## 3 Applications of Crosslinked PEI
### Adsorption of Heavy Metal Ions and Adsorption Models
To a solution of EGDE in toluene, a water solution of PEI and span surfactant was added dropwise. The crosslinking reaction was achieved easily at 45 \({}^{\circ}\)C for 4 h, and further washing and drying gave a solid adsorbent. The maximum uptake amount of Au\({}^{3+}\) was up to 944 mg g\({}^{-1}\) from a gold-containing water sample. However, the adsorption capacity for gold slightly decreased to 887 mg g\({}^{-1}\) in the presence of competitive ions, which is the case in gold-containing waste water. The little effect of the presence of competitive ions of gold adsorption is explained in terms of electrostatic attraction between the adsorbent and the analytes. Gold, under acidic conditions, exists in the form of AuCl\({}_{4}\)\({}^{-}\) (negatively charged), which is expected to form an electrostatic attraction with the positively charged adsorbent (protonation of the nitrogen of PEI is expected under acidic conditions). On the other hand, the metal cations will have repulsion with the positively charged adsorbent, which explains why the uptake of the positively charged metal ions was remarkably suppressed. Moreover, the polymer removed 88.7% of gold from water. The Langmuir and Freundlich equations were used to fit the experimental adsorption of Au(III) on the crosslinked polymer, but the Langmuir model (Equation (1)) [43] was found to best describe the adsorption on the polymer studied. The pseudo-first-order and pseudo-second-order kinetic equations were applied to fit the sorption kinetic data. The pseudo-second-order equation described the kinetic sorption procedure on the polymer, as evidenced by the high R\({}^{2}\) value (0.998). Gold is assumed to have been removed by an electrostatic interaction and or chelation and is shown in Figure 5.  
A glutaraldehyde-crosslinked PEI-coated polysulfone/_Escherichia coli_ bacterial biomass composite fiber (PEI-PSBF) was used as an adsorbent for Pd\({}^{2+}\) from acidic solutions [69]. The fiber was prepared by passing a DMF-dissolved polysulfone and _E. coli_ biomass through a spineret with a 0.1 mm diameter into deionized water. The extruded materials were collected, washed, and then lyophilized using a freeze dryer to yield the composite material (PSBF) [70]. The PSBF was the mixed with a 2.3% PEI solution and crosslinked by adding the desired amount of the crosslinker. The deionized water-washed material was dried using a freeze drier (TFD Series, Ilshinbiobase, Korea). The crosslinked PEI-coated PSBF was used to take up Pd\({}^{2+}\) and the adsorption capacity was found to be seven times higher and to have faster sorption kinetics in comparison with the adsorbent that was not coated with PEI (PSBF only). The kinetic data were well described by the pseudo-second-order kinetic model. The study revealed fast adsorption kinetics for Pd\({}^{2+}\), with an adsorption efficiency of 216.9 mg g\({}^{-1}\) (from Langmuir model) of the analyte with adsorption reaching  
Figure 5: Proposed gold chelation and electrostatic interaction with the crosslinked material [43]. at equilibrium in 240 min. On the other hand, the theoretical sorption capacities were studied (adsorption isotherms). In this case, the Freundlich model was best for PSBF while Langmuir model was best for the PEI-PSBF adsorbent. The adsorbent was recovered by releasing the Pd\({}^{2+}\) using a 0.1 M HCl/0.01 M thiourea solution mixture, with a desorption efficiency of the mixture of approximately 97.4%, and it was noted that the material can be reused for adsorption for up to five batches of adsorption and desorption processes. PEI in a Ca\({}^{2+}\)-alginate hydrogel matrix was crosslinked with glutaraldehyde to effectively adsorb and recover gold from acidic solutions [71]. Alginate, an anionic polysaccharide, forms stable hydrogels with divalent metal ions, including Ca\({}^{2+}\). The crosslinked material was achieved by the extrusion of a mixture of PEI and alginate onto a mixture of CaCl\({}_{2}\) and glutaraldehyde [72; 73].