## 3 Results and Discussion
### Pd(II) Sorption in Mono Metal System  
#### 3.2.1 pH Effect  
The pH effect was studied within the pH range of 0.3-4.0 adjusted by H\({}_{2}\)SO\({}_{4}\) or NaOH. The data shown in Figure 3 indicate that Pd(II) binding onto both _L. digitata_-based and _C crispus_-based beads is pH-dependent. The sorption of Pd(II) onto functionalized sorbents can be mainly attributed to: (1) coordination (i.e., via a ligand exchange mechanism on amine, carboxyl groups); and (2) electrostatic attraction between positively charged amine groups and anionic chloro-metal complexes. For the former one, a low pH is not favorable to metal sorption due to the increased competition between protons and Pd(II), while for the latter one, a low pH is usually required to positively charge the amine groups. It is noteworthy that, in this study, the concentration of HCl in the initial solution was around 0.09 M (diluted from stock solution), resulting in the predominance of chloroanionic species: PdCl\({}_{4}\)\({}^{2-}\) (96%), PdCl\({}_{3}\)\({}^{-}\) (3 \(\sim\) 4%), and PdCl\({}_{2}\)(aq) (0.1%) throughout the pH range. Therefore, Pd(II) binding occurs mainly through electrostatic attraction. Figure S5 shows the pH before and after the sorption process. The pH does not change after sorption for CC/PEI beads. However, for LD/PEI beads, due to a relatively higher pH\({}_{\text{PZC}}\) value of LD/PEI (7.79) than that of CC/PEI beads (6.80), the solution pH increases significantly after sorption when the initial pH is higher than 3. The pK\({}_{\text{a}}\) values of primary, secondary, and tertiary amine groups on bPEI were reported as 4.5, 6.7, and 11.6, respectively [15]. Thus, in acidic media, the protonation of amino groups leads to the improvement of the sorption of chloro-anionic palladium species through electrostatic attraction. In addition, the encapsulating matrix is made of alginate (i.e., guluronic and mannuronic acid groups with pK\({}_{\text{a}}\) of 3.65 and 3.38, respectively [42]) for _L. digitata_ and \(\kappa\)-carrageenanan (i.e., sulfonate groups of carrageenanan with pK\({}_{\text{a}}\) close to 4.9 [43]) for _C. crispus_. Indeed, [PERSON] et al. [44] reported that \(\kappa\)-carrageenanan is the predominant carrageenanan type in _C. crispus_. At a pH below 4, most of these groups are protonated and poorly active for binding palladium chloro-anions. When the pH\({}_{\text{eq}}\) is lower than 4, the maximum binding for both beads is observed at pH 1 with a sorption capacity of 0.88 \(\pm\) 0.03 mmol g\({}^{-1}\) for LD/PEI and 1.37 \(\pm\) 0.02 mmol g\({}^{-1}\) for CC/PEI beads. [PERSON] et al. [45] reported that a decrease of pH (below 4) reduced the amount of palladium sorbed on functionalized macroreticular Amberlite XAD resins with sulfur and nitrogen ligands. In their case, the Pd binding was mainly attributed to a coordinationmechanism; the competition from protons for the active binding sites when decreasing the solution pH would reduce the coordination between Pd(II) and the above ligands. While the pH continues decreasing (a greater amount of acid added), the sorption capacity decreases gradually. This could be due to the competition of a huge amount of SO42\({}^{-}\) in the solution (due to the effect of different anions will be discussed in the next section below). The dramatic increase in Pd(II) binding onto LD/PEI as pH\({}_{\text{eq}}\) increases to 4.7 could be attributed to the metal precipitation effect (the formation of low soluble Pd(II) species). Indeed, [PERSON] et al. [5] reported that the Pd(II) sorption onto activated carbon could be accompanied by microprecipitation phenomena when the pH > 3 (C\({}_{0}\): 50 mg L\({}^{-1}\), chloride concentration: 0.1 M, pH controlled by NaOH).