Molecular Insight into Water Desalination across Multilayer Graphene

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Molecular Insight of Water Desalination across Multilayer Graphene Oxide Membranes Bo Chen, Haifeng Jiang, Xiang Liu, and Xuejiao Hu ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b05307 • Publication Date (Web): 22 Jun 2017 Downloaded from http://pubs.acs.org on June 24, 2017

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ACS Applied Materials & Interfaces

Molecular Insight of Water Desalination across Multilayer Graphene Oxide Membranes

Bo Chen, Haifeng Jiang,* Xiang Liu, and Xuejiao Hu* Key Laboratory of Hydraulic Machinery Transients of Ministry of Education, School of Power and Mechanical Engineering, Wuhan University, Wuhan, Hubei 430072, China *Corresponding authors. E-mail addresses: [email protected] (H. Jiang), [email protected] (X. Hu).

ABSTRACT Transport of ionic solutions through graphene oxide (GO) membranes is a complicated issue because the complex and tortuous structure inside make it very hard to clarify. Using molecular dynamics (MD) simulations, we investigated the mechanism of water transport and ions movement across the multilayer graphene oxide. The significant flow rate is considerably influenced by the structural parameters of GO membranes. Due to the size effect on shrunken real flow area, there is disagreement between classical continuum model and nano-scaled flow. To eliminate the variance, we obtained modified geometrical parameters from density analysis, and used them in the developed hydrodynamic model to give a precise depiction of water flow. Four kinds of solutions (i.e. NaCl, KCl, MgCl2, and CaCl2) and different configurational GO sheets were performed to clarify the influence on salt permeation. It is found that the abilities of permeation to ions are not totally up to hydration radius. Even though the ionic hydration shell is greater than the opening space, the ions can also pass through the split because of the special double-deck hydration structure. For structure of GO, a smaller layer separation with greater offsetting gaps could substantially enhance the membrane’s ability to reject salt. This work establishes a molecular insight of the effects of configurational structure and salt species on desalination performance, providing useful guidelines for the design of multilayer GO membranes.

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KEYWORDS: multilayer graphene oxide, water flow, ions transport, hydrodynamics, molecular dynamics simulation

1. INTRODUCTION Graphene oxide (GO) materials have been widely studied recently because of its ease of production and intriguing properties in ions filtration,1-4 which have considerable potential in energy-efficient reverse osmosis (RO) desalination.5-9 With nanometer-sized open edge and interlaminated structure, GO-based stacked layers can effectively separate salts from saline water on account of different radius between water molecules and aqueous ions.10-13 Meanwhile, GO materials have shown more excellent permeability in contrast to the state-of-the-art commercial RO membranes, which is of great efficiency and economical values in RO desalination systems.14-19 In addition, some peculiar properties, such as the selective ion permeation20-21 and the great difference of permeability between water (unimpeded permeable) and other gases (impermeable),22 make GO films attract significant attentions as multifunctional membranes. In GO laminate films, the infiltrated network includes rich nano-structures, in combination of the defects on planus graphene sheets, open slit within graphene plane and the interlayer capillary between two flakes.23-25 Recently, much efforts have been made to figure out the transmembrane process of GO.26 Water molecules and ions have been investigated across nanopores on pristine graphene doped with functional groups, which could be considered as transport process through defects or slits on GO. It have been proved that graphene with hydroxyl-decorated pores could not only enhance the rejection ability of salt but also improve the permeation of water.15 Between the interlaminated GO sheets, the model of slipped-viscous flow has been cited to depict rapid water stream, which is greatly dependent to the oxidized region on GO plates.27-29 The confined water structure and the hydrogen interactions between water molecules and functional groups are found to enhance the surface friction as well as break down the fast flow regime.27, 30-32 However, most theoretical investigations have only considered 2


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part process of ionic aqueous solution transport through an idealized and simple GO system with variable characteristic parameters.33-35 The synthetic effect of complex porous structure of these multiple GO layers on the membrane’s performance are still unknown. In particular, it is difficult to clarify how the aqueous solution stream through the tortuous small-scaled passage and how the staggered gaps on different GO layers would influence the water permeability and salt rejection. In this work, we performed a pressure-driven flow simulation of ionic aqueous solution across bilayer GO membranes to investigate the effects of staggered nanoslits on desalination properties using the molecular dynamics (MD) simulation, as shown in Figure 1. On the one hand, we monitored the water flux across the membrane with variation of geometry parameters (i.e. width of gaps G and offsetting O between two staggered gaps) and made comparison with the infiltration predicted by the continuum model. Good agreement is obtained between the MD results and the developed theoretical continuum calculations with modified geometry parameters. In addition, four kinds of solutions (i.e. NaCl, KCl, MgCl2 and CaCl2) were carried out in different configurations and the trajectories of these ions were recorded. It is found that different ions have various transport regime through the nanoslit and nano-capillary because of different hydration structures.

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Figure 1. The initial configuration of the simulation system and the geometrical parameters characterizing the GO membrane. Gray, red, white, purple, and lime spheres represent carbon atoms, oxygen atoms, hydrogen atoms, cations, and anions, respectively. Ball and stick model denotes the saline water molecules and the stick model denotes the pure water molecules. The geometrical parameters G, O, W, and H stand for width of gaps, offset between two gaps, width of the laminate, and interlayer spacing distance, respectively.

2. HYDRODYNAMICS MODELIZATION Transmembrane transport across multilayer GO films can be considered as a 2D hydrodynamic problem involved in water flow past a thin screen with slits and interlayer flow between GO sheets.29 We considered a continuum hydrodynamic model of bilayer structure as depicted in Figure 2. An underlying assumption is that the multilayer membranes will have qualitatively similar effect of the specific bilayer geometry.34 Thus, we focused on the significant effects of characteristic configuration

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between two GO layers and the subsequent layers can be deduced as tandem repeat sequences. The synthesized model consists of three parts from the entrance to the exit of the bilayer GO plate. The flow resistance R was defined as = / to estimate the water permeation through membranes, where P represents pressure drop and Q represents flux. Firstly, the flow resistance at the entrance of a nanoslit can be estimated as:

=

(1)

Here η, G, and W denote the viscosity of water, the width of the nanoslit, and the width of the GO plate, respectively. It is generally utilized to investigate the steady flow through a single slit in an infinitely thin wall.36 Secondly, the turning flow at the entrance gap into interlaminated layers is described by the similar formula as Eq. (1). It can be considered as the half of flow through a slit of width of double interlayer distances H because there is only one edge at the gap and the other side is cut off by the plane surface.29 A modified entrance equation can be written as:

= 2 × ( )

(2)

Here η, H, and W express the viscosity of water, the interlayer spacing between two GO laminates, and the width of the GO plate, respectively. Finally, the fluid flows through a capillary channel between two staggered slits, which is given by the formula for plane Poiseuille flow:22, 27, 37

=

(3)

Here η, H, W, and O represent the viscosity of water, the interlayer spacing between two GO laminates, the width of the GO plate, and the length of the capillary channel (i.e. the offsetting of slits), respectively. The whole permeation resistance of the GO films is a combination of RSlit, RGap and RInterlayer in series connection. The complete model for bilayer structure is different under the circumstance that there is no offsetting (O = 0) between two gaps, which can be written as:

= 2 ；

O=0Å

= 2 + + ；

O≠0Å

5


(4) (5)


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Figure 2. Continuum hydrodynamic modelization of bilayer structure and geometrical parameters characterizing the GO membrane. Three parts of the flow processes from the entrance to the exit of the plate are marked in black dash rectangle. (a) The schematic diagram of flow at the entrance of a nanoslit. (b) The schematic diagram of flow at the entrance gap into capillary passage, where the portion in the 6


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red dash rectangle is the assumed symmetric part of flow through slit. (c) The schematic diagram of plane Poiseuille flow interlaminated between two plates.

3. SIMULATION MODEL AND METHOD The present system consisted of saline water reservoir (with NaCl, KCl, MgCl2, and CaCl2 concentration of 0.5 M) and pure water reservoir at two opposite ends of the simulation box, which was divided by a bilayer GO membranes. Both sides were bounded by rigid pistons in order to apply a transmembrane pressure. The initial configuration is depicted in Figure 1. We considered two 3 nm × 3 nm GO sheets as a separating membrane with interlayer spacing of H, corresponding to 7.431 Å. On both GO sheets there were nanoslits with width of G and the two slits were arranged in a staggered displacement of O. The molecular structure of GO plates is made of pristine graphene and hydroxyl functional groups distributed on interlayer side (at concentration c = nOH / nC = 0.2, where nOH and nC are the number of hydroxyl groups and carbon atoms, respectively). It has been generally utilized as the reasonable GO chemical structure because the hydroxyl is reported to remain rich in the long-living quasi-equilibrium state.28,38 We manufactured the nanoslits by deleting carbon atomic rings with attached hydroxyl groups as shown in Figure 3. The width of every carbon ring marked in shadow for deleting is 2.46 Å. We set the gap distances Gc-c from 6.15 to 9.84 Å and the interval width of the gap is half unit of carbon ring. The offsetting between two nanoslits ranged from 0 to 15.987 Å with the interval of carbon ring unit. All the configurational parameters above were performed to examine the effects of geometry on the performance of GO membranes. MD simulations were performed using the LAMMPS package.39 Period boundary conditions were used on all simulation dimensions. We chose the all-atom optimized potentials for liquid simulations (OPLS-AA)27-28, 38, 40 to describe the functional group (-C-OH) in GO sheets, which are widely used to cover essential many-body terms in interatomic interactions. The rigid simple point charge effective pair (SPC/E) model27-28, 30, 38, 40 were utilized for water molecules. The pair potential parameters between ions 7



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and water molecules were fitted to the binding energies of small clusters of ions in previous researches.41-42 Both of them include van der Waals and electrostatic terms. The potential parameters are given in Table 1. The characteristic length σ and energy parameter ε between different atoms were obtained by the common Lorentz-Berthelot combination rule.43 The van der Waals interactions are truncated at 1.0 nm, and the long-range Coulomb interactions are computed by utilizing the particleparticle particle-mesh (PPPM) algorithm.44 We performed the pressure-driven transmembrane flow from 50 MPa to 200 MPa by directly adding forces to pistons in non-equilibrium molecular dynamics simulations. Before the simulation, we exerted pressure on both the upper and the lower piston for 1 ns to get equilibrium. Then we increased the pressure of upper piston to force the saline water flow down and cross through the GO membranes. The simulation process lasted for a sufficiently long time (20 ns) at 298 K for data collection. The number of water molecules and ions from two reservoirs were recorded every 50 ps to get converged results. We employed the canonical ensemble (NVT) for the whole MD simulation. The post-processing was made by Visual Molecular Dynamics (VMD)45 and The Open Visualization Tool (OVITO).46

Figure 3. The schematic diagram of a gap by deleting one unit of carbon ring. Gray, red, and white spheres represent carbon atoms, oxygen atoms, and hydrogen atoms respectively. The area for deleting was marked in shadow.

Table 1. Potential Parameters of Atoms

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atom

σ (Å)

ε (kcal/mol)

charge(q)

C(C-C)

3.851

0.1050

0

C(C-OH)

3.550

0.0700

+0.15

O(C-OH)

3.070

0.1700

-0.585

H(C-OH)

0.000

0.0000

+0.435

O(H2O)

3.166

0.1553

-0.82

H(H2O)

0.000

0.0000

+0.41

Na

2.586

0.1046

+1

K

3.331

0.1046

+1

Mg

1.398

0.9153

+2

Ca

2.361

0.4704

+2

Cl

4.402

0.1046

-1

4. RESULTS AND DISCUSSION 4.1. Water Flow Rate. During the whole simulation, the number of water molecules and ions were tracked in the feeding water reservoirs, interlayer space and permeated water reservoirs. To justify the stabilization of the system, a typical temporal evolution of number of water molecules was obtained in Figure 4. The number of feeding water molecules marked with green decreased while the number of permeated water molecules marked with blue increased equally. The crossed area represents the number of water molecules interlaminated between GO sheets, which remained approximately constant. The linear variation of water molecules ensured that the water flowrate could be acquired steadily. In particular, we selected an interval for statistical domain between two representative time (i.e. tN=4/5 and tN=1/2, which stand for the time when feeding water molecules dropped to 4/5 and 1/2 of the whole, respectively). Because the flow is very slow in some specific structure, the fixed statistical time window cannot cover enough change of number of water molecules. The flowrate under that circumstance is hardly to maintain stable, and thus we chose the number-based statistical domain to eliminate the deviation. To obtain precise data in a finite simulation time, many researchers tend to apply a high-simulated

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pressure on the order of 100 MPa, which is significantly greater than the pressures employed in the RO plants (< 8 MPa). In order to clarify the effect of variable pressures on water permeation and salt rejection, we have investigated the water flow driven by different applied pressures ranged from 50 MPa to thousands MPa for the case of Gc-c = 6.15 Å and O = 0 Å. As depicted in Figure 5, the flow rate of the bilayer system rises linearly with increasing pressure. Applied pressures from 50 MPa to 200 MPa were performed in the following study to figure out the effects of geometry parameters. The linearity of water flowrate curves indicates that the results obtained at high pressures can be extrapolated to explore the water flux at low pressures in a RO system.

Figure 4. Typical temporal evolution of number of water molecules. The green domain depicts the number of water molecules in feeding reservoir and the blue domain depicts the number of water molecules in permeated reservoir. The crossed area of blue and green domain shows the number of water molecules in the interlayer. The tN=4/5 and tN=1/2 for this unique simulation are marked out.

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Figure 5. Membrane performance with different applied pressure. The dash dot line indicates the linear fit between flowrates and pressures. The partially enlarged figure inserted portrays the flowrate at low pressures.

The effects of width gap G and nanoslits offsetting O on water permeation have been investigated in detail. A model based on continuum hydrodynamics was considered to predict the flow resistance through the bilayer membranes. A shear viscosity η = 0.8937 mPa·s for pure water at 298.15 K was used in this simulation. Previous studies compared the water flowrate between classical calculations and MD results. They found that the flowrate of theoretical predictions is greater than that of MD results, so introduced exclusion distances ∆G and ∆H to eliminate the error between the results in continuum model and MD simulation.28-29 Water molecules cannot infinitely close to carbon atoms of the slits and channels, so the flow area must be less than the geometrical parameters. For water flow in macro scale, the volume of water molecules can be ignored compared to the passageway, so the shrunken area is negligible to the flow. However, if size of water molecule is comparable to the width of gap or interlayer

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separation, the reduced area would significantly influence the water flowrate. To obtain a precise flow rate, we specifically calculate the real area by number density analysis in configurational parameters Gc-c and Hc-c initially established. Here the Gc-c is measured between two carbon atoms at the edge of the gap, and the Hc-c is measured between two hydrogen atoms of the functional groups on GO sheets. The density distribution of oxygen atoms in water molecules near the entrance of the GO sheets is plotted in Figure 6. The blue region represents the screen that water molecules cannot traverse. The distances of gap set as Gc-c = 6.15 Å, 7.38 Å, 8.64 Å, and 9.84 Å are actually G = 2.50 Å, 3.75 Å, 5.50 Å, and 6.75 Å. The interval distance between the former two (G = 2.50 Å and 3.75 Å) and the latter two gaps (G = 5.50 Å and 6.75 Å) is corresponding to half unit of carbon ring. However, when the settled gap width Gc-c increases from 7.38 to 8.64 Å, the actually spacing change is slightly larger than that initially configured. It is because that the slit with G = 5.50 Å is accessible for two water molecules while the slit with G = 3.75 Å is only open to one as shown in the snapshot of Figure 7. As for interlayer flow, water molecules can hardly move near the wall of bilayer separation because of the adhered interaction between water molecules and hydroxyl groups, and thus the flow passage is narrower than that initially configured. The density distribution of oxygen atoms in water molecules between the interlamination of GO plates is plotted in Figure 8. Here we considered the region between two peaks of number density (marked as two dash lines) as the free flow, corresponding to H = 4.5 Å. All the structural parameters modified above were used in the formula of hydrodynamic model to give a precise theoretical prediction.

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Figure 6. The density distribution of oxygen atoms in water molecules near the entrance of the GO sheets.

Figure 7. The representative snapshot with different distances of nanoslit. Red, lime, and yellow spheres respectively represent carbon atoms, oxygen atoms, and hydrogen atoms, which make up the GO sheets. Purple, white, blue, and pink spheres correspondingly denote the oxygen atoms, hydrogen atoms, cations, and anions, which make up the ionic aqueous solution.

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Figure 8. The density distribution of oxygen atoms in water molecules between the interlamination of GO plates.

Primarily, a series of simple models that the different gaps of two GO sheets fully aligned (namely O = 0 Å) have been performed to investigate the influence of gap width on water movement. We carried out the theoretical calculation of water flux by using the parameters detected from the distribution map (shown in Figures 6-8), and made a comparison with results from MD simulation as shown in Figure 9. MD results marked as black scatters reveals that the water flowrate is of parabolic relation with slit width G, which closely meet the results predicted in continuum hydrodynamics model. Subsequently, a complex tortuous flow path (namely O > 0 Å) was considered by establishing different distances between two staggered slits as the model presented above. The flow path will be divided into two parts if the length in x direction is not long enough. One flows directly from upper slit towards lower slit and the other flows through period boundary and then enter into the lower slit, which made three permeation resistances in complex series-parallel connection. To simplify the hydrodynamics model in series connection and eliminate the effect of water flow through period boundary, we expanded the simulation 14


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box to two times in x direction. Figure 10 shows the water flux across the GO membrane as a function of slit offsetting. The water flowrate decreases for greater slits misalignment, because the staggered gaps on different layers can lead to an additional permeation resistance of the interlayer flow and the turning flow at the entrance gap into interlaminated layers. The scatters denote the declining water flowrate acquired from MD simulations, corresponding to the theoretical calculation from developed hydrodynamics modelization in Eqs. 1-5.

Figure 9. The water flux across the GO membrane as a function of slit offsetting. The scatters represent MD results and the line denote the theoretical calculation.

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Figure 10. The water flux across the GO membrane as a function of slit offsetting. The scatters represent MD results and the line denote the theoretical calculation. The dash line expresses the theoretical calculated flux with particular offset O = 0 Å.

4.2. Salt Rejection. As is known that GO membranes perform different capability of salt rejection in different kinds of ionic solution. We carried out four kinds of solutions (i.e. NaCl, KCl, MgCl2 and CaCl2) to clarify the salt permeation and the transmembrane process of ions with different hydrated radius. All the saline water was filtrated by GO membranes with the same configurational parameters. At first, fully aligned nanoslit (O = 0 Å) with gap width Gc-c = 9.84 Å (i.e. the real width G = 6.75 Å mentioned above) was used in the simulated system to figure out the influence of size constraint on the transport of the ionic hydration clusters. Figure 11 shows the salt rejection of four kinds of ions at different applied pressures. Salt rejection is defined as R = (Nf − Np) / Nf, where Nf is the initial number of salt ions inserted in the feed reservoir, while Np is the number of salt ions in the permeate reservoir at tN=1/2. It suggests that all kinds of ions could permeate through the GO membrane, and the salt rejection decrease linearly with the increase of applied pressures. From the linear fit of salt rejection to different ions, we can conclude that 16


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the abilities of permeation to ions are in the order K+ > Na+ > Mg2+ > Ca2+ for the same nanoslit. To further understand the nature of ionic water clusters flow through the nanoslit, we computed pair correlation functions between different ions and atoms in water molecules, which can imply the hydration structure and hydration shell of ions. As shown in Figure 12, radial distribution function (RDF) curves of Mg2+-Ow and Ca2+-Ow exhibit two distinct peaks, while that of Na+-Ow and K+-Ow only exhibit one. The sharp peaks indicate the highly ordered atoms around the ions, so there are two water shells around double-charged ions and only one around single-charged ions. Moreover, the first valleys of Mg2+-Ow and Ca2+-Ow RDF curves are wide and flat, showing that the first and second hydrated shells are clearly separated. The dash lines in Figure 12 represent the coordination number of ions, which is calculated by the integral of RDF curves. For single-charged ions, the first maximum of the RDF to hydrogen atoms in water molecules is at 3.15 Å for Na+ and 3.45 Å for K+, which means the calculated hydrated radius (close to the former study 3.2 Å for Na+ and 3.5 Å for K+).47 According to the coordination number curves, there are about 6 water molecules in the hydration shell of Na+ and 6.7 water molecules around in the hydration shell of K+. As for double-charged ions, the strong first peak reflects that the dense water cluster formed around ions, which should diffuse with ions in the solution. These hydrated water molecules are highly bounded to ions and are difficult to exchange with bulk water. The weak second peak denotes the secondary hydration shell with loose water cluster. The first maximum of the RDF to oxygen atoms is at 1.95 Å for Mg2+ and 2.45 Å for Ca2+ (in excellent agreement with the previous work 1.98 Å for Mg2+ and 2.43 Å for Ca2+).41, 48 Considering the two water shells, we define the hydration radius of Mg2+ as 4.25 Å and the hydration radius of Ca2+ as 4.55 Å (close to the previous study 4.28 Å for Mg+ and 4.58 Å for Ca+).41 The number of water molecules in the first shell around Mg2+ is 6 and around Ca2+ is 8 while in the second shell around Mg2+ is 22 and around Ca2+ is 30.4.

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Figure 11. The salt rejection to different ions of bilayer membrane. Black square, red circle, green up triangle, and blue down triangle represent the salt rejection to Na+, K+, Mg2+, and Ca2+, respectively.

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Figure 12. Pair correlation functions between different ions and atoms in water molecules. The black and red lines denote the function of ions in outerlayer and interlayer, respectively. The solid and dash lines represent radial distribution function and coordination number of ions, respectively. The left-hand axis and right-hand axis signify the radial distribution function (RDF) and coordination number, respectively. “Interlayer” means ions interlaminated between two GO sheets, and “outerlayer” means ions in permeated reservoirs or feed reservoirs.

According to RDF curves, the hydration size of Na+ and K+ is comparable to the breadth of nanoslit, so the permeability of Na+ and K+ are larger among four ions. The GO membrane shows better ability of salt rejection to Na+ than K+ though the former has smaller hydration radii, showing that the size relation is not a dominant factor on salt filtration for the small ions accessible to the narrow gap. For small-sized

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ions, the dielectric and hydrodynamic friction should be considered during the transport of solution. The diffusion coefficient of K+ is larger than that of Na+ calculated from Stokes law49 and Zwanzig’s theory,50 so the permeability of K+ is better than Na+. For large-sized ions, even though the hydration radii of Mg2+ and Ca2+ are greater than half width of the gap (G/2 = 3.375 Å), ions can still pass through the nanoslit. It is owing to the special structure of double-charged hydration cluster, which is like a double-deck sphere with rigid inner covered by soft surface. The first hydration shell is dense cluster and it can be considered as the rigid inner. The water molecules in secondary hydration shell weakly connect with the nuclear ions and they are like the elastic enclosure around the dense cluster. These water molecules would adjust their location to ensure the inner hydration shell to move across the gap. The schematic diagram of ions passing through nanoslit is depicted in Figure 13. If the hydration radius of ion is larger than the width of gap, the nanoslit can replace several water molecules from the outer hydration shell of the ions when passing through it. Then some water molecules of outer shell will get out of the constraint of secondary hydration shell until the inner ionic hydration shell go through the narrow gap. After the first hydration shell crossing over the split completely, the defected position of secondary hydration shell will attract some other water molecules in the permeated region to form a new hydration shell. The radii of first hydration shell is 2.65 Å for Mg2+ and 3.05 Å for Ca2+, which is smaller than half width of the slit. Thus, both of them could traverse GO membranes with small slit. To depict the coordination relation between water molecules and ions, the spatial evolution of coordination number inside ionic hydration shell during passing through the nanoslit is shown in Figure 14. The coordination number Nc in first hydration shell is invariant when the ions cross the split, corresponding to 6 water molecules for Mg2+ and 8 water molecules for Ca2+. In comparison, the coordination number Nc in secondary hydration shell declines obviously getting into the gap and subsequently increases leaving from the gap. The drop of coordinated water molecules ∆Nc are 4.15 for Mg2+ and 6.7 for Ca2+. The first hydration radii of Mg2+ is smaller than that of Ca2+ (R1Mg-H < R1Ca-H), so the bigger one need to dismiss more surrounding water molecules and cost more energy to break the hydrogen bonds. That is

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the reason why Ca2+ is more difficult than Mg2+ to infiltrate the bilayer GO membranes.

Figure 13. The schematic diagram of ions with great hydration radii during passing through the nanoslit.

Figure 14. The spatial evolution of coordination number inside double-charged ionic hydration shell

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during passing through the nanoslit. Square (marked with superscript 1) and circular (marked with superscript 2) scatters represent the coordination number in first and secondary hydration shell, respectively.

We also recorded the pair correlation functions of ions in different regions during ions transport from feeding reservoir to permeated reservoir. In the region out and between two GO layers, the function curves are plotted as black and red curves in Figure 12, respectively. For Na+ and K+, the peak of RDF curves in the region of interlayer is lower than that of outerlayer. It proves that the coordinated position around ions would be replaced by some hydroxyl groups in the layer, so the ions would attach to the wall when flowing through the nanocapillary between two GO sheets. As for Mg2+ and Ca2+, no obvious difference of the peaks between interlayer and outerlayer, because the larger hydration clusters could not enter into the nanochannel and are absorbed at the entrance of the channel. It can be inferred that gap offset and lamination separation could significantly influence the membrane’s ability to reject salt due to the nanocapillary between two slits. Therefore, we turn to the effect of GO layers’ geometry on salt rejection. The salt rejection of bilayer GO membranes with H = 6.7 Å and H = 4.5 Å at O = 23.4 Å at the same gap width Gc-c = 11.067 Å were compared in Figure 15. It indicates that the gaps with fully aligned offset (O = 0 Å) are weakly rejective to ions at 200 MPa. On the contrary, when the length of capillary increases to O = 23.4 Å at the same layer separation (H = 4.5 Å), the membrane is impermeable to ions even at high pressure, whereas ions could pass through the membrane if we enlarge the passage to H = 6.7 Å. The ions would be easily trapped by the functional groups on GO sheets when very close to them. Long and narrow capillary channel would absorb the ions with hydration radii lager than the interlamination spacing and refuse them to pass through the membrane into permeated reservoir. The ability to reject the salt would weaken to some degree with the increasing separation of interlayer. It indicated that enlarging gap offset and decreasing lamination distance could effectively enhance the salt rejection of GO membranes.

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In addition, the permeation behaviors of anions are various through different nano-structures in GO membrane. For fully aligned slits, both cations and anions could easily pass through the wide split established as Gc-c = 11.067 Å. Cations permeated through nanoslits while anions with equal quantity of charge also permeated through split at the same time, which obeys electro-neutrality in reservoirs. However, for the staggered slits, more anions permeated through the GO membrane than cations at the presence of nano-capillary. It is because the electronegativity of the GO sheets make cations absorbed near the wall and trapped in GO channels. The imbalanced transport of cations and anions may make permeated reservoirs electrified weakly, which have been observed in some experimental researches.20-21, 51-52

Figure 15. The salt rejection of bilayer membranes with different configurational parameters.

5. CONCLUSIONS In the present study, an imitated reverse osmosis pressure-driven flow was performed to investigate

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the effect of geometrical parameters and salt species on performance of GO membranes by means of classical MD simulation. We considered a developed continuum hydrodynamic description to illuminate the zigzag transport of water across multilayer GO laminates. The synthesized flow model can be divided into three parts, the entrance of a nanoslit, the conjunction between gap and passage and the interlayer inside capillary channel. The whole permeation of the GO films is dependent on the seriesparallel combination of three resistances in these three parts (namely RSlit, RGap and RInterlayer). We monitored variable configurational parameters to elucidate the effect of different structures. To eliminate the variance between classical model and nano-scaled flow, which is caused by the size effect on shrunken real flow area, we obtained modified geometrical parameters from density analysis. MD results show that the water flowrate is of parabolic relation with slit width G and decreases for greater slit alignment, quantitively in agreement with the theoretical prediction with modified geometrical parameters above. Four kinds of ions (i.e. NaCl, KCl, MgCl2 and CaCl2) were considered to clarify the salt permeation of ions with different hydration radius. For the same width of nanoslit, the ability of permeation to ions are in the order K+ > Na+ > Mg2+ > Ca2+, which is not consistent with the hydration radii of ions. For size of ions smaller than the width of slit (like Na+ and K+), the mobility friction should be considered during the transport of solution, so K+ is easier to permeate though membranes because of the greater diffusion coefficient. For some ions that the hydration radius is greater than the half gap width (like Mg2+ and Ca2+), the ions can also pass through the split, because these double-charged ions have special hydration structure like hybrid of hard and elastic sphere. Water molecules in first hydration shell are dense and adherent to ions while water molecules in secondary hydration shell are loose and will dismiss when getting the entrance into the nanoslit. It is more difficult for Ca2+ to infiltrate the bilayer GO membrane because more water molecules should be replaced from the RDF analysis. It is found that the gap offset and layer separation significantly influence the salt rejection of membranes. With greater offset and shrinking interlayer spacing, the salt rejection of GO membranes could dramatically increase. The aim of

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the results above is to assess the potential of multilayer GO membranes in desalination and help to understand the transport mechanism of water and ions across the tortuous nano-networks.

Notes The authors declare no competing financial interest.

ACKNOWLEDGEMENTS The authors acknowledge the support of the National Natural Science Foundation of China (No. 50906064), the China Postdoctoral Science Foundation (No. 2017M612498), and the Fundamental Research Funds for the Central Universities (No. 2042016kf0023). The numerical calculations have been done on the supercomputing system in the Supercomputing Center of Wuhan University.

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Graphical Table of Contents. 90x90mm (300 x 300 DPI)


Molecular Insight into Water Desalination across Multilayer Graphene

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