## 2 Results and Discussion
### Characterization of Materials
#### 2.1.3 Thermal Degradation--TGA Analysis  
The functionalization of APEI beads changes the thermal degradation of the material (Figure S2, due to the presence of new reactive groups grafted on the composite backbone. Several degradation steps can be identified:  
(1) 16-190/200 \({}^{\circ}\)C--the release of surface-absorbed water and constitutive water (inner water): the profiles are similar for APEI and AO-APEI (weight loss of 11%-15% and maximum DrDTG close to 97 \({}^{\circ}\)C) [40; 41; 42].  
(2) 190/200-264/304 \({}^{\circ}\)C--cleavage of saccharide rings and ester groups in alginate [43; 44], and analogs present in the algal biomass: the profiles remain close for the two materials (total weight loss: 41.17% for APEI and 34.6% for AO-APEI). Two peaks appear on the DrDTG curve for APEI at 218.6 and 300.12 \({}^{\circ}\)C, while for AO-APEI, the curve is relatively stable (variations leveled by the strong peak appearing at higher temperatures). This first step was assigned to the devolatilization of brown algae biomass (_Laminaria digitata_) with a strong exothermic peak at 235 \({}^{\circ}\)C.  
(3a) 304-560 \({}^{\circ}\)C: progressive mass loss for APEI associated with the degradation of PEI, and constituents of algal biomass (end of the main devolatilization step and char formation) [45; 46; 47]. The weight loss at this stage reaches 37.19% (total weight loss: 78.36%). Two small exothermic peaks are observed at 416.1 \({}^{\circ}\)C and 539.9 \({}^{\circ}\)C. In the thermal decomposition of crosslinked PEI/silica composite, [PERSON] et al. [48] reported a strong exothermic peak at 308 \({}^{\circ}\)C due to the decomposition of the organic fraction; the progressive loss of weight till 800 \({}^{\circ}\)C was assigned to the combustion of residual organic material and char.  
(3b) 264-474 \({}^{\circ}\)C: progressive mass loss (about 34.6%) for AO-APEI (cumulative weight loss: 59.2%). By comparison with APEI thermogram, this specific section is probably associated with the thermal degradation of amidoxime moiety. However, [PERSON] et al. [49] observed relatively weak changes in the thermograms of PEI and functionalized PEI (including amidoxime derivative). The differences may be attributed to different modes of interaction in the current complex system (algal biomass-alginate-PEI-glutaraldehyde-Ca).  
(4) 474-540 \({}^{\circ}\)C: strong weight loss (about 21.8%) associated with the thermal degradation of residual organic compounds and combustion of the char. The thermal degradation of AO-APEI requires a higher temperature than APEI. The strong exothermic peak is observed at 484.2 \({}^{\circ}\)C.  
The total weight losses are very close for the two materials: 78.4% for APEI and 81.0% for AO-APEI. The final solid probably corresponds to the inert calcium-based residue (alginate/algal biomass being ionotropically gelled with CaCl\({}_{2}\), in addition to the residues of calcium carbonate used for partial alginate extraction during the shaping/conditioning of APEI). The complexity of the structure of algal biomass (due to the presence of different polysaccharides and other cellulose-like or protein constituents) makes the interpretation of the profiles difficult. [PERSON] et al. [50] reported significant changes in the characteristic degradation temperatures of the most representative polysaccharides of brown macroalgae. This complexity is even reinforced by the additional contribution of PEI moieties.