Understanding adsorption of divalent metals ions (Mg, Ca) on Nitrogen-, Boron- doped, and defective graphene in nanofiltration process using van der Waals density functional method

Removal of divalent metal ions (Mg and Ca) by graphene membrane has a great implication for manufacturing chitin and chitosan in filtration process. Despite its importance, influences of the doping and vacancy in graphene on the adsorption of those metal ions remain unclear. Here, we study the adsorption of those metal ions on several graphene surfaces, namely pristine graphene (Gra), graphitic N- and B- doped graphene (N- and B-Gra), monovacancy graphene (MV-Gra), monovacancy graphene functionalized by an epoxy (O-MV-Gra), and monovacancy graphene functionalized by an hydroxyl group (OH-MV-Gra) by van der Waals density functional (vdW-DF) method. It was found all considered graphene surfaces have strong interactions with Ca, whereas Mg only chemisorbs on MV-Gra and B-Gra. Energetically, comparing with Ca adosprtion on pristine graphene, both B doping and vacancy creation strengthen the Ca adsorption, while N doping slight decreases it. The electronic structure analysis uncovers enhancement of the Cagraphene interaction by B doping and vacancy formation. Because of the results that have been observed, the removal of Ca ions from aqueous solution can be enhanced by the creation of nanopore or B doping in graphene, in which Ca atom are strongly captured by graphene.


Introduction
Shrimp shells are a rich source of bioactive substances like chitin, chiosan, carotenoids, and other chemical compounds [1][2][3][4].Extracting those bioactive substances from shrimp shell is crucial to increase the profit of processors and to mitigate the environmental population from shrimp shells waste [1][2][3][4].In the shrimp shell processing industry, the chitin is extracted through various cycles of hydrolysis and neutralization under acidic and alkaline conditions, respectively, following by filtration [1][2][3][4][5].After the hydrolysis and neutralization steps, the concentration of alkaline ions, e.g.Ca 2+ , K 1+ , and Na 1+ are significantly increased due to: (1) those ions dissolution from shrimp shell and (2) the base solution in the neutralization step [1][2][3][4][5].Those alkaline ions are then removed by filtration using ultrafiltration and nanofiltration.High-efficiency nanofiltration based on the polymeric membranes is very promising and widely used for Ca 2+ removal from the aqueous solution for this purpose [1][2][3][4][5].In particular, the incorporation of graphene or carbon-nanotube (CNT) into such polymeric membranes [6][7][8][9] is proved to be efficient to capture alkaline ions due to the excellent alkaline ions rejection of graphene or CNT [10][11][12][13][14][15][16].For instance, Nguyen et al synthesized the composite of CNT and nylon-66 and found that this composite exhibits a greater Ca 2+ rejection efficiency than original membrane [5,17].Joshi et al studied the permeation of ions and neutral molecules through micrometer-thick graphene-oxide (GO)-based membranes and speculated that the rapid permeation of small ions arises from the enhanced interactions between the GO membrane and ions that allows a high concentration of those ions inside the membrane [14].Zhu et al fabricated GO based membranes and showed that those membranes exhibits high water permeability and purification toward the rejection of methyl blue, which was recored up to with 99.88% [15].The creation of nanoscale pores in a layer of graphene also opens up a new strategy toward water purification [16].Surwade and co-workers in 2015 found that the single graphene layers with nanometer-sized pores exhibit a salt rejection rate of c.a. 100% and rapid water transport [16].
Unlike the numerous studies on the alkali metal ions (Na and K) capture for water desalination [18][19][20][21][22][23][24][25][26][27][28], there have been relatively few studies on the capture of divalent metal ions (Ca and Mg) by graphene [5,[29][30][31][32][33][34].Malhotraa et al [33] investigated the adsorption of several ions (Pb, As, Cu, Zn, Cr, Hg, Ni, Cd, Ca, Li, Fe) on pristine graphene by both experiments and density functional theory (DFT) calculations.Their results revealed that the charge transfer between graphene and metal ions plays an important role in binding of those ions with graphene.DFT calculation and experiments [20] showed that OH groups can stabilize alkali metal ions (Li, Ca, and K) capture.The interface between divalent metal ions (Ca and Mg) and the doped or functionalized graphenes remains elusive, which hinders the possibility of using graphene for the capture of divalent metal ions.
To provide the insights into the interface between divalent metal ions and graphene, we herein studied the adsorption of Mg and Ca on pristine (Gra), doped, and defective graphene surfaces by van der Waals density functional (vdW-DF) method [35,36].For the doped graphene, the single N and B substitution for a C atom of graphene (Nand B-Gras) are considered [21].For the defective graphene, monovacancy graphene (MV-Gra), monovacancy graphene functionalized by an epoxy (O-MV-Gra), and monovacancy graphene functionalized by an hydroxyl group (OH-MV-Gra) are studied.The structural properties and adsorption strength of Ca and Mg adsorbed on Gra, N-Gra,B-Gra, MV-Gra, O-MV-Gra, and OH-MV-Gra are analysed.The electronic structure origin of the cations adsorption is discussed based on electronic structure analysis.

Computational details
All our DFT calculations were performed by the Quantum ESPRESSO package [37] using the self-consistent vdW-DF method [35,36] with its spin extension [38].The rev-vdW-DF2 exchange-correlation functional [39] was used, which can describe the adsorption of several systems accurately [21,27,40,41].Core electrons were represented by Vanderbilt ultrasoft pseudopotentials with the GBRV library.The valence electron states were expanded in plane-wave basis set truncated with cut-off energies of 50 and 600 Ry for wave functions and augmented charge densities, respectively.All atoms were relaxed until total residual force threshold is <0.02 eV/Å.The solvation effect [22] that mimics the real conditions in water purification should be taken into account to study the interface between divalent metal ions and graphene surfaces.However, due to its huge computational cost, the solvation effect was neglected, the interaction between graphene and divalent metal ions in the vacuum condition were studied.Pristine, N-, and B-doped graphene (Gra, N-Gra, and B-Gra) surfaces were modeled by p(4 × 4) supercells, whereas the monovacancy graphene without and with the functionalized groups, i.e.MV-Gra, O-MV-Gra, OH-MV-Gra were modeled by larger p(5 × 5) supercells.Correspondingly, the k-meshes of 6 × 6 × 1 and 5 × 5 × 1 were employed of Brillouin-zone sampling [42] in structural optimizations for p(4 × 4) and p(5 × 5), respectively.To accurately calculate the density of states (DOS), the Γcentered 16 × 16 × 1 k-points mesh was employed.All slab model were separated by a vacuum region with a length of 16 Å in the surface normal direction.
To discuss the stability of graphene vacancy with the functionalized groups, free energy of formation (G f ) was calculated as, where E tot (F-MV-Gra), E tot (MV-Gra), E tot (H Here E tot (M/gra), E tot (gra), and ( ) E M tot iso are total energies of M adsorbed graphene surface, clean surface, and isolated M (M=Ca and Mg), respectively.With our definition, more negative adsorption energy implies stronger adsorbate-surface interaction.

Structural and electronic properities of graphene surfaces
We begin by discussing the structural and electronic properties of graphene substrates that we considered herein.Total magnetization of the graphene substrates is tabulated in table 1. Figure 1 depicts the atomic structure, band structure, and density of state (DOS) of Gra, N-Gra, and B-Gra.The stability of N-Gra and B-Gra have been discussed in our previous work [21].Upon the N substitutions for C site to from N-Gra, the electron rich nature of the N atom compared with C atom results in the downshift of the Dirac cone (figures 1 (e)  and (f)).On the contrary, the electron deficient nature of the B atom upshifts of the Dirac cone (figures 1 (j) and (k)).In both cases, the electronic structures of graphene near the Fermi level are dominated by 2p z orbital of C atoms and the doping opens the Dirac cone of the pristine graphene by an energy of 0.1 eV.
The nanopores in graphene are proved to enhance the salt rejection and improve the efficiency of graphenebased membranes [16,18,19,45,46], it is thus important to study the interaction between divalent metal ions and the vacancy of graphenes.Herein, we consider graphene surface with a monovacancy, i.  1) due to breaking of the symmetry.For O-MV-Gra, the most stable functionalized site is the hollow site between C1, C2, and C3 atoms, where O is trapped inside the defect sites [43] and the magnetism of monovacancy graphene is quenched due to the covalent bonding between O and C1, C2, and C3 atoms.For OH-MV-Gra, two stable structures are obtained where OH is in the intact (i-OH-MV-Gra) and dissociated (d-OH-MV-Gra) states.In i-OH-MV-Gra, OH only interacts with the C1 atom.In d-OH-MV-Gra, O binds to the C1 and C2 atoms and H binds to C1.Moreover, O and H in d-OH-MV-Gra are in top and bottom graphene planes with a large seperation.The d-OH-MV-Gra are stable than i-OH-MV-Gra by 2.56 eV, indicating a large exothermicity upon the O-H bond cleavage.Therefore, OH tends to dissociate at the defect site of graphene.Our finding is consistent with the previous work [44].We find that the OH functionlization in d-OH-MV-Gra results in the formation of a occupied flat band in spin-up channel and an unoccupied flat band in spin-down channel with total magnetization of 1.00 μ B (table 1).Wave functions corresponding to the highest occupied crystal orbital (O1) and the lowest unoccupied crystal orbital (U1) in spin-up and spin-down channels of d-OH-MV-Gra are plotted in figure 3 .The unpaired electron of

The adsorption of divalent ions (Mg and Ca) on graphene
The atomic models for divalent metal ions (Mg and Ca) adsorbed on Gra, N-Gra, B-Gra, MV-Gra, O-MV-Gra, d-OH-MV-Gra are illustrated in figure 4. Adsorption energy (E ads ) and vertical binding distance (h) are complied in table 2. We find that Ca interacts with all graphene surfaces more strongly than Mg does.On the pristine graphene surface, Mg-graphene interactions arise from the vdW attraction with a small E ads of −0.16 eV, [28] whereas electron exchange between Ca and substrate increases the binding strength of Ca to −0.89 eV and decreases vertical binding distance of Ca to 2.28 Å.The different bonding behavior is attributed to the difference in electronegativities between Mg and Ca (1.31 and 1.0, respectively).The lower electronegativity of Ca allows a facile electron exchange and thus increasing the Ca binding.Our finding is consistent with previous results [29,31,32].Estimated adsorption energies for divalent metal ions adsorbed on N-and B-doped graphene reveal that the divalent metal ions interacts repulsively (attractively) with N (B) site, respectively.This behavior is analogous to the Na and K adsorption on N-and B-doped graphene.For the Mg adsorption, vdW attraction dominates Mggraphene and Mg-N-Gra interactions, whereas the electron exchange further strengthens the binding of Mg to B-doped graphene by 0.66 eV.For Ca adsorption, N doping slightly increases E ads by 0.26 eV, while B doping significantly stabilizes the interaction with the surface by −1.32 eV.
For the adsorption of divalent metal ions on monovacancy graphene surfaces, stronger metal-graphene surfaces appear for Mg/MV-Gra, Ca/MV-Gra, Ca/O-MV-Gra, Ca/OH-MV-Gra comparing with pristine graphene.For Mv-Gra, the metal atoms are trapped inside the vacancy sites with increase in E ads by 1.69 and 2.85 eV for Mg and Ca, respectively, accompanying by decrease in vertical binding distance (table 2).For monovancancy graphene with the functionalied group, the interactions between Mg and O-MV-Gra and OH-MV-Gra become rather weak with a large seperation of 3.2 Å, thus the interaction arises mainly from the vdW attraction.In constrast, the interaction of Ca with O-MV-Gra and OH-MV-Gra remains strong in the range of chemisorption with E ads = −2.21and −2.23 eV, respectively.Comparing with Ca/Mv-Gra, E ads ʼs of those structures are reduced by 1.26 eV, whereas those adsorption energies are still more negative than that of Ca/Gra by 1.23 eV.Atomic geometry of Ca adsorbed O-MV-Gra (figure 4) indicates the bond formation of Ca with C atoms at the defect site results in an extrusion of the O atoms, i.e., the O atom moves out of the graphene plane outward Ca.The bonds lengths of Ca with neighboring C atoms are 2.30, 2.46, and 2.46 Å for Ca-C1, Ca-C2, and Ca-C3, respectively.From table 2, the shortest bond length in Ca/O-MV-Gra, i.e.Ca-C1 of 2.30 Å are elongated than that in Ca-MV-Gra (Ca-C3 of 2.27 Å), which arises from a competition in bonding formation of Ca and O with the C atoms at defect sites.For Ca/OH-MV-Gra, bond formation of Ca with the O sites is found with a bond length of 2.30 Å.Although more reactive C at the defected are terminated by O and H atoms in O-MV-Gra and OH-MV-Gra, our results reveal that Ca atom still chemisorbs on those surfaces with strong chemical bonds.

Electronic structure properties
We then analyze the electronic structure properties of Mg and Ca adsorbed on graphene.From Löwdin population analysis in table 2, one finds that the electron transfer from divalent metal to graphene surfaces takes place upon the strong binding formation in Mg/B-Gra, Mg/MV-Gra, and all cases of Ca adsorption.It indicates that divalent metal ions become positively charged and large electron transfer strengthens the adsorption.For Table 2. Adsorption energy (E ads ); the vertical binding distance (d) from the metal atom to the graphene surface; and effective Löwdin charge (Δq (M)) of divalent metal ions (Ca and Mg) on several graphene surfaces, i.e Gra, N-Gra, B-Gra, MV-Gra, O-MV-Gra, OH-MV-Gra.The distance (d) between divalent metal ions (M) and doping sites (N and B) and O (d(M-N/B/O)) and that of M with C atoms (C1,C2, and C3) at defect sites (See figure 4(b) for the labels) are listed.The effecive Löwdin charge is estimated by q = Z − q L , where Z and q L are total valance electron and Löwdin population, respectively.Percent increase in E ads relative to adsorption on the pristine graphene are reported in parentheses.

System
E ads (eV) instance, E ads increases from −0.89 eV in Ca/Gra to −3.47 eV in Ca/MV-Gra along with the increase in q from 0.59 to 0.96 e.We find that Ca atom donates nearly an electron on when it adsorbed on monovancancy graphene systems, namely MV-Gra, O-MV-Gra, and OH-MV-Gra.In contrast, the electron transfer does not take place between Mg and Gra, N-Gra, O-MV-Gra, and OH-MV-Gra and the adsorbed Mg remains neutral [28].This further confirms weak interactions in the range of −0.16 to −0.where ρ(Ca/S), ρ(Ca), and ρ(S) are total valence charge densities of adsorbed Ca, and isolated Ca and the graphene surface at their adsorption geometries, respectively.DOS and CDD of Ca adsorbed on the pristine and B-doped graphene are shown in figures 5 (a) and (b), respectively.From figure 5 (a), the electron rearrangement upon Ca adsorption on pristine graphene show the electron accumulation occurs at the C atoms and the area between Ca and the graphene surface, whereas the electron depletion occurs at the Ca site.As a result, an electron transfers from Ca to graphene, leaving the Ca 4s state vacant in the spin-down channel.For Ca/B-Gra, a similar bonding mechanism is found in which the electron transfer takes place from Ca to substrate.However, the red cloud at B site in Ca/B-Gra is larger than that at C in Ca/Gra and extends over a larger area, reflecting the fact that there is more electron transfer in B-Gra.The greater electron transfer is also evident in the upshift of Ca 4s states in which Ca 4s states at spin-down channel becomes partially occupied, leading to the stronger adsorption of Ca upon B doping.
DOS and CDD of Ca adsorbed on the monovancancy graphene are shown in figure 6. CDD's for Ca/MV-Gra, Ca/O-MV-Gra, and Ca/OH-MV-Gra show strong polarization characters in which charge depletion locates at Ca sites and charge accumulation locates at monovacancy graphene surfaces.This highlights the electron are transferred from Ca to monovacancy graphene surface, causing the Ca 4s states to become unoccupied (DOS of Ca 4s states are above Fermi level).From the CDD, upon Ca-C bond formation (Ca-C3, Ca-C1, and Ca-C3 bonds in Ca/MV-Gra, Ca/O-MV-Gra, Ca/OH-MV-gra, respectively), the electron density midway between the Ca atom and the C atoms is low and become negative, indicating an ionic bond.In the case of Ca/O-MV-Gra, CDD in space between the Ca atom and the O atom are negative, indicating the repulsion interaction between them.In contrast, in the case of Ca/OH-MV-Gra, the interaction between Ca and O is similar to Ca-C ones in which the electron accumulation locates at the Ca-C space and decrease from O to Ca sites, reflecting there an ionic bond between them.Consequently, we conclude that the enhancement of Ca binding to monovancancy site arises from the strong bonding character of Ca with C atoms at the defects sites.

Implication for the removal of calcium ions from the aqueous solution
Finally, implication of graphene membrane in removal of calcium ions from aqueous solution is discussed.In manufacturing of chitin and chitosan from shrimp shell [5], the removal of calcium ions from aqueous solution is important to ensure high-quality product.Experimentally, it was found that the incorporation of CNT into nylon-66 membranes facilities the Ca 2+ rejection efficiency by ten times compared to the original membrane [5].From our theoretical studies, it was found that Ca can be strongly trapped inside the graphene surface due to strong Ca-graphene surface interactions.Therefore, the origin for the high Ca ions removal from aqueous solution by graphene or multi-wall carbon nanotube [5] may be explained by the fact that the Ca ions are captured by graphene membrane with the strong adsorption capacity.Indeed, Meng et al studied Ca 2+ adsorption on GO membranes and found that Ca 2+ strongly adsorbed on functionalized sites of GO [48] as characterized by Raman spectra and Zeta potential.Sheng et al studied the removal of Ca 2+ and Cu 2+ by Fe 3 O 4 /GO-COOH [49].The high removal efficiency of Fe 3 O 4 /GO-COOH is attributed to a good adsorption capacity of GO and GO with the COOH group as characterized by x-ray power diffraction (XRD), Fourier transform infrared spectroscopy (FI-IR), and x-ray photoelectron spectroscopy (XPS) [49].The experimental results [48,49] are in good agreement with our DFT calculations.
From our DFT calculations, we find that Ca strongly adsorbs at monovancancy sites and B doping sites due to strong Ca-C bonds and B-doped graphene (table 2).Therefore, we expect that nanopores in graphene or B-doped graphene will enhance the Ca 2+ removal.We encourage the experiments to explore the incorporation of graphene based membrane with nanopore or B doping into polymeric membrane in the nanofiltration technology for removals of Ca ions.In particular, the adsorption of Ca should be investigated with Raman spectra, FT-IR, XPS, XRD, and Scanning electron microscopy-energy dispersive x-ray spectroscopy (SEM-EDS) [50][51][52][53].

Conclusions
In summary, we have investigated the adsorption of divalent metal ions (Mg and Ca) on pristine graphene, graphitic N-and B-doped graphene, monovacancy graphene, monovacancy graphene functionalized by an epoxy, and monovacancy graphene functionalized by an hydroxyl group.We have found that monovacancy graphene will be functionalized by O or OH group under the ambient conditions and OH will be cleaved due to strong interaction between C sites.We have found that Mg interacts weakly with graphene surface except for B-doped and MV-Gra, whereas Ca interact strongly with all considered graphene surfaces due to its lower electronegativity.Energetically, N-doping slightly decrease the Ca-graphene interaction, whereas B-doping and monovancacy graphene with and without O and OH group significantly increase the adsorption.Electronic structure analysis indicates that the divalent metal tends to donate electron to graphene surfaces and greater electron transfer results in stronger interaction.Moreover, our calculation have revealed that ionic bonds between Ca and C at defect sites are crucial for strengthening the interaction.Our result suggests that B-doping or monovancy can increase the capture of Ca due to the enhancement of divalent metal-graphene interaction, which maybe helpful in Ca ion removals.
e. MV-Gra and those functionalized by O (O-MV-Gra) and OH group in intact (i-OH-MV-Gra) and dissociated (d-OH-MV-Gra) state.The atomic structures of MV-Gra surfaces are shown in figure 2 (a) and the relative stabilties of those surfaces are depicted by phase diagram, which defined by the lowest G f in figure 2 (b).Electronic structures, namely band structures and density of state (DOS) of MV-Gra, O-MV-Gra, and d-MV-Gra surfaces are shown in figures 2 (c), (d), and (e), respectively.The optimized MV-Gra indicates the formation of a dangling bond between C1 and C2 atoms.Electronic structures in figure 2 (c) shows the spin polarization takes places upon the monovacancy formation with total magnetization of 1.22 μ B (table

Figure 2 .
Figure 2. (a) Atomic models of monovacancy graphene (MV-Gra); and MV-Gra functionalized by a epoxy (O-MV-Gra) and hydroxyl group in intact (i-OH-MV-gra) and dissociated (id-OH-MV-gra) state.(b) Phase diagram of monovacancy graphene surfaces defined the the lowest free energy of formation (G f ).The band structures in spin-up (the left row), in spin-down (the middle row), and density of states (the right row) of (c) MV-Gra, (d) O-MV-Gra, and (e) d-OH-MV-Gra. .

Figure 3 .
Figure 3. Wave functions corresponding to the highest occupied crystal orbital (O1) and the lowest unoccupied crystal orbital (U1) in spin-up and spin-down channels of d-OH-MV-Gra.

2
eV obtained for those adsorption systems mainly arise the vdW attraction.Density of state (DOS) and charge density difference (CDD) are employed to analyze the bonding mechanisms of Ca on various graphene surfaces.Charge density difference of the adsorbed Ca is calculated by r

Figure 5 .
Figure 5. Charge density difference (top) and projected density of state (bottom) of (a) Ca adsorbed on (a) graphene and (b) B-doped graphene.Isosurface is plotted at 0.002 -- e a 0 3 in which red and blue indicate electron accumulation and depletion, respectively.
2, and E tot (O 2 ) are total energy of graphene vacancy with the a functionalized group (F=O and OH), monovacancy graphene,isolated H 2 O, and O 2 , respectively.Here, N i , Δμ H , and Δμ O denote the number of atoms, deviation of chemical potential of H and O relative to the gasphased H 2 and O 2 , respectively.To estimate the binding strength of divalent metal ions (M) with graphene surfaces, adsorption energy (E ads ) was calculated by