## 3 Applications of Crosslinked PEI
### Adsorption of Heavy Metal Ions and Adsorption Models
The particles were collected and washed and subjected to etching with alkaline KOH to remove the bio-template (DE) and hence resulted a porous crosslinked PEI [75]. The size of 80% of the particles, as measured with 2000 (Malvern Instruments Ltd., U.K.), was found to be below 100 \(\upmu\)m, while the particles were within the range of 2-150 \(\upmu\)m. Interestingly, the copper ion uptake capacity of the etched GA-PEI resin was determined to be >8 times greater than non-etched GA-PEI-DE particles, revealing the importance of etching, which led to a more porous structure. The porous PEI material was also tested for its selectivity for ions and found to be more selective for copper ions compared to commercial resins (Purolite S930 Plus and Lewatit TP 220) [75], indicating the potential of the crosslinked material for binding copper ions in a water sample. The adsorption of copper was found to be very fast, with the adsorption reaching a capacity of 77% in 15 min and adsorption was completed within 1 h. The adsorption isotherms of etched GA-PEI-DE and Purolite S930 (commercial resin) were best described by the Langmuir model. In another work, aerogels were prepared by blending PEI with different materials such as chitosan [76] and alginate [77] for Cr\({}^{6+}\) adsorption. [PERSON] et al. prepared a cellulose/PEI nanofibril aerogel for Cu\({}^{2+}\) and Pb\({}^{2+}\) adsorption. The maximum adsorption capacities were calculated to be 357.44 mg g\({}^{-1}\) and 175.44 mg g\({}^{-1}\) for Cu\({}^{2+}\) and Pb\({}^{2+}\), respectively [78]. [PERSON] et al. prepared an aerogel by blending PEI/montmorillonite/sodium alginate/carboxylated chitosan and Ca\({}^{2+}\). The aerogel had high physical stability due to the various intermolecular forces existing between the blended materials. The material showed an adsorption ability toward Cu\({}^{2+}\) in aqueous solution. The 2.5 wt% PEI-containing material showed a maximum adsorption capacity of 203.99 mg g\({}^{-1}\)[79]. The material was also reusable, showing a 51.4% Cu\({}^{2+}\) removal efficiency after 10 cycles of adsorption and desorption studies. [PERSON] et al. prepared a three-dimensional porous aerogel from a chitosan-modified PEI crosslinked with ECH. The material was used to remove Cr\({}^{6+}\) from the environment and showed a maximum adsorption capacity of 445.29 mg g\({}^{-1}\)[76]. The adsorption kinetics and isotherm experimental data were fitted using adsorption models. A pseudo-second-order kinetic model and the Langmuir isotherm model were found to explain the experimental  
Figure 6: Photo of the crosslinked polyethylene imine material (texture dried and before drying) [31]. data. Moreover, the material has a high adsorption capacity after more than 10 adsorption and desorption cycles, demonstrating the stability and recyclability of the polymer. Table 1 shows a summary of PEI-based crosslinked materials and their performance in metal adsorption from aqueous solutions. Looking at the materials discussed in this review, the reactions conditions and the types of crosslinkers play significant roles. Among the widely used crosslinkers, glutaraldehydeheyde is at the forefront due to its fast reaction with PEI and due to its high tendency to crosslink PEI. As indicated in Table 1 (and discussed earlier), the glutaraldehydeheyde-crosslinked material (in the presence of an additive or not) showed excellent adsorption capacities for different metal cations, such as Cu\({}^{2+}\), Pd\({}^{2+}\), and Au\({}^{3+}\), in water. For example, a gold adsorption of 2300 mg g\({}^{-1}\) was reported by [PERSON] et al. [71] using a PEI/Ca\({}^{2+}\)-alginate hydrogel crosslinked with glutaraldehyde. Copper and lead adsorption reached up to 459 and 497 mg g\({}^{-1}\) in a glutaraldehydeheyde-crosslinked PEI/Fe\({}_{3}\)O\({}_{4}\)/corncob composite and PEI only material, respectively.