## 3 Results and Discussion  
### Characterization  
The SEM micrographs shown in Figure 2 clearly illustrate the porous structure of the beads. LD/PEI beads are characterized as more opened scaffolds with larger holes in the core of the beads compared to CC/PEI: the drying of the beads caused a more irregular surface for LD/PEI materials. The results of EDX analysis of the sorbents before and after Pd(II) sorption are shown in Supplementary Materials Figure S3. O and Ca elements in LD/PEI, and S and K in CC/PEI beads are associated with the embedding matrices. S in LD/PEI could be associated with fucoidan residues in the brown algae, while Na is due to the extraction process of the polymers (alginate or carrageenan), using Na\({}_{2}\)CO\({}_{3}\) and NaOH, respectively. EDX spectra of the beads after metal sorption suggest that Pd(II) has been successfully loaded. Moreover, Ca in LD/PEI beads is not detectable. However, no Ca-Pd ion exchange should occur since chloro-palladium complex anions are predominant (discussed in Section 3.2). Hence, the disappearance of the Ca peak is probably due to the Ca(II)-Na(I) or Ca(II)-H(I) exchange reaction (the pH of the initial solution (pH \(<\) 1) was adjusted to 1 using NaOH solution). Similarly, for CC/PEI beads after Pd(II) sorption, K is replaced by Na. The element cartographies of the cross-sections of the beads after Pd(II) sorption (shown in Figure 2) show that Pd is concentrated in the outer layer of LD/PEI beads, while for CC/PEI, it is homogeneously distributed in the whole mass of the beads. This phenomenon is probably due to the repulsive force of the outer Ca(II)-alginate barrier (\"egg box\" junctions) of LD/PEI beads; it is difficult for the branched polymer PEI to penetrate through the layer and get access to the internal compartment, resulting in a lower amount of loaded PEI inside LD/PEI. As a result, the metal uptake of LD/PEI beads is expected to be lower than that of CC/PEI (see next section). The distribution of Cl element is consistent with Pd distribution, confirming that Pd(II) is sorbed under the form of chloro-palladium complexes. The specific surface areas of dried beads (prepared by relatively similar procedures) were previously determined and showed values that did not exceed a few m\({}^{2}\) g\({}^{-1}\), two orders of magnitude lower than the values reached with activated carbon or some synthetic resins. The FTIR spectrophotometric analysis of raw sorbents, blank beads, and Pd-loaded beads was performed to identify the functional groups of the materials and to understand the binding mechanism. The spectra are shown in Supplementary Materials Figure S4, while the assignments of the main bands are reported in Supplementary Materials Table S1. The band observed in the spectrum of _L. digitata_ at 3278 cm\({}^{-1}\) corresponds to O-H vibration [26]. The band at 2935 cm\({}^{-1}\) is assigned to the C-H stretching [27]. The peaks at 1605, 1416, 1250, and 1022 cm\({}^{-1}\) represent COO-asymmetric stretching [28], COO-symmetric stretching [29; 30], CH\({}_{3}\) symmetric bending [31], and C-O-C anti-symmetric stretching [32; 33], respectively. For _C. crispus_ biomass, the main bands relate to -OH overlapping (3283 cm\({}^{-1}\)) [26], C-H stretching (2924 cm\({}^{-1}\)) [27], C=C stretching (1644 cm\({}^{-1}\)) [34], N-H bending and C-N stretching (1531 cm\({}^{-1}\)) [35], COO- symmetric stretching (1416 cm\({}^{-1}\)) [29; 30], S-O stretching (1152 and 1221 cm\({}^{-1}\)) [36; 37], C\(-\)O-C antisym. stretching (1152 and 1034 cm\({}^{-1}\)) [32; 33], and CH bending (696 cm\({}^{-1}\)) [38]. In a word, the main functional groups on _L. digitata_ are hydroxyl and carboxyl groups, while for _C. crispus_, besides these two reactive groups, sulfate groups are also identified. Indeed, brown algae (_L. digitata_) contain 31% of alginate which can provide a certain amount of carboxyl groups, while the carrageenan on red algae (_C. crispus_) bears ester sulfate groups. Both carboxyl and ester sulfate groups can be involved in metal binding.