## 2 Selected Strategy for Sorbent Synthesis--Rationales  
Chitosan (aminopolysaccharideacharide) has been widely investigated for metal sorption due to its hydrophilic character (associated with numerous hydroxyl groups) and the high reactivity of the amine groups [53; 54; 55]. Chitosan is characterized by its unique cationic behavior among carbohydrates. The protonation of the amine groups (at a pH below pKa, in the range 6.2-6.7) has been used for binding metal anions and anionic dyes. On the other hand, in near-neutral solutions, free amine groups can chelate metal cations. These hydroxyl and amine groups have been used for preparing numerous derivatives through the grafting of functional groups [56; 57; 58], or physical modifications (for preparing beads, fibers, membranes, foams, etc) [59; 60]. One of the main drawbacks affecting chitosan's application in water treatment consists of the poor porosity and the residual crystallinity of the biopolymer that may explain its slow mass transfer properties. This drawback can be overcome by using different strategies: (a) coating the biopolymer onto a highly porous support [61; 62], (b) re-conditioning the biopolymer (the dissolving of chitosan reduces its residual crystallinity and the gelling or neutralization step allows for the expansion of the hydrogel network, pending a strict control of the final drying step) [63], and (c) reducing the size of the sorbent particles [64]. Reducing the size of sorbent particles decreases the diffusion path and, consequently, the time required to reach the equilibrium, although this process necessitates the performance a difficult solid/liquid separation at the end of the operative steps. This disadvantage can be minimized through the incorporation of magnetic nanoparticles that facilitate the magnetic separation of the sorbent at the end of the process [65; 66]. In some cases, the preparation of magnetic sorbents proceeds through the simultaneous synthesis of magnetite nanoparticles and precipitation of chitosan (first, by mixing the Fe(III) and Fe(II) precursorswith chitosan before processing the hydrothermal precipitation at a controlled pH). Herein, the magnetite NPs were pre-synthesized before being embedded into chitosan hydrogel. The solubility of chitosan in acidic solutions (with the remarkable exception of sulfuric acid) usually requires the crosslinking of the biopolymer to reinforce the sorbent stability when acidic conditions are involved in the lifecycle of the sorbent (especially for metal desorption and sorbent recycling, [67]). In many cases, the crosslinking step results in a loss of sorption properties because amine groups are frequently involved in the crosslinks (typically, this is the case for glutaraldehyde crosslinker). When chelation mechanisms constitute the main binding mechanisms, the sorption capacity dramatically falls, contrary to ion exchange mechanisms, which are less affected. The sorption properties of raw chitosan for rare earths are relatively limited (see below, MC sorbent: crosslinked magnetic sorbent). Therefore, the functionalization is necessary for improving the potential of magnetic chitosan. Table S1 (Section SA in Supplementary Information) reports the maximum sorption capacities of a series of functionalized sorbents for REE(III) metal ions (some of which concern magnetic chitosan). It is remarkable to note that the beneficial effect of grafting new functional groups onto supports strongly depends on the metal. For example, in the case of the algal/PEI sorbent, the sulfonation of the hydrogel contributes to the material's strong sorption capacity for scandium (i.e., 3.16 mmol Sc g\({}^{-1}\)), while for cerium and holmium, the sorption levels remain much lower (i.e., 0.71-0.61 mmol g\({}^{-1}\)) [48]. The bi-functionalization of a support may increase the sorption performance, as in the case of La(III) and Ce(III) with alginate sorbent functionalized with poly-glutamate [68].