Observation and Analysis of Water Transport through Graphene Oxide

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Observation and Analysis of Water Transport Through Graphene Oxide Interlamination Bo Chen, Haifeng Jiang, Xiang Liu, and Xuejiao Hu J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b09753 • Publication Date (Web): 03 Jan 2017 Downloaded from http://pubs.acs.org on January 8, 2017

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The Journal of Physical Chemistry

Observation and Analysis of Water Transport Through Graphene Oxide Interlamination

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 Water transport inside graphene-based materials has drawn much attention nowadays because of its promising potential in ions filtration applications. Using Molecular Dynamics (MD) simulations, we investigated the mechanism of water transport inside the interlayer gallery between graphene oxide layers. The model of slipped-Poiseuille flow was cited to depict the characteristic transport of interlayer flow. This significant flow rate was related to slip velocity of water, which is constrained by hydrogen interactions between water molecules and hydroxyl groups. We find that hydrogen-bond networks are correlated with both functionalization and nanoconfinement. MD simulation results show that the slip velocity is negatively correlated with oxide concentration while independent of the array of hydroxyl groups, and the volumetric flux is linearly dependent to the slip velocity. It reveals that graphene oxide layers could get better water permeability after reduction.

INTRODUCTION Water is the backbone of industry, agriculture and economy all over the world.1 With the striking growth of population and industrial activities, freshwater and energy scarcity are the most severe challenge in the 21st century.2-3 Thus, water desalination is expected to play an increasingly crucial role to provide fresh and sustainable water for many water stressed communities and industrial sectors. 1

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Desalination processes are generally classified as thermal or membrane based technologies. Membrane process, such as reverse osmosis (RO), has been more prevalent in industrial development for several decades mainly due to its energy efficiency contrast to other desalination methods.4 However, there are some limitations in the use of these membrane methods, such as self-contamination, huge power requirements, low water permeability and so on.5 Nowadays many nanostructured materials have been investigated to improve the process of water purification. In particular, graphene-based membrane is identified as one of the most promising material for water desalination because of its outstanding ions filtration, high water permeability, feasible fabrication of functional group and so on.4-8 Surwade et al. manufactured nanoporous graphene (NPG) membrane through bombarding the suspended graphene by gallium ions and electrons, and they observed that water could pass through the NPG membrane quickly while the salt rejection could be 100% by controlling the radius of the nanopore.9 Using molecular dynamics simulations, Grossman have investigated that NPG membrane with pores decorated by hydrogen atoms or hydroxyl could not only effectively enhance the rejection of ions but also improve the permeation of water.10 Besides, NPG membranes with pores doped specific atoms can also be utilized for filtration and separation of mixed gases.11-13 Graphene oxide has been found recently as another membrane suitable for desalination because of its ease of fabrication, mechanical strength and industrial scale production compared to ordinary graphene sheets.14-17 Many researches have proved that the graphene-based membrane have excellent properties of salt selectivity and water permeability.18-19 In the work of Nair et al.12, mass leakage tests have been performed using spin-coating graphene oxide membranes. These sub-micrometer thick membranes are almost completely impermeable to gases like helium but allow unimpeded permeation of water vapor. Sun et al. have investigated a series of solutes in water through graphene oxide membranes and concluded that the heavy metal salts got the weakest permeability.15 The theoretical research related to water flow across multilayer graphene membranes have been explored by Yoshida via numerical simulation.20 They showed that results for the permeability calculated by continuum hydrodynamic

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model are in agreement with those obtained by MD simulations. All of researches above have demonstrated the outstanding transmembrane permeability of water, but it is still obscure in the mechanism of mass transport interlaminated graphene or graphene oxide sheets. In this work, we performed pressure-driven flow simulations to reveal the nature of interlayer flow between the graphene oxide sheets and to clarify the influence of surface functionalization in combination with layer distance on water permeation. The model of slipped-viscous flow is cited to elucidated the dynamics of fast water flow between the pristine graphene layers, while flow enhancement is reduced by hydrogen bonds between the surface and water molecules in graphene oxide sheets.20-21 We find that hydrogen-bond networks are correlated with both functionalization and nanoconfinement.

THEORY Interlayer water transport between graphene oxide sheets can be considered as the slipped Poiseuille flow confined between two flat plates separated by a distance d. Generally, the velocity profiles of no slip flow is parabolic:

=

∆

(

− ℎ )

(1)

where ∆p, η, l, D and h denotes for the pressure difference, the viscosity of water, the length of plates, the distance between two plates and the location perpendicular to the plate, respectively. The volumetric flux Q can be estimated by the integral of the velocity function:

= −

3


(2)


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where dp/dx expresses for the pressure gradient along flow direction and W is the width of the plate. In Refs. 12-14, the fast mass transport upon graphite sheet or through carbon nanotube is often attributed to the low-friction and super-lubricity phenomenon during water flow. Graphene oxide can be considered as two parts. The pristine graphene region, enhances the flow like water-graphite/water-carbon nanotube system. The oxidic region, reduces the enhancement of transport, because the hydrogen bonds between water molecules and hydroxyl groups capture the flowing water molecules near the wall and increase the friction between fluid and boundary. Therefore, interlayer flow between graphene oxide gallery is the coupling of super-lubricity flow and viscous flow. The flux ratio of part slippage flow to no slip flow can be estimated as: !"

= 1 + % /(−

)

(3)

where vs is the slip velocity, related to the concentration of oxide. With the growth of oxide concentration, the increasing number of hydrogen bonds apply stronger interaction between graphene walls and water molecules as well as reduce the effect of slipped-boundary and the slip velocity.

SIMULATION MODEL The molecular structure of graphene oxide generally consists of hydroxyl, epoxy, carbonyl groups, defective sites and open edges on the pristine graphene plane.14, 22 The hydroxyl groups are investigated in this work because they were reported to be able to remain rich in the long-living quasi-equilibrium state.23-24 The initial configuration was water sandwiched between two graphene oxide sheets, as shown in Figure 1a. The molecular structure of graphene oxide is presented in Figure 1b. For oxidized domain of graphene oxide, we constructed hydroxyl function groups at concentration c = nOH / nC ranged from 0 (pristine graphene) to 25%, where nOH and nC are the number of hydroxyl groups and carbon atoms, respectively. Different layer distances of capillary channels at c = 10% were also performed in this study.

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There were 1200, 1800, 2400, and 3000 water molecules inserted initially corresponding to interlayer distance h of 1.1, 1.5, 1.9, and 2.3 nm, respectively. Besides, the influence of uniform and random distribution of hydroxyl groups was investigated as well. Molecular dynamics (MD) simulations were performed using the LAMMPS package.25 The simulation system dimensions are 15×3×3 nm in x, y, z, respectively, where period boundary conditions were used on all dimensions. The all-atom optimized potentials for liquid simulations (OPLS-AA) were used for graphene oxide, which are widely used to capture essential many-body terms in interatomic interactions. The rigid simple point charge effective pair (SPC/E) model were used for water molecules. Both of them include van der Waals and electrostatic terms.23-24, 26 The potential parameters of atoms are given in Table 1. The characteristic length σ and energy parameter ε between water molecules and carbon atoms were obtained by the common Lorentz-Berthelot combination rule.27 The van der Waals interactions are truncated at 1.2 nm, and the long-range Coulomb interactions are computed by utilizing the particle-particle particle-mesh (PPPM) algorithm.28 We performed the pressure-driven water flow by directly adding forces to water molecules in nonequilibrium molecular dynamics simulations, which was widely used to investigate fluid flow.24, 29 The simulation process lasted for a sufficiently long time (4 ns) at 298 K to reach equilibrium, and the sample evolved for 1 ns for data collection. The coordinates and velocities of all the atoms were recorded every 50 ps to get converged results. All the MD simulations were performed in constant number of particles, volume and temperature (NVT) ensemble. The post-processing was made by Visual Molecular Dynamics (VMD)30 and The Open Visualization Tool (OVITO).31

Table 1. Potential Parameters of Atom Atom

σ（Å）

ε（Kcal/mole）

C（C-C）

3.851

0.105

C（C-OH）

3.550

0.070

5



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O（C-OH）

3.070

0.170

H（C-OH）

0.000

0.000

O（H2O）

3.166

0.1553

H（H2O）

0.000

0.000

(a)

(b)

Figure 1. Atomic structure of graphene oxide (a) Initial configuration of simulation (b) Structure of graphene oxide sheets. Gray, red, white and pink spheres represent for carbon atoms, hydrogen atoms and oxygen atoms in hydroxyl, hydrogen atoms and oxygen atoms in water molecules, respectively.

RESULTS AND DISCUSSION We specifically noted that the pressures applied in our works were significantly greater than the pressures employed in RO plants (< 8 MPa).10 To obtain precise data for water flux in a finite simulation 6


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time, a high simulated pressure on the order of ~1000 MPa was performed in this simulation. To justify this approach’s reasonability, we investigated the water flow driven by different applied pressures ranged from 11.1 MPa to 850 MPa, which was interlaminated between graphene oxide sheets with the same interlayer distance and oxide concentration (h = 1.9 nm, c = 10%). The velocity profile at every pressure obviously presented the characteristic of parabolic distribution as shown in Figure 2. It reveals that the model of Poiseuille flow is also suitable for low pressure drop. In Figure 3, the linearity of water flux scaling with driving pressure insured that results obtained at high pressure can be extrapolated to calculate the water flux from lower net driving pressures in an RO system. Especially, the circle dot in Figure 3 represents for the pressure we performed in the simulation of different oxide concentration and interlayer spacing followed.

Figure 2. Velocity profiles along z axis for different pressures ranged from 10 MPa to 850 MPa.

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Figure 3. Volumetric flux as a function of applied pressure, where the square scatters represents for the MD simulation results and the dash dot line denotes for the fitting plot of relation between flux and driven pressure. Especially, the circle dot represents for the pressure in the simulation followed.

We have investigated the effects of oxide concentration and interlayer spacing in detail. The representative snapshots of water flow between graphene sheets and graphene oxide layers are illustrated in Figure 4. It is observed that water flows in the channel of graphene sheets with the formation of 0.05nm-thick vacuum region along the gallery walls. It is mainly due to the hydrophobic interaction between water and graphene, which induces fast water transport by low-friction and super-lubricity within the pristine graphene channels. In contrast, water molecules are easy to attach on the hydrophilic oxidic regions because of the hydrogen bonds between water molecules and hydroxyl groups. These arguments were made by assuming that the reduced capillary driven flow sandwiched between graphene oxide layers breaks down the expected flow enhancement. In order to quantify the effect of oxidic regions on pristine graphene sheets on water transport, variable concentrations of hydroxyl groups are monitored during the simulation, and the well8


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characterized velocity profiles are exhibited in Figure 5. It is clearly shown that the velocity profile for flow changes from low curvature (c < 10%) to parabolic one at high c values, and the parabolic viscous flow characteristics covered all the concentrations with some fluctuations when it is greater than 10%. The parabolicity of velocity profile implies that the viscous flow between parallel plates in continuum hydrodynamics, which can be calculated by the Poiseuille solution of the Navier-Stokes equations. Specially, at c = 0, namely water flow between graphene sheets, the velocity profile is nearly planus, showing the unimpeded water transport in basal graphene nanochannels. In contrast, the hydroxyl groups would reduce the enhancement of water flow.

(a)

(b)

Figure 4. Represented snapshots of water flow (a) Interlayer flow between graphene oxide (b) Interlayer flow between graphene. Red, white, pink, blue and light yellow spheres represent for carbon atoms, hydrogen atoms and oxygen atoms in hydroxyl, hydrogen atoms and oxygen atoms in water molecules, respectively.

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(a)

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(b)

Figure 5. Velocity profiles along z axis for different oxide concentration (a) c = 0-0.1 (b) c = 0.1-0.25

To obtain the flux of water through the graphene oxide layers with slipped-boundary, we get the function of velocity profiles by parabolic fitting, and the volumetric flux Q can be estimated by integral of velocity function as shown in Figure 6a-d. The slip velocity as a function of c values is exhibited in Figure 6e. It is obvious that the flux and slip velocity are negatively correlated with oxide concentration while they get little fluctuation at high values, in consistent with Poiseuille flow. The flux ratio as a function of slip velocity is presented in Figure 6f, and the profile is linear as predicted in Eq. (3). It follows that water transport between graphene oxide layers has great relationship with hydroxyl groups on basal plane. Besides, the velocity profiles of uniform and random array of hydroxyl groups at the same oxide concentration of 5% (c = 0.05) on graphene-derived sheets have been monitored as shown in Figure 7. There are little differences in distribution of velocity along z axis, and thus it reveals that water diffusion is independent of the arrangement of functional groups at the same oxide concentration.

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(a)

(b)

(c)

(d)

(e)

(f)

Figure 6. (a)-(d) Velocity function at low concentration (e) Relationship between concentration and slip velocity (f) Relationship between flux ratio and slip velocity.

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Figure 7. Velocity profiles along z axis for different array of hydroxyl groups, where the red and black curve denote for random and uniform array, respectively, and the inserted pictures are molecular structure of two kind of graphene oxide sheets (c = 0.05).

In addition to the oxide concentration, the interlayer spacing also has a great influence on the water transport. The interlayer diffusion was performed through a range of layer distances from 1.1 nm to 2.3 nm. For all of layer distances, H2O molecules behave as the same of those in bulk water and continuum flow. Figure 8 shows the velocity profiles of water flow sandwiched between different layer distances. The average value of velocity increases along with expanding the interlayer spacing because the flow velocity is cubic relation with distance between layers according to Eq. (1). In order to estimate the permeability of variable interlayer spacing, a characteristic permeation parameter Lp was defined as Lp=Q/ (W∆P), where Q is the volumetric flux, W is the width of plates and ∆P is the driven pressure. Volumetric flux is calculated by integral of velocity function in Figure 8 and the width of plates and the driven pressure are set at the initial configuration. As presented in Figure 9, these scatters are obtained by MD simulation and the solid line represents for theoretical calculation of viscous flow. The value of 12


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Lp in large layer spacing is greater than theoretical prediction because there are more hydrogen interactions in small interlayer distance and it can enhance the resistance of water flow near wall between two sheets.

Figure 8. Velocity profiles distributed along z axis through different layer distances

Figure 9. Permeation parameters as a function of interlayer distance, where the scatters denote for the

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MD simulation results and the line represents for theoretical calculation of viscous flow.

More evidence about interactions between water molecules and graphene oxide sheets are exhibited in number density profiles and pair correlation functions. The distribution of number density of water molecules in z direction through variable layer distances is presented in Figure 10. More molecules lie near the interlamination interface than the center of interlayer because the hydrogen interactions make water molecules bound to hydroxyl groups during flow and it is also the reason why flow velocity is almost 0 near the boundary. Water molecules at the center of interlayer can be considered as free flow with low friction in the study of Devanathan’s group.21 The number density of free molecules increases with the expanding layer distance, which means the impeditive interactions from hydroxyl groups to water transport are less at larger interlayer spacing. Figure 11 exhibits the pair correlation functions between hydroxyl groups oxygen atoms (Og) and water oxygen atoms (Ow) and that between hydroxyl group hydrogen atoms (Hg) and water oxygen atoms (Ow) for different layer distances. The Ow-Og distribution has a first peak at 0.27 nm indicating strong interactions between water molecules and hydroxyl groups. With expanding the interlayer spacing, the height of this peak decreases, which shows less molecules binding to hydroxyl groups. A similar trend is seen in the Hg-Ow pair correlation function and the longer range structure as well as the second and subsequent peaks starts to disappear, indicating that water molecules move away from hydroxyl groups and perform free flow. Therefore, the hydrogen interactions will be reduced and the water flow rate will be enhanced through large-distance gallery. That’s the reason why permeation parameter function deviated from theoretical cubic-relation calculation of viscous flow. Overall, our results indicated that graphene oxide could act as a high-permeability membrane for water filtration. For illustrative purposes, the theoretical performance of interlayer flow between graphene oxide (GO) (c = 0.15) as well as reduced graphene oxide (RGO) (c = 0.05) in our simulations is plotted in Figure 12, by contrast with the experimental performance of commercial reverse osmosis

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(RO) membranes from Pendergast et al32 and nanoporous graphene (NPG) from Grossman et al10. The water permeability of five kinds of RO membranes (MFI Zeolite, seawater RO, brackish RO, nanofiltration and High-flux RO) is not exceeding 1 L/cm2/day/MPa and that of NPG ranged from 39 to 66 L per cm2·day·MPa. The interlayer flow examined in this work could reach a 3-4 orders of magnitude higher than commercial RO.

Figure 10. Number density profiles of water through different interlayer distances

Figure 11. Pair correlation functions between (a) oxygen atoms in hydroxyl groups and water molecules

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(b) hydrogen atoms in hydroxyl groups and oxygen atoms in water molecules for the different interlayer distances

Figure 12. Performance chart for interlayer flow between GO as well as RGO versus functionalized nanoporous graphene and existing technologies.

CONCLUSIONS This article has performed slipped-viscous flow interlaminated between graphene oxide sheets using Molecular Dynamics simulations. Water transport can be enhanced through the graphene oxide gallery at low oxide concentration, while the flow velocity and volumetric flux in this flow regime are greater than that in classical Poiseuille flow. It is the hybrid flow of two characteristic transport mechanism. In one way, water contacting on hydrophobic graphene surface will form a 0.05-nm-thick vacuum layer, which greatly eliminates the friction between water and boundary while enhances the flow rate through

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the interlamination. In another way, the hydrogen interactions between water molecules and hydroxyl groups hinder the molecules flow near graphene oxide surface, and thus make velocity of water flow tend to parabolic distribution. The simulation results reveals that the enhanced flow rate is negatively correlated with the oxide concentration as well as hydrogen interactions below an oxide concentration of 10%, while is consistent at variable concentration of high values. It is mainly because of the limited contact area between water and boundary surface, and thus it reaches the saturation of hydrogen bonds at high concentration. We find that hydrogen-bond networks are correlated with both functionalization and nanoconfinement. It tends to yield more hydrogen bonds at high oxide concentration and in narrow interlayer space, but it is independent to the arrangement of hydroxyl groups. These results presented will be useful in understanding the nature of water transport through graphene oxide interlamination and can be utilized to predict and design innovative reverse-osmosis membrane for desalination.

ACKNOWLEDGEMENTS The authors acknowledge the support of the National Natural Science Foundation of China (No. 50906064) and the Fundamental Research Funds for the Central Universities (No. 2042016kf0023).

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Behavior of Graphene Oxide Aqueous Solutions: A Comparative Experimental and Molecular Dynamics Simulation Study. Langmuir 2012, 28, 235-41. (24) Wei, N.; Peng, X.; Xu, Z. Understanding Water Permeation in Graphene Oxide Membranes. ACS Appl. Mater. Inter. 2014, 6, 5877-5883. (25) Plimpton, S. Fast Parallel Algorithms for Short-Range Molecular Dynamics. J. Comput. Phys. 1995, 117, 1-19. (26) Jorgensen, W. L.; Maxwell, D. S.; Tirado-Rives, J. Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids. J. Am. Chem. Soc. 1996, 118, 11225-11236. (27) van Gunsteren, W. F.; Weiner, P. K.; Wilkinson, A. J. Computer Simulation of Biomolecular Systems: Theoretical and Experimental Applications; Springer Science & Business Media, 2013; Vol. 3. (28) Hockney, R. W.; Eastwood, J. W. Computer Simulation Using Particles; CRC Press, 1988. (29) Wei, N.; Peng, X.; Xu, Z. Breakdown of Fast Water Transport in Graphene Oxides. Phys. Rev. E 2014, 89, 012113. (30) Humphrey, W.; Dalke, A.; Schulten, K. VMD: Visual Molecular Dynamics. J. Mol. Graph. Model. 1996, 14, 33-38. (31) Stukowski, A. Visualization and Analysis of Atomistic Simulation Data with Ovito-the Open Visualization Tool. Model. Simul. Mater. Sci. Eng. 2009, 18, 015012. (32) Pendergast, M. M., Hoek E. M. V. A Review of Water Treatment Membrane Nanotechnologies. Energy Environ. Sci. 2011, 4, 1946-1971.

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TOC Graphic

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Figure 1. Atomic structure of graphene oxide (a) Initial configuration of simulation. Gray, red, white and pink spheres represent for carbon atoms, hydrogen atoms and oxygen atoms in hydroxyl, hydrogen atoms and oxygen atoms in water molecules, respectively. 299x118mm (300 x 300 DPI)


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Figure 1. Atomic structure of graphene oxide (b) Structure of graphene oxide sheets. Gray, red, white and pink spheres represent for carbon atoms, hydrogen atoms and oxygen atoms in hydroxyl, hydrogen atoms and oxygen atoms in water molecules, respectively. 299x118mm (300 x 300 DPI)



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Figure 2. Velocity profiles along z axis for different pressures ranged from 10 MPa to 850 MPa. 210x177mm (300 x 300 DPI)


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Figure 3. Volumetric flux as a function of applied pressure, where the square scatters represents for the MD simulation results and the dash dot line denotes for the fitting plot of relation between flux and driven pressure. Especially, the circle dot represents for the pressure in the simulation followed. 34x26mm (600 x 600 DPI)



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Figure 4. Represented snapshots of water flow (a) Interlayer flow between graphene oxide. Red, white, pink, blue and light yellow spheres represent for carbon atoms, hydrogen atoms and oxygen atoms in hydroxyl, hydrogen atoms and oxygen atoms in water molecules, respectively. 152x72mm (300 x 300 DPI)


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Figure 4. Represented snapshots of water flow (b) Interlayer flow between graphene. Red, white, pink, blue and light yellow spheres represent for carbon atoms, hydrogen atoms and oxygen atoms in hydroxyl, hydrogen atoms and oxygen atoms in water molecules, respectively. 152x73mm (300 x 300 DPI)



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Figure 5. Velocity profiles along z axis for different oxide concentration (a) c = 0-0.1 214x177mm (300 x 300 DPI)


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Figure 5. Velocity profiles along z axis for different oxide concentration (b) c = 0.1-0.25 218x177mm (300 x 300 DPI)



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Figure 6. (a)-(d) Velocity function at low concentration. 69x57mm (600 x 600 DPI)


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Figure 6. (e) Relationship between concentration and slip velocity. 35x28mm (600 x 600 DPI)


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Figure 6. (f) Relationship between flux ratio and slip velocity. 69x57mm (600 x 600 DPI)



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Figure 7. Velocity profiles along z axis for different array of hydroxyl groups, where the red and black curve denote for random and uniform array, respectively, and the inserted pictures are molecular structure of two kind of graphene oxide sheets (c = 0.05). 255x177mm (300 x 300 DPI)


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Figure 8. Velocity profiles distributed along z axis through different layer distances. 214x173mm (300 x 300 DPI)



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Figure 9. Permeation parameters as a function of interlayer distance, where the scatters denote for the MD simulation results and the line represents for theoretical calculation of viscous flow. 35x26mm (600 x 600 DPI)


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Figure 10. Number density profiles of water through different interlayer distances. 259x177mm (300 x 300 DPI)



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Figure 11. Pair correlation functions between (a) oxygen atoms in hydroxyl groups and water molecules. 220x177mm (300 x 300 DPI)


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Figure 11. Pair correlation functions between (b) hydrogen atoms in hydroxyl groups and oxygen atoms in water molecules for the different interlayer distances. 222x173mm (300 x 300 DPI)



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Figure 12. Performance chart for interlayer flow between GO as well as RGO versus functionalized nanoporous graphene and existing technologies. 34x21mm (600 x 600 DPI)


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TOC Graphic 85x40mm (300 x 300 DPI)


Observation and Analysis of Water Transport through Graphene Oxide

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