## 3 Results and Discussion
### Phosphorus Removal in Batch Adsorption Experiments  
The Table 2 presents the results of calculating the constant and correlation coefficient (R2) of adsorption. The data matched the evaluated isotherm equations very well, as shown in Figure 3. High correlation coefficients (\(R^{2}\) > 0.99) indicated that the Langmuir model matched the experimental data in this study acceptably well. The adsorption of phosphorus removal could be described well by the Langmuir isotherms with a correlation value of R\({}^{2}\) = 0.9894 which indicated that chemisorption was the dominant process and suggested the monolayer adsorption. The maximum amount of phosphorus required to form a monolayer is equal to 6.31 mg/g. This value showed that HAOPs had a high capacity to remove phosphorus. Additionally, the \(n\) value was higher than 1 which indicated that the adsorption intensity was favorable at higher concentrations. However, the Freundlich adsorption model also fitted the data well which indicates that the multi-molecular layer adsorption coexisted in this process. These observations were in agreement with the work reported earlier [36]. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multicolumn{3}{c}{**Langmuir Isotherm Model**} & \multicolumn{3}{c}{**Freundlich Isotherm Model**} \\ \hline \multirow{2}{*}{Qm (mg/g)} & \multirow{2}{*}{\(\mathbf{K_{L}}\) (L/mg)} & **Correlation** & \multirow{2}{*}{**K\({}_{\mathbf{F}}\) (L/mg)\({}^{1/n}\)**} & **n (-)** & **Correlation** \\  & & **Coefficient R2** & & & **Coefficient R2** \\ \hline
6.31 & 1.85 & 0.9894 & 0.49 & 2.62 & 0.8904 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Parameters of [PERSON] and [PERSON] isotherms. Figure 2: SEM images of the HAOPs layer (**a**) 100 \(\upmu\)m, (**b**) 50 \(\upmu\)m and (**c**) 20 \(\upmu\)m.  
The adsorption kinetics of phosphorus onto dynamic membrane adsorber was investigated using the pseudo-first-order, pseudo-second-order models. Kinetics of phosphorus adsorption by HAOPs were fitted to the pseudo-first-order (Equation (7)) and pseudo-second-order (Equation (8)) models:  
\[Q_{t}=Q_{e}\Big{(}1-e^{-k_{1}t}\Big{)} \tag{7}\]  
\[Q_{t}=\frac{(Q_{e})^{2}k_{2}t}{1+Q_{e}k_{2}t} \tag{8}\]  
where \(k_{1}\) and \(k_{2}\) are first- and second-order adsorption rate constants. For the initial phosphorus concentration of 18.2 mg/L, the pseudo-second-order equation fitted the experimental data better with a correlation coefficient R\({}^{2}\) = 0.9924, when compared to the first-order model R\({}^{2}\) = 0.7785. In addition, the difference between the experimental and theoretical adsorbed masses at equilibrium for the pseudo-second-order was lower than 5% (Table 3). The separation parameter \(R_{L}\) (between 0.02 and 0.14) indicates the adsorption nature to be favorable. Earlier studies demonstrated that metal hydroxides have a high affinity to phosphorus compounds, especially aluminum hydroxides [6; 12; 33; 36; 37]. [PERSON] et al. [36] revealed that the adsorption capacity is determined mainly by the population of surface functional groups on the adsorbents. The mechanisms of phosphorous adsorption by alumina-based adsorbents have been investigated in previous studies [16; 33; 34; 35; 36; 37; 38; 39; 40; 41; 42; 43; 44; 45; 46; 47; 48; 49; 50; 51; 52]. [PERSON] et al. [42] revealed that the chemisorption of phosphorous compounds is associated with the displacement of the surface hydroxyl groups. Furthermore, [PERSON] et al. [36] reported that the mechanism of  
Figure 3: Phosphorus adsorption on dynamic membrane adsorber.