Article pubs.acs.org/JPCB
Molecular Dynamics Simulation of Water Transport Mechanisms through Nanoporous Boron Nitride and Graphene Multilayers Majid Shahbabaei and Daejoong Kim* Department of Mechanical Engineering, Sogang University, Seoul 121-742, Republic of Korea S Supporting Information *
ABSTRACT: In this study, molecular dynamics simulations are used to investigate water transport mechanisms through hourglass-shaped pore structure in nanoporous boron nitride (BN) and graphene multilayers. An increase in water flux is evidenced as the gap between the layers increases, reaching a maximum of 41 and 43 ns−1 at d = 6 Å in BN and graphene multilayers, respectively. Moreover, the BN multilayer exhibits less flux compared to graphene due to large friction force and energy barrier. In BN, the friction force dramatically increases when the layers are strongly stacked (d = 3.5 Å), whereas it would be independent of the layer separation when the layers are sufficiently spaced (d ≥ 5 Å). In contrast, it was shown that the friction force is independent of the layer spacing in graphene. On the other hand, water molecules across the BN exhibits larger energy barriers compared to graphene when the layers are highly spaced at d = 8 Å. Consistent with the result reported for the flux, the axial diffusion coefficient of water molecules in graphene increases with layer spacing, reaching a maximum of 6.8 × 10−5 cm2/s when the layers are spaced at d = 6 Å.
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INTRODUCTION Demand for potable water is increasing because of the reduction in reliable fresh water sources and increase in global population. Therefore, it is necessary to search for technologies that can convert nonconventional water sources into fresh water. Seawater is one such abundant source which can be reached by most of the countries in the world. In order to utilize seawater as potable water, it is required to remove the high salinity. Desalination technologies are intended for the removal of dissolved salts that cannot be removed by conventional treatment processes. Osmosis is the phenomenon of water flow through a semipermeable membrane that blocks the transport of salts or other solutes through the membrane. When two aqueous solutions are separated by a semipermeable membrane, water will flow from the side of low solute concentration to the side of high solute concentration. The flow is stopped, or even reversed by applying external pressure on the side of higher concentration. In such a case, the phenomenon is called reverse osmosis (RO). The major advantage of RO is the lower energy consumption due to the absence of an evaporation step. Although the transport in the solution circulating in the space between the membranes is important, it is the ion and water transport in the membranes that determine the performance of membrane process. Membranes emerged as a viable means of water purification in the 1960s with the development of high performance synthetic membranes. Implementation of membranes for water treatment has progressed using more advanced membranes © 2017 American Chemical Society
made from new materials and employed in various configurations. Millions of years ago, nature created biological membranes. The most important feature of a biomembrane is that it is a selectively permeable layer. This means that the size, charge, and other physio-chemical properties of the particles, molecules, atoms, or substances attempting to permeate it will determine whether they succeed or not. Membranes are developed to preferentially permeate species. For this reason, permeation tests are probably the most powerful technique to characterize membranes. The performance or efficiency of a membrane process is dictated by the permeability and selectivity of the membrane. Recently, novel membranes made by carbon nanotube (CNT) arrays have been investigated for desalination.1 Although many experimental and theoretical studies have demonstrated that CNTs allow fast molecule transport rate,2−7 the low salt rejection rate limits their industrial applications. In more recent theoretical and experimental studies, nanoporous graphene,8−13 graphene oxide,14,15 and MoS216 have shown that they could be used as highly selective and permeable filtration membranes. To date, only graphene and graphene oxide membranes have been extensively investigated as filtration membranes, a few groups attempted to study the BN monolayers. Compared to graphene, BN sheets exhibit high Received: December 19, 2016 Revised: February 28, 2017 Published: March 23, 2017 4137
DOI: 10.1021/acs.jpcb.6b12757 J. Phys. Chem. B 2017, 121, 4137−4144
Article
The Journal of Physical Chemistry B thermal conductivity and stability, electrical insulation, high chemical stability, and high resistance to oxidation.17−22 Recently, BN nanotubes have shown excellent water permeation potential compared to CNTs of similar length and diameter.23 Recent experimental studies on graphene oxide have shown that producing carbon material in molecular-level porous structure with well-tuned pore sizes and interlayer separations could be achieved.24−27 To date, most studies have considered water permeation or water desalination through monolayer systems with changing in several key parameters including nanopore size, chemistry, etc. However, a few studies have investigated water permeation properties through multilayer nanoporous membranes.28 Aquaporins (AQPs) have a homotetramer structure with each subunit having an hourglass shape. The unique shape of aquaporin water channels, suggesting an hourglass shape approximately 20 Å in length and 3 Å in the narrowest diameter at the center of the channel,29,30 plays a key role in fast water conduction. Understanding the mechanism of flow in aquaporin water channels can result in achieving high water permeation through semipermeable membranes. Recently, an experimental study using transmission electron microscope (TEM) tomography31 suggested that solid-state nanopores have an hourglass-shape more than a cylindrical structure. Our recent study showed that hourglass-shaped pore structure in multilayer nanoporous graphene (with constant layer separation) is suggested to be a more efficient design for achieving higher flux, compared to cylindrical pore. We also found that the hydrophilicity effect can double the flux inside hourglassshaped pore.32 In the present study, we investigate water transport properties through hourglass-shaped pores in multilayer nanoporous BN and graphene using MD simulation. In particular, we examine the interlayer spacing effect on fast water transport rate through BN and graphene multilayers.
Figure 1. Schematic of nanoporous (a) boron nitride (BN) and (b) graphene multilayers with layer separation of d, (c) in which constructed in an hourglass-shaped structure.
potential. The boron and nitride atoms in the BN and carbon atoms in the graphene layers were artificially set to be frozen (to reduce the computational cost) as well as uncharged particles. Lennard-Jones interactions between water molecules (oxygen) and graphene (C) and boron nitride (B and N) were set as σO−O = 0.3169 nm, εO−O = 0.1515 kcal/mol, σO−C = 0.3190 nm and εO−C = 0.0956 kcal/mol, and σB−O = 0.3311 nm, εB−O = 0.12465 kcal/mol, σN−O = 0.3267 nm and εN−O = 0.14965 kcal/mol, respectively. The long-range Coulomb interactions are considered using the Ewald method,37 and by applying SHAKE algorithm,38 the water molecules are held rigid. Over 2000 extended simple point charge (SPC/E) water molecules were simulated in the reservoirs for 1 ns to attain equilibrium state. Next, by applying 800 MPa pressure difference crossing the pores, nonequilibrium simulations were conducted for 1 ns to attain a steady-state system. Effective simulation data was obtained subsequently for 5−8 ns nonequilibrium simulations (separately for the layer separation of 3.5, 5, 6, and 8 Å for graphene and BN systems).
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SIMULATION MODELS AND DETAILS We performed MD simulations to investigate the layer separation (d) effect on water transport phenomena through hourglass-shaped pores in multilayer nanoporous boron nitride (BN) and graphene membranes. Graphene and BN samples were generated using VMD nanotube builder.33 The simulation models were symmetrically constructed by assembling seven BN and graphene monolayers by replicating the hourglassshaped aquaporin water channel with diameter changing from 5 to 8 Å, as shown in Figure 1. Graphene and BN layers were introduced by removing adjacent carbon atoms in the center of layer and selecting pores without sharp edges (see the Figure S1 of the Supporting Information for the details). The interlayer separation varies from d = 3.5, 5, 6, and 8 Å while connecting to a reservoir (31.9 × 34.3 × 30.0 Å3) filled by water molecules. Nonequilibrium MD simulations are implemented using the large-scale atomic/molecular massively simulator (LAMMPS).34 A constant external force f is applied on all water molecules inside the reservoir in z axial direction of the layers with the aim of modeling a pressure-driven flow.35 The simulations were performed in the NVE ensemble (constant number of water molecules, constant volume, and constant energy) with a dissipative particle dynamics (DPD) thermostat36 to maintain a constant temperature of 300 K. A time step of 0.5 fs is chosen in order to ensure accurate simulated behavior of water molecules between bulk region and layers. The periodic boundary conditions are applied in three dimensions. A cutoff of 10 Å is used for the Lennard-Jones (LJ)
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RESULT AND DISCUSSION Water molecules are pushed into the pore systems from the reservoirs by the applied pressure ΔP, which creates flux and permeability through the membranes. By counting the number of water molecules which completely pass the multilayers along the -z direction, the water flux was calculated. Figure 2 shows the variation of water flux as a function of the layer separation
Figure 2. Number of water flux as a function of layer separation. 4138
DOI: 10.1021/acs.jpcb.6b12757 J. Phys. Chem. B 2017, 121, 4137−4144
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The Journal of Physical Chemistry B
Figure 3. (a) RDFs between the oxygen of water (Ox) and boron (B) and nitrogen (N) of boron nitride and carbon of graphene (CG), and the RDFs between the oxygen of water molecules while crossing the BN and graphene with layer separation of (b) d = 3.5 Å, and (c) d = 8 Å.
discussed in the following. However, when the layers are sufficiently spaced (d ≥ 6 Å), the density distribution indicates virtually similar behavior in BN and graphene multilayers (see Figure S4 of the Supporting Information). The structure of water molecules in BN and graphene can be shown using radial distribution function (RDF).41 Figure 3a exhibits the radial distribution functions (RDFs) between the oxygen of water molecules (Ox) and boron (B) and nitrogen (N) of boron nitride and carbon of graphene (CG). Although, RDFs between water molecules and the atoms of the surfaces (a monolayer of BN and graphene) indicate identical shapes with a minimum located at the same position, the intensity of the RDFs of the BN surface suggests more favorable interplay between water and BN surface. It illustrates that the density increases in the vicinity of the BN surface in comparison to graphene. Therefore, such a very strong interplay between oxygen of water molecules and BN surface (high wetting feature of the BN layer) will reduce water transport rate, especially when the layers are strongly stacked (d = 3.5 Å). Figure 3b exhibits the RDFs between the oxygen of water molecules across the BN and graphene with layer separation of d = 3.5 Å. The RDF for graphene shows zero for a short distance which is due to strong repulsive forces. For both surfaces, the position of the first maximum and the magnitude of peaks are different which exhibits different hydration number. The first peak corresponds to the nearest neighbor
for BN and graphene multilayers. As the layer separation increases, the water flux increases, which is in agreement with the very recent study.39 It indicates that the water flux increases with increasing the layer separation, reaching a maximum of 41 and 43 ns−1 at layer separation of d = 6 Å for BN and graphene multilayers, respectively. When the layers are highly spaced (d = 8 Å), the water flux decreases in both the cases, suggesting that water flux is affected by the energy barrier of the layer separation. It is shown that the water flux through multilayer membranes could be maximized by tuning the layer spacing. Moreover, the graphene shows higher water flux compared to BN, in agreement with the very recent study on water permeation through bilayer BN and graphene.40 Our results suggest that two factors lead to flux reduction in BN compared to graphene which incorporate larger friction force and energy barriers as the gap between the layers increases, as explained later. When the gap between the layers is increased, the water density increases across the membranes as shown via the pair correlation functions (see the Figure S2 of the Supporting Information). When the layers are strongly stacked (d = 3.5 Å), the BN and graphene show less densities compared to other cases (d ≥ 3.5 Å) because there is no space for water molecules. In the case of small gap between the layers (d ≤ 5 Å), the BN shows lower density compared to graphene (see Figure S3 of the Supporting Information) due to the larger friction force and strong interplay between water molecules and wall surface, as 4139
DOI: 10.1021/acs.jpcb.6b12757 J. Phys. Chem. B 2017, 121, 4137−4144
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The Journal of Physical Chemistry B
Figure 4. (a) Friction force between water molecules and the surfaces as a function of time for the layer separation of 3.5 A. (b) Comparison of friction force between water molecules and the BN surface as a function of time with layer separation of 3.5 and 8 A. (c) Comparison of friction force between water molecules and the surface as a function of the layer separation.
shell, and the subsequent maxima suggest the subsequent nearest neighbor shells, which is highlighted for BN. Therefore, strong formation of bridges between water molecules and the BN layers can be understood when the layers are highly stacked (d = 3.5 Å). In addition, to show the layer spacing effect on hydration structure of the surfaces, the RDFs between the oxygen of water molecules were calculated when the layers are sufficiently spaced. Figure 3c shows the RDFs between the oxygen of water molecules crossing the BN and graphene in the case of the layer separation of d = 8 Å. In both surfaces, the RDFs for oxygen−oxygen start with small peaks at the same positions, showing high intensity for BN. However, the maximum peak of RDFs indicates higher intensity for graphene at different position in comparison to BN, which suggests larger hydration number in graphene multilayer. We believe that this phenomenon will potentially reduce the energy barriers (the vacant spaces between water molecules) between water molecules inside graphene, which is led to higher flux compared to BN when the layers are highly spaced (d = 8 Å). Friction force as an interfacial property plays a key role in understanding of transport mechanisms at nanoscale. Figure 4a shows the friction force between water molecules and the surfaces as a function of simulation time when the layers are
strongly stacked (d = 3.5 Å). We used the method described in the work,42 where the friction force equals the total tangential force of the pore atoms on the water molecules. Specifically, the friction force at a given time and position is computed as the sum of the forces acting on the wall atoms, estimated by the Lennard-Jones potential, in the flow direction for the corresponding time step. As shown in Figure 4a, the friction force on two surfaces differ drastically, with the larger friction force on BN surface. Although, in comparison to graphene, the friction force is larger for BN at the starting of the simulation, it dramatically increases after a short time (∼30 ps). Therefore, this large friction force can reduce the flow rate through BN multilayer in the case of highly stacked layers (d = 3.5 Å). In contrast, compared to BN, in graphene multilayer, the friction force indicates lower magnitude with no significant fluctuation during simulation. The inset shows the difference between the friction forces in BN and graphene before 30 ps simulation. This larger friction force for BN is in agreement with the very recent ab initio study about friction force of water on graphene and boron nitride sheets.43 A comparison of friction forces between water molecules and the BN surface with layer separation of 3.5 and 8 Å is given in Figure 4b. Although, at the starting of the simulation, the friction force is lower in the case 4140
DOI: 10.1021/acs.jpcb.6b12757 J. Phys. Chem. B 2017, 121, 4137−4144
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The Journal of Physical Chemistry B
Figure 5. Profiles of the potential mean force (PMF) for water molecules in BN and graphene multilayers with layer separation of (a) 3.5 Å and (b) 8 Å.
Figure 6. Free energy of occupancy fluctuation as a function of (a) number of water molecules and (b) number of hydrogen bonds inside BN and graphene multilayers with layer separation of d = 3.5 Å.
of d = 3.5 Å in comparison to d = 8 Å, the friction force on BN with layer separation of d = 3.5 Å drastically increases after a short simulation time (∼30 ps). On the other hand, whereas at the starting of the simulation, the friction force is larger for BN with layer separation of d = 8 Å, overall, it exhibits lower friction force during the whole simulation time compared to the strongly stacked layers (d = 3.5 Å). Therefore, it can be found that the friction force in BN multilayer highly reduces when the gap between the layers is sufficiently increased. To further show the friction force on the surfaces, the effect of interlayer spacing on friction force in BN and graphene multilayers is given in Figure 4c. The plot describes a comparison of friction forces between water molecules and the surfaces as a function of the layer separation. As shown in Figure 4c, the friction force decreases as the layer separation increases in BN multilayer. It also suggests that the friction force in BN will be independent of the layer separation when the layers are sufficiently spaced (d ≥ 5 Å). On the other hand, the plot describes that, qualitatively, the friction force in graphene multilayer will be independent of the interlayer distance. In addition, in the case of the layer separation of d = 3.5 Å, the BN multilayer indicates the larger friction force compared to graphene, which might come from
strong interplay between water molecules and boron and nitrogen of BN. To monitor the prospective of water permeation through BN and graphene multilayers, one can calculate the potential of mean force (PMF). Radial distribution function (RDF), g(x), describes how the atomic density varies as a function of the distance from one particular atom. Because density is another way to describe probability, so it is related to the PMF.44 In fact, we can generate the PMF from RDF, by using the relation PMF(x) = (−kBT)Lng(x). Figure 5 illustrates the profiles of the potential mean forces (PMFs) for water molecules crossing the BN and graphene multilayers with layer separation of 3.5 and 8 Å. As shown in Figure 5a, when the layers are strongly stacked (d = 3.5 Å), the graphene shows larger PMF compared to BN. However, when the layers are sufficiently spaced (d = 8 Å), the BN shows larger energy barriers (more empty spaces between water molecules which suggests a weak interaction between them) compared to graphene. In the case of d = 3.5 Å, although the BN shows lower energy barriers compared to graphene, it exhibits smaller water flux, which corresponds to larger friction force. As shown in Figures 4c and 5b, it can be found that the friction force rather than the energy barrier has a dominant 4141
DOI: 10.1021/acs.jpcb.6b12757 J. Phys. Chem. B 2017, 121, 4137−4144
Article
The Journal of Physical Chemistry B
Figure 7. (a) Axial diffusion coefficient of water molecules and spatial variation of n in graphene and BN multilayers with layer separation of 3.5 Å. (b) Axial diffusion coefficient of water molecules and spatial variation of n in graphene multilayer with layer separation of 3.5 Å.
48 molecules, 41 being the most probable. Compared to BN, the higher occupancy of the graphene multilayer can be attributed to the weak interactions between water−water and water−wall, as seen from the results presented for RDFs. Figure 6b indicates the free energy of occupancy fluctuation as a function of the number of hydrogen bonds inside BN and graphene multilayers with layer separation of d = 3.5 Å. As shown in Figure 6b, an enhancement of water density between the BN layers can be found. The wetting characteristics of water on BN surfaces, which comes from the preferential interplay between water molecules and surface, will increase the number of hydrogen bonds close to the BN surfaces, as seen from the result presented for RDF. In this case, a high tension between the BN layers would have occurred, as Garnier et al. have shown in their study for the bilayer BN. Diffusion plays a key role in water transport in confined environments. The axial diffusion coefficient of water molecules can be computed from the mean square displacement (MSD) of the center of mass of the water molecules, using
