## 2 Crosslinking of PEI and Reaction Mechanisms  
The chemical crosslinking of polymers involves covalently bonding of one part of a polymer chain to another polymer chain. Often, small molecular crosslink are used to join the polymer chains. Crosslinking reactions enhance the stability and mechanical strength of the polymer material and change the physical state of the material to make it suitable for practical applications. PEI, being a nitrogen-rich organic polymer, is known to be effectively crosslinked using small molecular crosslinkers to give a three-dimensional network that can retain its structure during adsorption processes. The traditionally used chemical crosslinkers include glutaraldehyde, glyoxal, dichloroethane, ECH, triglyceridesltrimethylpropane ether, etc. (Figure 2), and follow various crosslinking reaction mechanisms. However, in general terms, the reaction take place between the lone pair of electron-possessing nitrogen atoms of PEI and the electrophilic centers found in the molecular/polymeric crosslinkers. The crosslinking of PEI with dialdehyde-containing molecules such as glyoxal and glutaraldehyde has been reported by different research groups and is known to yield a highly stable material. The crosslinking reaction can be achieved easily by mixing PEI and the crosslinker and stirring at room temperature to yield a yellowish/orangish powder [31]. The crosslinking reaction can also be carried out by dipping a PEI-coated surface in a crosslinker solution [32]. The reaction is expected to take place between the nitrogen of the polymer with the electron-deficient carbonyl group of the crosslinkers. Studies of the mechanisms of the reaction between glutaraldehyde and PEI have revealed that the reaction involves more than one type of mechanism. The first possible pathway reported is Schiff base formation, where a C=N double bond is formed between the two reacting functional groups (Scheme 1) [9; 31; 32]. Schiff base formation has been confirmed from an IR study where C=N stretching was detected at 1650 cm\({}^{-1}\), while the appearance of sharp peaks at 2937 and 2850 cm\({}^{-1}\) were assigned to a C-H bending mode, and a low-frequency mode of C-H bending appeared at 1453 cm\({}^{-1}\). The introduction of polar groups such as OH, COOH, and C=O on the surface of inert materials will assist in adhesion and the preparation of stable polar coatings. The material to be coated on the modified surface is then applied using coating techniques such as spraying, vapor deposition, printing, dipping, and other known film-making techniques [33]. [PERSON] et al. [34] studied an alternative coating method whereby an  
Figure 2: Molecular, oligomer, and polymeric crosslinkers used to crosslink polyethylene imine. oxidized surface was treated with 1:1 mixture by weight of PEI and glutaraldehyde at a total solid content of 1% in water that was suitable for effective adhesion enhancement. Complete crosslinking occurs when the water is evaporated to leave a polymerized red/orange solid that is no longer soluble in water. The proposed mechanism for the crosslinking reaction involves aldol condensation polymerization of the glutaraldehyde crosslinker with a dehydration reaction producing an ethylenic double bond and a carbonyl group in conjugation with the carbonyl group attached to the backbone of the glutaraldehydepolymer. The presence of the basic amino group in PEI catalyzes the polymerization reaction of glutaraldehyde. The carbonyl group of the polymerized glutaraldehyde and the amine of the PEI undergo a Schiff base reaction to form a conjugated amine bond (Scheme 2) in the subsequent reaction step [16; 34]. To better understand the nature of the crosslinked material, the individual reactants (PEI and glutaraldehyde) before crosslinking and the mixture of PEI-glutaraldehyde, [PERSON] et al. used \({}^{13}\)C NMR spectroscopy. The NMR spectrum of glutaraldehyde in water is more complex with peaks appearing from 0 to above 200 pm.