## 2 Crosslinking of PEI and Reaction Mechanisms
The crosslinking reaction proceeds via an amine alkylation reaction between the alkyl bromide of the crosslinker and the amine groups of the branched PEI, with bromine being substituted with amine functional group of the amine. [PERSON] et al. used bromoalkyl phenyl attached to a triazene core unit as a crosslinker (2\(A\),6-tris-(4-bromomethyl-3-fluoro-phenyl)-1,3_5-triazine (4 BMFPT)) for PEI, as shown in Scheme 8, for CO\({}_{2}\) selective capture at ambient temperature [53]. Different materials with different mixing ratios of the crosslinker to PEI were synthesized. The materials prepared were characterized with IR, elemental analysis, and SEM, and the materials were tested for their performance in CO\({}_{2}\) capture. It is important to note that the direct capture of CO\({}_{2}\) from air is not facile, as a material with a high selectivity and strong reactivity with CO\({}_{2}\) is required [54]. Hence, careful control of the reaction conditions to ensure the presence of amine functionalities is  
Figure 7: Synthesis of gels and porous polymers by an aza-Michael addition reaction of PEI with polyethylene glycol diacrylate (PEGDA) [51]. necessary to achieve a high CO\({}_{2}\) adsorption capacity and fast kinetics. The crosslinking reaction of PEI with 4 BMFPT was performed by stirring at 82 \({}^{\circ}\)C for three nights, and the solid was washed with a multitude of solvents. The product was also washed with KOH to remove the HBr formed during the reaction. The dried materials showed colors ranging from pale yellow to darker to deep orange, depending on the feed ratio of the monomers. The final materials were also found to have a course to spongy texture, depending on the feed ratio of the monomers. The PEI-4 BMFPT crosslinked material resulted in spherical particles. The adsorption kinetics of the crosslinked material were found to be fast and reached a CO\({}_{2}\) adsorption of 2.31 mmol g\({}^{-1}\) under 1 atm, 90% CO\({}_{2}\)/Ar at 30 \({}^{\circ}\)C.  
A trichloro-substituted triazine crosslinker (2,4,6-trichloro-1,3,5-triazine, TCT) was used to crosslink PEI by [PERSON] et al. to prepare a material for the efficient recovery of gold from waste water, and the reaction is shown in Scheme 9 [55]. The reaction is a nucleophilic aromatic substitution reaction carried out at 70 \({}^{\circ}\)C with molar ratios from 10:1 to 2:1 (PEI to TCT ratio). The reactions yielded pale-yellow precipitates with a 35-85% yield. The \({}^{13}\)C NMR peaks associated with PEI in the aliphatic region were broad, featureless bands in the crosslinked material, which are indications of the formation of a rigid material. This is in contrast to the sharp peaks seen in the \({}^{13}\)C spectrum of the pristine PEI, supporting the occurrence of reaction between the crosslinker and PEI. A relatively sharp peak appearing at 165 ppm corresponds to the aromatic carbons of TCT, indicating that the substitution reaction between PEI and TCT occurred. In the IR study, the C-CI stretching/bending vibrations associated with the TCT crosslinker (at 1267 and 850 cm\({}^{-1}\)) disappeared from the spectrum of the crosslinked material, supporting the expected CI substitution by the amine. Details about its use for Au\({}^{3+}\) adsorption are discussed in Section 3.1. **Scheme 9. ** Crosslinking of PEI with triazine moiety-containing molecules with a good leaving group [53; 55]. The crosslinking of PEI using ECH to reduce its water solubility and engineer the material's properties was also studied in the past, and the crosslinked polymer was used for the removal of metal ions and dyes [21; 56; 57]. [PERSON] et al. prepared crosslinked PEI using ECH in the presence of a NaOH solution at 50-70 \({}^{\circ}\)C, which formed a gel like material in few minutes. In this case, the mechanism involves both nucleophilic substitution of the chlorine from ECH and ring opening of the three-membered ring (Scheme 10) [21]. The metal adsorption characteristic is briefly discussed in Section 3.1 below. [PERSON] et al.