Molecular Dynamics of Equilibrium and Pressure-Driven Transport

Sep 11, 2013 - (29) Insight into the effects of varying surface chemistry on the pressure-driven flow may aid the design of systems with good surface ...
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Molecular Dynamics of Equilibrium and Pressure-Driven Transport Properties of Water through LTA-Type Zeolites Salomon Turgman-Cohen,† Juan C. Araque,† Eric M. V. Hoek,‡ and Fernando A. Escobedo*,† †

Department of Chemical and Biomolecular Engineering, Cornell University, 120 Olin Hall, Ithaca, New York 14853-5201, United States ‡ Department of Civil & Environmental Engineering and California NanoSystems Institute, University of California Los Angeles, 5732 Boelter Hall, Los Angeles, California 90095-1593, United States S Supporting Information *

ABSTRACT: We consider an atomistic model to investigate the flux of water through thin Linde type A (LTA) zeolite membranes with differing surface chemistries. Using molecular dynamics, we have studied the flow of water under hydrostatic pressure through a fully hydrated LTA zeolite film (∼2.5 nm thick) capped with hydrophilic and hydrophobic moieties. Pressure drops in the 50−400 MPa range were applied across the membrane, and the flux of water was monitored for at least 15 ns of simulation time. For hydrophilic membranes, water molecules adsorb at the zeolite surface, creating a highly structured fluid layer. For hydrophobic membranes, a depletion of water molecules occurs near the water/zeolite interface. For both types of membranes, the water structure is independent of the pressure drop established in the system and the flux through the membranes is lower than that observed for the bulk zeolitic material; the latter allows an estimation of surface barrier effects to pressure-driven water transport. Mechanistically, it is observed that (i) bottlenecks form at the windows of the zeolite structure, preventing the free flow of water through the porous membrane, (ii) water molecules do not move through a cage in a single-file fashion but rather exhibit a broad range of residence times and pronounced mixing, and (iii) a periodic buildup of a pressure difference between inlet and outlet cages takes place which leads to the preferential flow of water molecules toward the low-pressure cages.

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INTRODUCTION The transport properties of liquids and gases through zeolitic materials have been extensively studied due to their potential applications in gas separations,1 pervaporation2−5 and reverse osmosis.6 Depending on pore structure, zeolite membranes7−9 can compete with the standard membrane solutions in these applications. Although there is much experimental10−13 and numerical14 research on the diffusion of gases and liquids within bulk zeolitic materials, the same cannot be said of pressure-driven transport through zeolite membranes. Envisioned reverse osmosis and pervaporation processes based on zeolite membranes operate under hydrostatic pressure drops, and information on the fluxes achievable under the operating conditions of these unit operations can aid in the design and development of such separation systems. In the field of reverse osmosis, interfacially polymerized polyamides are enhanced by addition of LTA zeolite nanoparticles,15 and the resulting thin film nanocomposite (TFN) membranes exhibit 2−3 times higher permeability relative to pure polyamide membranes while maintaining similar salt selectivities.15−18 LTA zeolites consist of a three-dimensional pore structure including large cavities (∼11 Å diameter) termed α-cages and smaller ones (∼6 Å diameter) termed β-cages. The α-cages are separated by rings of 4−5 Å in diameter consisting © 2013 American Chemical Society

of eight oxygen atoms (8R windows). A hypothesized explanation for the increased water permeability observed in nanocomposite thin films is preferential flow of water through zeolite molecular sieve pores.17,18 Such a hypothesis could be directly tested by attaining sufficient insights into the mechanisms and rates of pressure driven water flux through pure LTA zeolite films. Pure zeolite membranes have been investigated as potential materials for reverse osmosis and pervaporation. Kumakiri et al. hydrothermally synthesized LTA membranes and performed permeation experiments of a 10% ethanol in water solution at various pressures.19 They found water permeability an order of magnitude lower than commercially available polymeric membranes.6 Their membranes were stable to hydrostatic pressure drops of 4 MPa. Pera-Titus et al. investigated similar membranes supported by a porous, hollow α-alumina support for water/ethanol dehydration separations. Water fluxes of 0.2 kg m−2 h−1 were reported at room temperature with a 80% (mol/mol) water feed.20 Cho and co-workers investigated pervaporative desalination of seawater and pure water using Received: December 20, 2012 Revised: September 5, 2013 Published: September 11, 2013 12389

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Figure 1. Snapshot of simulation cells used for pressure driven flow simulations. In the shaded blue areas a constant external force is applied on all water oxygen atoms. The yellow areas are defined as the membrane with a thickness of 24.555 Å and correspond to the regions at which the flux is measured. Green spheres represent zeolite framework atoms, and orange ones represent Na+ ions.

LTA membranes and reported water flux data and rejection percentage for a number of ionic species found in seawater.21 Fluxes for pure water were 0.241 kg m−2 h−1 at 42 °C. Finally, Li et al. investigated the performance of MFI zeolite membranes (∼3 μm thickness) in desalination applications. For a 0.1 M NaCl solution, the water flux was 0.112 kg m−2 h−1 at a 2 MPa applied pressure drop.22 Although experimental measurements are crucial to gauge the performance of the zeolite membrane, they may not provide intrinsic transport properties of zeolitic crystals; all known experimental studies to date involved polycrystalline membranes with nonzeolitic pores though which water and ions could bypass the zeolite internal pore structure. In this respect, computer simulations could enable elucidation of molecular transport through defect-free zeolite membranes and, therefore, approximate the intrinsic properties of the zeolite in question. In addition, computer simulations have been used to investigate the equilibrium permeation through biological,23 nanotube,24 and simplified model pores.25 In some cases, intermittent pore permeation was observed,25 a phenomenon consistent with some of our results. One of the first simulation studies of zeolite systems is due to Lin and Murad,26 who simulated the flow of water through a ZK-4 membrane driven by osmotic pressure. The osmotic pressure gradient was created by two membranes that separated regions of high and low salt concentrations. Recently, the pressure-driven flux of salt water solutions (0.5 M NaCl) through zeolitic imidazolate framework-8 (ZIF-8) membranes was investigated by nonequilibrium molecular dynamics (MD) simulation.27 Two graphene plates acted as pistons inducing a pressure drop across the membrane. Water fluxes in the order of to 105 kg m−2 h−1 for pressure drops from 50 to 150 MPa, which are several orders of magnitude larger than what has been experimentally reported with LTA type materials. However, no experimental data are available for such systems, and the large fluxes simulated seem surprising given the hydrophobicity of ZIF-8 and the narrow cavities connecting the larger pores (3.4 Å in diameter). During the time frame of the simulation (10 ns) no Cl− or Na+ ions permeated the ZIF-8 membrane, suggesting their suitability in reverse osmosis, water desalination applications.27 Interfacial properties of thin film membranes are also important for their performance, and it is well-known that strong structuring of water is observed at the hydroxyl-capped

LTA surface.28 The role of water structuring on pressure-driven transport of water and solutes through zeolites is, to our knowledge, unexplored. In membrane design, chemical surface modification is becoming a key element in tailoring membrane properties such as their resistance to fouling.29 Insight into the effects of varying surface chemistry on the pressure-driven flow may aid the design of systems with good surface properties and efficient water flow. In this article, we use nonequilibrium molecular dynamic (MD) simulations to investigate pressure driven transport through bulk and thin membranes of LTA zeolite. We tested two end-capping chemistries for the membrane models: one hydrophilic (hydroxyl terminated) and one hydrophobic (ethyl terminated). By comparing the measured water flux in bulk vs membrane systems, we can estimate the effect of the water/ zeolite interface on the pressure-driven flow and provide some insight into the feasibility of using zeolite membranes in waterbased separation systems. By varying the end-capping chemistry of the zeolite film, we are also able to probe the effect on pressure-driven transport between hydrophilic and hydrophobic membranes. Finally, we explore qualitatively the mechanism of the pressure-driven transport through LTA type membranes.

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MODELS AND METHODOLOGY Bulk Zeolite at Equilibrium. We modeled one full cubic unit cell (side length of 24.555 Å) of LTA with periodic boundary conditions. To better match the zeolite chemistry to those used in TFN membrane experiments,30 we use a model zeolite framework with Si/Al = 1.67 that follows Lowenstein’s rule.31 This modification leads to a less negative framework and to a lower number of Na+ ions needed to balance the system charge. It also results in a slight asymmetry in the distribution of Si and Al atoms in the membrane, a feature that will be relevant when interpreting our results. We adopt the potentials of Faux and co-workers32−34 with the exception that the threebody potential is replaced by a truncated Vessal version.35 The net negative charge of the model zeolite framework is balanced by the presence of 72 Na+ ions.10,32 The zeolite structure was hydrated by adding up to 224 water molecules (fully hydrated unit cell) by means of Monte Carlo insertions.36 We implement the SPC/E water model37 as a rigid framework with a bond length of 1.0 Å and tetrahedral HOH angle. For nonequilibrium simulations of the pressure-driven transport in the bulk 12390

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Figure 2. Simulation snapshots. (a) Shows a single water molecule occupying each of the middle 8R windows. Spheres in yellow represent silicon, red oxygen, and pink aluminum. The blue molecules represent water, and the gray cylinders are the framework atom connectivity. (b, c) Side view of OH and CH2CH3 terminated zeolite surfaces, respectively. The sizes of the atoms represent in a scaled manner the van der Waals radius perceived by a water oxygen atom. Additional views of the interface and rings can be found in refs 28 and 38.

barostat only applied to the water molecules. This was necessary so that the barostat does not deform the zeolite framework while achieving the target pressure. The time constants for the barostat and thermostat were 0.5 ps, which are in the typical range for SPC/E water simulations. Equilibrium MD in the NPT ensemble was performed at 298 K and 1 atm, and NVT simulations were performed on the NPT-preequilibrated systems. The Ewald summation technique with a precision of 10−6 was used to calculate the long-range electrostatic interactions. Quaternions were used to keep the water molecules rigid with an error tolerance of 10−5. For the simulations of the hydrophobically modified zeolite, the SHAKE algorithm with a tolerance of 10−8 was used to fix the bond length between Al/Si, CH2, and CH3 groups. Nonequilibrium simulations of pressure-driven flow were performed in (i) a membrane system with hydrophilic interfaces, (ii) a membrane system with hydrophobic interfaces, and (iii) the bulk zeolite system; the setup for each of these scenarios is described in turn below. For the membrane systems, we induce pressure-driven flow by first submerging the fully hydrated membrane in a bath of 1980 water molecules. We double the number of water molecules relative to the equilibrium simulations to limit the effect of the external force to an area far away from the zeolite membrane. The simulation cell thus constructed is then NPT equilibrated at 298 K and 1 atm until the bulk water density is recovered away from the zeolite. During subsequent NVT simulations, a constant external force was applied along the z direction on the oxygen atoms of all water molecules located in the first and last 5 Å of the simulation cell (see top frame in Figure 1). With this approach we can readily calculate the pressure drop across the membrane as44,45

material, three full cubic unit cells of hydrated LTA were used (Figure 1). Thin Zeolite Membrane. We obtained the zeolite membrane by disrupting the periodicity of a single bulk unit cell in the Z direction. Atoms were added so that the membrane was D4R (double four oxygen rings) terminated on both sides, and the orientation of these double rings was perpendicular to the surface.38 The resulting structure is not fully coordinated, and 32 hydroxyl groups (16 of each side of the membrane) are added to complete it (Figure 2b). The {1,0,0} surface is the most stable surface as determined by electron/force microscopy experiments28 and the second most stable according to lattice minimization calculations.38 The potentials and charges assigned to the OH groups were obtained from the work of Baram and Parker.39 Addition of the capping OH groups yields a zeolite framework that in combination with the Na+ ions carried a net negative charge. This excess charge was redistributed among the oxygen atoms of the zeolite framework resulting in a deviation of 0.1% from the original oxygen charge. The hydrated zeolite slab was submerged in a bath of 990 water molecules, and the equilibrium properties of water in and around the zeolite were determined. To investigate a less polar surface, we construct a membrane in which the hydroxyl groups are replaced with hydrophobic, united-atom ethyl groups (Figure 2c). The charges used for the united-atom ethyl group and the carbon bonded silicon and aluminum atoms were obtained from Abraham et al.40 by scaling the original charges on Si and Al by a fixed factor and keeping the charge ratios of Si to CH2 constant. The LennardJones parameters for the united atoms were obtained from the OPLS41 force field, and the rest of the force field parameters were obtained from the work of Zhang et al.42 We note that this is a simplistic description of a hydrophobic-modified zeolite membrane and that our main objective is a qualitative assessment of the surface effects when the surface/water interaction is weaker. Methodology. All simulations were performed with the DL_POLY 2.20 and DL_POLY Classic packages.43 Simulations were conducted in the NVT and NPT ensembles with a Nose−Hoover thermostat/barostat. We modified the NPT routine in DL_POLY to control the pressure by changing only one dimension (z) of the simulation cell and so that the

ΔP =

Fzn w Axy

(1)

were Fz is the magnitude of the applied force, nw is the number of water molecules to which the external force is applied, and Axy is the area of the xy-plane of the simulation cell. We have also determined the pressure drop using equation of state data46 and report these results as Supporting Information. For the pressure-driven simulations a thermostat time constant of 12391

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where μz is the z component of the dipole moment and |μ| is the magnitude of the dipole moment vector. The function cos(θ) can discriminate between water molecules with dipoles preferentially pointing in the positive or negative z direction, and SZ can identify dipoles that are parallel (SZ = 1) or perpendicular (SZ = −0.5) to the z-axis. The profiles were calculated by binning the simulation cell in 0.5 Å intervals and averaging within the bins. The flux of molecules during pressure driven-flow was measured by counting the number of water molecules crossing xy-planes at the entrance, middle, and exit of the zeolite membrane for at least 15 ns and averaging the results. For the bulk zeolite, the mid-unit cell in the model was taken as the effective “membrane” for evaluating the flux. The error in the flux was estimated by using a variable number (depending on equilibration and production times) of 1 ns simulation blocks. The system was assumed at equilibrium when the difference between 1 ns blocks exhibited no systematic drift (see Supporting Information). The flux at lower imposed pressure drops is difficult to measure due to the low number of water crossing events during the simulation. To illustrate this point, experimental measurements of LTA membrane permeability are on the order of 10−19 m2 Pa−1 s−1, which would require approximately 120 ns for a single molecule crossing event at ΔP = 0.1 MPa, a prohibitively long simulation. We define the entrance and exit of the zeolite membrane as the locations of the 8R (Figure 2) windows and not the end positions of the capping hydroxyls or united atom ethyl groups. The flux (JZ), applied pressure drop (ΔP), and thickness (LZ) of the zeolite may be used to measure permeabilitythe flux normalized by the pressure drop per unit thickness.

0.1 ps was used to remove heat from the system effectively. The magnitudes of the external force applied correspond to pressure drops in the range 50−400 MPa. These large pressure drops are necessary because the water permeability through LTA membranes is low, and it would take prohibitively long simulations to measure it at experimentally relevant pressures (see discussion below). To oppose the applied external force and prevent the zeolite framework from drifting, a quartic potential acts on the atoms of the zeolite framework to constrain them to their initial position while maintaining their ability to undergo thermal vibration. The quartic potential is chosen due to its softness at small displacements and hardness at large displacements relative to the harmonic alternative. Note that end-capping hydroxyl and ethyl groups are not constrained by the quartic potential. Similar methods for nonequilibrium MD have been previously used to investigate water transport through biological membranes with transmembrane pores44,45 and of Lennard-Jones fluid through slit pores of various geometries.47 Compared to the method of Hu et al.,27 the approach implemented here allows the simulation to reach a stationary steady state at which the flux can be measured. Furthermore, the external force only perturbs the system in a small area away from the zeolite, preventing nonphysical artifacts in the properties of interest. Finally, the method is easy to implement requiring only small modifications to the external force subroutines of the DLPOLY 2.20 package. The method, however, does not permit the structure of the zeolite to vary in response to the applied pressure (due to the constraining forces). This is also the reason that the zeolite framework does not collapse under such heavy load. The method then assumes that the zeolite membrane is stable no matter the pressure drop applied across it. For the bulk zeolite, we induce and measure a flux in a manner analogous to that of the membrane systems. An external force is applied to the first and last 5 Å of a periodic simulation cell consisting of three unit cells of the LTA framework (see bottom frame in Figure 1). The resulting system has a dimension in the z direction of 73.665 Å, and the external force is applied along approximately 13% of the system’s volume. The perturbations extending from the region where the external force is applied could introduce some unphysical effects in a small simulation cell like ours. However, as we will show below for the membrane systems, the small 8R windows of the zeolite framework seem to compartmentalize the simulation cell and to prevent the pressure drop to affect the water structuring inside the zeolite material. Data analysis for the bulk, equilibrium system involved the measurement of the hydration energy and the estimation of the diffusivity of water molecules inside the zeolite by monitoring their mean-squared displacement. For membrane simulations, we gain insight into the structure of water near the zeolite surface by computing profiles of the density, the projection of the water dipole in the z direction, cos(θ), and the orientational order parameter (SZ) as a function of the position along the z coordinate. The last two parameters are defined as cos(θ) =

SZ =

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RESULTS AND DISCUSSION Equilibrium Properties of Water in Bulk LTA. We compute the hydration energy of bulk LTA at Si/Al = 1.00 for comparison to previously published results. We use the dehydrated zeolite as a reference state and compare the energy of the system as the water load increases. The energy of water molecules as a function of water loading is shown in Figure 3 and is almost identical to that reported by Faux et al.34 We can estimate the hydration energy per mole of water by the slope of a line fit to the data. At Si/Al = 1.00 the heat of hydration is 69 kJ/mol while at Si/Al = 1.67 it is 65 kJ/mol. We also compute the diffusion coefficients (DH2O) by measuring the meansquared displacement of the water molecules during 5 ns of simulation time. For Si/Al = 1.67, we observe that as a function of water loading DH2O first increases (at low loading) and then decreases (at high loading). The reason for this maximum in DH2O is well-known.34 Once the initial water molecules have adsorbed at the most energetically favorable adsorption sites, subsequent molecules adsorb to sites with smaller binding energies, resulting in an overall increase in diffusion. When all adsorption sites are occupied, water molecules can only diffuse from adsorption sites to interstitial sites that would not be occupied at the lower energy state, resulting in a decrease of overall mobility at high loadings. Our water diffusion results are 1 order of magnitude lower than those of Faux et al.34 and seem to be most consistent with experimental data from ref 49 but less so with experimental data from other reports.10,48,49 They also exhibit the expected trend as the Si/Al ratio increases. The difference with the diffusion results of Faux et al. may be due to several factors

μZ |μ ⃗ |

3 cos(θ ) − 1 2

(2)

(3) 12392

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Nonequilibrium simulations of the bulk, hydrophilic membrane, and hydrophobic membrane systems were performed to study the properties of water in and around the zeolite and to calculate the water flux. Figure 5 shows the

Figure 3. Energy of the zeolite water system (top) and the selfdiffusion coefficient of water (bottom) as a function of water loading (top) inside the bulk zeolite. The numbers in the legend represent the Si/Al ratio.

including the truncated form of the three-body potential used in this work and the different thermostatting methods. The diffusion of water within the zeolite framework was also monitored as the temperature was varied (Figure 4). At Si/Al =

Figure 5. Pressure drop (top), flux (middle), and permeability (bottom) for the LTA zeolite membrane system.

pressure drop, fluxes, and permeabilities as a function of the external force for the three systems investigated. We measure a lower pressure drop (in Figure 5, top panel) in the bulk systems relative to the membrane due to the lower number of molecules the external force acts on (relative to the membrane systems). In both hydrophilic and hydrophobic membranes, ΔP increases linearly with the applied force. The flux as a function of ΔP decreased in the order bulk > hydrophilic > hydrophobic system. This suggests that surface barrier effects could play a role in pressure-driven transport through LTA membranes. As the flux becomes more accurate (at high ΔP), we measure the permeabilitythe flux normalized by the membrane thickness and driving forceto compare it to experimental values. For the hydrophilic membrane the permeability is 1.58 × 10 −19 m 2 Pa −1 s −1 , which agrees well with the experimentally6,19,22 determined one of ≤10−19 m2 Pa−1 s−1 for similar, but much thicker, membrane systems. In contrast, the hydrophobic membrane has a permeability 3 times lower, indicating that surface barrier effects may play a more significant role in resisting flow in this case. This result contrasts many observations for other pore systems in which hydrophobic membranes exhibited higher permeations due to their lack of affinity for the water molecules. An explanation for this difference is that in our study only the surface of the membrane has been hydrophobized while the internal surface of the pores remains hydrophilic. We did not compute a permeability for the bulk system since its membrane thickness is not well-defined. If one assumes, however, that the equivalent thickness of our bulk system is the thickness of the three unit

Figure 4. Self-diffusion coefficient of water inside the bulk zeolite as a function of temperature. The numbers in the legend represent the Si/ Al ratio.

1.67 we observed higher water diffusion coefficients, indicating a higher mobility of water in the silicon-rich zeolite framework, which may lead to improved transport properties in the system. This observation is in agreement with pulsed field gradient NMR measurements10 and is consistent with the observed decrease in the heat of hydration for higher Si/Al ratio: such zeolites contain lower number of cations that bind water strongly, likely enhancing the mobility of adsorbed water molecules. 12393

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measures exhibit almost identical profiles inside the zeolitic material, indicating that our modifications preserved the integrity of the membrane and only altered the surface region. In both hydrophilic and hydrophobic cases, the density of water far away from the zeolite surface decays to the value for the pure SPC/E water model. The fact that water in between the zeolite surface and the external force region behaves like bulk water is an indication that a sufficiently large “buffer” zone exists to relax away any direct perturbation of the external force on water structure. (Given the small isothermal compressibility of water, the higher upstream pressure caused by the external force should only translate into a very small increase in water density.) Just outside the zeolite surface we observe a series of density peaks and valleys as has been previously observed.38 For the hydrophilic membrane, the peak nearest to the surface has a maximum density approximately 50% higher than bulk water. We attribute the observed flux decrease relative to the bulk membrane to the formation of this adsorbed water layer. To illustrate why these layers contribute to a reduced membrane flux, we computed the residence time of water in the density peak region and compare it to that of bulk water (see Supporting Information). For the hydrophilic membrane and a 50 MPa pressure drop, the average residence times of water were 42.5, 134, and 160 ps for bulk, upstream peak, and downstream peak, respectively. These observations suggest that water in the high-density peak region is more structured and less mobile, creating a free energy barrier to flow. A similar, yet lower density, peak appears in the case of a hydrophobic membrane. If our explanation above were complete, a larger flux for the hydrophobic membrane would be expected relative to the hydrophilic one. As we saw in Figure 5, this is not the case. To explain this, we note the development of a depletion region near the surface of the hydrophobic zeolite (at ±15 Å) where the water density is nearly zero. This depletion layer develops due to the water repelling nature and the large excluded volume of the ethyl groups. We posit that the combined effects of this depletion region and the highdensity adsorbed water contribute to the lower permeability of the ethyl-capped membrane. We note that an unintended consequence of hydrophobizing the membrane is a higher mobility of Na+ ions located near the edges of the zeolite. Some of these sodium ions drift from their equilibrium positions, further obstructing the 8R windows and restricting the water flow. The dipole moment, cos(θ), and order parameter (SZ) also exhibit interesting trends. In the case of the hydrophilic surface, cos(θ) does not decay to the bulk value of zero, instead decaying to a small value. We attribute this residual polarization to the high polarity of the zeolite surface and the limited size of the simulation cell, although it may also partially reflect that water molecules may flow more efficiently for certain dipole moment orientations. However, the lower polarity of the hydrophobic surface allows the water to reach its bulk value. At the zeolite surface, we also observe the formation of peaks and valley in these properties. For both hydrophilic and hydrophobic membranes, we observe that the water dipole moment is, on average, pointing along the positive z-direction at the zeolite inlet while it points in the negative z-direction at the zeolite outlet. This indicates that water align in a similar fashion relative to the zeolite surface and combined with the peaks observed in the SZ profile we can deduce that the water hydrogen atoms point toward the zeolite surface in these regions. This effect appears stronger in the hydrophobic zeolite,

cells, then the permeability of the bulk is approximately 16 times that of the surface at ΔP ≈ 100 MPa. Using this estimate and assuming a resistance-in-series type mass transfer model (see eq S1 in Supporting Information), we extrapolate that a membrane with 50 times the thickness of the one modeled here would have an equivalent overall mass transfer coefficient 4 times smaller than the thin membrane we simulated. While surface barriers will expectedly be less important to permeability for thicker membranes, one should keep in mind that a cross-flow among zeolite cells occurs (violating the resistance-in-series scenario), and additional surface barriers may also appear at interfacial grain boundaries in the bulk regions. Our results can be put in the context of the TFN membranes developed by Hoek and co-workers17 with the caveat that our model is approximate and does not reflect the complex chemical environment within TFN membranes: the measured permeability for the zeolitic membranes are roughly 1 order of magnitude lower than those of pure polyamide films.6 Thus, our simulations suggest that preferential flow paths through the zeolite particles may not explain the enhanced permeabilities observed in TFN membranes. An alternative hypothesis is that preferential flow paths do occur around the zeolite particles and not through them. The larger fluxes observed in the composite films may be due to molecular-scale voids between the nanoparticles, to changes in polyamide cross-linked structure and film morphology50 (for high rejection TNF membranes), and may also be related to their apparent resistance to physical compaction relative to pure polymeric analogues.51 To explore the possible reasons for the decreased water flux through small zeolites frameworks relative to bulk zeolites, we look at the density, z-component of the dipole moment, and the order parameter of the water molecules as a function of the z-coordinate (Figure 6). These parameters should provide insight into surface induced structuring of water. All three

Figure 6. Concentration (top), cos(θ), and SZ as a function of position along the z-axis for bulk (green), OH-terminated (black), and CH2CH3-terminated (red) zeolite membranes. The blue dotted lines represent the approximate location of the 8R windows and the property values for pure bulk water. 12394

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but the peaks correspond to the aforementioned water depletion region, and therefore, just a few molecules exhibit the strong directional preference. Figure 7 shows the density, cos(θ), and SZ as a function of the applied external force. As expected, we observe a difference

Figure 8. Left: schematic representation of list of water crossing event through 8R windows for the OH-capped system at ΔP = 400 MPa. The different colors represent the set of cages at which a particular water molecule entered the zeolite. The sequence of symbol shapes represents the order in which the molecules crossed the particular 8R window. Single-file motion of water molecules would have resulted in conserved color and symbol sequences, going from left-to-right, along successive (same label) cages. Right: depiction of the relative positions of the different cages (appearing as cubes for simplicity) as marked in the left panel; note that periodic boundary conditions apply along the x- and y-axes.

Figure 7. Concentration (top), cos(θ), and SZ as a function of position along the z-axis and ΔP. On the left side ΔP = 0 MPa (black), 50 MPa (red), 100 MPa (green), 200 MPa (magenta), and 400 MPa (blue). On the right side ΔP = 0 MPa (black), 50 MPa (red), 100 MPa (green), 150 MPa (magenta), and 200 MPa (blue).

in bulk water density between the membrane’s upstream and downstream regions. This is due to the pressure drop generated across the membrane by the external force. We also highlight the similarity between the equilibrium systems and the membranes with an applied external force. The “fingerprint” region inside the zeolite is almost invariant as a function of ΔP, indicating the external force has no effect in the way the water structures in and around the zeolitic membrane. We now focus on a tentative characterization of the mechanism of water transport through LTA zeolite. These zeolites are composed of large α-cages (∼11 Å in diameter) separated by small windows composed of rings of oxygen atoms (8Rs, ∼4−5 Å in diameter).10 These 8R windows are known to form a steep diffusional barrier for larger nonpolar molecules such as alkane chains.14 Water however fits through these 8R windows, and snapshots of our simulations indicate that a single water molecule occupies each 8R windows at a time (see for example Figure 2). The water molecules occupying the 8R windows are stable in their positions, and they can spend substantial time until a different water molecule displaces them. A possible transport mechanism is then single-file diffusion (like in narrow carbon nanotubes), in which water molecules push each other one-by-one until they can displace the ones occupying the 8R windows. However, true single-file diffusion is an unlikely scenario due to mixing of water within the α-cages of the zeolite structure and interdiffusion of water molecules along the nonflow axes. To confirm this, we show a number of molecules that traversed all three sets of 8R windows of the zeolite membrane (entrance, middle, and exit; Figure 8) during the ΔP = 400 MPa hydrophilic simulation. We also divided the zeolite membrane into four pairs of coupled cages (one after the other in the z direction) to see if single-file diffusion is, in effect, happening. Each shape and color represents a unique

particle. The shape indicates the order in which the water molecules entered the zeolite membrane and the colors indicates in which of the four upstream 8R windows they entered the zeolite. As depicted in the figure, the order in which the molecules cross the three different planes varies. Furthermore, we observe a number of molecules entering through one pair of cages and exiting through a different one, indicating intercage switching in the x and y directions and effectively ruling out single-file diffusion as a mechanistic description. To further characterize the transport kinetics of water though the zeolite, we obtained the residence time distribution for water molecules inside a single α-cage (based on 588 events where a molecule entered a cage through one channel and exited through another). For reference, we also plot in Figure 9a the distributions corresponding to the limiting ideal flow behaviors of a plug-flow reactor (PFR) which has the narrowest distribution and a continuously stirred tank reactor (CSTR) which has the broadest distribution. Perfect single-file diffusion is consistent with plug-flow since in such a case we would expect water molecules to spend approximately the same amount of time inside a zeolite cage. In Figure 9a we see instead that each α-cage roughly approaches the CSTR behavior, indicating significant mixing of water molecules within the zeolite cages. Note that since the number of water molecule per cage is small (∼30), stochastic fluctuations have a strong influence on the distribution of residence times. Interestingly, some water molecules move through a cage 12395

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circles). As time progresses, the difference between the number of molecules in the inlet and outlet cages oscillates, and most crossing events across the central set of 8R windows seem to occur when there are more molecules in the inlet cages than in the outlet ones. Intermittent permeation of water in simple pore models in equilibrium was also observed in a previous simulation study,25 suggesting that this phenomenon could arise from the fluctuations needed at the ends of a narrow channel for water molecules to fill it. In our case, the pressure gradient likely controls the frequency of such fluctuations, and we hence suggest a pulsating mechanism in which the internal pressure in the inlet cages builds up until a water molecule is able to displace the water molecule occupying a central 8R window. Since it is difficult to compute an internal cage pressure, we explore the differences in water occupancy between inlet and outlet cages. To this end, we compute the joint occupancy distributions in inlet and outlet cages by counting the number of molecules in the cages at each time step and building a two-dimensional histogram of the inlet and outlet occupancies. Figure 11 shows contour plots of these distributions at various pressures and for hydrophilic and hydrophobic membranes. For hydrophilic membranes, we detect a buildup of water molecules in the inlet cages of the zeolite relative to the outlet cages as evidenced by the appearance of the contour curves below the diagonal. This observation is true even in the ΔP = 50 MPa case for which a net forward flux cannot be measured in the time frame of our simulation. Furthermore, we observe a steady shift of the center of the contour plot further below the diagonal, indicating that the likelihood of observing higher occupancy in the inlet cages relative to the outlet cages increases with the pressure drop. In the case of the hydrophobic membrane, the trends are not as clear. There is an asymmetry in the populations of inlet and outlet cages even at equilibrium conditions (ΔP = 0 MPa) with the outlet cages showing larger water occupancy. This is a direct consequence of the aforementioned asymmetric distribution of Al and Si atoms in the zeolite structure (a consequence of increasing the Si/Al ratio). This asymmetry is accentuated in the case of the hydrophobic system since the Al and Si atoms attached to the ethyl groups have scaled charges compared to Si/Al atoms in the bulk zeolite. Furthermore, lower charges at the surface of the zeolite result in some of the Na+ ions drifting from their equilibrium positions and into the α-cages and 8R windows. These two effects explain the

Figure 9. (a) Representative plot of the normalized residence time distribution for the zeolite membrane. The data are for the hydrophilic system at ΔP = 200 MPa. The mean residence time is τ = 7120 ps. The dotted and dashed lines represent the distributions for the limiting cases of a plug flow reactor “PFR” representing single-file motion (a delta function) and a continuously stirred tank reactor “CSTR” (an exponential decay ∼ e−t/τ/τ), respectively. (b) Water trajectories for events with residence times approximately equal to 0.1τ (left) and 1.0τ (right).

quickly while others are stuck inside for very long times, resulting in a very broad range of residence times that underscore a diversity of transition pathways. Figure 9b shows sample trajectories of such fast and slow water molecules. In Figure 10, we show the number of water molecules (smoothed by averaging over 50 consecutive simulation snapshots) approximately occupying the four sets of coupled α-cages. We also label events in which a water molecule jumps in the forward direction from inlet to outlet cages (black

Figure 10. Smoothed water population for inlet (red) and outlet (green) cages as a function of simulation time for the 400 MPa hydrophilic membrane. From top to bottom cages A, B, C, and D. The circles represent water crossings through 8R window events. 12396

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Figure 12. Average difference between water occupancy in the inlet and outlet cages when a positive flux was registered across the middle 8R windows (black squares), a negative one (red circles), and for the entire data set (green triangles) for the hydrophilic (left) and hydrophobic (right) membranes. The dotted line represents the average population difference at ΔP = 0 MPa. The error bars correspond to one standard deviation.

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CONCLUSIONS Herein, we modeled pressure-driven water transport through zeolite membranes with hydrophilic and hydrophobic surfaces. Relative to the bulk zeolite, both hydrophilic and hydrophobic membranes exhibit lower fluxes, suggesting the presence of surface barriers to water flow. We found good agreement between simulated fluxes through hydrophilic zeolites and experimental measurements of similar, albeit much thicker, zeolite membranes. For both hydrophilic and hydrophobic membranes, we found dense water regions near the zeolite surface, whereas a water depletion layer also formed near the hydrophobic zeolite surface. The dense water layer creates a barrier because water molecules therein are pinned and more ordered. A low water density trough (well below the bulk density) signals a hydrophobic region that water molecules tend to avoid. The combination of dense and sparse water density regions near the hydrophobic membrane is consistent with its lower permeability compared to that of the hydrophilic membrane. Inside zeolite crystals, uniaxial single-file diffusion of water (i.e., as in aligned carbon nanotubes) appears unlikely due to significant intracage mixing and intercage diffusion perpendicular to the axis defined by the applied pressure gradient. By monitoring the joint probability distribution of water occupancy in inlet versus outlet cages and the occurrence of flow events, we find evidence to support a spontaneous pulsating mechanism wherein a periodic buildup of a pressure difference between inlet and outlet cages takes place, leading to preferential flow of water molecules toward the low-pressure cages. This cyclic behavior is more apparent in the case of the hydrophilic membrane. The importance of several design factors became apparent when considering the effect of zeolite interface chemistry on water transport, which may warrant further investigation. As indicated before, interfacial structuring of water molecules at the zeolite surface may play a significant role in the pressure driven transport across the membrane. In the case of hydrophobically capped zeolites, diffusion of the cations resulted in partial obstruction of the flow pathways, potentially reducing the permeability of the hydrophobic material and

Figure 11. Contour histograms of the joint distribution of water occupancy in outlet vs inlet cages. Left panels: from top to bottom for the hydroxyl-capped membrane ΔP = 0, 50, 100, 200, and 400 MPa. Right panels: for the ethyl-capped membrane ΔP = 0, 50, 100, 150, and 200 MPa. The dotted diagonals are the inlet = outlet lines.

asymmetric occupancy of the hydrophobic zeolite. Charge asymmetry effects and large fluctuations in water occupancy values notwithstanding, the contour plots for the hydrophobic membrane do not exhibit a clear trend with varying pressure drop. The presence of the ethyl groups and the severe water depletion layers at the zeolite surface seem to prevent a clear coupling between ΔP and the water occupancy data. To support the hypothesis of a pulsating mechanism, we look at the correlation between water occupancy data and the flux events observed during the simulation. Specifically, we partition the water occupancy data set in cases in which a net forward or a net backward flux was observed across the middle set of 8R windows and obtain the average occupancy for these partitioned data sets. In the hydrophilic case, we observe similar trends to those in the contour plots, with the difference between inlet and outlet cages increasing with the pressure drop (Figure 12, left). We also observe a definite correlation between the water occupancy differences depending on forward or reverse net flux events. In the case of forward flux, we observe a larger difference relative to the full data set while the opposite is true in the case of the reverse flux. This is strong evidence supporting a pulsating flow mechanism. The same observation is true of the hydrophobic membrane, although as with the contour plots, no clear trend with pressure drop is observed. Surface barrier effects have been previously attributed to entrance52 or exit barriers.53 Since the water structuring around the zeolite remained symmetric and systematic differences between entrance and exit fluxes were not detected in our system, it is unclear whether entrance or exit effects were dominant in slowing down the transport across the membranes; in fact, our results suggest that entrance and exit barriers are comparable contributors. 12397

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(5) Bowen, T. C.; Noble, R. D.; Falconer, J. L. Fundamentals and Applications of Pervaporation through Zeolite Membranes. J. Membr. Sci. 2004, 245, 1−33. (6) Pendergast, M. T. M.; Hoek, E. M. V. A Review of Water Treatment Membrane Nanotechnologies. Energy Environ. Sci. 2011, 4, 1946. (7) Bein, T. Synthesis and Applications of Molecular Sieve Layers and Membranes. Chem. Mater. 1996, 8, 1636−1653. (8) Caro, J.; Noack, M. Zeolite Membranes − Recent Developments and Progress. Microporous Mesoporous Mater. 2008, 115, 215−233. (9) Caro, J.; Noack, M.; Kölsch, P.; Schäfer, R. Zeolite Membranes − State of Their Development and Perspective. Microporous Mesoporous Mater. 2000, 38, 3−24. (10) Kärger, J.; Ruthven, D. M. Diffusion in Zeolites and Other Microporous Solids, 1st ed.; Wiley: New York, 1992; p 605. (11) Ruthven, D. M. Diffusion in Zeolitesa Continuing Saga. Adsorption 2010, 16, 511−514. (12) Wang, R.; Baran, G.; Wunder, S. L. Packing and Thermal Stability of Polyoctadecylsiloxane Compared with Octadecylsilane Monolayers. Langmuir 2000, 16, 6298−6305. (13) Brandani, S. In Adsorption and Phase Behaviour in Nanochannels and Nanotubes; Dunne, L. J., Manos, G., Eds.; Springer: Dordrecht, 2010; pp 195−212. (14) Smit, B.; Maesen, T. L. M. Molecular Simulations of Zeolites: Adsorption, Diffusion, and Shape Selectivity. Chem. Rev. 2008, 108, 4125−84. (15) Jeong, B.-H.; Hoek, E. M. V.; Yan, Y.; Subramani, A.; Huang, X.; Hurwitz, G.; Ghosh, A. K.; Jawor, A. Interfacial Polymerization of Thin Film Nanocomposites: A New Concept for Reverse Osmosis Membranes. J. Membr. Sci. 2007, 294, 1−7. (16) Ghosh, A. K.; Hoek, E. M. V. Impacts of Support Membrane Structure and Chemistry on Polyamide−Polysulfone Interfacial Composite Membranes. J. Membr. Sci. 2009, 336, 140−148. (17) Lind, M. L.; Ghosh, A. K.; Jawor, A.; Huang, X.; Hou, W.; Yang, Y.; Hoek, E. M. V Influence of Zeolite Crystal Size on ZeolitePolyamide Thin Film Nanocomposite Membranes. Langmuir 2009, 25, 10139−45. (18) Lind, M. L.; Jeong, B.-H.; Subramani, A.; Huang, X.; Hoek, E. M. V. Effect of Mobile Cation on Zeolite-Polyamide Thin Film Nanocomposite Membranes. J. Mater. Res. 2009, 24, 1624−1631. (19) Kumakiri, I.; Yamaguchi, T.; Nakao, S. Application of a Zeolite A Membrane to Reverse Osmosis Process. J. Chem. Eng. Jpn. 2000, 33, 333−336. (20) Pera-Titus, M.; Fité, C.; Sebastián, V.; Lorente, E.; Llorens, J.; Cunill, F. Modeling Pervaporation of Ethanol/Water Mixtures within “Real” Zeolite NaA Membranes. Ind. Eng. Chem. Res. 2008, 47, 3213− 3224. (21) Cho, C. H.; Oh, K. Y.; Kim, S. K.; Yeo, J. G.; Sharma, P. Pervaporative Seawater Desalination Using NaA Zeolite Membrane: Mechanisms of High Water Flux and High Salt Rejection. J. Membr. Sci. 2011, 371, 226−238. (22) Li, L.; Dong, J.; Nenoff, T. M.; Lee, R. Desalination by Reverse Osmosis Using {MFI} Zeolite Membranes. J. Membr. Sci. 2004, 243, 401−404. (23) de Groot, B.; Grubmüller, H. Water Permeation across Biological Membranes: Mechanism and Dynamics of Aquaporin-1 and GlpF. Science 2001, 294, 2353−2357. (24) Hummer, G.; Rasaiah, J. C.; Noworyta, J. P. Water Conduction through the Hydrophobic Channel of a Carbon Nanotube. Nature 2001, 414, 188−90. (25) Allen, R.; Melchionna, S.; Hansen, J.-P. Intermittent Permeation of Cylindrical Nanopores by Water. Phys. Rev. Lett. 2002, 89, 175502. (26) Lin, J.; Murad, S. A Computer Simulation Study of the Separation of Aqueous Solutions Using Thin Zeolite Membranes. Mol. Phys. 2001, 99, 1175−1181. (27) Hu, Z.; Chen, Y.; Jiang, J. Zeolitic Imidazolate Framework-8 as a Reverse Osmosis Membrane for Water Desalination: Insight from Molecular Simulation. J. Chem. Phys. 2011, 134, 134705.

suggesting that the equilibrium positions of cations is an important factor in determining the permeability of the membrane. We also observed that the distribution of Al and Si atoms affects the net diffusive properties of the solvent inside the zeolite and that this distribution correlates with water occupancy of the α-cages. In terms of water mobility through the bulk membrane, zeolite materials that have larger cages and openings between cages will likely exhibit reduced steric hindrance to water transport. In terms of water transport through the membrane interfaces, many potential physical and chemical modifications of the zeolite surface could be explored to discourage the formation of strong adsorption or depletion layers, e.g., by controlling the grafting density of selected capping groups or by introducing weakly polar groups that could disrupt the ordering of water molecules without repelling them altogether. The observed fluxes through zeolites were lower than fluxes reported for pure polyamide films typically used to make reverse osmosis membranes, which does not support the hypothesis that the improved fluxes of TFN membranes are due to preferential water flow through zeolites. One should bear in mind, however, that the interfacial chemical environment of actual TFN membranes is not fully characterized but is expected to be far more complex than the simple model adopted here.

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ASSOCIATED CONTENT

S Supporting Information *

Sample equilibration criteria, independent measurements of pressure drop across the membrane, residence time in the high water density peaks, and details of the resistance in series model. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; Tel 607-255-8243 (F.A.E.). Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This publication was based on work supported by Award KUSC1-018-02, made by King Abdullah University of Science and Technology (KAUST). The authors are also grateful to computer cycles supplied by the Extreme Science and Engineering Discovery Environment (XSEDE) which is supported by National Science Foundation Grant OCI1053575.

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