## 2 Crosslinking of PEI and Reaction Mechanisms
It was suggested this difference is due to the number of hydroxyl groups found in the sorbents, which considerably affected the CO\({}_{2}\) adsorption. This can be taken yet as another example that reveals that the property  
Figure 4: Proposed structures of crosslinked and pristine polyethylene imine [37]. of the final material will depend on the nature of the crosslinker. Hence, a careful choice of the crosslinker and reaction conditions has a paramount importance in governing the structure of the material and its efficiency in absorbing target analytes. Scheme 4 shows the crosslinking reaction of PEI with ethylene glycol diglycidyl ether (EGDE). The reaction is between the amine of the PEI and the reactive three-membered epoxy ring in a nucleophilic attack, which opens the ring of the epoxide to form a hydroxyl group-containing product. The crosslinked polymer was prepared in a facile reaction that involves a reverse suspension polymerization reaction [43]. The EGDE crosslinker was first dissolved in a desired amount of toluene and the water-soluble PEI and a non-ionic surfactant and emulsifier (Span 80) were dropped into the organic phase and the reaction mixture was heated at 45 \({}^{\circ}\)C for 4 h to produce the crosslinked material. The beads produced were rinsed with methanol and pure H\({}_{2}\)O before being dried at 50 \({}^{\circ}\)C overnight. The prepared material was characterized by multiple techniques to understand its morphology and elemental composition. The SEM study revealed the polymer to have a regular sphere shape, and the surface was found to be relatively smooth. An IR study of both the monomers and the final crosslinked polymer was conducted. The result showed the disappearance of a peak at 911 cm\({}^{-1}\) associated with the epoxy ring, which indicated the occurrence of the reaction. Moreover, the band at 1654 cm\({}^{-1}\), which is associated with N-H deformation, weakened, which supports a crosslinking reaction. The crosslinked polymer was found to have 69.4%, 14.5%, and 16.1% atomic percentages of O, N, and C, respectively, from an XPS wide-scan spectrum study. The amounts of primary amines, secondary amines, and tertiary amines were calculated to be 29.6%, 45.9%, and 24.6%, respectively. The result shows that the crosslinked material is potentially suitable for Au\({}^{3+}\) adsorption, for which the material was prepared. In fact, the crosslinked polymer gave a high sorption capacity and high selectivity for Au\({}^{3+}\) due to its high density of amine and hydroxyl groups on the surface, which is discussed in a later section in more detail. Poly(ethylene glycol) diglycidyl ether (PEGGE, Mn = 500 g/mol) and 1,4-butanediol diglycidyl ether were used as crosslinkers of PEI at low temperature (below 0 \({}^{\circ}\)C) (an ice templating technique), as has been described by [PERSON] et al. (Scheme 5) [47] and [PERSON] et al. [48]. The process of the crosslinking reaction involved the mixing of the PEI and the crosslinker, vortexing, and subsequently freezing the mixture in liquid nitrogen or a dry ice-acetone bath to yield PEI 196 and PEI 78, respectively [47], or freezing the mixture at \(-15\) \({}^{\circ}\)C [48]. PEI 196 and PEI 78 are discussed hereafter. The frozen materials were then thawed at room temperature, and the samples were collected carefully from the vial. A SEM study of both materials (PEI 196 and PEI 78) revealed the formation of porous crosslinked materials. The degree of crosslinking was estimated from an XPS study by looking at the ratio of the C-O to C-N bonds in the crosslinked materials. A lower C-O to C-N bond ratio will imply less crosslinking, as the oxygen will come from the crosslinker. The result showed PEI 196 to have a lower C-O to C-N bond ratio and hence a lower degree of crosslinking [47], which is expected due to the very low reaction temperature (\(-196\)\({}^{\circ}\)C). The better crosslinking reaction of PEI 78 has also resulted a lower percentage of primary and secondary amines in the final material as compared to its counterpart (PEI 196).