# Potentiality of Rod-Type Chitosan Adsorbent Derived from Sewage Sludge
## 3 Results and Discussion
### Optimization of Rod-Type Biosorbent Modification Conditions
#### 3.2.2 Effect of Material Content in Biosorbent  
The amounts of sludge and chitosan were important variables affecting sorption performance. Figure 1b shows the effects of sludge content on As(V) removal onto RCS. The sludge content affected the biosorbent surface and thus the As(V) removal capacity of the biosorbent. For further details, adsorption results were compared with pseudo-first-order and pseudo-second-order kinetics modeling. These models have been employed to investigate the adsorption dynamics of pollutants onto the biosorbents in relation to time and to estimate the rate of the process. They also help explain biosorption mechanisms and potential rate-controlling steps that may include mass transport and chemical reaction processes [21]. The pseudo-first-order equation is:  
\[q_{t}=q_{e}\Big{(}1-e^{-k_{1}t}\Big{)} \tag{2}\]  
where \(q_{e}\) is the amount of adsorbate adsorbed (mg/g) at equilibrium, \(q_{t}\) is the amount of adsorbate adsorbed (mg/g) at time \(t\) (min), and \(k_{1}\) (min\({}^{-1}\)) is the rate constant. The pseudo-second-order equation is usually associated with a situation in which the rate of direct adsorption or desorption controls the overall sorption kinetics, and typically describes the removal behavior of metals [22; 23]. An integrated form of the pseudo-second-order equation can be expressed as:  
\[\frac{t}{q_{t}}=\frac{1}{k_{2}\cdot q_{e}^{2}}+\frac{t}{q_{e}} \tag{3}\]  
or  
\[\frac{q_{t}}{t}=\frac{h}{1+k_{2}q_{e}t} \tag{4}\]  
where \(h\) (g/mg\(\cdot\)h) is the initial sorption rate and \(k_{2}\) (g/mg\(\cdot\)h) is the rate constant. The rate constant, initial sorption rate, and modulus values were calculated from different equilibrium metal sorption equations and are shown in Table 2. Equilibrium uptake (\(q_{e}\)) increased with increasing sludge fraction in RCS. Comparing the rate constant and initial adsorption rate, RCS containing 4.0% sludge showed the fastest adsorption rate. From these results, it can be seen that 4.0% was satisfactory in terms of speed, but 6.0% was the optimal adsorption amount. In order to increase adsorption capacity, it was decided to produce an adsorbent containing more than 6.0% sludge. In this study, the optimal sludge content was determined to be 6.0% because more weight was placed on adsorption capacity. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \multirow{2}{*}{\begin{tabular}{c} **Sludge** \\ **Content** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{\
\begin{tabular}{c} **Chitosan** \\ **Content** \\ **(\%)** \\ \end{tabular} } & \multirow{2}{*}{
\begin{tabular}{c} **Diameter** \\ **(mm)** \\ \end{tabular} } & \multicolumn{4}{c}{**Pseudo-First-Order**} & \multicolumn{4}{c}{**Pseudo-Second-Order**} \\ \cline{4-10}  & & & \(K_{1}\) & \(q_{e}\) & \(R^{2}\) & \(K_{2}\) & \(q_{e}\) & \(R^{2}\) & \(h\) \\  & & & **(1/h)** & **(mg/g)** & **(-)** & **(g/mg\(\cdot\)h)** & **(mg/g)** & **(-)** & **(mg/g\(\cdot\)h)** \\ \hline
2.0 & 4.0 & 0.2–0.3 & 0.96 & 0.09 & 0.9889 & 0.13 & 14.64 & 0.9995 & 28.65 \\
4.0 & 4.0 & 0.2–0.3 & 1.13 & 0.08 & 0.9855 & 0.14 & 14.84 & 0.9995 & 29.94 \\
6.0 & 4.0 & 0.2–0.3 & 0.79 & 0.09 & 0.9636 & 0.11 & 16.08 & 0.9990 & 27.33 \\
6.0 & 3.0 & 0.2–0.3 & 0.84 & 0.12 & 0.9395 & 0.19 & 13.69 & 0.9996 & 35.55 \\
6.0 & 4.0 & 0.2–0.3 & 1.58 & 0.06 & 0.9422 & 0.10 & 16.66 & 0.9956 & 27.63 \\
6.0 & 5.0 & 0.2–0.3 & 1.28 & 0.06 & 0.9628 & 0.07 & 16.16 & 0.9963 & 18.48 \\
6.0 & 6.0 & 0.2–0.3 & 0.78 & 0.08 & 0.9475 & 0.06 & 16.69 & 0.9931 & 16.55 \\
6.0 & 4.0 & 0.2–0.3 & 0.81 & 0.09 & 0.9759 & 0.09 & 15.78 & 0.9984 & 22.42 \\
6.0 & 4.0 & 0.5–0.6 & 1.63 & 0.04 & 0.9192 & 0.06 & 16.82 & 0.9916 & 16.13 \\
6.0 & 4.0 & 0.8–0.9 & 0.95 & 0.08 & 0.9969 & 0.08 & 15.47 & 0.9971 & 19.47 \\
6.0 & 4.0 & 1.0–1.2 & 0.64 & 0.08 & 0.9911 & 0.06 & 15.70 & 0.9992 & 14.84 \\ \hline \end{tabular}
\end{table} 
Table 2: Comparison of pseudo-first-order model and pseudo-second-order model parameter values for different sludge contents, chitosan contents, and diameters of the biosorbent.