# Removal of Chromium(VI) by Chitosan Beads Modified with Sodium Dodecyl Sulfate (SDS)
## 3 Results and Discussion
### Kinetic Studies  
An adsorption kinetics study was conducted to explore the relationship between the adsorption amount \(q_{\rm t}\) and time \(t\). According to Figure 14, the adsorption content of Cr(VI) by SDS-chitosan beads increased significantly within 96 h. The quick adsorption within the initial 24 h indicated that uptake of Cr(VI) was mainly caused by chemical sorption or surface complexation. This might be associated with the abundant exposure of sorption sites on the adsorbent surface. As the sorption sites were gradually occupied by Cr(VI), the adsorption rate of Cr(VI) became slower with a lapse of time and ultimately, approached equilibrium [66; 67]. For the purpose of comprehending the adsorption kinetics in more detail, the pseudo-first-order, pse For the purpose of comprehending the adsorption kinetics in more detail, the pseudo-first-order, pseudo-second-order, and intraparticle diffusion kinetic models were applied to explain the kinetic sorption process [68; 69]. The fitting curves of pseudo-first-order and pseudo-second-order models are presented in Figures 15 and 16, respectively. The calculated parameters, along with the correlation coefficient (\(R^{2}\)) of these models, are presented in Table 5. The adsorption kinetics based on the experimental values were both in good agreement with the pseudo-first-order and pseudo-second-order kinetic models judging from the high correlation coefficients. The fitness of the pseudo-first-kinetic model implied that the rate-controlling step might involve chemisorption or chemical bonding between Cr(VI) and the functional groups of adsorbents. On the other hand, the rapid phase in the initial step \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Metal**} & \multirow{2}{*}{**T (\({}^{\circ}\)C)**} & \multicolumn{3}{c}{**Langmuir Isotherm**} & \multicolumn{3}{c}{**Freundlich Isotherm**} \\  & & \(Q_{max}\)(mg/g) & \(R_{L}\) & \(R^{2}\) & \(K_{F}\)(mg/g) & **1/n** & \(R^{2}\) \\ \hline Cr(VI) & 25 & 3.23 & 0.308\(\times 10^{-4}\) & 0.960 & 3.01 & 0.700 & 0.921 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Isotherm parameters for Cr(VI) adsorption onto the SDS beads. Figure 14: Pseudo-first-order and pseudo-second-order plot of Cr(VI) adsorption on the SDS-chitosan beads. Figure 13: The Freundlich isotherm of Cr(VI) adsorption on the SDS-chitosan beads. of the adsorption process may imply physical adsorption or exchange at the adsorbent surface [61; 70]. Although the adsorption data could be well-described by the pseudo-first-kinetic model, the diffusion of Cr(VI) into pores could play an important role for Cr(VI) adsorption on the adsorbent, since SDS-chitosan beads are porous structures. Therefore, an intraparticle diffusion model was also applied to elucidate the diffusion mechanism and to investigate whether the film or pore diffusion was the controlling step in the adsorption process. The plots of \(q_{\text{t}}\) versus \(t^{1/2}\) for the adsorption of Cr(VI) fitting as an intraparticle diffusion model are provided in Figure 17. From this figure, it is revealed that plural processes influence the adsorption process for the adsorption of Cr(VI) by SDS-chitosan beads. In the pseudo-first-kinetic model, the adsorption rate was very high. This may be attributed to the film diffusion of Cr(VI) through the hydrodynamic layer to the surface of SDS-chitosan beads and the diffusion of Cr(VI) through the boundary layer to the external surface of the adsorbent. As the sorption on the external surface reaches saturation, Cr(VI) can enter into the pores of the SDS-chitosan beads and be adsorbed on the internal surface of the mesopores. It is considered that the intraparticle diffusion starts to fall down and reaches an equilibrium stage with the lowering of the Cr(VI) concentration in solution [61; 71]. Figure 16: Pseudo-second-order linear kinetic model of Cr(VI) adsorption on the SDS-chitosan beads. Figure 15: Pseudo-first-order linear kinetic model of Cr(VI) adsorption on the SDS-chitosan beads.