## 2 Crosslinking of PEI and Reaction Mechanisms
Strong \({}^{13}\)C NMR peaks have been observed at around 100 ppm and in the region below 50 ppm. The complex NMR spectrum is attributed to the tendency of glutaraldehyde to form a mixture of isomers, such as cyclic hemiacetals, when it is in water [35]. The \({}^{13}\)C NMR spectrum of the branched PEI, on the other hand, gave eight sharp peaks, where seven of them appeared in the aliphatic region. A \({}^{13}\)C NMR study of the crosslinked material (after the PEI and glutaraldehyde were kept together for some time) was also conducted by the research group. In the spectrum, peaks associated with glutaraldehyde disappeared and a broadening of peaks were observed, which were both attributed to the formation of a rigid polymer network. The presence of an imine bond in the crosslinked material was also proposed, as a new peak at 174 ppm appeared while the peak at 205 ppm disappeared [34]. It is known that reactive amino functional group-containing molecules or polymers react with aldehydes and acids. [PERSON] et al. prepared crosslinked PEI for a CO\({}_{2}\) adsorption study [36]. The crosslinkers used in the study were a glyoxal solution (GOX, 40 wt% in H\({}_{2}\)O) and oxalic acid (OA). The authors observed an increase in the viscosity of the material with time, indicating the occurrence of a crosslinking reaction. The reaction was performed in methanol by dissolving 1 g of PEI (MW = 1200 g/mol) and mixing it with the crosslinker (glyoxal/oxalic acid) dissolved in 1 mL of methanol. After heating the mixture for 6 h at 60 \({}^{\circ}\)C, the solvent was evaporated, and the material left was cured by heating to 80 \({}^{\circ}\)C for 6 h under stirring and finally heating at 100 \({}^{\circ}\)C for 6 h under vacuum to remove water and other low-molecular-weight adsorbed molecules. The materials prepared were named 2.5 GOX-PEI and 2.5 OA-PEI, where the numbers refer to the molar ratio of the crosslinker to nitrogen atoms in PEI. Like the previous study reported by [PERSON] et al. [37], \({}^{13}\)C NMR was used to study the crosslinking reaction mechanism and propose the structure of the crosslinked PEIs. The structure of the pristine PEI showed \({}^{13}\)C peaks all below 60 ppm (aliphatic region), which is a clear indicator of the aliphatic carbon atoms (methylene groups), and the structure proposed for PEI is shown in Figure 1. The 2.5 GOX-PEI and 2.5 OA-PEI materials also gave distinct and sharp peaks, unlike the broadened peaks reported when ECH and 1,3-butadiene diepoxide (BDDE) crosslinkers are used. Moreover, weak peaks were observed around 165 ppm for 2.5 GOX-PEI, while the 2.5 OA-PEI material gave a peak at 165 and another peak above 170 ppm. The peak appearing at around 165 ppm for 2.5 GOX-PEI is assigned to the carbon atom of carbonyl group of an amide structure [36], which was interpreted as the crosslinking reaction with glyoxal proceeds via amide bond formation instead of the imine bond formation. Moreover, the ratio of primary, secondary, and tertiary amines found in the crosslinked materials were calculated based on the \({}^{13}\)C NMR spectrum. A slight increase in the tertiary amine content that was found in 2.5 GOX-PEI (31.9%) as compared to PEI (29.1%) was interpreted as the preferred reaction of glyoxal with the secondary amine and hence supporting the proposed amide bond formation in the crosslinking reaction. However, the tertiary amine content showed a decrease in the 2.5 OA-PEI material compared to PEI and 2.5 GOX-PEI. The inconsistency in the ratio of the tertiary amine to secondary to primary amines in 2.5 OA-PEI could also arise from quaternary ammonium cation and carboxylate anion formation, which potentially underestimates the tertiary amine concentration in the structure.