Water Permeation and Ion Rejection in Layer-by-Layer Stacked

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Water Permeation and Ion Rejection in Layer-by-Layer Stacked Graphene Oxide Nanochannels: A Molecule Dynamic Simulation Xiaoning Yang, Haiwei Dai, and Zhijun Xu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b05337 • Publication Date (Web): 12 Sep 2016 Downloaded from http://pubs.acs.org on September 13, 2016

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The Journal of Physical Chemistry C is published by the American Chemical Society. 1155 Sixteenth Street N.W., Washington, DC 20036 Published by American Chemical Society. Copyright © American Chemical Society. However, no copyright claim is made to original U.S. Government works, or works produced by employees of any Commonwealth realm Crown government in the course of their duties.

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The Journal of Physical Chemistry

Water Permeation and Ion Rejection in Layer-by-layer Stacked Graphene Oxide Nanochannels: A Molecule Dynamic Simulation

Haiwei Dai, Zhijun Xu, Xiaoning Yang* State Key Laboratory of Material-Orientated Chemical Engineering, College of Chemistry and Chemical Engineering, Nanjing Tech University, Nanjing 210009, China

*: To whom correspondence should be addressed E-mail: [email protected] (X. Yang); Telphone: 86-025-83587184 1

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Abstract: Layer-by-layer assembled graphene oxide (GO) has been considered as high-efficient novel membrane material. However, its performance of water permeation and ion rejection still remains largely unresolved. Herein we constructed a model of GO membrane using laminate nanochannels with aligned flexible multilayered GO sheets, on which functional groups were randomly distributed based on the Lerf-Klinowski model. The water permeation and ion rejection in the flexible GO membranes with various pore widths and surface oxidization degrees were simulated. Our results indicate water flow rate in the GO nanochannels is significantly slowed down, which is quantitatively equivalent with the prediction using no-slip Poiseuille equation. The simulated results suggest the capillary channels within GO stacked laminated membranes might not always work as the major flow route for water to permeate. It is observed that confined water structure becomes more disordered and loose within the corrugated GO nanochannels. The interfacial friction provides huge corrugation of surface energy landscape for water moving, and largely suppresses the water flow. The microscopic mechanism of ion rejection has been ascribed to the size exclusion of ion hydration and the surface interaction from functional groups. Overall, our results provide new physical pictures for capillary channels in GO-related stacked membranes.

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Introduction Graphene oxide (GO) with intriguing properties1-4 and ease of preparation and scaling up5 has demonstrated great potential in nanofluidics, electronics, supercapacitors, and biological area.6-9 Among these applications, multilayered GO membranes provide novel pore structures for water purification and separation. In this aspect, GO layers could be easily fabricated or assembled into laminate structures with interlayer distance on nanometer scales.4,5,7 This unique stacked laminate structure allows water molecules to permeate through the interconnected network formed by corrugated GO nanosheets. Meanwhile, the GO-based multilayered membranes show excellent retention of solute molecules. At present, extensive experimental

methods,

including

pressure-driven

ultrafiltration,10

vacuum

filtration11,12 or drop-casting method13, have been developed to fabricate free-standing GO laminates membranes. These experimental studies also indicate that the layer distance of adjacent GO sheets could be controlled by degree of hydration inside the nanochannel.14-16 In the GO-based stacked membranes, the percolated network features rich microstructure3,11,17 with inclusion of the interlayer capillary gallery and the open space between edges of neighboring sheets or the pores within graphene planes. Molecular permeation through the interconnected network of GO membrane occurs through both the interlayer gallery and the interedge voids or graphene pores. However, it has been generally accepted that the capillary nanochannels between GO sheets have been considered as the critical route for molecule permeation.18 3



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Furthermore, it was hypothesized that the interconnected nanochannels have two types of regions: functional and pristine.5 The former acts as spacers to keep adjacent graphene sheets apart, whereas the unoxidized pristine region provides a capillary channel that allows ultrafast water transport. Very recently, pressure-driven water transport inside the rigid nanochannel, formed by pristine graphene sheets, has been simulated,19 and ultrafast water flow rate was observed. In addition, the aligned stacked model of GO membrane has been studied20 with the rigid capillary channels of pristine graphene walls in order to characterize the potential of selective removal of radioactive technetium from contaminated water. It should be noted that this flow capillary model with pristine graphene regions in GO-based laminate membranes is still lack of enough direct proof with large debates. Ultrahigh-resolution transmission electron microscopy (TEM) has revealed that the synthesized GO sheet possesses a high density of oxygen-containing functional groups with 82% area corresponding to oxidized region, but only 16% pristine graphene region.17 According to the Lerf-Klinowski model,21 the oxidized region and pristine region are just discretely and randomly distributed on GO plane without continuous region. Talyzin et al.22 reported the structure of GO membranes in liquid water, and they declared that water permeation through GO membranes is not limited in unoxidized regions of GO flakes and the widely suggested “pristine graphene capillaries”1 might not be existent. In order to realize the water flow nature in GO nanochannels, it is necessary to consider the reasonable chemical feature on basal plane of GO sheets. 4


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Although extensive experiments have been conducted regarding the synthesis preparation and separation performance for the GO membranes, the flow behavior and confined structures between hydrophilic corrugated GO sheets still remain largely unexplored. Currently, massive arrays of nanochannels formed by flexible GO sheets with average interlayer spacing around 10 Å have been fabricated, which could be used for preparing nanofluidic devises.7,23,24 Therefore, investigating the microscopic behavior of flow and structure confined in two-dimensional corrugation GO nanochannels will provide new microscopic understanding of water permeation through GO-based laminate membranes. Meanwhile, this result will be important and valuable to the development of nanofluidics devices. With the above in mind, in this paper, a layer-by-layer stacked GO membrane with corrugation fashion was constructed, thereby forming unique multi-layers nanofluidic channels almost parallel to the flow direction. In our work, the Lerf-Klinowski GO model was applied to represent GO chemical structure. Interlayer distance of GO laminates membrane could be controlled based on the initial water content in order to reflect the actual pore widths of GO membrane. Non-equilibrium molecular dynamics (MD) simulations were conducted to investigate the water permeation and salt rejection in the multilayered GO membrane models. The confined structures and flow friction of water within the corrugation nanochannels has been explored.

Simulation Models and Method In this work, we considered the 40Å×80Å GO sheet with epoxy and hydroxyl 5



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functional groups randomly distributed on the two both sides by following the Lerf-Klinowski model,21 which has been extensively accepted as the reasonable GO chemical structure.25,26 Since hydroxyl and epoxy groups were reported to be in long-lived equilibrium state,27 the carboxyl groups were not considered here. In addition, the well-known Lerf-Klinowski GO model has also shown the absence of carboxylic acids on the periphery of the basal plane.21,26 Therefore, in order to make focus on the effect of GO surfaces and avoid complexity, we did not include the carboxyl groups at GO edges in our present GO model. In the surface distribution of functional groups on graphene sheets, we used the previous rule that a large fraction of hydroxyl and epoxy were bonded to carbon atoms next to each other.3 We considered two types of GO surfaces with oxidization concentrations being 20% (C10O1(OH)1 denoted as GO1) and 40% (C10O2(OH)2 denoted as GO2), which are defined as the number of oxygen-containing groups divided by the carbon atoms on graphene sheet. This choice of oxidization concentration was based on the oxidation degrees of GOs fabricated in different experimental methods1,28,29 measured by XPS, which are in the range of 0.20-0.44.22,30 The two GO models were shown in Figure S1. All molecular dynamic simulations were performed using the LAMMPS package.31 Tersoff-Brenner force field32 was employed to describe the effective many-body interactions for carbon atoms within each graphene sheet. This force field is a non-additive pair potential, where three-body terms are included, and it takes the nature of chemical bonding and environment into account in a complex and 6


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reasonable way. The Tersoff-Brenner force field has been widely used for carbon-based materials.33,34 The all-atom optimized potentials for liquid simulations (OPLS-AA) force field was implemented for the functional group atoms35,36 and SPC/E model37-41 was used for water molecules. For the interaction between graphene and water, the Lennard-Jones (L-J) potential 4ε [(σ / r )12 − (σ / r ) 6 ] between carbon and oxygen atoms of water molecules with the parameters ε=0.392 kJ·mol-1 and σ=3.19 Å37,39,42 was adopted, which is able to reproduce the experimentally measured water contact angle on graphite surfaces.42 All the sp2 carbon atoms in GO were treated as uncharged atoms. The charges of functional group atoms in the GO sheet were adopted from the reference 43, in which ab initio quantum computation was used to obtain the atomic charge model for functional groups in GO. All the L-J parameters using in this simulation were listed in Table S1. We employed the Lorentz–Berthelot mixing rule for the L-J interactions between different particles. The particle-particle particle-mesh (pppm) method was applied to calculate the long-range electrostatic interaction. The laminate GO membranes were firstly constructed by stacking four parallel GO sheets approximately parallel to each other and forming four flow channels, as shown in Figure 1. At present, layer-by-layer assembly GO membrane has been experimentally fabricated with different interlayer distances designed for separation and purification of organic and salt solutions.1,11,13,44,45 For salt-containing aqueous solutions, Han11 and Hu45 prepared GO laminate membranes with ~10 Å pore width, showing moderate ion retention. In the study by Nair et al.,1 the intersheet gaps of GO 7



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membrane were also maintained to 9 Å and all solutes with hydrated radii larger than 4.5 Å were blocked. According to previous experimental reports,15,16,46 the layer-to-layer spacing of GO measured by XRD and neutron scattering experiments showed highly sensibility to humidity and the typical interlayer distances range from 6.0 to 11.0 Å, depending on the atmospheric relative humidity. In order to control the specified interlayer spacing between the GO sheets, we initially placed water molecules with certain content (wt%), which is defined as water mass percentage relative to the mass of each graphene sheet. Herein, a preliminary MD simulation was conducted to determine the quantitative relation between the interlayer distance and the water content. The detailed simulation procedure and mechanism analysis were given in the supporting information. As seen in Figure S2, the interlayer distance between GO sheets varies from 5.5 to 12.4 Å with increasing water content. Comparatively, the GO2 sheets with larger oxidization degree produce more swelling of interlayer spacing. This simulation result is in good agreement with the experimental observation in the previous studies.15,16 In addition, our simulation result is also consistent with the previous simulation study.14 These results might provide a validation that the combined force field used in this work should be reasonable. A certain amount of water molecules were placed into the interlayer pores between the parallel GO sheets so that channel distances from 7.5-12.4 Å were initially set before the non-equilibrium MD simulation. In the non-equilibrium MD simulation, the size of simulation box is 40 Å in the x direction and over 250 Å in the z direction. The box length of y direction was adjusted according to the interlayer 8


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distance. Three-dimensional periodic boundary conditions were applied. The GO membranes with four-layer GO sheets were placed in the middle of the simulated box with the carbon atoms of the left and right corner edges fixed to prevent whole structure shifting. Water molecules were added into the channels in order to maintain the initial pore widths. Four initial water contents for two types oxidation GO membranes were investigated, which were denoted as: GO1-25 wt%, GO1-30 wt%, GO1-35 wt%, GO1-40 wt%, and GO2-25 wt%, GO2-30 wt%, GO2-35 wt%, GO2-40 wt%. These GO-based nanochannels correspond to the initial pore widths 7.5, 8.4, 9.5, 10.6 Å for GO1, and 8.7, 9.7, 11.0, 12.4 Å for GO2, respectively, which are close to the pore widths for the typical GO laminate membranes.5,11,47 On both sides of the membrane, two reservoirs were connected. 8000 water molecules and 90 Na+ and 90 Cl- were randomly distributed in the left bulk reservoir. 1500 water molecules were placed in the right reservoir. One rigid graphene plate as the piston was placed at the left side of the simulation box and external force was imposed to the plate. The carbon atoms in the plate were treated as the uncharged L–J sphere.35,36 To generate the desired pressure difference ( ∆P ), the applied force ( f ) was exerted on each carbon atom of the piston based on the equation, f = ∆P ⋅ A / n ,48 where A is the area of the graphene plate and n refers to the total number of carbon atoms of the plate. The hydrostatic pressure difference ranged from 100 to 400 MPa. In the non-equilibrium MD simulation, it was quite common to apply high pressure simulation in order to reduce thermal noise and enhance signal/noise ratio within a nanosecond timescale.37,40,49 The canonical ensemble (NVT) was employed in the whole 9



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simulation. According to our simulations, during the non-equilibrium process, the interlayer spacing between GO sheets could achieve certain fluctuation around the initial pore widths.

Results and Discussion Flow Behavior: We firstly simulated the water permeation across the GO membranes. Figure 2a and 2b show the water fluxes (in unit of ns-1) as a function of applied pressure difference for different GO pores. The water flux was calculated when stable pressure-driven flow has been achieved with water molecules completely occupying the nanochannels. The water flux appears linear increase with external pressures, demonstrating a stable hydraulic flow mode. Although the applied pressure is significantly higher than what is typical for actual desalination operation, the flow scaling linearly with pressure difference could be applied to extrapolate the results at low pressures.49 According to our results, the water flow rates in our GO nanochannels are generally 2-3 orders of magnitude smaller than those in pristine graphene nanochannels19 and carbon nanotube pores50. This huge difference might reflect the effect of functional groups of GO surfaces. In the GO laminate membrane, the GO sheet is usually flexible (see Figure 1) with certain corrugation during the permeation simulation process. Figure S3 presents the average fluctuating degree of two neighboring GO sheets under different pressures. In general, the sheet corrugation degree is insensible to pressure, and the maximum fluctuation is below 1Å. It is observed that the GO1 sheet undulates a little greatly than GO2. Due to the flexible feature of GO membranes, the interlayer distance of 10


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adjacent sheets displays distribution, as shown in Figure S4. Most of them distribute around the initial pore width, whereas GO1-30 wt% shows two peaks in the distribution, which will be further discussed in the following section. In the subsequent analysis, we used the average spacing between sheets to signify the pore width. We compared the simulated flux with that predicted from the no-slip Poiseuille equation of fluid mechanics,1,37 in which the flux ( Qno − slip ) is expressed as, Qno− slip = −

d 3∆PW 12ηL

(1)

where d is the effective distance of water layer. ∆P is pressure difference along z-axis and W, L represent the width and length of GO sheet. η is the shear viscosity used for confined water (SPC/E water model at 300 K).51 Accordingly, the flow enhancement factor could be quantified by ε = Qsimulated / Qno − slip . As seen in Figure 2c, the calculated enhancement factor is 1.0-1.4 for GO1 channels, but only 0.4-0.6 for GO2 channels. As compared with the Poiseuille flow, the water flow rate in the GO channels does not show flow enhancement, which usually occurs in nanopores formed by pristine graphenes and carbon nanotubes.19,52 This result might imply that the water flow in GO channels exhibits the non-slip Poiseuille flow behavior. From the slopes of flux profiles in Figures 2a and 2b, the water permeability could be computed and shown in Figure 2d by using the channel cross-area as the permeation area. The water permeability increases with the pore sizes in GO channels, and this behavior is qualitatively consistent with no-slip Poiseuille flow equation. The breakdown of water

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flow in GO nanochannel is probably caused by a combination of the friction resistance from the GO corrugation surfaces and the enhanced molecular viscous effect in the GO confined pores. As shown in Figure 2d, the permeability values range from 104.4 to 860.4 L·m-2·h-1·bar-1 for various pore widths, which are close to the previous simulated permeability for the GO framework (GOF)53 membranes with graphene sheets covalently interconnected by linear linker. At present, experiments10,11,44,47,54 have been conducted to measure the pressure-driven water flow through GO-based laminate membranes. In the actual GO laminate membrane with rich microstructures, water molecules can transport through both the interlayer galleries and the open spaces between edges of neighboring graphene sheets or the defect pores on the graphene plane. Thus, it is inappropriate to directly compare our simulated permeability to experimental measurements, because here we only considered the water flow within the nanochannels. In previous works, the measured water permeability of GO laminate membranes with interlayer spacings of ~10 Å11,39 were found to have about four to six orders of magnitude higher than those from the non-slip Poiseuille flow equation. Generally, the huge difference could be attributed to the so-called ultrafast slip flow within the GO channels and the direct passing through the intersheet gaps or pore defects. According to our simulated results, we find the water flow in GO nanochannels is highly inhibited and the corresponding flow rate is quantitatively equivalent to the non-slip Poiseuille flow. In view of the above results, it could be speculated that the water permeation in the stacked GO laminate 12


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membranes reported in literatures11,39 mainly occurs in the pores or defects of GO membranes, including the edge of neighboring sheets and the porous structure. These pore defects increase molecular transporting through GO membranes. For instance, our supplementary pressure-driven MD simulation (data not shown) shows that for water transporting through single-layer porous GO membranes with pore size of 7.5-10.0 Å, permeability can achieve the values of 200-1000 L·m-2·h-1·bar-1. Moreover, our simulated results advise that, in some cases, the interlayer gallery formed by GO sheets could not serve as the major flow route for water permeation through GO stacked membranes. Wei et al.37 also simulated the water flow in the sandwich-like distributed GO nanochannels with pristine region placed between oxidized regions. The flow enhancement, compared to the Poiseuille flow, was reported to be 8.05, which is not able to match or support the high measured permeability of water with several orders of magnitude larger than the non-slip Poiseuille flow.11,39 Thus, this might further support the speculation and suggestion that the so-called pristine graphene region within GO channels might not be feasible in the description of flow behavior of GO stacked laminate membrane. To further characterize the water flow characteristics in the GO nanochannels, in Figures 3a and 3b, we showed the typical water velocity profiles across the channel cross-area. Compared to the plateau-like flow between pristine graphene sheets,37,55 the velocity profiles in GO channels distributes scattered across the nanochannels with convex features. This means that there is large viscous shear nature between confined water layers, which could suppress the flow rate. A close inspection of 13



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Figures 3a, b suggests that the velocity profile turns to be somewhat parabolic shape owing to strong surface effect, which causes almost immobility of water molecules near GO surfaces. This agrees with the non-slip Poiseuille flow with zero velocity near boundary surfaces. We calculated the average velocity for all GO membranes in Figure 3c and find that average flow velocity increases with the average layer distance. This is consistent with the variation of water permeability with the pore width (Figure 2c). For the two GO membranes, water inside the GO1 nanochannel transports faster than that of GO2 with similar pore width. This could be due to weaker interaction felt by water in GO1 that has fewer functional groups. The average velocity of water in the GO channels is from 0.1 to 1.7 m/s, which is two orders of magnitude smaller than those observed in pristine graphene pores and carbon nanotube.52,56 However, the velocity value reported here in GO channel is close to the values in hydroxyl functional graphene pores.57 This smaller velocity for water molecules flowing through the GO channels implies that there exists larger flow friction resistance arising from the graphene oxide surfaces. It should be noted that this low flow behavior could be somewhat related to the sudden expansion and construction in the GO channels with the inclusion of entrance and exit. Previous molecular simulations58 have shown there exists thermodynamics resistance for water molecules entering the carbon nanotubes from bulk phase. Fluid mechanics computation59 also demonstrated energy dissipation mainly occurs solely near the entrance and exit of the cylindrical channel with a zero-friction surface. In general, pressure loss probably exists at entrance and exit for 14


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limited pore length,60 however, the pore end-effect might become unimportant in our hydrophilic GO channels due to enhanced surface friction. In the following section, we will give further discussion and analysis regarding the pore end-effect. It’s known that nanopore flow is associated with the corresponding confined structure configuration. In this section, we studied the confined water structure in different GO channels. Generally, the steady water flow inside the laminate GO pores can be generated, when water molecules gradually fill the GO channels under a constant external pressure, and the structure of water inside GO channels remains quite stable. Figure 4 shows the typical density profiles of oxygen and hydrogen atoms of water molecules along y-direction confined within different GO nanochannels, respectively. Similar structure features could be obtained in other pressure conditions. For comparison, the relevant simulation snapshots are also shown. In the GO1-25 wt% pores, corresponding to the average pore width of 7.5 Å, a single-layer density peak in both hydrogen and oxygen density profiles can be obtained between the GO sheets, wherein the water molecules are oriented parallel to the GO planes. Although the radial distribution functions (Figure S5) for this monolayer water shows several enhanced peaks, the water structure does not appear ordered structure feature, which is in contrast with the observation in the pristine pores.41,61,62 As the pore width increasing (from GO1-30 wt% to GO1-40 wt%), multiplied density peaks can be formed in the density profiles. However, we observe obvious merging between the density peaks, suggesting the change in the orientational preference of water molecules with the enhanced disturbing from confined molecules. 15



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For GO2 channels, the density profiles become wide along with unresolved peaks, which is obviously different from those observed in smooth and rigid pristine graphene pores.63 The difference of density profile between pristine graphene and GO sheets is mainly attributed to the effect of surface oxidized functional groups. It can be clearly seen from the snapshots that water molecules in the GO2 channels distribute more loosely with no clear molecular layers. This enhanced disordered water structure in GO2 might suppress the flow rate, as compared to GO1. In short, our simulation demonstrates that there exists liquid-like structure for water confining and flowing within the GO channels, and the layered ice-like structure observed in pristine graphene capillary61 is unlikely occurred. It is interesting to note that in the GO1-30 wt% membrane (Figure 4), the two adjacent interlayer channels show distinct water density profiles, in which one channel shows one density peak and double density peaks appear in another channel. This phenomenon can be related with the occurrence of two distinctive channel sizes in the GO1 membrane. As seen in Figure S4, in the GO1-30% channel, when stable water flow is achieved, the initial pore width (8.4 Å) can be transferred into two different average interlayer distances, 7.2 Å and 10 Å, which is consistent with the flexible nature of GO sheets (Figure S3). Actually, according to previous potentials of mean forces (PMF) profile64 between two GO sheets, two PMF minima at ~7 Å and ~10 Å, corresponding to a single layer and bilayers of confined water, respectively, are separated by a free energy barrier at ~8.3 Å between GO sheets. This means that the transfer of interlayer distances between GO sheets is driven by interaction free 16


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energy. In Figure 5, we show the effective confined densities of water molecules as a function of applied pressure differences. It can be seen that water density increases slightly with pressure difference, consistent with the minor pressure dependence of confined water density in CNTs.65 The effective density in GO channels is around 0.60~0.85 g/m3, smaller than the values in pristine graphene slit pore63 and carbon nanotube.65 The smaller density reported here could be attributed by the presence of surface functional groups, which exclude the water molecules near the GO surfaces because of steric repulsion. We also investigate the hydrogen-bonding (HB) structures for water inside the GO pores. Figures S6 shows the proﬁles of water-water (WW) HBs and water-GOs (WF) per water molecule, along the y direction in the GO channels. Here we used the geometric criterion definition of hydrogen bonds.66 The HB proﬁles are symmetric with respect to the pore centers. The average WW HB number is reduced near GO surfaces, as compared with the results in graphene pores.63 This behavior is due to the formation of HBs between water molecules and the surface functional groups, which plays a competitive action in the WW HB formation. Figure 6 shows the number distribution of HB between the two types of functional groups (hydroxyl and epoxy) and the neighboring water molecules. It is observed that a single hydroxyl group could form more HBs with water molecules, as compared with epoxy group. This means that hydroxyl groups have stronger affinity with water molecules. In addition, we investigated the dynamics stability of HB 17



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between water and functional groups by calculating two time correlation functions of HB (Figure 6b): Continuous HB correlation function SHB (t ) and intermittent HB correlation function C HB (t ) ,67 which are defined as,

S HB (t ) =

< h ( 0 ) h (t ) > < h ( 0 ) H (t ) > , and C HB (t ) = < h (0) h (0) > < h ( 0) h ( 0) >

(2)

where H (t ) = 1 represents that HB pair remains continuously from t=0 to time t, and zero otherwise. h (t ) = 1 represents the formation of HB at time t, and zero otherwise.

S HB (t ) describes the dynamics of HB breaking as it is related to the continuous presence of HB and C HB (t ) describes the structure relaxation of HBs. As shown in Figure 6, it is obvious that both S HB (t ) and C HB (t ) of hydroxyl groups decay more slowly than epoxy groups, which means hydrogen bond between water and hydroxyl is more stable and remains less relaxed. The stable HB formation between hydroxyl groups and water molecules also agrees with the corresponding stronger binding interactions. To further characterize the interfacial layer structures of water, we calculated the two-dimensional (x-z plane) density distributions for water molecules near GO surfaces whose location corresponds to the first peaks of density profiles. The water densities (Figure 7) do not show the uniform distributions, which are different from that observed on pristine graphene surfaces.68 There exist obvious depletion regions in the surface contact layer on GO surfaces, suggesting that functional groups could exclude water molecules. Comparatively, hydroxyl groups could produce larger blank regions than epoxy groups, possibly because of different sizes. This uneven and 18


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undulated water distribution near GO planes is supposed to impede the surface flow, further reducing the flow rate through the GO channels. It was observed that this effect become enhanced near GO2 sheets due to denser surface functional groups. The liquid flow friction for pure water molecules confined within the GO nanochannels was quantified to characterize interfacial flow resistance. The friction coefficients can be expressed via linear response theory in terms of a Green-Kubo (GK) relationship at equilibrium38,57 introduced as λ=

1 Ak BT

∞

∫ 0

< Fx (t ) Fx (0 ) > dt

(3)

where Fx (t ) is the time-dependent force acting along the water flow direction on GO sheet with surface area A. The friction coefficient was evaluated from the plateau of the integrations about force auto-correction function shown in Figure S7. Following the previous treatment, we chose the time that corresponds to first zero of the force autocorrelation function as the upper limits for integration.69 Figure 8a shows the results of the friction coefficient in the different GO membranes investigated. The friction coefficients ( λ ) display around 0.78×106 and 1.15×106 Ns·m-3 for GO1 and GO2, respectively, with minor dependence on the layer distance of GO channels. This friction coefficients reported here for GO surfaces are close to the value for hydroxyl-functionalized graphene,57 but are two orders of magnitude higher than that for pristine graphene.38 The larger friction coefficients are in good agreement with the slow flow rate in GO nanochannels.

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According to the above results, in our hydrophilic GO slit pores, there is enhanced interfacial friction resistance within the pore interior. This suggests that the entrance and exit effects might become weak to some extent. For example, in previous work,61 it was remarked that as interfacial friction within nanochannels increases, the pore end-effect will make a decreasing contribution. In addition, in our simulation system, the anchored functional groups on GO surface near the entrance could enhance the attractive interaction between water molecules and the channel entrance. This pressure loss in entrance, which is caused by breaking the network of hydrogen bonds in the bulk water, can be greatly compensated by increased interactions between water molecules and the functional groups near the hydrophilic entrance.70 Therefore, for the GO nanochannels with enhanced interfacial friction action, the resistance contribution due to end-effect probably becomes smaller, as compared with the hydrophobic pores with low friction. However, this remark needs to be confirmed and further comprehensive study is necessary. According to the GK relation, the friction coefficients can be rewritten as λ =< F 2 > ×τ F /( Ak BT ) ,55 where the decorrelation relaxation time τ F characterizes

the decay degree of the force-force autocorrelation function. It can be seen from Figure 8b that the plot of λ versus < F 2 > / A for water confined within GO slits shows approximate linear relationship, suggesting the change of the friction coefficients λ could be directly correlated with the mean-square force < F 2 > . The similar relation has been obtained for flow friction behavior in graphene.38,55 In our GO systems, the small relaxation time ( τ F =15 fs) signifies the fast relaxation of 20


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lateral force, probably due to the flexible nature of GO sheets. At present, the dependence of water friction coefficients on the pore sizes remains controversial in literatures.38,71 However, our result is consistent with the water friction confined in graphene slit pores38 and implies that for GO surface, the similar liquid-solid interaction strength holds for irrespective of pore widths. Actually, the large friction coefficients ( λ ) of water in the GO nanochannels are highly associated with the corrugation of the potential energy landscape ( ∆E )72 felt by the water molecules in the contact layer and an approximate relation holds with λ ∝ ∆ E 2 . Thus, we simulated the two-dimensional potential energy distributions between single water molecule in the contact layer and the GO surfaces. As shown in Figure 9, the energy landscapes of GOs are corrugated and undulated and the maximum energy difference can achieve 25 kJ/mol, which is dramatically distinct from the behavior in smooth, roughness-free pristine graphene channel.38,55,73 This might explain the extremely high friction undergone by water in the GO channels where the water permeates slowly. This simulation result is consistent with the previous observation74 that the retarded dynamics of intercalated water molecules in GO interlayer is due to the strong interaction of water with the surface functional groups. In Figure S8, the similar energy profiles of GO channels with different layer distances can explain the invariant friction coefficients. Meanwhile, from the potential landscape, the enhanced interaction strength causes the immobile water layer near the GO surfaces, which agrees well with the non-slip Poiseuille flow behavior exhibited above. As shown in Figure 9, it is observed that the GO2 energy profile is more 21



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corrugated than that of GO1, possibly due to more functional groups on the GO2 sheet. This is consistent with the relatively larger friction coefficient on GO2 nanochannel. We then decomposed the potential energy landscapes into the Coulombic and L-J contributions. The Coulombic energy ranges from -20 to 5 kJ/mol, while the L-J energy shows a small values ranging from -5 to 5 kJ/mol (Figure 9). This indicates that the electrostatic interaction from GO surfaces provides more significant influence on the friction coefficients.

Ion Rejection: As desalination membrane, we also evaluated the ion rejection for the GO nanochannels. Ion rejection (R) was calculated by the following equation, R = 1 − C1 / 2 / C 0 ,49 where C 0 is the initial ion concentration of feed solution and C1/ 2

is the concentration of permeated side when half water molecules transport through the membrane. As seen in Figure 10a, the ion rejection is 100% for the GO membranes with average interlayer distances smaller than 9.5 Å and no ions permeation through the GO membrane can be observed after 16 ns pressure-driven simulation. For the GO membranes with large interlayer distance, the salt rejection decreases with increasing the interlayer distance and the applied external pressure. The ion rejection performance for the GO nanochannels with largest interlayer distances is similar with the experimental results.11,45 For better understanding of ion rejection behavior in the GO pores, the number density profiles of ions along the flow direction (z-axis) are shown in Figure 10b for GO1-30 wt% membrane with the channel spanning approximately from 0 to 80 Å. It is observed that most ions accumulate in the left pore entrance and only a small 22


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fraction of ions can permeate into the GO pores. In particular, for the GO nanochannels with smaller pore sizes, no NaCl ions could enter into the pores during the simulation time. Overall, the ions are generally blocked by the pore entrance of GO channels and only few could struggle to permeate into. In general, the molecular mechanism of the ion rejection has been well recognized by the pore steric hindrance on hydration ions.40,75 When ion permeating into the GO pores, several water molecules should be peeled off due to the formation of hydration ions (for detail, see Figures S9, S10). This will result in the energetic penalty,40 which makes it difficult for ions to permeate into the membrane pores. With the increase of external pressure, the energy barrier is more easily overcome, thus the ion rejection decreases with increasing the applied pressure. We also made a supplementary simulation regarding the motion trajectories of several typical ions near the pore entrance during the non-equilibrium simulation. As shown in Figure S11, the ions always stay the region near the pore entrance with large position fluctuation, further exhibiting the slit pore has obvious size-sieving barrier on the ion permeation. In addition, the pore confinement makes ion translocation unfavorable within the GO membrane pores. Figure S12 shows the MSDs for several ions within the GO slit pores. The MSDs are noticeably smaller than those in the bulk reservoir. This result could provide further support to our conclusion. It has been demonstrated that ions in the GO channels usually feel surface attraction (Figure S13) which leads to less mobility of the ions. The slow mobility of ions will further enhance the ion rejection when passing through the GO pores. We find that the ion rejection in the GO1-40 wt% 23



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membrane, with smaller interlayer distance, is lower than that of the GO2-35 wt% membrane. This difference could be explained as the different pore surface interactions toward the ions. As seen in Figure S11, the Na+ and Cl- feel obvious surface attraction when confined within the GO pores and the surface interaction becomes increased for ions in the GO2 pore. Our simulation demonstrates that the GO-based nanochannels provide an effective barrier for ion transport. The laminate GO membranes with average pore width below 9.5 Å could achieve excellent NaCl rejection.

Conclusions In this work, MD simulation has been conducted to study water permeation and ion rejection in layer-by-layer assembled free-standing GO membrane. At first, we constructed the GO-based laminate membrane model by aligning flexible GO sheets paralleled to each other. The chemical structure of GO sheet was constructed based on the Lerf-Klinowski model. The GO channel width can be modified by initial interlayer water content and the obtained pore width corresponds to the typical pore size in actual GO laminate membranes. Water flow rate in the corrugated GO capillary channel is obvious lower than that observed in the channel between pristine graphene sheets. The water flow behavior in the GO channel with the Lerf-Klinowski chemical structures is quantitatively equivalent with the no-slip Poiseuille flow model without flow enhancement. Our simulated results suggest that, in some cases, the interlayer gallery formed by GO sheets could not serve as the major flow route for water permeation through GO membranes. Flow velocity of water in the GO channel is found to be around 0.1-1.7m/s with almost immobility near GO surfaces. The confined water structure in 24


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the flexible GO nanochannels has been shown in this work. Enhanced disordered and loose water structure is more obvious with the increase of oxidation degree and the undulated water structure in contact water layer caused by functional groups could suppress the water flow. The friction coefficient of water flow in the GO channel is two orders of magnitude higher than that for pristine graphene pores and it increases with the surface oxidation degree. The hydrogen bond interaction between water and functional groups is found to be responsible for the enhanced surface friction. The interaction energy landscape of GO surfaces has huge energy barrier felt by water and higher oxidation degree of GO surface causes more corrugated energy barrier. We finally evaluated the ion rejection when passing through the GO pores. Our result demonstrates that the laminate GO membranes with reasonable interlayer distances exhibit high ion rejection ability. The size-exclusion of ion-hydration and the ion affinity interaction from GO sheets provide the joint contribution to the ion rejection. Our result provides new understanding of water flow nature in GO-based laminate membranes and it is important in designing new functional nanofluidic devices.

Supporting Information Details of some simulation methods and supplementary figures. This material is available free of charge via the Internet at http://pubs.acs.org.

Notes The authors declare no competing financial interest.

Acknowledgments This work was supported by the National Natural Science Foundation of China under Grants 21376116, 973 National Basic Research Program of China (2015CB655301), Research funding from State Key Laboratory of Materials-Oriented Chemical Engineering (ZK201404), and A PAPD Project of Jiangsu Higher Education Institution. 25



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Figure 1. Lateral view of the simulation system of GO laminate membrane, showing that GO membrane was placed in the center of the box and two chambers on the both sides of the membrane. Simulation box is marked between two the blue dash line. Carbon atoms in GO sheets are shown as green plate, oxygen in red sphere, hydrogen in white, Na+ in blue, and Cl- in green, respectively.



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Figure 2. a,b) Water flux across the GO1 and GO2 nanochannels with different interlayer distances as a function of applied pressures difference. c) Water flow enhancement (ε) of GO1 and GO2 channels. d) Water permeability of two GO nanochannels as a function of the average interlayer distances, red for GO1 and blue for GO2.


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Figure 3. a,b) Two typical flow velocity profiles of water molecule in four water channels of GO1-40 wt% and GO2-40 wt% membranes. The red line indicates average velocity value. c) The average flow velocity of water molecules as a function of applied pressure for all GO membranes.



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Figure 4. Atomic snapshot structures of water molecules inside GO1 and GO2 nanochannels for different water contents under pressure-driven flow condition; the atomic density profiles along the thickness direction (y) for oxygen atoms (blue) and hydrogen atoms (red) of water molecules.


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Figure 5. The variation of the effective water densities as a function of the pressure difference applied to GO membranes during the infiltration process, left for GO1 and right for GO2. Water density was calculated on the basis of the effective interlayer distances.



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Figure 6. a) Probability distribution of HB between functional groups on both GO sheets and the neighboring water molecules. b) Intermittent HB correlation function CHB(t) (left) and continuous HB correlation function SHB(t) (right) functions of HB for water and functional groups on the graphene inside GO1 and GO2 nanochannels, solid line for hydroxyl and dash line for epoxy.


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Figure 7. a,b) Two-dimensional surface density distribution of oxygen atoms in water molecules whose location corresponds to the first atomic density peaks inside the GO1-40 wt% and GO2-40 wt% nanochannels. For a better understanding, corresponding GO sheet and functional groups are also shown, red circle for hydroxyl and yellow circles for epoxy.



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Figure 8. a) Friction coefficient for water within both GO1 and GO2 channels as functions of the interlayer distances. b) Function dependence of the friction coefficient versus the static mean-squared forces for all GO membranes. The decorrelation time τF is calculated from the slope.


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Figure 9. Typical interaction energy landscape felt by water molecule in the contact layer of water inside both GO nanochannels, left for GO1-40 wt% and right for GO2-40 wt%. The interaction energy is then decomposed into the Coulombic contributions (panels b,e) and the Lennard-Jones contributions (panels c,f).



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Figure10. a) Salt rejections for all GO1 and GO2 membranes versus the applied pressure. Lines of the GO membranes denoted as “other membranes” with smaller interlayer distances show the 100% ion rejection. b) Density profile of ions (Na+ and Cl-) along z-axis in GO1-30 wt% membrane. GO membrane spans approximately from 0 to 80 Å as GO model shown in the figure.


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Water Permeation and Ion Rejection in Layer-by-Layer Stacked

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