## 2 Results and Discussion
### Sorption Properties
#### 2.2.3 Sorption Isotherms  
Sorption isotherms are reported at pH\({}_{0}\) 6 (pH\({}_{\rm eq}\) ranging between 6.8 and 7.3) in Figure 4. The shape of the curve follows the usual Langmuir profile: (a) initial steep increase of sorption capacity followed by (b) a saturation plateau. The maximum sorption capacity tends to 189 mg Sr g\({}^{-1}\) (2.16 mmol Sr g\({}^{-1}\)). The duplicate experiments confirm the reproducibility in the sorption properties (obtained on two different stocks of beads).  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Model** & **Parameter** & **1 st Series** & **2 nd Series** \\ \hline Experiment & \(\rm q_{eq,exp.}\) (mg Sr g\({}^{-1}\)) & 74.6 & 77.7 \\ \hline \multirow{3}{*}{FIGURE} & \(\rm q_{eq,1}\) (mg Sr g\({}^{-1}\)) & 76.4 & 79.2 \\  & \(\rm k_{1}\times 10^{2}\) (min\({}^{-1}\)) & 3.27 & 3.44 \\  & \(\rm R^{2}\) & 0.973 & 0.981 \\ \hline \multirow{3}{*}{PSORE} & \(\rm q_{eq,2}\) (mg Sr g\({}^{-1}\)) & 89.2 & 91.8 \\  & \(\rm k_{2}\times 10^{4}\) (L mg\({}^{-1}\) min\({}^{-1}\)) & 4.30 & 4.53 \\  & \(\rm R^{2}\) & 0.957 & 0.969 \\ \hline \multirow{3}{*}{RIDE} & \(\rm D_{e}\times 10^{9}\) (m\({}^{2}\) min\({}^{-1}\)) & 6.7 & 7.0 \\  & \(\rm R^{2}\) & 0.962 & 0.975 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Uptake kinetics for Sr(II) sorption onto AO-APEI. The parameters of the models.  
Figure 3: Uptake kinetics for Sr(II) removal using AO-APEI sorbent. Modeling of kinetic profiles with the PEORE (**a**) and the RIDE (**b**) models (pH\({}_{0}\): 6.0; pH\({}_{\rm eq}\): 7.1; SD: 0.2 g L\({}^{-1}\); C\({}_{0}\): 55.5 and 50.0 mg Sr L\({}^{-1}\) for 1 st and 2 nd series, respectively; room temperature: \(25\pm 1\)\({}^{\circ}\)C; agitation speed: 140 rpm).  
The experimental profiles are fitted by the Langmuir, Freundlich, and Sips equations. The Freundlich and the Sips equations show very similar fitted curves, which are less accurate than the curve simulated by the Langmuir equation. Table 2 reports the parameters of the models and relevant determination coefficients. The sorption capacity at saturation of the monolayer \(\mathrm{q_{m,L}}\) is close to 207 mg Sr g\({}^{-1}\) (i.e., 9.3% higher than experimental value). The affinity coefficient (i.e., b) tends to \(2.29\times 10^{-2}\) L mg\({}^{-1}\).  
Table 3 compares the sorption properties of a series of sorbents. AO-APEI is part of the most efficient Sr(II) sorbents. The maximum sorption capacity is consistent with the values reported for amidoximated chitosan [72]. However, calixarene-based extractant immobilized on a composite silica/polymer resin shows much higher sorption from nitric acid solutions (i.e., 454 mg Sr g\({}^{-1}\)). The combination of fast uptake and high levels of metal recovery makes the material very attractive.  
\begin{table}
\begin{tabular}{c c c c} \hline
**Model** & \(\mathbf{R}^{2}\) & **Parameter** & **AO-APEI Sorbent** \\ \hline Experiment & & \(\mathrm{q_{m,exp.}}\) (mg Sr g\({}^{-1}\)) & 189.3 \\ \hline Langmuir & 0.988 & \(\mathrm{q_{m,L}}\) (mg Sr g\({}^{-1}\)) & 206.9 \\  & & \(\mathrm{b_{L}}\times 10^{2}\) (L mg\({}^{-1}\)) & 2.29 \\ \hline [PERSON] & 0.971 & \(\mathrm{K_{F}}\) & 41.2 \\  & & \(\mathrm{n_{F}}\) & 3.89 \\ \hline Sips & 0.977 & \(\mathrm{q_{m,S}}\) (mg Sr g\({}^{-1}\)) & 384.1 \\  & & \(\mathrm{b_{S}}\times 10^{2}\) (L mg\({}^{-1}\)) & 8.81 \\  & & \(\mathrm{n_{S}}\) & 2.48 \\ \hline \end{tabular}
\end{table}
Table 2: Sorption isotherms for Sr(II) binding onto AO-APEI. The parameters of the models.  
Figure 4: Sorption isotherms for Sr(II) removal using AO-APEI sorbent. Modeling (\(\mathrm{pH_{0}}\): 6.0; \(\mathrm{pH_{eq}}\): 7.1; SD: 0.2 g L\({}^{-1}\); temperature: \(25\pm 1\)\({}^{\circ}\)C; contact time: 48 h; agitation speed: 140 rpm).