Molecular insights on Ca2+/Na+ separation via graphene-basednanopores:The role of electrostatic interactions to ionic dehydration

Yumeng Zhang,Yingying Zhang,Xueling Pan,Yao Qin,Jiawei Deng,Shanshan Wang,Qingwei Gao,Yudan Zhu,,Zhuhong Yang,Xiaohua Lu

1 College of Chemical Engineering,State Key Laboratory of Materials-oriented Chemical Engineering,Nanjing Tech University,Nanjing 211816,China

2 College of Chemical Engineering,Nanjing Forestry University,Nanjing 210037,China

3 School of Chemical Engineering,State Key Laboratory of Chemical Engineering,East China University of Science and Technology,Shanghai 200237,China

Keywords:Separation Microstructure Molecular simulation Modified graphene nanopores Metal-ions Nanoconfinement

ABSTRACT Ca2+/Na+ separation is a common problem in industrial applications,biological and medical fields.However,Ca2+and Na+have similar ionic radii and hydration radii,thus Ca2+/Na+separation is challenging.Inspired by biological channels,group modification is one of the effective methods to improve the separation performance.In this work,molecular dynamics simulations were performed to investigate the effects of different functional groups (COO-,) on the separation performance of Ca2+ and Na+through graphene nanopores under an electric field.The pristine graphene nanopore was used for comparison.Results showed that three types of nanopores preferred Ca2+to Na+,and Ca2+/Na+selectivity followed the order of GE-COO- (4.06) ＞GE (1.85) ＞(1.63).Detailed analysis of ionic hydration microstructure shows that different nanopores result in different hydration factors for the second hydration layer of Ca2+ and the first layer of Na+.Such different hydration factors corresponding to the dehydration ability can effectively evaluate the separation performance.In addition,the breaking of hydrogen bonds between water molecules due to electrostatic effects can directly affect the dehydration ability.Therefore,the electrostatic effect generated by group modification will affect the ionic hydration microstructure,thus reflecting the differences in dehydration ability.This in turn affects the permeable and separation performance of cations.The results of this work provide perceptive guidelines for the application of graphene-based membranes in ion separation.

1.Introduction

The separation of metal ions such as Ca2+/Na+separation is a common problem in industrial applications,biological and medical fields[1–5].For example,the Ca2+is necessary to remove from Na+solution in the Chlor-alkali industry,because the existence of Ca2+affects the production efficiency of alkali production [4].Also,selective recognition of Ca2+and Na+plays an important role in the cell signal transduction and is responsible for initiating electrical signals in excitatory systems such as nerves and muscles for organisms [6,7].However,Ca2+and Na+have similar ionic radii(Ca2+:0.099 nm,Na+:0.095 nm) and hydration radii (Ca2+:0.332 nm,Na+:0.324 nm),thus the highly efficient separation of Ca2+/Na+separation is still challenging.

Membrane separation technology has the advantages of low energy consumption and high efficiency and has been widely used to solve the major problems in the fields of water resources,energy and environment[8–12].As a new type of two-dimensional material,graphene has excellent electrical properties,good thermal conductivity and mechanical properties due to its atomic-level thickness.Moreover,graphene -based nanoporous membranes have the advantages of high permeability and high selectivity.Therefore,graphene is often chosen as the materials to study the separation behavior [13–22].For example,Zhao et al.[23] for the first time prepared a monolayer graphene membrane with high density and precise subnanopores,and the separation performance of the membrane for sieving gas mixtures reached a new level.Zhang et al.[20]prepared a surface-charged graphene oxide membrane by altering the surface charge density of graphene.The membrane showed excellent salt rejection (～93%) and ultrahigh water permeability (from～15 to～56 L·m-2·h-1·bar-1,1bar=0.1 MPa),which far exceeded the performance limit of the most advanced nanofiltration membrane (salt rejection:from～40% to～98%;water permeability:from～5 to～14 L·m-2·h-1·bar-1).The above examples illustrate that graphene-based membranes via the control of pore size and surface charge have achieved remarkable results in gas separation and desalination.

However,existing membrane materials have limited performance in ionic separation.To design better ion separation membranes,a better understanding of the molecular mechanisms of ion transport in nanoscale confinement is needed[24].The separation or conduction behavior of ions in an aqueous solution especially under nanoconfined conditions is accompanied by ionic hydration.The differences in ionic hydration microstructure further affect the separation performance of ions [25–31].For examples,Sahu et al.[30,31] used molecular dynamics (MD)simulations to investigate the separation mechanism of K+/Cland proposed that the ionic selectivity depended only on geometry and hydration.Up to now,it is still difficult to study the ionic hydration microstructure during ion transport.Due to the lack of experimental techniques with a spatial and temporal resolution,it is difficult to observe the dynamic changes in the complex ionic hydration microstructure at the nanoscale (e.g.,dehydration).Molecular simulation is an effective means to describe the interface-induced fluid microstructure and the abnormal interfacial phenomena can be understood at the molecular level [32,33].Therefore,molecular simulation is widely used to study the separation or transport behavior of ions in an aqueous solution.

Inspired by biological channels,group modification is one of the effective methods to improve separation performance [5,34–36].Hinted by the water channel,Cohen-Tanugi and Grossman[37,38] design the graphene pores modified with hydrogen and hydroxyl groups to separate ion and water.Results showed that the hydroxyl-modified pore showed higher water flux,whereas the hydrogen-modified pore showed higher salt rejection.He et al.[39] investigated the separation of K+and Na+through graphene nanopores modified with negatively charged carboxylate and carbonyl groups using MD simulations.They found that the effect of charged groups on water molecules in the ionic hydration layer could affect the way ions passing through pores,which in turn further affected K+/Na+selectivity.Garcia-Fandino et al.[40]employed MD simulation to study the permeability and selectivity of Ca2+,Na+and K+in carbon nanotubes with negatively charged carboxylate groups and found that Ca2+had obvious selectivity compared with monovalent cations.Corry studied the desalination performance of carbon nanotubes modified with carboxylate group and amine group by MD simulation.Results showed modification of charged groups could improve the desalination performance of carbon nanotubes [41].Experimentally,Zhang et al.[42] prepared a positively charged composite nanofiltration membrane for desalination and found that salt rejection increased while water flux decreased.Xu et al.[43] prepared a permselective MOF membrane modified by amino for the separation of monovalent and divalent cations.The results showed that the membrane had ultra-high selectivity and excellent stability.

As mention above,the functional groups provide the electrostatic effect on the ionic hydration microstructures,and further control the permeable and separation performance of metal cations.Therefore,investigating the effect of the electrostatic effect(i.e.,electrostatic attraction and repulsive) caused by the modified groups to ionic hydration microstructure may reveal the mechanism of ion separation.This work focused on studying the effects of functional groups on the separation performance of Ca2+and Na+through graphene nanopores under an electric field using MD simulation.Negatively charged carboxylate and positively charged amine groups were selected as the research objects and compared with the pristine graphene nanopore,as the negatively charged carboxylate in the biological Ca2+channel plays a critical role in the selectivity [5,34] and experimental results show that the amino modified membrane has excellent ion separation performance [43].Furthermore,the relationship between the microstructures of cations and their separation performance at the nanoscale was investigated.The following questions will be addressed:(I) How do the modified functional groups affect the Ca2+/Na+selectivity? (II) What are the underlying contributions to the confined Ca2+/Na+selectivity at the molecular level?

2.Simulation Models and Method

The simulation model is shown in Fig.1.Graphene nanopore with a diameter of 1.02 nm was obtained by removing the carbon atoms from the central region of the graphene sheet.The diameter of the graphene nanopore was defined as the distance between two opposite carbon atoms.The graphene sheet was placed in the middle of the periodic box(4.29 nm×4.25 nm×5.00 nm),perpendicular to the Z-axis.In the simulation boxes,there are CaCl2and NaCl mixed solutions with the concentration of 0.25 mol·L-1,which is widely used in molecular simulation studies on the behavior of ionic separation [44–46].In this work,three types of graphene nanopores (pristine,modified with three negatively charged carboxylate groups and modified with three positively charged amine groups,labelled as GE,GE-COO-and GE-NH3+) were designed to investigate the effect of groups on the separation performance of Ca2+/Na+.

Fig.1.Model of a graphene nanopore in the middle and the two reservoirs filled with CaCl2 and NaCl mixed solutions on both sides of the graphene sheet.(a)lateral view of the simulation box,(b)pristine,(c)modified with three amine groups and(d)modified with three carboxylate groups graphene nanopores with a diameter of 1.02 nm.The blue,pink and green spheres represent Na+,Ca2+and Cl-,respectively,while the silver spheres represent the carbon atoms.The red,purple and white spheres represent O,N and H atoms.The blue arrow represents the direction of the electric field applied to the system.

The GROMACS software package was used for all simulations[47].VMD package[48]was used to view the visual configuration.The OPLS-AA [49] field parameters were used for ions,functional groups and carbon atoms,and the SPC/E [50] model was used to describe the solvent water molecules.The force field parameters used in this work are shown in Table 1.The non-bonded interactions between atoms were treated as a combination of Lennard-Jones and coulombic pairwise interactions,defined as

Table 1 Force field parameters used in the simulations

In Eq.(1),εijand σijrepresent energy and size parameters,respectively,and follow the Lorentz-Berthelot mixing rule.

After energy minimization,the Parrinello-Rahman coupling method[51]was used to perform 5 ns NPT for the equilibrium system firstly.The separation selectivities of Ca2+/Na+confined in three types of monolayer graphene nanopores under electric field condition were investigated by performing 105ns production simulations.The coordinates were saved every 1.0 ps and those for the last 100 ns were used for further analysis.The V-rescale[52]thermostat was coupled with fluid molecules at 300 K.A cutoff of 1.0 nm was used to compute the short-range van der Waals interactions.The long-range electrostatic interactions with a real-space cutoff of 1.0 nm were calculated using the PME solver[53].Periodic boundary conditions were implemented in all three directions.In all simulations,a transmembrane voltage (V) was applied along the Z-axis.The voltage was calculated by V=-E×Lz,where Lzcorresponds to the length of the simulation box along the Z-axis.In previous studies,the electric field has been widely used as a driving force to investigate ion separations [54–57].The electric field intensity used in this work was 0.2 V·nm-1,and the corresponding transmembrane voltage was 1.0 V.

3.Results and Discussion

The number of cations through the nanopores as a function of time and Ca2+/Na+selectivity were used to evaluate the effects of functional groups with positive and negative charges on the separation performance of Ca2+/Na+confined in the graphene nanopore with a diameter of 1.02 nm(Section 3.1).Then the spatial distributions of functional groups and cations were studied to explain the variations in the separation performance (Section 3.2).Finally,the ionic hydration microstructure analyses of confined cations,including radial distribution function (RDF) between cations and water molecules,hydration factor and hydrogen bond structures,were analyzed to clarify the underlying mechanisms at the molecular scale (Section 3.3).

3.1.The number of cations through the nanopores as a function of time and Ca2+/Na+ selectivity

The flux and selectivity are two important parameters to evaluate the separation performance [58].In this work,the ionic flux refers to the number of a type of ion passing through the nanopore.Selectivity is defined as the ratio of the number of cations through nanopores.Therefore,the number of cations through the different nanopores as a function of time under an applied electric field and their corresponding Ca2+/Na+selectivities were calculated [39,59].To more clearly observe the flux change with time evolution,the data of last 20 ns were selected for drawing,as shown in Fig.2.

Fig.2(a),(b)show that the number of Ca2+and Na+through pristine and positively chargedgraphene nanopores increase at almost the same rate with time,indicating that the Ca2+/Na+selectivity is almost not affected by the extension of simulation time.Therefore,it is confirmed that in practical applications,although the flux will increase with the extension of simulation time,the order of selectivity caused by different graphene-based nanopores will not change much.Fig.2(c) shows that the number of Ca2+and Na+through the negatively charged COO--modified graphene nanopore needs to be buffered for a while and then increased.With the extension of simulation time,the increasing rate of the number of Ca2+through nanopores is significantly higher than that of Na+,indicating that higher Ca2+/Na+selectivity is expected to be achieved.Fig.2(d) shows the Ca2+/Na+selectivity ratio of the different modified nanopores with diameters of 1.02 nm under an electric field of V=1 V.As illustrated in Fig.2(d),three types of graphene nanopores have a preference for Ca2+over Na+.The order of the Ca2+/Na+selectivities is GE-COO-(4.06) ＞GE (1.85) ＞(1.63).

Fig.2.The numberofcations through a)GE,b)GE-andc)GE-COO-nano poreswith diameters of 1.02 nm as a function of time under an electric field of V=1 V and d)correspondingCa2+/Na+ selectivities.Theblackdashed linerepr esents aCa2+/Na+ ratioof1.0.

3.2.Spatial distributions of functional groups and cations

3.2.1.Three-dimensional coordinates of the graphene sheet and functional groups

In Section 3.1,it was found that different functional groups had a great influence on both flux and selectivity.Typically,the functional group can affect ion transport by steric effect and electrostatic interaction [24].However,it is still controversial whether the steric effect of the functional group on ion transfer disappears in the electric field condition because electric field renderers the group far away from the pore center[39,54].Hence,it is necessary to reveal the differences in flux and selectivity caused by the steric effect or electrostatic interaction of modified group.To address this,we calculated the average position of the functional groups over the 100 ns simulation time,using the pristine graphene sheet as a reference.

The three-dimensional coordinates of the graphene sheet and the functional groups were shown in Fig.3.The coordinates of the center of mass of a COO-were used to represent those of the COO-.The coordinates of nitrogen atoms were used to characterize those ofas the nitrogen atom is near the center of mass of aAs can be seen from the projection on the X–Y plane in Fig.3(red part),the diameter of the graphene nanopore is maintained due to the modified-group departure from the pore center.Namely,the differences in flux and selectivity for various nanopores are mainly the roles of different modified groups,whereas the steric effect of modified groups.

Fig.3.The three-dimensional coordinates of the graphene sheet and functional groups.(a) GE,(b) (c) GE-COO-.The represents coordinates of the center of mass of a COO-.

3.2.2.X–Y planar density distributions of cations

To investigate the distribution characteristics of cations,we adopted the two-dimensional planar density distributions of cations inside the pristine,COO--modified and-modified graphene-based nanopores in the X–Y direction,as shown in Fig.4.A brighter color means a higher density.

There are similarities and differences among the three types of graphene-based nanopores.For each type of nanopores,Ca2+is mainly distributed near the center of the nanopore,and the central region is the brightest.The distributions of Na+are more dispersed and lighter than those for Ca2+.This observation indicates that Ca2+occupies a favorable position in the middle of the nanopores,which is preferred to pass through the nanopore.

Comparing the three types of nanopores,it is found that the distributions of Ca2+in COO--modified nanopore are the most concentrated,followed by pristine graphene nanopore,whereas those of-modified nanopore are the most dispersed.The main reason is that the negative charge of COO-has a strong attraction effect on Ca2+,whereas the positive charge ofhas a strong repulsion effect on Ca2+.The distributions of Na+in the three types of nanopores are similar,and all of them are relatively dispersed.This is because Ca2+is already in a favorable pathway to impede the passage of Na+.This phenomenon,known as ionic Coulomb blockade,has also been observed in biological ion channels and subnanometer pores[60–62].This indicates that functional groups affect the distributions of cations further affecting the flux and selectivity of cations.Based on the above analysis,three types of nanopores prefer Ca2+to Na+,and the order of the Ca2+/Na+selectivities is GE-COO-＞GE ＞GE-NH3+,which is consistent with the results in Section 3.1.

Fig.4.X–Y planar density distributions of Ca2+ and Na+ within GE,GE-COO- and graphene-based nanopores with diameters of 1.02 nm under 1 V electric field.Horizontal and vertical axises represent the coordinates along the X and Y direction of the graphene sheet,respectively.

3.2.3.The number density distributions of cations along the Z-axis

To further analyze the differences of Ca2+and Na+passing through these three types of nanopores driven by an electric field,we calculated the number density distributions of Ca2+and Na+along the Z-axis(perpendicular to the plane of the graphene sheet).As shown in Fig.5,Z=0 is the position of the graphene sheet and the direction of the electric field is along the positive direction of the Z-axis.

For pristine graphene nanopores,the main peak position of Ca2+at the entrance side (Z ＜0.0 nm) is at Z=-0.423 nm,the same as that of Na+,indicating that it is the same degree of difficulty for Ca2+and Na+to approach the nanopore.However,the peak value of Na+is very low (0.269),that is,the amount of aggregation is extremely small.Combined with the two-dimensional density distributions,this is because Ca2+occupies a favorable position in the center of the nanopore and thus has a repulsive effect on Na+.The peak values of Ca2+and Na+at the exit side (Z ＞0.0 nm) are very low,indicating that the difficulty of two ions leaving the nanopore is not significantly different.Therefore,for pristine graphene nanopore,the selectivity depends on the difficulty of entering the nanopore.Since Ca2+is easier to enter the nanopore than Na+,the pristine graphene nanopore prefers Ca2+to Na+.

For the graphene nanopore modified with positively chargedthe main peak positions of Ca2+and Na+at the entrance side(Z ＜0.0 nm)are at Z=-0.582 nm and Z=-0.542 nm,respectively.This indicates that Na+is closer to the nanopore than Ca2+,and the peak values of both are similar(0.494 and 0.442,respectively).This is because Ca2+is more repelled by a positive charge.On the exit side (Z ＞0.0 nm),the main peaks of Ca2+and Na+are in the same position,but the peak value of Ca2+(1.611) is 3.2 times of that of Na+(0.498),indicating that the positive repulsion effect makes Ca2+depart from the nanopore more easily.Therefore,for the graphene nanopore modified with positively charged NH3+,the selectivity depends on the difficulty of departing from the nanopore.Since Ca2+is easier to depart from the nanopore than Na+,themodified graphene nanopore prefers Ca2+to Na+.

Fig.5.The number density distributions of (a) Ca2+ and (b) Na+ along the Z-axis under GE,GE-COO- and nanopores with diameters of 1.02 nm under 1 V.Z=0 represents the position of the graphene sheet (the graphene sheet is perpendicular to the Z-axis).

For the graphene nanopore modified with negatively charged COO-,the main peak positions of Ca2+and Na+at the entrance side(Z ＜0.0 nm)are at Z=-0.408 nm and Z=-0.448 nm,respectively.This indicates that Ca2+is closer to the nanopore than Na+,and the peak value of Ca2+(4.3) is 7.1 times of that of Na+(0.605).This is because Ca2+is more attractive to the negative charge.On the exit side (Z ＞0.0 nm),the main peaks of Ca2+and Na+are in the same position,but the peak value of Ca2+(5.707) is 11.3 times that of Na+(0.504),indicating that Ca2+departs from the nanopore more easily.The main reason is that the difference in the hydration number of two cations near the pore and in the bulk.The difference in Ca2+is greater than Na+,thus Ca2+is easier to return to the bulk relative to Na+(for detail,see 3.3.2 and Fig.S1 in the Supplementary Material).Therefore,for the graphene nanopore modified with negatively charged COO-,the selectivity was influenced by both the difficulty of getting in and out of the nanopore.Since Ca2+is easier to get in and out of the nanopore than Na+,the COO--modified graphene nanopore prefers Ca2+to Na+.

Comparing the entrance side (Z ＜0.0 nm) of the three types of nanopores,the main peak position of Ca2+in the COO--modified nanopore is closest to the nanopore (Z=0.0 nm) and showing the highest peak value,followed by the pristine graphene nanopore,whereas those ofnanopore is the farthest from the nanopore with the least peak value.As mentioned above,the peak value of Na+in pristine nanopore is so small that it could almost be ignored,thus we focus on comparing two modified nanopores.The main peak of Na+is closer to the COO--modified nanopore than that of theone,which is because of the electrostatic effect,that is,like charges repel but opposite charges attract.Both Ca2+and Na+are affected by the electrostatic effect.On the exit side (Z ＞0.0 nm),the peak values of Ca2+and Na+in pristine nanopore are quite small,thus we also focus on comparing two modified nanopores.The main peak positions of Ca2+and Na+are closer to the-modified graphene nanopore,and the peak value ofis smaller than that of the COO--modified one.Combined with the analysis of the entrance side,cations in COO--modified nanopore are easier to not only enter but also depart from the nanopore.For detailed location coordinates and peak values,please refer to Table S1 in the Supplementary Material.

In conclusion,for all three kinds of nanopores with a diameter of 1.02 nm,Ca2+is preferred over Na+.Moreover,COO--modified nanopore is more conducive for Ca2+to pass through,followed by pristine and-modified nanopores.This indicates that the electrostatic interaction of the functional groups plays an important role when the cations pass through nanopores,consistent with the results of separation performance in Section 3.1.

3.3.Analysis of ionic hydration microstructures

3.3.1.Radial distribution function between cations and water molecules

The ionic hydration microstructure is a key indication for reflecting ionic separation performance in nanoconfined space[27,29,63],including the hydration of the ions on the surrounding water molecules and the hydrogen bonding between water molecules [28].

The RDF between the ions and water molecules was first analyzed to obtain the hydration radius of the ions,as shown in Fig.6.The value of the hydration radius depends on the location of the RDF trough.It can be seen from Fig.6 that the radii of the first hydration layer of Ca2+and Na+are about 0.332 nm and 0.324 nm respectively.The radius of the second hydration layer of Ca2+is about 0.572 nm,and there are slight differences among the three types of nanopores.Since the second peak of RDF between Na+and water molecules is not obvious,only the first hydration layer of Na+is considered in this study.These results are consistent with literature reports [26,64].According to the above phenomenon,we discover that the strength of ion-water for Ca2+and Na+with different hydration layers is different,which may influence ion separation.

3.3.2.Hydration factor analysis

The hydration factor proposed by Zhou et al.[65]is an essential index to evaluate the strength of ion-water for different layers[29,66–68].The hydration factor of cation is defined in Eq.(2)and (3),where N and θ represent the number and orientation of water molecules in the hydration layer,respectively.Moreover,the closer the hydration factor is to 1,the more ordered the water in the hydration layer is.

Fig.6.Radial distribution function of water molecules around (a) Ca2+ and (b) Na+.

Fig.7.Hydration factors of Ca2+ and Na+ at the nanopore entrance and the bulk solution.Ca-f,Ca-s and Na-f represent the first hydration layer of Ca2+,the second hydration layer of Ca2+ and the first hydration layer of Na+ respectively.

The hydration factors of Ca2+and Na+in the nanopore and bulk are plotted in Fig.7.It can be seen from Fig.7 that the hydration factor of the first hydration layer of Ca2+is close to 1.This means that the strong interaction between Ca2+and water molecules leads to the highly orderly water molecules in the hydration layer,indicating that Ca2+belongs to the ion with strong hydration ability.Therefore,the second hydration layer of Ca2+needs to be considered,as shown in red data in Fig.7.Compared with the three nanopore and bulk,we found that the hydration factors in the first hydration layer of Ca2+were all slightly smaller than that of the bulk.The order of the hydration factor in the first hydration layer of Ca2+is bulk ＞GE-COO-＞GE ＞GE-It is difficult to remove the first layer of water due to the strong hydration of the first Ca2+hydration layer.However,hydration factors of the second hydration layer of Ca2+fluctuate around 0.3,indicating that its hydration is weak and the second layer of water is easy to be removed.For pristine and-modified nanopores,the hydration factors of the second hydration layer of Ca2+are stronger than that of the bulk,that is,water molecules in the second hydration layer are more ordered.For COO--modified nanopore,it is the opposite of the other two nanopores.The hydration factors of the first hydration layer of Na+fluctuate around 0.6,which is between the first and second hydration layers of Ca2+.This indicates that Na+has a weaker interaction with water molecules and is the ion with weak hydration ability,which is consistent with the RDF results in Section 3.3.1.The hydration factors of Na+of the three nanopores are weakened compared with that of the bulk,and the order of hydration factors is consistent with that of the first hydration layer of Ca2+.

Besides,Fig.7 also shows that the pristine,-modified,and COO--modified nanopores result in different hydration factors for the second hydration layer of Ca2+and the first layer of Na+.For Ca2+and Na+,such different hydration factors corresponding to the dehydration ability can effectively evaluate the separation performance [30,31,62,68].Therefore,to more clearly describe the dehydration differences in various nanopores,a parameter φCa-s/Na-fwas defined in Eq.(4),where FCa-sand FNa-frepresent the hydration factors of the second layer of Ca2+and the first layer of Na+,respectively.

Fig.8.The ratios of the hydration factor of the second layer of Ca2+ and the first layer of Na+ in three nanopores.

The smaller the ratio and the larger the difference are,the more favorable the separation of Ca2+/Na+is.From Fig.8,we can see intuitively that the order of the ratio in three types of nanopores is as follows:GE-COO-＜ GE ＜This shows that COO--modified nanopores are more conducive to the Ca2+/Na+separation.Pristine and-modified graphene nanopores also have separation performance,but it is significantly less than that of COO--modified one.This result is consistent with the results of Ca2+/Na+selectivity in Section 3.1.

3.3.3.Hydrogen bond analysis

The hydration phenomenon originates from the competition between the ion-water and water-water.Hence,the breaking of the hydrogen bonding network between water molecules corresponds to the change of ionic hydration microstructures.When the ionic hydration is strong,the water molecules in the hydration layer will present a specific orientation,which is not conducive to the formation of hydrogen bonds.Therefore,we further analyzed the average number of hydrogen bonds per water molecule along the Z-axis between in and beyond the first hydration layer,as shown in Fig.9.

The geometric criteria are used to determine the formation of hydrogen bonds [69–73].A hydrogen bond is formed between two water molecules (one acts as a donor and the other acts as an acceptor) when the following two criteria are simultaneously satisfied.The distance between the oxygen atoms in the donor and acceptor water molecules is less than 0.35 nm.(II) The O—H···O angle is less than 30°.

Fig.9 shows that the average hydrogen bond number of water molecules between in and beyond the first hydration layer is smaller than that of the bulk when Ca2+and Na+pass through three types of nanopores.In addition,the order of the average hydrogen bond number of water molecules at the nanopore(Z=0)is GE-＞GE ＞GE-COO-.For Ca2+,the smaller the average hydrogen bond number is,the weaker the interaction between the water molecules and the easier it is for the outermost water molecules to be removed.This indicates that the second layer of water is the easiest to be removed when Ca2+passes through COO--modified nanopore.In other words,among three types of nanopores,Ca2+is the easiest to pass through COO--modified nanopore.Therefore,the difficulty ranking of Ca2+through the three nanopores is GE-＞GE ＞GE-COO-.The case for Na+is the opposite of Ca2+,because the first hydration layer of Na+is its outermost layer.Therefore,the weaker the hydrogen bond is,the more unfavorable the removal of the outermost water molecules.Among three types of nanopores,Na+is the most difficult to pass through COO--modified nanopore.Therefore,the difficulty ranking of Na+through the three nanopores is as follows:GE-COO-＞GE ＞GE-This result was consistent with the hydration factor analysis in Section 3.3.2.The order of hydration factors in the first layer of Na+is:GE-COO-＞GE ＞GE-The stronger the ionic hydration is,the harder the water molecules are to be removed.In conclusion,the order of Ca2+/Na+selectivity is GE-COO-＞GE ＞GE-which is consistent with the results in Section 3.1.

Fig.9.The average number of hydrogen bond per water molecule along the Z-axis between in and beyond the first hydration layer of (a) Ca2+ and (b) Na+.

4.Conclusions

In this work,MD simulations were used to study the effects of different functional groups (COO-,) on the separation performance of Ca2+and Na+through graphene nanopores under an electric field.The pristine graphene nanopore was used as a reference.The pore size and electric field were set at 1.02 nm and 1 V.Analyses of the number of cations through the nanopores as a function of time,Ca2+/Na+selectivity,spatial distributions of functional groups and cations and ionic hydration microstructures led to the following conclusions.

(I) Three types of graphene nanopores have a preference to Ca2+over Na+and the order of the Ca2+/Na+selectivities is GECOO-(4.06)＞GE(1.85)＞GE-(1.63).It can be seen that the selectivity of ions through COO--modified graphene nanopore is 2.5 times that of-modified one.

(II) Spatial distributions of functional groups and cations show that differences in flux and selectivity for various nanopores are mainly the roles of different modified groups,whereas the steric effect of modified groups.Analyses of ionic hydration microstructures discover that different nanopores result in different hydration factors for the second hydration layer of Ca2+and the first layer of Na+.Thus,we define a ratio of the hydration factor of the second layer of Ca2+to the first layer of Na+for quantitatively describing the dehydration differences in various nanopores.Such differences can effectively evaluate the separation performance.On the other hand,the hydration phenomenon originates from the competition between the ion-water and water-water.Hence,the breaking of the hydrogen bonding network between water molecules corresponds to the change of ionic hydration microstructures.In conclusion,the functional group provides the electrostatic effect on the ionic hydration microstructure,thus reflecting the differences in dehydration ability,which further controls the permeable and separation performance of metal cations.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This work was supported by the National Science Foundation of China (21878144,21838004 and 21776123),the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (21921006).We are grateful to the High Performance Computing Center of Nanjing Tech University for supporting the computational resources and the National Supercomputer Center in Guangzhou.

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2021.10.023.

Nomenclature

E electric field intensity

F the hydration factor of cation in the hydration layer

GE pristine graphene

GE-COO-graphene modified with three negatively charged carboxylate groups

Lzthe length of the simulation box along the Z-axis

MD molecular dynamics

N the number and orientation of water molecules in the hydration layer

q charge of atom,e

RDF radial distribution function

U(rij) the interaction energy between sites i and j,kJ·mol-1

V transmembrane voltage

ε Lennard-Jones energy constant,kJ·mol-1

θ orientation of water molecules in the hydration layer

σ Lennard-Jones length constant,nm

ΦCa-s/Na-fthe hydration factors of the second layer of Ca2+and the first layer of Na+