## 3 Results and Discussion  
### Characterization of the Sorbents  
The full characterization of the sorbents is detailed in Section SB (SI). Herein, the main characteristics are summarized. The particles are characterized as elongated irregular objects with rounded edges (Figure S1 Supplementary Material). The average size of the microparticles of MC-UR/S is 6 \(\pm\) 4 \(\upmu\)m. The embedded nanoparticles (NPs) of magnetite are visible in the TEM images (Figure S2, with a size of around 5-7 nm). The magnetic properties of MC-UR/S were quantified by vibrating sample magnetometry to 18.7 emu g\({}^{-1}\), with limited coercivity and remanence. The particles are superparamagnetic (Figure S3). This low value can be explained by the effect of the polymer coating of the magnetic NPs and the low fraction of magnetite in the composite. Indeed, the TGA analysis shows that the residual weight (after reaching 800 \({}^{\circ}\)C) shows a progressive decrease with the functionalization of the MC material, reaching 56.0%, 45.2% for MC-UR, and decreasing to 26.4% for the sulfonated sorbent (Figure S4). In addition, the TGA profiles show three main transitions corresponding to water release, followed by the depolymerization of chitosan, together with the degradation of the end products (urea and sulfonated ends), before recording the degradation of the char. Intermediary sub-waves are also observed (and confirmed by the DrTG profiles, Figure S5), which are probably associated with the degradation of functionalizing moieties. The analysis of the FTIR spectra for MC-UR and MC-UR/S at different stages of use (raw, after Ce(III) sorption, and after five cycles of re-use) shows, firstly, information regarding the presence of reactive groups (amine, amide, carbonyl, and sulfonate) and their interactions with cerium. Several characteristic bands of these functional groups are shifted after metal binding and desorption (Figure 1, Table S2a). However, these changes may result not only from the interaction of the sorbent with Ce(III). Indeed, the change in the environmental conditions, such as the pH for processing the sorption (i.e., at pH 5) or the drastic acidic solution for processing the metal desorption  
Figure 1: FTIR spectra—(**a**) MC-UR and (**b**) MC-UR/S, raw, after Ce(III) sorption, and after 5 th desorption. (i.e., 0.2 M HCl), may also affect the chemical state of these reactive groups (and their relevant vibrations in the FTIR spectra). In Section SB, the comparison of the spectra with those of the sorbents conditioned at pH 5 and exposed to 0.2 M HCl solutions is presented in Figures S6-S9 and Table S2b,c. The discussion of the relevant differences shows specific modifications in the large band at 3430-3370 cm\({}^{-1}\), which is assigned to the overlapping of \(\
u\)(OH) and \(\
u\)(NH) vibrations, at \(\approx\)1450 and \(\approx\)1375 cm\({}^{-1}\) (amide and amine groups, respectively), and at \(\approx\)1250-1050 cm\({}^{-1}\), associated with \(\
u\)(C-O) and \(\delta\)(OH)) for MC-UR and with \(\
u\)(S-O) for MC-UR/S. The investigation of the effects of metal desorption and sorbent recycling also shows substantial changes (appearance/disappearance of the signals and shifts in their characteristic wavenumbers, Figures S7 and S9, Table S2c). Despite these changes in the FTIR spectra, the full desorption of the metal and the weak loss in the sorption capacity (see Section 3.2.5) mean that these chemical modifications hardly affect their sorption performances. The elemental analysis of the sorbent identified the iron content as being in the range 30.7-32.5% (Table S3), meaning a higher value than that deduced from the TGA analysis (at least for MC-UR/S). The successful animation (urea grafting, for MC-UR) and sulfonation (for MC-UR/S) are also demonstrated by the increase in the nitrogen content (around 6.5%, \(w\)/\(w\); \(\approx\)4.6 mmol N g\({}^{-1}\)) and the appearance of the S element (around 3.3%, \(w\)/\(w\); \(\approx\)1 mmol S g\({}^{-1}\)).