Speciation of Hexavalent Chromium in Aqueous Solutions Using a Magnetic Silica-Coated Amino-Modified Glycidyl Methacrylate Polymer Nanocomposite

A new magnetic amino-functionalized polymeric sorbent based on glycidyl methacrylate was synthesized and used in the separation of chromium Cr(VI) oxyanions sorption from aqueous solutions in a static batch system. The kinetic and isothermal parameters of the sorption process were determined. The experimental data were best fitted by a pseudo-second-order model with R2 = 0.994 and χ2 = 0.004. The sorption process of Cr(VI) removal by amino-functionalized sorbent was controlled by both intraparticle diffusion and liquid film diffusion. The equilibrium results showed that the sorption process is best described by the Freundlich model, followed closely by the Sips isotherm model, with a maximum sorption capacity of 64 mg/g. Quantum chemical modeling revealed that the sorption sites on the sorbent surface are fragments with diethylenetriamine and aminopropyl silane groups that coated the magnetic nanoparticles. The calculations showed that Cr(VI) oxyanions (Cr2O72−, CrO42− and HCrO4−) bind to both sorption sites, with diethylenetriamine centers slightly favored. The X-ray photoelectron spectroscopy (XPS) spectra demonstrate that the chromium bound to the sorbent in the form of Cr(III), indicating that the Cr(VI) can be converted on the surface of the sorbent to a less harmful form Cr(III) due to the sorbent’s chemical composition.


Introduction
The predominant valence states of chromium in the environment are trivalent Cr(III) and hexavalent Cr(VI). Hexavalent chromium form has a variety of adverse effects on human health, including skin rash, weakened immune system, decreased pulmonary function, gastrointestinal and neurological issues, cytotoxicity, genotoxicity, etc., as opposed to trivalent chromium, which is biologically vital for the human body (25-35 µg/day) and influences sugar and lipid metabolism [1,2]. The main sources of Cr(VI) are leather and textile manufacturing, as well as the paint and pigment industry. According to the U.S. Environmental Protection Agency (EPA), the maximum permitted total chromium concentration in drinking water is 0.1 mg/dm 3 , while the World Health Organization (WHO) and Europe [Council Directive 98/83/EC on the quality of water intended for human consumption] limited allowable concentration at 0.05 mg/dm 3 [3]. In recent decades, chromium contamination of water was a global issue, particularly in regions with intense mining, industrialization, and ineffective waste management, such as South Africa, Pakistan, China, and India. Recent research revealed an increase in Cr(VI) ions in India's water systems where the mining industry developed [4,5], as well as an alarming 1.38-fold increase in China's average chromium concentration compared to the background [6]. The fact that the

Preparation of Magnetic Sorbent 2.2.1. Silanization of Fe 3 O 4 Nanoparticles by APTMS
Magnetite nanoparticles (5 g) were dispersed in a toluene/methanol solution (100 cm 3 50/50 by weight) and sonicated for 30 min. After that, 50 cm 3 of solvent was evaporated, and 50 cm 3 of methanol was added. This operation was repeated twice to remove excess water. Then, APTMS (5 cm 3 ) was added to the suspension and stirred for 3 h at 323 K, then cooled down to room temperature, followed by decantation and thorough rinsing with ethanol. Finally, the obtained coated magnetic nanoparticles were dried in a vacuum at 333 K for 3 h and named Fe 3 O 4 @APTMS.

Synthesis of Amino-Functionalized Magnetic Nanocomposite
Magnetic nanocomposite (Fe 3 O 4 @APTMS/PGME) was synthesized by suspension copolymerization of 29.2 g of GMA and 19.5 g of EGDMA and AIBN as an initiator (0.5 g) in the presence of an inert component (51.0 g of cyclohexanol and 12.8 g of tetradecanol) and 4.55 g of Fe 3 O 4 @APTMS. The monomer phase was sonicated at 300/600 W in an ultrasonic water bath Sonic 12 GT (Sonic, Niš, Serbia) and transferred in the aqueous phase that consists of 225.0 g of deionized water and 2.25 g of PVP. Copolymerization was carried out under an N 2 atmosphere at 348 K for 2 h, then at 353 K for another 2 h with a stirring rate of 250 rpm. Synthesized copolymer particles were repeatedly rinsed with distilled water and ethanol, kept in ethanol for 12 h, and dried overnight in a vacuum oven at 323 K. The obtained Fe 3 O 4 @APTMS/PGME was classified with 0.15, 0.30, and 0.63 mm sieves.
A sample of magnetic nanocomposite (particles with diameters in the range of 0.15-0.30 mm) was additionally functionalized with diethylenetriamine, as described previously [31]. The resulting amino-functionalized magnetic nanocomposite was labeled as Fe 3 O 4 @APTMS/PGME-deta.

Characterization of Magnetic Sorbent
SEM-EDX analysis of Fe 3 O 4 @APTMS/PGME-deta was performed by scanning electron microscope using a JEOL JSM-6610LV instrument (JEOL Ltd., Tokyo, Japan). In order to make them conductive, samples were coated with a thin gold layer (the gold thickness was 15 nm) in a high-vacuum evaporator prior to scanning. TEM analysis was performed on the JEM-1400 Plus Electron microscope (JEOL USA, Inc., Peabody, MA, USA), with a voltage of 120 kV and LaB6 filament. FTIR spectra were recorded in ATR mode using a Nicolet 380 spectrometer (Thermo Scientific, Waltham, MA, USA) over the range of 400-4000 cm −1 with a resolution of 2 cm −1 . XPS analysis was carried out using a SPECS, PHOIBOS100 spectrometer (SPECS Surface Nano Analysis GmbH, Berlin, Germany) and dual anode Al/Ag monochromatic source. The survey XPS spectra were taken using a monochromatic Al Kα line with an energy step of 0.5 eV in FAT 40 mode, while high-resolution spectra were taken with an energy step of 0.1 eV in FAT 20 mode. XRD patterns were recorded with an Ital Structure APD2000 X-ray diffractometer (G.N.R. S.r.l., Turin, Italy) in a Bragg-Brentano geometry using Cu Kα radiation (λ = 1.5418 Å) and step-scan mode (range: 10-70 • 2θ, step-time: 1.0 s, step-width: 0.02 • ). The program Powder Cell (Federal Institute for Materials Research and Testing, Berlin, Germany) was used for approximate phase analysis. Field dependence of isothermal magnetization M(H) at T = 300 K was measured on a SQUID-based commercial magnetometer Quantum Design MPMS-XL-5 (Quantum Design, Inc., San Diego, CA, USA) in the applied DC fields up to 5 T.
The point of zero charge of Fe 3 O 4 @APTMS/PGME-deta was determined by the technique of evaluating the change of initial and equilibrium pH values [32]. For this purpose, the initial pH of 0.01 mol/dm 3 NaCl solutions (20 cm 3 in a series of erlenmeyer flasks) was adjusted between 2 and 11 using 0.1 mol/dm 3 NaOH or 0.1 mol/dm 3 HCl. Equilibrium pH was determined after adding 50 mg of sorbent and mixing for 24 h at room temperature [25]. The initial pH values were plotted against ∆pH to obtain the point where the initial pH equals the final pH (pH PZC ).

Sorption Experiments
Amino-functionalized magnetic nanocomposite was evaluated as a Cr(VI) sorbent under static batch conditions at unadjusted pH (pH = 5.9) at room temperature (T = 298 K). Based on our previous studies, in order to determine the sorption rate, 0.2 g of Fe 3 O 4 @APTMS/PGME-deta was brought into contact with 20 cm 3 (25 mg/dm 3 ) of the Cr(VI) solution. For 60 min, Cr(VI) solutions (20 cm 3 ) with concentrations ranging from 1 to 180 mg/dm 3 were in contact with 0.2 g of Fe 3 O 4 @APTMS/PGME-deta to determine the sorption isotherm. For the sorption thermodynamics studies, additional experiments were performed at 298, 310, 329, and 343 K with an initial Cr(VI) ions concentration of 25 mg/dm 3 . At predetermined intervals, sample aliquots were extracted and analyzed using inductively coupled plasma optical emission spectrometry, ICP-OES (model iCAP 6500, Thermo Scientific, Waltham, MI, USA).
The amount of Cr(VI) sorbed per unit mass of magnetic sorbent, i.e., the sorption capacity, Q (mg/g), was determined using Equation (1): where C i (mg/dm 3 ) and C (mg/dm 3 ) are the initial and final concentrations in the solution following sorption, respectively, V (dm 3 ) is the volume of the solution, and m (g) is the mass of the magnetic sorbent.

Quantum Chemical Modeling
The optimization of possible dimers containing oxyanion and its sorption site (derivatives of deta, APTMS, and ethyl hydroxide) was performed in the Gaussian09 program (Gaussian, Inc., Wallingford, CT, USA) using B3LYP functional, 6-311 g ** basis set for non-metals and lanl2dz basis set for chromium. Optimized structures were used for the prediction of binding energies between the mentioned species on the same level of theory as well as optimization. The solvation energies were included and calculated by the implicit solvation model (SMD) (dielectric constant (ε) for water was 78.39). The binding energy values were calculated based on Equation (2): where: ∆E V is the energy of interaction within the dimer (or binding energy), E O−A is the energy of the optimized structure of dimer, E O is the energy of the optimized structure of oxyanion, and E A energy of the optimized structure of sorption site, which represents a model molecule for sorption center on sorbent surface. The basis set superposition error (BSSE) was included by using the standard (Boys-Bernardi) counterpoise procedure [33].

Characterization of Fe 3 O 4 @APTMS/PGME-Deta
The magnetic polymer sample functionalized with diethylenetriamine (Fe 3 O 4 @APTMS/ PGME-deta) was porous with a pore diameter corresponding to half of the pore volume of 286 nm and a specific pore area value of 37 m 2 /g, as determined by mercury porosimetry [21]. The sample Fe 3 O 4 @APTMS/PGME-deta was also fully characterized using SEM, TEM, ATR-FTIR, XRD, and SQUID magnetometry. Figure 1a shows the SEM images of smooth spherical shape particles and cross-sections with the typical macroporous morphology formed by suspension copolymerization, consisting of the pores within microspheres, interstitial cavities between the microspheres, and pores between the agglomerates of the microspheres [34]. In addition, TEM image ( Figure 1b) confirms the encapsulation of Fe 3 O 4 nanoparticles (dark areas), which are dispersed in the gray copolymer matrix.
where: ΔEV is the energy of interaction within the dimer (or binding energy), is the energy of the optimized structure of dimer, EO is the energy of the optimized structure of oxyanion, and EA energy of the optimized structure of sorption site, which represents a model molecule for sorption center on sorbent surface. The basis set superposition error (BSSE) was included by using the standard (Boys-Bernardi) counterpoise procedure [33].

Characterization of Fe3O4@APTMS/PGME-Deta
The magnetic polymer sample functionalized with diethylenetriamine (Fe3O4@APTMS/PGME-deta) was porous with a pore diameter corresponding to half of the pore volume of 286 nm and a specific pore area value of 37 m 2 /g, as determined by mercury porosimetry [21]. The sample Fe3O4@APTMS/PGME-deta was also fully characterized using SEM, TEM, ATR-FTIR, XRD, and SQUID magnetometry. Figure 1a shows the SEM images of smooth spherical shape particles and cross-sections with the typical macroporous morphology formed by suspension copolymerization, consisting of the pores within microspheres, interstitial cavities between the microspheres, and pores between the agglomerates of the microspheres [34]. In addition, TEM image ( Figure 1b) confirms the encapsulation of Fe3O4 nanoparticles (dark areas), which are dispersed in the gray copolymer matrix. Grafting of the magnetite surface through silanization was confirmed by the ATR-FTIR spectrum ( Figure 2). Namely, the band at 1060 cm −1 for Si-O-Si stretching, as well as stretching Si-O vibration at 965 cm −1 confirm the presence of silanized magnetite [20]. The strong peak originating from Fe-O vibrations at ~570 cm −1 confirms the successful incorporation of magnetite nanoparticles [35]. The characteristic bands for crosslinked methacrylate copolymer at ~2939 cm −1 , ~1456 cm -1 , and ~1389 cm -1 (methyl and methylene stretching and bending vibrations of C-H bond), 1723 cm −1 (C=O stretching vibrations), 1261 cm −1 , and 1153 cm −1 (stretching C-O-C vibrations) also appeared in Fe3O4@APTMS/PGME-deta spectra [36,37]. The absorption bands for the epoxy ring vibrations at ~850 cm −1 and ~1260 cm −1 indicate incomplete functionalization of epoxy groups. Furthermore, the bands at 1562 cm −1 and 1656 cm −1 (stretching N-H vibrations of primary and secondary amine groups), 750 cm −1 (wagging N-H vibrations) as well the broad band at ~3700-3050 cm −1 (stretching N-H and O-H vibrations) confirmed the amino-functionalization [25,38]. Grafting of the magnetite surface through silanization was confirmed by the ATR-FTIR spectrum ( Figure 2). Namely, the band at 1060 cm −1 for Si-O-Si stretching, as well as stretching Si-O vibration at 965 cm −1 confirm the presence of silanized magnetite [20]. The strong peak originating from Fe-O vibrations at~570 cm −1 confirms the successful incorporation of magnetite nanoparticles [35]. The characteristic bands for crosslinked methacrylate copolymer at~2939 cm −1 ,~1456 cm −1 , and~1389 cm −1 (methyl and methylene stretching and bending vibrations of C-H bond), 1723 cm −1 (C=O stretching vibrations), 1261 cm −1 , and 1153 cm −1 (stretching C-O-C vibrations) also appeared in Fe 3 O 4 @APTMS/PGME-deta spectra [36,37]. The absorption bands for the epoxy ring vibrations at~850 cm −1 and 1260 cm −1 indicate incomplete functionalization of epoxy groups. Furthermore, the bands at 1562 cm −1 and 1656 cm −1 (stretching N-H vibrations of primary and secondary amine groups), 750 cm −1 (wagging N-H vibrations) as well the broad band at~3700-3050 cm −1 (stretching N-H and O-H vibrations) confirmed the amino-functionalization [25,38].
The existence of magnetite phase Fe 3 O 4 was confirmed in Fe 3 O 4 @APTMS/PGME-deta  [39]. Additionally, the broad peak at 2θ = 10-30 • indicated the existence of an amorphous polymer coating layer on the surface of iron oxide nanoparticles. A similar observation was reported for magnetic polymer-bentonite composite [19].  [39]. Additionally, the broad peak at 2θ = 10-30° indicated the existence of an amorphous polymer coating layer on the surface of iron oxide nanoparticles. A similar observation was reported for magnetic polymer-bentonite composite [19].     [39]. Additionally, the broad peak at 2θ = 10-30° indicated the existence of an amorphous polymer coating layer on the surface of iron oxide nanoparticles. A similar observation was reported for magnetic polymer-bentonite composite [19].    deta. The hysteresis loop M(H) curve showed a very fast increase in magnetization with the saturation magnetization value (Ms) of 6.8 Am 2 /kg, indicating that the Fe3O4@APTMS/PGME-deta can be facilely separated from aqueous solutions by applying an external magnetic field and reuse. Based on the pHPZC value of 7.9 ( Figure 5), the positively charged Fe3O4@APTMS/PGME-deta surface at pH < pHPZC electrostatically attracted negatively charged Cr(VI) ions and, thus, enabled their efficient removal. On the other hand, due to electrostatic repulsion at pH > pHPZC, the negatively charged Fe3O4@APTMS/PGME-deta surface did not promote the Cr(VI) ions sorption.  Based on the pH PZC value of 7.9 ( Figure 5), the positively charged Fe 3 O 4 @APTMS/PGMEdeta surface at pH < pH PZC electrostatically attracted negatively charged Cr(VI) ions and, thus, enabled their efficient removal. On the other hand, due to electrostatic repulsion at pH > pH PZC , the negatively charged Fe 3 O 4 @APTMS/PGME-deta surface did not promote the Cr(VI) ions sorption.
deta. The hysteresis loop M(H) curve showed a very fast increase in magnetization with the saturation magnetization value (Ms) of 6.8 Am 2 /kg, indicating that the Fe3O4@APTMS/PGME-deta can be facilely separated from aqueous solutions by applying an external magnetic field and reuse. Based on the pHPZC value of 7.9 ( Figure 5), the positively charged Fe3O4@APTMS/PGME-deta surface at pH < pHPZC electrostatically attracted negatively charged Cr(VI) ions and, thus, enabled their efficient removal. On the other hand, due to electrostatic repulsion at pH > pHPZC, the negatively charged Fe3O4@APTMS/PGME-deta surface did not promote the Cr(VI) ions sorption.

Chromium Sorption onto Fe 3 O 4 @APTMS/PGME-Deta
Previously, Cr(VI) sorption was studied on non-magnetic amino-functionalized macroporous GMA-based copolymer from concentrated metal solutions (0.05 mol/dm 3 ) and at low pH values (pH = 1.8) [40]. In this study, sorption capacity was tested on mag-netic Fe 3 O 4 @APTMS/PGME-deta in diluted solutions with a concentration of 25 mg/dm 3 (0.48 mmol/dm 3 ). All experiments were performed at pH = 5.9 and 298 K, i.e., close to ambient conditions, in order to come as close as feasible to actual environmental concentrations.
The kinetic data were analyzed with theoretical models of PFO, PSO, Elovich, Avrami, and fractional power. The nonlinear regression method was used to fit the data to determine the best-fit kinetic model. For that purpose, two error functions, coefficient of determination (R 2 ) and chi-square statistic test (χ 2 ), were used for analysis. The used nonlinear fitting equations of the kinetic data are presented in Table S1.
As seen in Figure 6, the sorption at the initial stage was rapid (up to 10 min), and the process then gradually slowed down to 50 min when the uptake equilibrium and saturation was attained. The sorption half-time, t 1/2 (the time required to reach 50% of the total sorption capacity), was approximately 2 min, and the sorbent saturation was achieved after 40 min. These results indicate that most Cr(VI) ions were sorbed at the binding sites of Fe 3 O 4 @APTMS/PGME-deta on and/or near the surface. The calculated kinetic parameters and the error calculation are summarized in Table 1.

Chromium Sorption onto Fe3O4@APTMS/PGME-Deta
Previously, Cr(VI) sorption was studied on non-magnetic amino-functionalized macroporous GMA-based copolymer from concentrated metal solutions (0.05 mol/dm 3 ) and at low pH values (pH = 1.8) [40]. In this study, sorption capacity was tested on magnetic Fe3O4@APTMS/PGME-deta in diluted solutions with a concentration of 25 mg/dm 3 (0.48 mmol/dm 3 ). All experiments were performed at pH = 5.9 and 298 K, i.e., close to ambient conditions, in order to come as close as feasible to actual environmental concentrations.
The kinetic data were analyzed with theoretical models of PFO, PSO, Elovich, Avrami, and fractional power. The nonlinear regression method was used to fit the data to determine the best-fit kinetic model. For that purpose, two error functions, coefficient of determination (R 2 ) and chi-square statistic test (χ 2 ), were used for analysis. The used nonlinear fitting equations of the kinetic data are presented in Table S1.
As seen in Figure 6, the sorption at the initial stage was rapid (up to 10 min), and the process then gradually slowed down to 50 min when the uptake equilibrium and saturation was attained. The sorption half-time, t1/2 (the time required to reach 50% of the total sorption capacity), was approximately 2 min, and the sorbent saturation was achieved after 40 min. These results indicate that most Cr(VI) ions were sorbed at the binding sites of Fe3O4@APTMS/PGME-deta on and/or near the surface. The calculated kinetic parameters and the error calculation are summarized in Table 1. Based on error function values (lowest χ 2 and highest R 2 ) calculated for different kinetic models, the fitting degree is as follows: PSO > PFO > Avrami > Elovich > fractional power kinetic models. Additionally, the experimental value of sorption capacity at equilibrium, Qe exp , (1.2 mg/g) is closer to the calculated value of equilibrium sorption capacity, Qe calc , for the PSO model (1.12 mg/g) than the value of the PFO (1.04 mg/g) and Avrami equation (1.07 mg/g). The experimental data are most consistent with the PSO kinetic model, indicating that the rate of sorption is dependent on the affinity of the sorbate to the sorbent, i.e., the oxyanion and properties of the magnetic nanocomposite. It also refers to chemisorption, which involves interactions that alter the electronic structure of the sorbent's active site and the oxyanion [41].  Based on error function values (lowest χ 2 and highest R 2 ) calculated for different kinetic models, the fitting degree is as follows: PSO > PFO > Avrami > Elovich > fractional power kinetic models. Additionally, the experimental value of sorption capacity at equilibrium, Q e exp , (1.2 mg/g) is closer to the calculated value of equilibrium sorption capacity, Q e calc , for the PSO model (1.12 mg/g) than the value of the PFO (1.04 mg/g) and Avrami equation (1.07 mg/g). The experimental data are most consistent with the PSO kinetic model, indicating that the rate of sorption is dependent on the affinity of the sorbate to the sorbent, i.e., the oxyanion and properties of the magnetic nanocomposite. It also refers to chemisorption, which involves interactions that alter the electronic structure of the sorbent's active site and the oxyanion [41].
For the study of the rate-controlling step of the chromium sorption process, four (IPD, Bangham, Boyd, and LFD) models were utilized. The used equations of the four diffusion models are presented in Table S1, while values of obtained relevant parameters are given in Table 2. The IPD plot ( Figure S1a) indicates three diffusion stages: boundary layer diffusion, intraparticle diffusion, and equilibrium stage, where IPD slows down [42]. However, all three straight lines of the fitting curve do not pass through the origin, indicating that intraparticle diffusion is not the only rate-controlling step of chromium sorption. The plots of Bangham and Boyd models (Figures S1b and S1c, respectively) confirmed this result [29,43]. LFD model assumes that the slowest stage of the sorption process is diffusion through the boundary layer of the sorptive solution [44]. Although the LFD plot ( Figure S1d) deviated from the origin, the high R 2 value (R 2 = 0.943) suggested the definite influence of film diffusion on chromium sorption by Fe 3 O 4 @APTMS/PGME-deta sorbent.
The Langmuir, Freundlich, Tempkin, Dubinin-Radushkevich, Toth, and Sips isotherm models were used to describe the equilibrium data by employing nonlinear fitting forms (Table S2). The calculated values of parameters and the plot of six applied isotherm models are presented in Table 3 and Figure 7, respectively. Table 3. Parameters and error function data for isotherm models obtained by nonlinear fitting for the chromium sorption onto Fe 3 O 4 @APTMS/PGME-deta.

Isotherm Model Parameter Value
Langmuir Q m , L (mg/g) 8.22 Considering R 2 and χ 2 values, the sorption isotherm models fitted the experimental data in the order of Freundlich > Sips > Toth > Langmuir > Dubinin-Radushkevich isotherm > Temkin isotherm. The Freundlich model describes heterogeneous systems and reversible sorption and is not restricted to the formation of monolayers. The value of K F is related to the degree of sorption, while the Freundlich constant (1/n) is a measure of the deviation of the sorption from linearity; the more heterogeneous the surface, the 1/n value is closer to zero [41]. The Freundlich constant obtained in this study was 0.65 (corresponding to an n value of 1.54), indicating favorable sorption. The value of the free energy of sorption calculated from the Dubinin-Radushkevich model was 59.5 kJ/mol, suggesting that the process of chromium removal onto Fe 3 O 4 @APTMS/PGME-deta was chemisorption governed by particle diffusion mechanism [45]. According to the Sips model, the maximum sorption capacity was 64.13 mg/g. Additionally, the Sips exponent (m = 0.68) was less than 1, indicating the predominance of chromium sorption on a heterogeneous surface. that the process of chromium removal onto Fe3O4@APTMS/PGME-deta was chemisorption governed by particle diffusion mechanism [45]. According to the Sips model, the maximum sorption capacity was 64.13 mg/g. Additionally, the Sips exponent (m = 0.68) was less than 1, indicating the predominance of chromium sorption on a heterogeneous surface. The maximum Cr(VI) sorption capacity of Fe3O4@APTMS/PGME-deta obtained from the Sips isotherm model was compared with different magnetic sorbents having a wide range of sorption capacities ( Table 4). The literature review focused on studies published in the last decade, and the choice was made according to the structural similarities of the sorbents with our sorbent in terms of functional groups and/or the incorporated coated and uncoated magnetite. Unlike the majority of sorbents listed in Table 4 that were tested in a highly acidic environment, Fe3O4@APTMS/PGME-deta was used at an unadjusted pH, closer to real conditions. In that manner, the waste production and secondary pollution were minimized, making Cr(VI) sorption process with Fe3O4@APTMS/PGME-deta low-cost, economical, and environmentally friendly. Bearing that in mind, it can be said that Fe3O4@APTMS/PGME-deta has a reasonable capacity for Cr(VI) sorption from aqueous solutions.  The maximum Cr(VI) sorption capacity of Fe 3 O 4 @APTMS/PGME-deta obtained from the Sips isotherm model was compared with different magnetic sorbents having a wide range of sorption capacities ( Table 4). The literature review focused on studies published in the last decade, and the choice was made according to the structural similarities of the sorbents with our sorbent in terms of functional groups and/or the incorporated coated and uncoated magnetite. Unlike the majority of sorbents listed in Table 4 that were tested in a highly acidic environment, Fe 3 O 4 @APTMS/PGME-deta was used at an unadjusted pH, closer to real conditions. In that manner, the waste production and secondary pollution were minimized, making Cr(VI) sorption process with Fe 3 O 4 @APTMS/PGMEdeta low-cost, economical, and environmentally friendly. Bearing that in mind, it can be said that Fe 3 O 4 @APTMS/PGME-deta has a reasonable capacity for Cr(VI) sorption from aqueous solutions.   A thermodynamic investigation was conducted at four temperatures in the 298-343 K range. Table 5 shows the thermodynamic parameters of chromium sorption calculated from experimental data using Equations (3)-(5) [28]: where C e (mg/dm 3 ) and C a (mg/dm 3 ) are the concentration of chromium ions in solution at equilibrium and the amount of chromium ion sorbed onto Fe 3 O 4 @APTMS/PGME-deta at equilibrium, respectively, R (8.314 J/mol K) is the universal gas constant, T (K) the absolute temperature and ∆G 0 (kJ/mol), ∆S 0 (kJ/mol K), and ∆H 0 (kJ/mol) are the change of standard Gibbs free energy, standard entropy, and standard enthalpy, respectively. Negative ∆G 0 values at all temperatures imply spontaneous sorption of chromium on the magnetic nanocomposite sorbent, but positive ∆H 0 values suggest the process is endothermic. A positive value of ∆S 0 indicates the sorbent's affinity for chromium oxyanion and a higher probability of solid-liquid phase interactions leading to structural changes on both the magnetic nanocomposite and the oxyanion, which is characteristic of chemisorption.

Chromium Sorption Mechanism
In order to understand the interaction mechanism between chromium oxyanions and Fe 3 O 4 @APTMS/PGME-deta, the SEM-EDX (Figure 8), FTIR ( Figure 9) and XPS analyses (Figure 10) of the samples before and after sorption were performed.
Negative ΔG 0 values at all temperatures imply spontaneous sorption of chromium on the magnetic nanocomposite sorbent, but positive ΔH 0 values suggest the process is endothermic. A positive value of ΔS 0 indicates the sorbent's affinity for chromium oxyanion and a higher probability of solid-liquid phase interactions leading to structural changes on both the magnetic nanocomposite and the oxyanion, which is characteristic of chemisorption.

Chromium Sorption Mechanism
In order to understand the interaction mechanism between chromium oxyanions and Fe3O4@APTMS/PGME-deta, the SEM-EDX (Figure 8), FTIR ( Figure 9) and XPS analyses (Figure 10) of the samples before and after sorption were performed.
The EDX spectrum confirmed the presence of all expected elements (C, O, N, Fe, Si, Cr). The N peaks showed an amino-functionalization, Fe peaks suggested the incorporation of magnetite, while the presence of the Si peak evidenced the silanization of magnetite particles. After sorption, the presence of a Cr peak was observed on the particle surface as well as on the cross-section, thus proving successful sorption. As shown in Figure 8d stronger Cr peak on the cross-section indicated that intraparticle diffusion has a great influence on sorption. Due to gold coating on Fe3O4@APTMS/PGME-deta, the EDX spectra show Au peak. Figure 8. EDX spectra and SEM images for Fe3O4@APTMS/PGME-deta of (a) particle surface and (b) cross-section before sorption and (c) particle surface and (d) cross-section after chromium sorption.
As can be observed from FTIR spectra, the intensity and position of some characteristic peaks of the magnetic nanocomposite sorbent after chromium sorption were changed. After chromium sorption, two new peaks at 933 cm −1 and 802 cm −1 appeared, which could be assigned to Cr-O bond [29,59]. The band of O-H and N-H stretching vibration at 3275 cm −1 shifted to higher wavenumbers. The intensity of N-H bending vibration at 1656 cm −1 slightly increased, while the bands at 1562 cm −1 and 750 cm −1 disappeared, which can be attributed to the formation of N-Cr bond [60].     The EDX spectrum confirmed the presence of all expected elements (C, O, N, Fe, Si, Cr). The N peaks showed an amino-functionalization, Fe peaks suggested the incorporation of magnetite, while the presence of the Si peak evidenced the silanization of magnetite particles. After sorption, the presence of a Cr peak was observed on the particle surface as well as on the cross-section, thus proving successful sorption. As shown in Figure 8d stronger Cr peak on the cross-section indicated that intraparticle diffusion has a great influence on sorption. Due to gold coating on Fe 3 O 4 @APTMS/PGME-deta, the EDX spectra show Au peak.
As can be observed from FTIR spectra, the intensity and position of some characteristic peaks of the magnetic nanocomposite sorbent after chromium sorption were changed. After chromium sorption, two new peaks at 933 cm −1 and 802 cm −1 appeared, which could be assigned to Cr-O bond [29,59]. The band of O-H and N-H stretching vibration at 3275 cm −1 shifted to higher wavenumbers. The intensity of N-H bending vibration at 1656 cm −1 slightly increased, while the bands at 1562 cm −1 and 750 cm −1 disappeared, which can be attributed to the formation of N-Cr bond [60].
In the full-range scan of the XPS spectra (Figure 10a), the common peaks of C 1s, O 1s, N 1s, Si 2p, and Fe 2p were observed before sorption. After sorption, the new peak of Cr 2p (~580 eV) appeared, which confirmed the successful sorption of Cr ions on Fe 3 O 4 @APTMS/PGME-deta. The HRES spectrum of Cr 2p with curve-fitting is shown in Figure 10b. The peaks centered at 576.5 eV and 585.8 eV could be assigned to Cr 2p 3/2 and Cr 2p 1/2 , respectively. The Cr 2p 3/2 peak was deconvoluted into two subpeaks at 575.8 eV and 578.1 eV that can be ascribed to the Cr(III) and Cr(VI) states. Additionally, the Cr 2p 1/2 spectrum was fitted with two peaks located at 585 eV and 587.2 eV, which can be associated with Cr(III) and Cr(VI) species [61]. To further investigate the interactions between chromium and Fe 3 O 4 @APTMS/PGME-deta, HRES N 1s spectra of the aminofunctionalized nanocomposite before and after the sorption of chromium were analyzed. The HRES N 1s spectrum before sorption (Figure 10c) was deconvoluted into two peaks at 399.2 eV and 400.2 eV, which were consistent with the presence of non-protonated primary and secondary amine groups [62]. After sorption (Figure 10d), two new peaks at 395.0 eV and 401.2 eV appeared, which can be assigned to protonated amino groups and N-Cr bond [63].
Bearing in mind that the initial solution contained only hexavalent chromium, the appearance of Cr(III) peaks in XPS spectra can be explained by the reduction of some Cr(VI) species on the Fe 3 O 4 @APTMS/PGME-deta surface during the sorption process. The chemical route behind this removal and reduction of Cr(VI) to Cr(III) by magnetic polymer nanocomposite Fe 3 O 4 @APTMS/PGME-deta was not fully explored. It is assumed that the removal mechanism for hexavalent chromium consists mostly of electrostatic attraction by the sorbents surface, electron migration, and coordination reaction [64]. Under experimental conditions, at the initial stage, chromium oxyanion could be absorbed by electrostatic attraction with hydroxyl and amino functional groups of the Fe 3 O 4 @APTMS/PGMEdeta. After sorption, the surface charge of the sorbent remained positive but became less positive upon contact with the negatively charged Cr(VI) species [65]. The Cr(VI) signals found by XPS ( Figure 10) result from HCrO 4 − oxyanion interaction with the hydroxyl and amino groups. This interaction does not affect the oxidation state of Cr species. However, chromium can be reduced to the trivalent form in the vicinity of an electrondonating functional group, such as a hydroxyl group. Following chromium reduction, hydroxyl groups are oxidized to the carbonyl in this process. On the surface of the sorbent, Cr(III) species can coordinate with amino groups by forming covalent bonds with N atoms [66]. XPS analysis results confirmed that some Cr(VI) species become free trivalent chromium ions.

Quantum Chemical Calculations
Our previous works demonstrated that calculating the coordination bond energy for the chemisorption of metal ions on the polymer gives excellent agreement with the experimentally determined maximum sorption capacities [27,67]. Quantum chemical modeling of physisorption and calculation of the energy of non-covalent binding proved to help explain the binding mechanism of oxyanions to the polymer and the affinity of individual oxyanions for the polymer [21].
The nature of chromium oxyanion binding at the active sites of sorbent was studied by quantum chemical modeling. Analyzing the sorbent's chemical composition within its unit structure shows possible binding active sites: a diethylenetriamine-derived fragment (called a "detaOH residue"), an (aminopropyl)triethoxysilane-derived fragment (called an "APTMSOH residue") ( Figure S2), as well as (aminopropyl)silane groups derived from APTMS, which coated the surface of magnetic nanoparticles before it is incorporated into the polymer in situ [68].
The introduction of the hydroxyethyl group to the deta and APTMS skeleton is very important from the point of view of supramolecular chemistry because the number of donor groups for hydrogen bonding is increased. In addition, the OH group is a better donor for hydrogen bonding than the NH 2 group; hence, detaOH and APTMSOH species will be used to model sorption.
Depending on the pH value, deta could be protonated (pKa values for deta are 4.42, 9.21, and 10.02), and the distribution of different ionic/neutral forms of deta (deta-H 3 3+ , deta-H 2 2+ , deta-H + , and deta) is shown in Figure S3 [69]. We assumed that the distribution of detaOH species would be similar to that of deta species because adding a hydroxyethyl group to deta should not cause drastic changes in the acid-base characteristics of detaOH. The free amino groups of (aminopropyl)silane fragments are protonated to pH less than 10 (pK a = 10.6 for APTMS); hence, the positively charged surface of the silane layer is a potentially good absorbent for negatively charged oxyanions [70]. Model systems for estimation of the binding energies of oxyanions to the copolymer include all molecular fragments, which under experimental conditions, could be found on the surface of the polymeric nanocomposite ( Figure 11) Depending on the pH value, deta could be protonated (pKa values for deta are 4.42 9.21, and 10.02), and the distribution of different ionic/neutral forms of deta (deta-H3 3+ deta-H2 2+ , deta-H + , and deta) is shown in Figure S3 [69]. We assumed that the distribution of detaOH species would be similar to that of deta species because adding a hydroxyethy group to deta should not cause drastic changes in the acid-base characteristics of detaOH The free amino groups of (aminopropyl)silane fragments are protonated to pH less than 10 (pKa = 10.6 for APTMS); hence, the positively charged surface of the silane layer is a potentially good absorbent for negatively charged oxyanions [70]. Model systems for estimation of the binding energies of oxyanions to the copolymer include all molecular frag ments, which under experimental conditions, could be found on the surface of the poly meric nanocomposite (Figure 11): double and triple protonated detaOH species (detaOH H2 2+ and detaOH-H3 3+ ), protonated species formed by condensation of two APTMS (2APTMS-H2 2+ ) or three APTMS (3APTMS-H3 3+ ), and their hydroxyethyl derivatives (2APTMSOH-H2 2+ and 3APTMSOH-H3 3+ ). At pH = 5.9, the dominant species are hydrogen chromate (HCrO4 − ) and chromate (CrO4 2− ) ions and, to a lesser extent, dichromate (Cr2O7 2− ) ions. Optimized structures o combinatorial configurations of HCrO4 − , CrO4 2− , and Cr2O7 2− and six sorption sites were used as the model systems to calculate the interaction energies within the complex structure ( Figure 12). The results of the calculations are shown in Table 6.
Quantum chemical calculations showed that the CrO4 2− ion, unlike HCrO4 − and Cr2O7 2− ions, undergoes neutralization after binding to the sorption sites, except to   (Table S3). Namely, the double negative charge is distributed over four oxygen atoms in the case of the chromate ion, while in the case of the dichromate ion, over seven oxygen atoms. Therefore, the oxygen atoms of the chromate ion were partially more negative and, therefore, more strongly attract the amine hydrogen atoms from the sorption sites. H 2 CrO 4 and HCrO 4 − ion were formed as products of neutralization, with a lower negative charge than the initial CrO 4 2− ion. As a result of neutralization, there was also a decrease in the positive charge of the sorption sites, as well as a decrease in attractive electrostatic forces. Therefore, the binding energies of the newly formed Cr(VI) species were significantly lower than the binding energies of Cr 2  ). Accordingly, one can assume that CrO 4 2− ion has a significantly higher affinity for all sorption sites than HCrO 4 − and Cr 2 O 7 2− ions. However, after neutralization, its binding energies decreased due to the reduction in electrostatic interactions between the newly formed species.
The mechanism of oxidation by chromium (VI) species was well known, and chromic acid, one of the most commonly used oxidizing agents, reacts with diverse substrates, among them alcohols. The selective oxidation of primary and secondary alcohols into their corresponding aldehydes (or carboxylic acids) ketones can also be achieved using polymersupported chromic acid [71]. The used polymer has positively charged amine groups, which facilitate oxidation by forming esters with chromic acid. Calculations showed that oxyanions have the ability to bind to positively charged amine groups and ethylhydroxyl groups of the detaOH-H 2 2+ , detaOH-H 3 3+ , 2APTMSOH-H 2 2+ , or 3APTMSOH-H 3 3+ sorbent. Accordingly, it should be expected that oxidation of the alcohol group will occur, as well as the formation of Cr(III) species. Cr(III) oxyanion, which is less toxic than Cr(VI), binds to N atoms directly by forming covalent bonds [66]. The sorption of Cu(II), Co(II), Cd(II), and Ni(II) ions by amino-functionalized chelating macroporous copolymers poly(GMA-co-EGDMA)-amine and sorption selectivity of the subject copolymers were successfully quantified experimentally and modeled by quantum chemical calculations [27,31,67]. According to these results, coordination of the diethylenetriamine group from Fe 3 O 4 @APTMS/PGME-deta to the Cr(III) ion can be expected.

Conclusions
This investigation showed that macroporous magnetic nanocomposite synthesized by suspension copolymerization in the presence of silanized magnetite nanoparticles and functionalized with diethylenetriamine (Fe 3 O 4 @APTMS/PGME-deta) was found to be an effective sorbent for hexavalent chromium in aqueous solutions at low concentration. Detailed characterization confirmed the presence of silanized magnetite and amino-functionalization. The obtained magnetic polymer possessed exceptional performances (excellent chemical and thermal properties), a prerequisite for successful commercialization strategies. On the other hand, reliable modeling of sorption kinetics is crucial from both scientifical and technological standpoints. The sorption half-time was approximately 2 min, with a saturation time of 40 min. Kinetic analysis indicated that the sorption rate of Cr(VI) was controlled by liquid film diffusivity and intraparticle diffusion, while equilibrium and thermodynamic studies revealed that the process is spontaneous and endothermic and that chemisorption is involved. The mechanism of sorption of Cr(VI) oxyanions was discussed through a synergy of experimental analysis and modeling approach, which accounted for the possible protonated states of the sorbent, the equilibrium forms of Cr(VI) species in solution, as well as possible non-covalent interactions responsible for their attraction. Namely, the quantum chemical calculations identified two potential binding sites for Cr(VI) oxyanions on the surface of the sorbent (deta and APTMS). The appearance of Cr(III) peaks in XPS spectra of Fe 3 O 4 @APTMS/PGME-deta after chromium sorption indicated that the Cr(VI) removal was a combination of chemical sorption (the first step in the sorption mechanism) and the conversion of Cr(VI) to Cr(III) on the sorbent surface (the second step in the sorption mechanism). Both binding sites have the ability not only to bind Cr(VI) species to the sorbent but also the possibility to reduce Cr(VI) to a less harmful form of Cr(III) ions in their reaction with the OH group from the active sites. This fact makes Fe 3 O 4 @APTMS/PGMEdata nanocomposite more advanced and convenient over other sorbents, which cannot reduce Cr(VI). The wide range of polymer action, stability, and sorption diversity makes it suitable for commercial and industrial water purification. The possibility of surface modification with various functionalized groups of methacrylate-based polymers ensures multipurpose use as one of the main principles of the circular economy, a new production and consumption business model, which includes optimal use of resources, reduction in raw materials consumption, and giving second life of harmful and precious metals.
Supplementary Materials: The following supporting information can be downloaded at: https:// www.mdpi.com/article/10.3390/ma16062233/s1, Table S1: Kinetic models equations; Table S2: Equations for isotherm models; Table S3: The calculated energies of interactions (in kcal/mol) between CrO 4 2− ion and sorption sites, including the species formed in the reaction of neutralization; Figure S1: The plots for (a) IPD, (b) Bangham, (c) Boyd and (d) LFD models for removal of chromium on Fe 3 O 4 @APTMS/PGME-deta; Figure S2: The reaction of epoxy groups with deta and APTMS and formation of appropriate detaOH and APTMSOH derivatives; Figure S3: The structures and distribution of different deta forms (detaH 3 3+ , detaH 2 2+ , detaH + , and deta) depending on pH value.

Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.