Design of an amino-functionalized chelating macroporous copolymer poly(GMA-co-EGDMA) for the sorption of Cu(II) ions

Polymer-based, highly porous nanocomposites with functionalized ligands attached to the core structure are extremely efficient in the detection, removal and recovery of metals through the process of sorption. Quantumchemical models could be helpful for sorption process analyses. The sorption of Cu(II) ions by amino-functionalized chelating macroporous copolymers poly(GMA-co-EGDMA)-amine and sorption selectivity of the subject copolymers, ethylenediamine (en), diethylenetriamine (dien) and triethylenetetramine (trien), were successfully modelled by quantum chemical calculations. Considering the crystal structures from CSD and experimental conditions during the formation of metal complexes, the most frequent mononuclear complexes are those with the tetradentate teta ligand, while binuclear complexes are formed when the metal ion is in large excess. Although the en-copolymer was the most effective functionalized one, higher maximum sorption capacities (Qmax) were observed for the dienand trien-copolymers, due to their abilities to form binuclear complexes. The enthalpy term has the greatest contribution to the total Gibbs energy change of reaction for the formation of mononuclear Cu(II) complexes (ΔGaq), while the solvation energy of the reaction has the greatest contribution in the formation of binuclear complexes. The results of the study indicate that small amines with the ability to form binuclear complex are the best choice for functionalization of the considered copolymer.

(Received 21 January, revised 12 April, accepted 15 April 2019) Abstract: Polymer-based, highly porous nanocomposites with functionalized ligands attached to the core structure are extremely efficient in the detection, removal and recovery of metals through the process of sorption.Quantumchemical models could be helpful for sorption process analyses.The sorption of Cu(II) ions by amino-functionalized chelating macroporous copolymers poly(GMA-co-EGDMA)-amine and sorption selectivity of the subject copolymers, ethylenediamine (en), diethylenetriamine (dien) and triethylenetetramine (trien), were successfully modelled by quantum chemical calculations.Considering the crystal structures from CSD and experimental conditions during the formation of metal complexes, the most frequent mononuclear complexes are those with the tetradentate teta ligand, while binuclear complexes are formed when the metal ion is in large excess.Although the en-copolymer was the most effective functionalized one, higher maximum sorption capacities (Q max ) were observed for the dien-and trien-copolymers, due to their abilities to form binuclear complexes.The enthalpy term has the greatest contribution to the total Gibbs energy change of reaction for the formation of mononuclear Cu(II) complexes (ΔG aq ), while the solvation energy of the reaction has the greatest contribution in the formation of binuclear complexes.The results of the study indicate that small amines with the ability to form binuclear complex are the best choice for functionalization of the considered copolymer.

INTRODUCTION
The Earth's crust naturally contains heavy metal compounds, the concentration of which is increased in places such as bedrocks, or can be found as ores in rocks.2][3] Consequently, the amounts of heavy metals deposited on the Earth's surface are considerably higher compared to natural background concentrations.Heavy metals accumulate over time and since they are non-decomposable or non-biodegradable, they are the long-term health and environmental hazards.Very rarely, acute effects appear when considerable amounts of heavy metals are accidentally released into the environment. 4Various methods of heavy metal removal have been developed and are still being developed: physicochemical (membrane filtration, chemical precipitation, ionexchange, adsorption), electrochemical (electrocoagulation, electroflotation, electrodeposition) biological 5 (biosorption, by bacteria and microorganism, activated sludge process, biofilter, anaerobic digestion, stabilization ponds) and current (membrane filtration, photo-catalysis, nanotechnology) methods.Process of sorption is efficient in the detection and removal of heavy metals. 6Recently, nanocomposite carbon-7 (activated carbon, carbon nanotubes, fullerenes, graphene), polymer-8,9 silica- [10][11][12][13][14][15][16][17][18][19][20] and natural-based [21][22][23][24] nanocomposites, highly porous materials designed for heavy metal adsorption, are being intensively developed. 6he features of the above-mentioned composites are environmental stability, high specific surface area and strength of the core (carbon, polymer and silica), and in synergy with the reactivity of attached ligands to specific metal ions make them efficient, specific and sensitive metal ions sorbents.This allows fast and cheap detection, complete removal or recovery of metals from contaminated waters.
The physicochemical method of remediation through precipitation of Cu(II) ions using chelating agents has proved to be very efficient in fulfilling environmental regulation guidelines. 39Chelating homopolymers and copolymers are highly selective sorbents of heavy metal ions from aqueous solutions. 40Efficient and selective polymers consist of cross-linked polymer structures (core) and functional groups (ligands) that have the ability to form adequate interactions with heavy metals.These functional groups are the key for the selective chelation of heavy metals.Within functional groups, coordination bonding with metal ions is achieved through N, O, P and S atoms. 41,42acroporous copolymers based on glycidyl methacrylate (GMA) are especially interesting, since they contain an epoxide ring in their structures.Optionally, the ease of opening the epoxide ring offers the possibility for the introduction of a ligand with an iminodiacetate, thiol, pyrazole or amino group. 43The GMA molecule is a convenient basis for the relatively simple formation of different metal ions and organic compound sorbents.][46][47][48][49] An incredible number of possible structures that could be synthesized, demands a theoretical evaluation of the most appropriate ligand for the sorption of a particular compound.Recently, through the process of polymerization of GMA monomer together with ethylene glycol dimethacrylate (EGDMA), a macroporous copolymer poly(glycidyl methacrylate-co-ethylene glycol dimethacrylate) (poly(GMA-co-EGDMA)) has been synthesised.The final products were obtained through functionalization of the copolymer poly(GMA-co-EGDMA) with three different amines (Scheme 1): ethylenediamine in poly(GMA-co--EGDMA)-en, diethylenetriamine in poly(GMA-co-EGDMA)-dien and triethylenetetramine in poly(GMA-co-EGDMA)-trien.These three amino-functionalized copolymer samples showed differences in the efficacy of Cu(II) sorption from aqueous solutions, which is expressed as the polymer capacity of sorption in mmol of adsorbed ions per gram of the polymer, Q (mmol g -1 ).The process of sorption itself is a rapid one, while the capacity of sorption depends on the ligand.The sorption capacity rises from -en to -dien (around 1.75 times larger), but there is no difference for -dien and -trien copolymer, i.e., the values are practically identical. 40heme 1.The structure of chelated copolymer poly(GMA-co--EGDMA), functionalized through the reaction of amines (en, dien and trien) with the epoxide ring of the original copolymer.
The aim of this study was to explain experimentally the obtained trend for Cu(II) by applying theoretical techniques to predict the selectivity of the ligands.The complex molecular system of each of the three copolymers is comprised of a recurring structural unit.Therefore, it is possible to discuss Cu(II) ion and copolymer reactions within the macromolecule at the unit segment level.The unit segment would be the Cu(II) ion with coordinated amino ligands.A large number of such segments (up to several thousands) that can be found in the solution where the sorption occurs include a sorbent/metal ion system.The unit segment, crucial for metal-ligand bonding is, in itself, a complex of metal ions and amino ligands, the geometry and stability of which can be predicted by statistical analysis of data taken from the crystal structures and quantum chemical calculations.

METHODOLOGY
Possible coordination modes of triethylenetetramine (trien) ligand in crystal structures, extracted from Cambridge Structural Database (CSD, version 5.38, November 2016), 51 were investigated by applying statistical analysis of the obtained data.
The quantum chemical calculations were performed in the Gaussian09 program 52 applying the B3LYP functional.The 6-311++g** basis set was used for non-metal elements and the lanl2dz basis set for Cu 2+ .The initial complex geometries of possible isomers were optimized at the same level of theory, and the parameters obtained by optimization were used to evaluate Gibbs free energies for the reactions of complex formation.In these reactions (Eq.( 1)), the hydroxyamine obtained in the ring opening reaction (marked as L), reacts with the hexaaqua complex, forming the corresponding complex with the coordinated amine: In Eq. ( 1), L represents enOH, dienOH or trienOH ligand (Scheme 1), n represents the hapticity of ligands, while a equals 1 for mononuclear and 2 for binuclear complexes.The SMD method and the aforementioned level of theory were applied for the solvation energy (ΔE s ) calculations (Eq.( 2)): The Gibbs energy change of reaction (1) in aqueous solution (ΔG aq ) was estimated according to the following equation: Δ ΔG g , the Gibbs energy change of the reaction (1) in vacuum (Eq.( 4)), includes the enthalpy change (ΔH) and entropy change (ΔS), connected through the following equation: The enthalpy change of the reaction is determined by Eq. ( 5): Δ H = ΔE e + ΔE t + pΔV (5)   in which ΔE e stands for the electronic energy change, ΔE t is the thermal energy change, and pΔV is the work performed in a reaction.

Crystallographic analysis of the structures from CSD
Crystal structure analysis is a very useful tool used in conformational analysis and in supramolecular chemistry.In this particular case, the primary interest was to gather information from the crystal structure analysis about coordination geometries of complexes with Cu(II) ion and the trien ligand, as well as the abundance of each geometry observed.Considering the complexes of Cu(II) and the substituted trien ligand from CSD, the most frequent ones are mononuclear complexes of the Cu(II) ion with tetradentate trien ligand geometries, while the second most abundant are binuclear complexes in which two N atoms of the trien ligand are coordinated to each metal ion.Taking into consideration the experimental conditions during trien complex formation, it was observed that binuclear binding occurs when the metal ion is in excess compared to the trien ligand (more than two times).The abundance of mononuclear complexes of Cu(II) and the tetradentate trien ligand are distributed as follows: by far the most frequent are those with square pyramidal (71 %), followed by octahedral (26 %) and square planar (3 %) complex geometry.
When only the Cu(II) complexes with unsubstituted trien ligand (17 crystal structures) are taken into account, a similar trend was observed.Mononuclear complexes with the tetradentate trien ligand are the most frequent (10 structures), while binuclear (2 structures) and polynuclear complexes (5 structures) with the tetradentate trien ligand are less abundant (Fig. 1).Structures with a bridging trien ligand were not found.Complexes with a square-pyramidal geometry (15 structures) are much more numerous than complexes with a square-planar geometry (2 structures).The values of the torsion angle T (N1-N2-N3-N4 angle) are in the range from 0 to 20°, indicating a planar or trans conformation of the trien ligand.

Experimental conditions during the sorption of Cu(II) ions for functionalized copolymers
As previously concluded, the quantity ratio of metal ions and ligands influences the mode in which the ligand is coordinated to the metal.For that purpose, both the quantity of Cu(II) ions and the corresponding copolymer amino-functionalized groups were determined (Table I), in sorption studies of the Cu(II) ion. 42Poly(GMA-co-EGDMA)-en contains 1.12 mmol, poly(GMA-co-EGDMA)--dien 0.81 mmol and poly(GMA-co-EGDMA)-trien) 0.65 mmol amino-functionalized groups. 42Considering the number of amino-functionalized groups (fg) in the copolymer, the quantity of the metal ion is significantly higher in all three cases (Table I).The Cu(II) ion is in an excess, so the complete quantity of the Cu(II) ion would not be sorbed.If the Cu(II) ions formed the mononuclear enOH, dienOH or trienOH complexes, the maximum sorption (Q max = f(t)) would be different.According to the number of amino-functionalized groups, en-functionalized copolymer should have the highest and the trien-functionalized one should have the lowest Q max value.However, dien-and trien-functionalized copolymers have greater Q max values.One of the reasons could be the ability of these ligands to form binuclear complexes.The en-functionalized copolymer is the most effectively functionalized one (53 %), followed by the dien-(38 %) and trien-functionalized copolymer (31 %), which is inverse to their molecular lengths.Similar Q max values of dien-and trien-ligands are quite unlikely given the number of functionalized groups.However, the shortest amine (en) more easily penetrates inside the initial poly(GMA-co-EGDMA) copolymer, thus functionalizing a larger number of epoxide rings.
In aqueous solutions Cu(II) ion exists as a hexaaqua complex.The sorption of this metal strongly depends on the ability of its hexaaqua complex to penetrate near the amino-functionalized groups of the corresponding copolymer.This complex is more voluminous and less flexible than the considered amines (en, dien and trien), resulting in its lower penetrability than the amines.Indicators are the theoretical Q max values (Table I), which are in cases of en-functionalized and dien-functionalized copolymers significantly higher than the experimentally determined Q max values.

Quantum chemical calculations for trienOH complexes
To confirm the above-proposed assumption, quantum chemical calculations were performed to evaluate the Gibbs energy change (ΔG aq ) that accompanies the formation of mononuclear and binuclear Cu(II) complexes with the trienOH ligand in aqueous solution.For this purpose, the complex geometries obtained through optimization of four possible isomers of mononuclear complexes and one binuclear Cu(II) complex were used.Depending on the mutual positions of coordinated oxygen atoms from aqua and trienOH ligands, initial isomers of octahedral complexes with pentadentate trienOH ligand (N 1 ,N 2 ,N 3 ,N 4 ,O-trienOH) could be a cis or trans isomer.Upon the optimization, dissociation of a water molecule (Wd) from an octahedral mononuclear complex occurs.The newly formed complexes take square pyramidal geometry (Fig. 2).The apical position is occupied by an OH group ([Cu(N 1 ,N 2 ,N 3 ,N 4 ,O--trienOH)] 2+ complex), or by the NH group of the trienOH ligand The tetradentate N 1 ,N 2 ,N 3 ,N 4 -trienOH ligand in octahedral mononuclear complexes leaves a space for two aqua ligands in the cis or trans positions.Optimized complexes take square pyramidal geometry, likewise in complexes with pentadentate trienOH ligand (Fig. 2).One of the aqua ligands is released, while the other one remains in the apical position of the square pyramidal ([Cu(H 2 O)(N 1 ,N 2 ,N 3 ,N 4 -trienOH)] 2+ ) complex.As far as the coordinated N atoms are concerned, they are in equatorial position (trans geometry of a tetradentate ligand).
The structures obtained by the optimization were used to calculate the Gibbs free energy change in the formation reaction of these complexes out of the Cu(II) hexaaqua complex (Eq.( 1)).
Interestingly, the results of the optimization are in agreement with the results of the crystallographic analysis, which is strong confirmation that the square pyramidal geometry of the Cu(II) complexes is the most frequent one in crystal structures.
The enthalpy of the formation reaction of Cu(II) complexes with the trienOH ligand, corresponding to the sum of electronic energy change (ΔE e ), thermal energy change (ΔE t ), and work (pΔV), has the greatest contribution to the total Gibbs energy change in aqueous solution (ΔG aq ).
An exothermal process is indicated by the negative sign of enthalpy.On the other hand, contributions from the entropy (TΔS term) and solvation energy (ΔG aq −ΔG g ) are significantly lower than those from the enthalpy term.The formation of a complex without coordinated OH-group is energetically more favourable, by only about 5 % (Table II).
The structure the geometry of which is based on crystallographic data was used as a model system for quantum chemical calculations for binuclear Cu(II) complexes with the trienOH ligand.The first two N atoms (N 1 and N 2 ) are coordinated to one Cu(II) ion in the square pyramidal complex, while the other two N atoms (N 3 and N 4 ) along with the OH group are coordinated to the second Cu(II) ion (Fig. 3).Upon the optimization, one aqua ligand was dissociated from the Cu(II) ion to which the N 1 and N 2 atoms of the trienOH ligand are coordinated, leading to a change towards the square planar geometry of that Cu(II) ion.The other Cu(II) ion remains in the square pyramidal geometry.The enthalpy change of this reaction has positive sign (endothermal reaction), which is compensated by the entropic term (TΔS).However, the greatest contribution to the spontaneous nature of the reaction originates from the solvation energy of the reaction.[

Quantum chemical calculations for enOH and dienOH complexes
As in the trienOH complexes, the initial structures of all possible isomers of mononuclear enOH and dienOH complexes of Cu(II) ion were optimized, with the geometries of all possible coordination isomers (Table III).The optimized structures of the complexes with the highest values of the Gibbs energy changes for reactions of the complex formation in an aqueous solution (ΔG aq ) are shown in Fig. 4.
Unlike the most stable dienOH complex, the most stable structure of an enOH complex does not contain a coordinated OH group.Both enOH and dienOH complexes have higher ΔG aq values than those of trienOH complexes, while dienOH complex displayed the highest ΔG aq value.This trend could be * 1 kcal = 4184 J explained by a larger number of chelate rings in the dienOH complex, compared to the enOH complex.Although the most stable trienOH complex has the greatest number of chelate rings, it is the least stable complex, since chelate rings are condensate and, as such, under a higher ring strain than the rings of the most stable dienOH complex.

CONCLUSIONS
By comparing the Gibbs energy change (ΔG aq ) for mononuclear and binuclear trienOH complex, it could be concluded that the formation of mononuclear complexes is a slightly more favourable (spontaneous) process.These results are in agreement with the combined potentiometric-spectrophotometric study of a Cu(trien) complex, 52 which showed that the mononuclear complex with a tetradentate trien ligand is dominant.This type of complex already occurs at pH 2.5, reaching its maximum at pH 5.In that study, a binuclear complex was not experimentally detected, which could be explained by the fact that the synthesis is conducted in a solution in which the quantity of ligands is four times that of Cu(II) ions.However, it is possible to calculate the equilibrium constant of the reaction in the process of complex formation from the Gibbs energy change (ΔG = −RTln K).The functional dependence of this equilibrium constant versus the [Cu(H 2 O) 6 ] 2+ complex concentration is linear in the reaction where a mononuclear complex is formed, or square for binuclear complex formation.In accordance with the Le Chatelier principle, an increase in metal ion concentration shifts the equilibrium towards trienOH complex formation.As a surplus in concentration of Cu(II)aqua complex versus trienOH ligand is more pronounced, the proportion of binuclear complex in the product increases.Therefore, it is reasonable to assume that, in case of a trien-functionalized complex, the adsorption of Cu(II) ion occurs as a result of the formation of binuclear complexes, since the concentration of Cu(II) ions is about four times higher than the quantity of ligands (functionalized groups of copolymers).For the same reasons, the formation of binuclear complexes with a dien-functionalized copolymer could be expected, but in this case, the concentration of Cu(II) ions is three times that of ligands.

TABLE I .
The quantities of Cu(II) ions and amino-functionalized groups (in mmol) in the corresponding copolymer, obtained in the process of the experimentally conducted sorption of Cu(II) ions.Theoretically Q max(theor) and experimentally Q max(exp) determined values of the maximum sorption of Cu(II) ion, expressed in mmol g-1 a The quantities of functionalized groups (fg) are calculated per g of the copolymer sample used in the experiments; b theoretical Q max values calculated per g of the copolymer, considering that mononuclear Cu(II) complexes are formed; c the theoretical Q max values calculated per g of the copolymer, considering that binuclear Cu(II) complexes are formed