## 3 Applications of Crosslinked PEI
### Adsorption of Heavy Metal Ions and Adsorption Models
Solid formation was accompanied by ionotropic gelation and a crosslinking reaction. The two other materials prepared and tested for gold uptake consisted of PEI, alginate, and CaCl\({}_{2}\) (without crosslinking), and pristine (consisting only alginate and CaCl\({}_{2}\)). The materials were washed and solid products were obtained by freeze drying. The adsorbent capacities of the three materials for gold were tested. While the glutaraldehyde-crosslinked material showed an adsorption capacity of 2300 mg g\({}^{-1}\), the non-crosslinked material showed an adsorption capacity of 1400 mg g\({}^{-1}\) for gold. The pristine material consisting of alginate and CaCl\({}_{2}\) showed poor gold adsorption (4.81 mg g\({}^{-1}\)). The desorption of gold was achieved using thiourea/HCl, and its best combination resulted in the leaching out of 97% of the gold from the adsorbent. The gold binding mechanisms were studied and elucidated with the aid of XRD and XPS as involving sequential electrostatic interaction and reduction by the amine, hydroxyl, and aldehyde groups. PEI was crosslinked with glutaraldehyde and glyoxal in the presence of hydroxypropyl methylcellulose (HPMC) in a typical beaker reaction at room temperature to yield an orangish-reddish crosslinked material (Figure 6). The resulting material was a jelly before it was put into an oven for drying. The crosslinked material was mixed with a copper ion-spiked water solution and stirred at room temperature to evaluate the copper binding capacity of the adsorbent material. The bulk crosslinked material was found to be efficient at removing copper ions from water within a short period of time. The study showed that the copper adsorption of the material was up to 350 mg g\({}^{-1}\) for the crosslinked polymer, which has HPMC as an additive, and leached out later. However, the two other crosslinked polymers--one without HPMC but crosslinked with glutaraldehyde and the second materials crosslinked with glyoxal--showed a lower copper adsorption capacity. The adsorption of Cu\({}^{2+}\) on the crosslinked PEI is best described by a pseudo-second-order kinetic model (Equation (4)), as revealed by the high R\({}^{2}\) value of a linear plot plot of t/qt versus \(t\). The material is also reusable for repeated adsorption batches after the release of adsorbed copper ions in 2% HNO\({}_{3}\)[31]. [PERSON] et al. used PEI to crosslink cellulose nanocrystals for effective use as adsorbent of rare earth elements (REEs) from water and recovery of the REEs. Apart from the role of PEI in crosslinking the cellulose nanocrystals, it will also act as a coordination cite and hence bind the REEs in an aqueous solution. The use of PEI as a crosslink avoids the use of toxic crosslink as well. The crosslinked material prepared gave adsorption capacities of 0.611, 0.670, and 0.719 mmol g\({}^{-1}\) for La\({}^{3+}\), Eu\({}^{3+}\), and Er\({}^{3+}\), respectively, with the primary and secondary amines playing roles in the binding process. Rare earth elements have similar chemical properties and hence are difficult to separate when they are found together in a sample. However, this PEI-crosslinked cellulose adsorbent showed a binding preference toward Er\({}^{3+}\) compared to La\({}^{3+}\) and Eu\({}^{3+}\), which makes the crosslinked material interesting for a real application [74]. The synthesis of porous crosslinked PEI was found to be interesting to increase the adsorption capacity and the adsorption kinetics of heavy metal cations. In this regard, PEI-coated diatomaceous earth (DE) was crosslinked with glutaraldehydehyde, with the DE serving as bio-template. The template was removed in subsequent steps to yield a porous structure. The synthesis of the adsorbent involved the dispersion of washed DE into a solution containing PEI in 0.5 mol L\({}^{-1}\) NaCl to yield a 10 wt% (DE plus PEI) dispersion. The solid dispersion was collected after centrifugation and crosslinked with a glutaraldehyde solution (0.5 wt%).