## 2 Results and Discussion
### Sorption Properties  
#### 2.2.1 The pH Effect  
Figure 2 compares the effect of pH on Sr(II) sorption for APEI and AO-APEI sorbents (including reproducibility testing). The sorption capacity of raw material (APEI) slightly increases with pH, up to 7, and tends to slightly decrease above pH 7.1: the qeq value never exceeds 22 mg Sr g\({}^{-1}\). The grafting of amidoxime groups significantly improves Sr(II) uptake: the sorption capacity linearly increases with equilibrium pH from 17 mg Sr g\({}^{-1}\) at pH 1, up to 85 mg Sr g\({}^{-1}\) at pH 7.3. Above pH 7.8, the sorption capacity tends to decrease but maintains a sorption capacity close to 72 mg Sr g\({}^{-1}\) at pH 8.3-9.1. Strontium speciation (not shown) in synthetic solutions (prepared with nitrate salts) shows that the metal is present under the form of free Sr\({}^{2+}\) species, in the whole pH range. So, the pH can only influence strontium sorption through its impact on the sorbent (protonation/deprotonation of reactive groups). In acidic solutions (pH below 2) all the reactive groups held on alginate, algal biomass, PEI, and amidoxime groups are protonated: the protons enter in competition with Sr(II) for metal binding. The sorption capacities remain below 10 mg Sr g\({}^{-1}\) for APEI. While increasing the pH, the progressive deprotonation of reactive groups increases sorption efficiency: the enhancement is relatively limited for APEI due to a marginal sorption on carboxylate groups, hydroxyls and free amine groups of PEI (not engaged in crosslinking with alginate chains and glutaraldehyde). On the opposite hand, for AO-APEI, the strong increase in sorption capacity means that the amidoxime groups represent the most reactive groups for Sr(II) binding, especially with progressive deprotonation and the decrease of proton competition. This is consistent with the pHPZC value of AO-APEI: at pH below 6.15, the global surface charge is positive, with the highest value around pH 3-4. A progressive decrease is observed between pH 4 and 6. At pH close to 7.3, the sorbent shows maximum Sr(II) sorption capacity. The sorbent is negatively charged (pH being higher than pHPZC). Above this value, the sorption begins to decrease because of the possible charge screening effect of Na\({}^{+}\) (resulting from pH control with NaOH solution) [65; 66]. The excess of cations partially shields negatively charged functional groups (such as OH\({}^{-}\) and COO\({}^{-}\)); in addition, it prevents anion-anion repulsion and increases Na\({}^{+}\) ion exchange; this was emphasized by the appearance of Na 1\(s\) signal on the XPS survey analysis of the sorbent after metal sorption. The sorption of Pb(II) on amidoxime-functionalized zeolite hybrids reached an optimum value at pH close to 6 [39]. [PERSON] et al. [67] reported similar trends for the sorption of Cu(II), Ni(II), Co(II), Cr(III), and Fe(III) on tapioca-cellulose functionalized with poly(amidoxime) ligands. In the case of amidoxime-grafted chitosan, [PERSON] et al. [68] observed a continuous increase in sorption capacity between pH 1 and 8 for Sr(II), while for Ba(II) the sorption capacity tended to stabilize at pH 7. For Cu(II) sorption on amidoximated starch embedded in chitosan beads, [PERSON] et al. [69] reported a strong increase in binding capacity above pH 2 and up to pH 5; it is noteworthy that at pH 1.5, the sorption of the divalent cation was negligible. Figure S5 shows the pH change during metal sorption. The pH remains stable between pH 1 and 3 and between 7 and 9, while between 4 and 6, the equilibrium pH varies by 1 pH unit. This pH variation does not affect metal speciation and does not cause metal precipitation. The distribution ratio (K\({}_{\rm d}\) = qeq/Ceq, L g\({}^{-1}\)) is plotted in log\({}_{10}\) units as a function of equilibrium pH (Figure S6). The plots are characterized by two segments: (a) increasing slope below pH 7.1 (+0.144 and +0.80) (b) decreasing slope above pH 7 (\(-\)0.074 and \(-\)0.064).