## 2 Results and Discussion
### Characterization of Materials
#### 2.1.4 Chemical Characterization of Sorbent--FTIR and XPS Analyses  
Figure S3 shows the FTIR spectra of the different materials: not only for successive compounds produced during the functionalization of APEI beads but also after metal sorption, metal desorption, and after five recycling cycles. Table S2 shows the assignments of the main peaks appearing on these spectra. The peak at 2198 cm\({}^{-1}\) (C\(\equiv\)N stretching vibration) clearly demonstrates the effective nitrilation of the amine groups with chloroacetonitrile. This band disappears after amidoximation: the functionalization is quantitative. [PERSON] et al. [51] identified this vibration at 2244 cm\({}^{-1}\) on poly(acrylonitrile) grafted kenaf cellulose. They also observed the disappearance of this band after amidoximation and the appearance of new bands at 1677 and 1647 cm\({}^{-1}\) (corresponding to C=N stretching and N-H bending vibrations). The FTIR spectrum of CN-APEI also shows a significant shoulder at 1760-1750 cm\({}^{-1}\), which is usually assigned to carboxylate groups. For AO-APEI, the band is overlapped with the C=N group of amidoxime; this makes the identification of these amidoxime-based vibrations difficult. Actually, the amidoximation is followed by the widening of the C=N band at 1612 cm\({}^{-1}\), which is associated with the overlapping of carboxylic/carboxylate groups. This was also assigned to the tautomerization effect on the amidoxime group [47]. The sorption of Sr(II) slightly affects the FTIR spectra; the most relevant changes are the weak shifts of the C-N stretching and C-O symmetric stretching vibrations towards higher wavelengths, the shift of C-N stretching (in primary amines) and C-O-C asymmetric stretching towards lower wavelengths and the slight increase in the wavelength of C=N and C=O stretching vibrations. This confirms that the functional groups most  
involved in Sr(II) sorption are the reactive groups of amidoxime ligand. However, it is important to note that some of these reactive groups are also present in PEI and alginate-like constituents of algal biomass. Figure 1 shows the XPS survey spectra of the materials (at different steps of the synthesis and after metal desorption). The presence of calcium is assigned to the ionotropic gelation of alginate-based materials (for preparing APEI) beads). The N 1\(s\) peak is identified on the different materials (PEI, proteins of algal biomass, associated with the effects of nitrilation and amidoximation). The sorption of Sr(II) is confirmed by the Sr 3\(d\) peak; the Na 1\(s\) peak also appears after metal sorption. Sodium hydroxide was used for pH control; therefore, a residual amount of Na(I) ions may co-exist in the sorbent, due to absorption in the porous network or partial ion-exchange with Ca(II) on alginate. Tables S3 and S4 report the HRES spectra of the most representative signals of characteristic elements. Table S5 summarizes the assignments of these peaks and their variations with sorbent synthesis, metal binding, and after metal desorption. Five peaks (relative to C 1\(s\)) are identified as C(C, H) and adventitious C at 284.27 eV [44], C-(NH, NH\({}_{2}\)) at 285.41 eV [44], C-O, C=N at 286.08 eV [52], C=O, C-O-C at 287.6 eV [53], and O=C-O, O-C-O at 288.44 eV [52]. The N 1\(s\) signal on raw material (APEI) is deconvoluted into two peaks: at 399.2 eV and 401.34 eV assigned to C-N, C=NH, -NH, and to N\({}^{+}\), respectively [47; 54]. For O 1\(s\), three peaks are identified at 529.29 eV, at 530.7 eV, and at 532.27 eV for O-Ca, C=O, and C-O, and OH, respectively [55; 56; 57]. Table S5 confirms the grafting of nitrile groups; this is correlated to the appearance (or reinforcement) of the C\(\equiv\)N group on C 1\(s\) at 287.32 eV, N 1\(s\) at 398.3 eV signals, and by the significant decrease in the atomic fraction of C-NH or C-NH\({}_{2}\) groups [58].