## 3 Results
### Adsorption Experiments of Polymers Towards Methylene Blue
#### 3.3.4 Effect of Initial Dye Concentration  
Batch experiments were performed at different MB concentrations (5-100 mg/L). The polymers were mixed with MB during 24 h at pH 6. The amount of MB adsorbed depending on the initial concentration is present in Figure 8.  
According to Figure 8, the amount of MB adsorbed by the polymer increases from 8 to 51 mg/g with the increase of the initial MB concentration from 5 to 100 mg/L. This increasing of the concentration gradient acts as the driving force. The polymer obtained from PEDGE 500 (PEGCD1) was more efficient compared to those obtained from PEDGE 640 (PEGCD2) and EDGE (EGCD). Figure 8: **(Top)** Effect of the initial concentration of MB on the adsorption capacity (mg/g) of MB by EGCD, PEGCD1 and PEGCD2; and **(Bottom)** effect of the initial concentration of MB on the percentage of MB adsorption. With different initial concentrations of MB, it has been observed that the yield of adsorbed MB decreases with the increase in the concentration of the MB solution. When the concentration of MB is low, the equilibrium is rapidly reached because they are many sites available for adsorption. At high MB concentrations, more active sites were occupied and the percentage of additional MB adsorbed was lower, if compared to the initial concentration. According to these results, adsorption isotherms were investigated to fit the best model. In this way, batch experiments were conducted with various concentrations of MB (10-100 mg/L). Other parameters were kept constant (adsorbent mass = 30 mg, time = 24 h, Syncore vial speed = 260 rpm and pH = 6). The modeling of the adsorption equilibrium consists of representing the equilibrium relationship between the quantity of MB in the liquid phase and that adsorbed on the material by application of the Langmuir model and the Freundlich model [71; 72]. The Langmuir isotherm is generally used when the adsorption is a monolayer with a specific homogeneous binding site while, for Freundlich isotherm, it rather meets a multi-layer adsorption process with a heterogeneous surface. The MB adsorption was fitted to both Langmuir and Freundlich models. Since values of the correlation coefficient for the Freundlich isotherms were not significant compared to Langmuir model, the Freundlich isotherms are not described in this study. The Langmuir model (Equation (3)) is the following one:  
\[\frac{C_{e}}{Q_{e}}=\frac{C_{e}}{Q_{m}}+\frac{1}{Q_{m}K_{L}} \tag{3}\]  
For the Langmuir equation, \(C_{e}\) (mg/L) is the concentration of MB at equilibrium; \(Q_{e}\) (mg/g) is the uptake capacities at equilibrium; \(Q_{m}\) (mg/g) is the maximum adsorption capacity; and \(K_{L}\) (L/mg) is the Langmuir equilibrium constant. Figure 9 depicts the linear fit of the isotherm data for PEGCD2. All the parameters for the Langmuir model for EGCD, PEGCD1 and PEGCD2 are listed in Table 2.  
Figure 9: Plots of adsorption of MB onto the PEGCD2 polymer following the Langmuir model. The linear regression line of Ce/Qe versus Ce allows to calculate the Langmuir constants \(K_{L}\) and \(Q_{m}\). The separation factor \(R_{L}\) was calculated through the following equation (Equation (4)). \[R_{L}=\frac{1}{1+K_{L}C_{0}} \tag{4}\]  
where \(K_{L}\) is the Langmuir constant (L/mg); and \(C_{0}\) is the initial concentration (mg/L). The correlation coefficients (\(R^{2}\)) indicate the best fit between the experimental and calculated adsorption data according to the Langmuir isotherm. MB adsorption data fitted the Langmuir model with correlation coefficients between 0.92 and 0.99. The value of \(R_{L}\) gives an indication if the type of isotherm is favorable (\(0<R_{L}<1\)), unfavorable (\(1<R_{L}\)), linear (\(R_{L}=1\)) or irreversible (\(R_{L}=0\)) [73]. EGCD, PEGCD1 and PEGCD2 have \(R_{L}\) values much smaller than 1.0, indicating a strong affinity between MB and the polymers. The maximum amount of MB (\(Q_{\text{max}}\)) adsorbed by PEGCD and EGCD was compared to other CD polymers recently reported in the literature (Table 3).