg/g); K\({}_{2}\) corresponds to the maximum monolayer adsorption capacity of adsorbent (mg/g) which can be correlated with the variation of the suitable area and porosity of the adsorbent; \(K_{1}\) is the Langmuir adsorption constant (L/mg); and C\({}_{0}\) corresponds to the initial concentration of CV. \(RL\) is a dimensionless equilibrium parameter that explains the favorability of adsorption process. \(RL\) is calculated using Equation (5), the adsorption is unfavorable when \(RL>1\), linear when \(RL=1\), favorable when \(0<RL<1\), and irreversible when \(RL=0\). The Freundlich isotherm [27] is an empirical model not limited to monolayer coverage alone, but also describes multilayer adsorption. It is applicable to adsorption processes that occur on heterogonous surfaces showing an exponential distribution of active sites and their energies. The model is expressed as follows:  
\[Q_{e}=KC_{e}{}^{1/n} \tag{6}\]  
where, \(K\) and \(1/n\) correspond to the adsorption capacity (L/mg) and the adsorption intensity, respectively. The later indicates the relative distribution of the energy and the heterogeneity of the adsorbent sites. N values lower than one designate a cooperative adsorption, whereas values larger than one indicate a more heterogeneity in the surface and a favorable adsorption. Likewise, the Elovich isotherm (Equation (7)) assumes that adsorption increase exponentially with adsorption sites implying a multilayer adsorption [28; 29]. \[Q_{e}=A*K*C_{e}e^{-(\frac{Q_{e}}{A})} \tag{7}\]  
where, \(A\) and \(K\) correspond to the maximum sorption capacity and sorption constant, respectively. Conversely, the Redlich-Peterson isotherm (Equation (8)) is a mix of the Langmuir and Freundlich isotherms. The numerator comes from the Langmuir isotherm and approaches to the Henry region at infinite dilution [30]. Therefore, the mechanism of adsorption does not follow an ideal monolayer adsorption [31]. At high liquid-phase concentrations of the adsorbate, it reduces to the Freundlich equation. It is applicable in either homogenous or heterogeneous systems due to its versatility. The model is expressed as follows:  
\[Q_{e}=\frac{A*C_{e}}{1+k*C_{e}{}^{\beta}} \tag{8}\]  
where, \(A\) corresponds to the Redlich-Peterson isotherm constant (Lg\({}^{-1}\)), \(B\) is a constant (Lmg\({}^{-1}\)), and \(\beta\) is an exponent that lies between zero and one. Similarly, the Sips isotherm (Equation (9)) combines the Langmuir and Freundlich isotherms, altogether. This model predicts adsorption on heterogeneous surfaces, thereby avoiding the limitation of increased adsorbate concentration normally associated with the Freundlich model [32]. Thus, at low adsorbate concentration this model reduces to the Freundlich model, but at high concentration of adsorbate, it predicts the Langmuir model (monolayer adsorption).