Water and Solute Transport Governed by Tunable Pore Size Distributions in Nanoporous Graphene Membranes Doojoon Jang,† Juan-Carlos Idrobo,‡ Tahar Laoui,§ and Rohit Karnik*,† †

Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, United States Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States § Department of Mechanical Engineering, King Fahd University of Petroleum and Minerals, Dhahran 31261, Saudi Arabia ‡

S Supporting Information *

ABSTRACT: Nanoporous graphene has the potential to advance membrane separations by offering high selectivity with minimal resistance to flow, but how mass transport depends on the structure of pores in this atomically thin membrane is poorly understood. Here, we investigate the relationship between tunable pore creation using ion bombardment and oxygen plasma etching, the resulting pore size distributions, and the consequent water and solute transport. Through tuning of the pore creation process, we demonstrate nanofiltration membranes that reject small molecules but offer high permeance to water or monovalent ions. Theoretical multiscale modeling of transport across the membranes reveals a disproportionate contribution of large pores to osmotic water flux and diffusive solute transport and captures the observed trends in transport measurements except for the smallest pores. This work provides insights into the effects of graphene pore size distribution and support layer on transport and presents a framework for designing atomically thin membranes. KEYWORDS: graphene, pore size distribution, mass transport, concentration polarization, nanofiltration, desalination

W

introduce pores in graphene. Although these methods produce pores with a finite size distribution, molecular dynamics simulations on water and solute transport are typically performed across a single graphene pore.13−15,27−29 Moreover, the few experimental measurements of transport across nanoporous graphene report a wide range of transport properties,16−19,30 typically without analysis of the pore size distribution. Previous attempts to quantitatively relate nanometer or sub-nanometer pores to water transport were limited by measurements on a single membrane with large uncertainty, with the majority of the pores being too small to permit the passage of water molecules.18 Therefore, with the exception of membranes with pores that are significantly larger than the solute or solvent molecules,16 these studies have not elucidated the structure−function relationship between the nanoporous graphene pore structure and the resulting transport properties. Furthermore, understanding of the relationship between the pore creation treatments and the resulting pore density and size distribution in graphene has remained inadequate. Conse-

ater scarcity and rising demand for clean water around the world1,2 urge advances in efficient membrane technologies for water purification and desalination. Nanoporous graphene has recently risen as a promising material for next-generation water purification membranes due to its atomic thickness,3,4 inherent impermeability,5 high mechanical strength,6 and capacity to sustain selective nanopores in its lattice,7 and it is predicted to exhibit excellent rejection of salt or contaminants while offering minimal resistance to flow.8 Owing to these unique properties, graphene has potential to overcome the trade-off between permeability and selectivity9,10 and vulnerability to chlorine,11 which are major challenges of current reverse osmosis (RO) and nanofiltration (NF) membranes. Inspired by a number of molecular dynamics studies predicting ultrahigh water permeability across a nanopore in single-layer graphene,12−15 technologies have been developed to create pores in graphene and to measure transport of water and solutes,16−19 suggesting the feasibility of harnessing nanoporous graphene as membranes for water purification and other applications. A variety of methods including electron beam,20,21 ion irradiation,22−24 chemical or plasma etching,17,18,25,26 UVozone,7 and their combinations have been reported to © XXXX American Chemical Society

Received: June 20, 2017 Accepted: September 18, 2017

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Figure 1. Procedure for graphene membrane preparation and two-step pore creation. (a) Transfer of CVD graphene to didecylamine-treated polycarbonate track etch (PCTE) membrane. (b) Defect mitigation and pore creation in graphene lattice. Step 1. Interfacial polymerization (IP) on the fabricated graphene membrane to mitigate leakage across large defects and tears. Step 2. Gallium ion bombardment using focused ion beam (FIB) to nucleate defect sites. Step 3. Oxygen plasma treatment on the bombarded graphene to grow the defects into larger pores in a controllable manner. (c) Graphene lattice viewed from the top after interfacial polymerization (step 1), gallium ion bombardment (step 2), and oxygen plasma treatment (step 3). The schematics are not drawn to scale. APSammonium persulfate; HMDAhexamethylenediamine; APCadipoyl chloride.

RESULTS AND DISCUSSION Membrane Preparation and Pore Creation. Graphene membranes were fabricated via polymer free, direct transfer of graphene to a polycarbonate track etch (PCTE) membrane with 200 nm pore size18 (see Methods and Figure 1a). Any large defects or tears in graphene introduced during the transfer process permit leakage of solutes and consequently deteriorate membrane selectivity.18,25 To mitigate such leakage, interfacial polymerization (IP) was performed, after transferring graphene to the PCTE membranes, to form nylon-6,6 plugs in the PCTE pores underlying tears or large defects in graphene18 (Figure 1b). To introduce a high density of selective pores in graphene, a two-step process of gallium ion bombardment followed by oxygen (O2) plasma etching was pursued. Ion bombardment has been reported to nucleate reactive defects in graphene, which selectively grow into larger pores upon etching.22,23,25 In our previous study,18 acidic potassium permanganate (KMnO4 in H2SO4) was used as an oxidative etchant, but only a small fraction (∼10%) of the resulting pores were permeable to water. Additionally, leakage sealing from nylon plugs formed by interfacial polymerization was partially compromised after extended exposure to the acidic etching environment, diminishing membrane selectivity. Therefore, we replaced the acid etch with oxygen plasma treatment on the bombarded

quently, a comprehensive picture that relates pore size distribution in graphene to its transport properties has not yet emerged, which is prerequisite to realizing membranes with high selectivity and permeance. Development of predictive analytical models that tie in the fabricated pore size distributions and the support pore structure to the overall membrane transport properties, validated by experimental measurements, is essential to guide the design of such membranes tailored to different applications. In this paper, we experimentally investigate osmotic water flux and size-selective solute diffusion across nanoporous graphene with a high density (∼1013 cm−2) of pores tunable with ion bombardment and oxygen plasma etching. We use high-resolution aberration-corrected scanning transmission electron microscopy (STEM) to elucidate the relationship between ion bombardment and oxygen plasma treatment and the resulting pore size distributions. Finally, we develop an analytical model of transport that relates the fabricated pore size distributions to the overall membrane transport properties. The model agrees with the experimental measurements and provides insights into the key factors that govern transport across nanoporous graphene membranes. B

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Figure 2. Effect of pore creation processes on osmotically driven water transport and diffusive solute transport. (a) Schematic of measurement setup with two reservoirs separated by graphene membrane. For water flux measurements, draw (graphene) side is filled with glycerol ethoxylate solution and feed (PCTE) side is filled with deionized water. For KCl and Allura Red (AR) diffusion measurements, feed (graphene) side is filled with 0.5 M KCl/1 mM Allura Red in 0.5 M KCl, respectively, while permeate (PCTE) side is filled with deionized water/0.5 M KCl. (b) Water permeance as a function of oxygen plasma etch time. Blue-filled markers are from high-dose vertical ion bombardment followed by plasma. Different combinations (low-dose vertical/inclined/no bombardment + plasma) are also shown. (c) Normalized diffusive permeance of KCl (green) and Allura Red (red) as a function of oxygen plasma etching time. Right: high-dose vertical or no bombardment. Left: low-dose vertical or inclined bombardment. (d) Selectivity of KCl flux over Allura Red flux as a function of oxygen plasma etching time. Right: high-dose vertical or no bombardment. Left: low-dose vertical or inclined bombardment.

For graphene subjected to vertical (incidence angle of 0°) ion bombardment at a high density of 6 × 1013 cm−2, water permeance, defined as the measured water flow rate normalized by draw solution osmotic pressure and the PCTE pore area (10% of total membrane area) as the reference area, initially decreased with plasma exposure for short etching time up to 20 s. However, it increased monotonically with further etching, exceeding the permeance of conventional seawater RO membranes31 (Figure 2b). The highest permeance of 3.6 × 10−11 m Pa−1 s−1 (or 13.0 L m−2 h−1 bar−1) observed at 75 s was comparable to performance of nanofiltration (NF) membranes31 rejecting 98% of MgSO4 and almost an order of magnitude greater than the permeance achieved in our previous study.18 The consistent rise in water permeance by over an order of magnitude is indicative of the emergence or growth of water-permeable pores arising from plasma etching. Water permeance of membranes subjected to the same plasma etch conditions, but without ion bombardment, was lower at

graphene to selectively oxidize and grow the nucleated defects into water-permeable pores, while maintaining the integrity of the leakage-sealing nylon plugs. Although plasma alone can produce nanopores in graphene,17 we hypothesized that nucleating defects with ion bombardment prior to plasma etching would result in a higher pore density. Graphene was irradiated by 1 or 8 keV gallium ions using a focused ion beam (FIB) at an incidence angle and dose of 0 or 52° and (0.5−6) × 1013 cm−2, respectively. After the bombardment, graphene membranes were etched in an inductively coupled plasma cleaner for a desired period of time (see Supporting Information, Section 1). Water and Solute Transport Measurements. We first investigated how membrane transport properties depend on the pore creation process. For this purpose, osmotically driven water flux across the nanoporous graphene was measured in a diffusion cell (Figure 2a) with an osmotic pressure difference imposed by a glycerol ethoxylate draw solution (see Methods). C

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50 s of plasma etching with permeance comparable to vertical ion bombardment at a density of 6 × 1013 cm−2 (Figure 2b,c). However, Allura Red permeance remained low, which indicates that the 8 kV inclined bombardment was able to introduce and sustain sub-nanometer pores after plasma exposure, resulting in a high KCl/Allura Red selectivity of 38 at 50 s etch (Figure 2d, left panel). Pore Diameter Distribution from STEM Imaging. To relate the pore creation process to the resulting pore size distributions and the membrane transport properties, pore size distributions were obtained by analyzing several annular dark field aberration-corrected STEM images for each pore creation condition, where pore density was calculated as the ratio of pore count to total inspected area. The samples for imaging were prepared via two different methods to complement the limitations of each other. In the “direct transfer” method, chemical vapor deposition (CVD) graphene grown on copper was directly transferred to transmission electron microscopy (TEM) grids using a polymer-free method and subjected to identical ion bombardment and plasma etching as that performed on the graphene membranes. On the other hand, in the “PCTE transfer” method, graphene was transferred from the graphene−PCTE membranes used for transport measurements to TEM grids, allowing us to image a representative subset of the actual pores across which water and solute transport was measured (see Methods and Figure 3a). Pore imaging on the direct transfer graphene revealed that increasing exposure to plasma monotonically increased the pore density and also enlarged the pores in the graphene lattice, whether it was bombarded or not (Figures 3b,c and S1). For vertically bombarded graphene, the pore density increased significantly from 0.39 × 1013 cm−2 to 1.59 × 1013 cm−2 as the plasma etching time increased from 10 to 30 s. Upon additional etching, the density remained almost unchanged (1.64 × 1013 cm−2 for 50 s etch) but was accompanied by a decreased number of smaller (≤0.18 nm) pores and emergence of larger outliers around 1.5 nm, which coincides with higher KCl and Allura Red permeance at 50 s than at 30 s etch time. It suggests that once the reactive areas around defect sites are lost during the initial etching stage, subsequent growth of existing pores or merging of adjacent small pores will occur in preference to nucleation of new defect sites in the graphene lattice, as reported by Warner et al.20 In the absence of ion bombardment, the observation of pores in graphene demonstrates that oxygen plasma alone is able to nucleate and grow pores in graphene, as previously reported.17 With additional etching, both pore size and density increased, but the pore density was consistently lower than that in the ionbombarded case (Figure 3c), which explains the lower permeance in the absence of ion bombardment for a given etching time (Figure 2b,c). Nevertheless, it does not imply that the role of ion bombardment is merely a forward shift in plasma time, as measured transport characteristics evolve with plasma etching in distinctly disparate manners for graphene without ion bombardment. Regardless, we observe that all pore creation conditions give rise to a high concentration of extremely small pores (single or double vacancies) and a sparse distribution of larger pores. This observation suggests that, rather than a uniform increase in size of the nucleated defects, oxygen plasma tends to enlarge only a few of the defects into larger pores while the other defects remain close to their original size. Surprisingly, the pore density measured from vertically bombarded graphene in PCTE transfer was lower by an

least by a factor of 2, suggesting that the combination of ion bombardment and plasma etching enables faster water transport. Potassium chloride (KCl, ∼0.66 nm hydrated diameter for both K+ and Cl−) and Allura Red (546 Da, ∼1 nm Stokes diameter) were selected as model solutes to probe transport by diffusion under a concentration gradient (see Methods). Measurements for each species were normalized by the bare PCTE membranes’ permeance (KPCTE ≈ 6.36 × 10−5 and 1.99 × 10−5 m s−1 for KCl and Allura Red, respectively) to compare any selectivity beyond that due to differences in molecular diffusivity. Both KCl and Allura Red exhibited transport trends similar to water, with an initial decline for short plasma exposure followed by a monotonic increase with further etching (Figure 2c, right panel). However, KCl transport showed a steep surge at 30 s and consistently increased with further plasma etching, whereas Allura Red experienced a much more gradual increase and saw resistance to diffusive transport even at 90 s of etching. This preferential transport of KCl over Allura Red indicates that ion bombardment followed by plasma etching created pores in the sub-nanometer or nanometer regime. The KCl/ Allura Red selectivity, defined as the ratio of the absolute diffusive permeance (flux normalized by concentration difference), increased from 7.4 to 31.2 after 30 s of plasma etching and then gradually declined as the membranes became more permeable to Allura Red (Figure 2d, right panel). Rise and decline in selectivity demonstrates that graphene nanopores can be easily tuned by simply controlling the plasma etching time after bombardment. The membranes exposed to plasma etching without ion bombardment showed similar trends but resulted in a lower selectivity of 16.5 at 30 s etch time that remained nearly unchanged with additional etching. This plateau in selectivity is likely due to the simultaneous increase in the number densities of both KCl-permeable and Allura Redpermeable pores with plasma etching (see Figure 3c). However, the selectivity in the case without ion bombardment also eventually decreased to 5.4 after 600 s of plasma etching (not shown in the plot). The faster decrease in selectivity in the ionbombarded case may be due to the greater susceptibility of ionbombarded graphene to plasma etch. To confirm that the nylon plugs are not susceptible to oxygen plasma, interfacial polymerization was performed on bare PCTE membranes without graphene. KCl and Allura Red diffusion measured across the nylon-plugged membranes did not increase even after 60 s of plasma etching (Figure 2c, left panel), indicating that any change in transport originated primarily from graphene pore creation and growth, not from damaged nylon plugs. To further elucidate the role of ion bombardment, water and solute transport measurements were also carried out with different bombardment parameters (Figure 2b,c). When bombarded at one-third of the original density, graphene membranes showed 3−5-fold lower water and solute transport for 50 s of etching, implying that the enhancement in transport was closely dependent on nucleation of defect sites due to bombardment. We also investigated bombardment at an incidence angle of 52°, dose of 0.55 × 1013 cm−2, and acceleration voltage of 8 kV, which has a high (80−90%) probability of nucleating defects in the form of complex vacancy defects or amorphous areas as compared to predominantly single or double vacancies from vertical irradiation at 1 kV.25,32 Both water and KCl transport showed significant increase after D

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Figure 3. Annular dark field aberration-corrected STEM images of graphene pores and estimation of pore diameter distribution. (a) Schematic of PCTE transfer method to transfer graphene from PCTE to a TEM grid. (b) Representative STEM images of graphene pores from direct transfer at different oxygen plasma etching time with (top) and without (bottom) ion bombardment. Scale bars are 1 nm. (c) Direct transfer: Pore diameter distributions for all of the pore creation conditions in panel b. Pore density (text) and log-normal probability density function (red) are shown for each condition. Inset shows magnified view for pores larger than 0.495 nm. (d) PCTE transfer: Pore diameter distribution, pore density, and log-normal probability function for ion bombardment followed by 30 s or 50 s of oxygen plasma etching. For all images and distributions with ion bombardment, the ion beam incidence angle was 0° (vertical) with a density ∼6 × 1013 cm−2.

order of magnitude than that of direct transfer (Figure 3d). The discrepancy might have originated from contamination from the polycarbonate support, since dissolving polycarbonate with chloroform can leave polymer residues, covering some of the smaller pores. The pore density was slightly lower at 50 s than 30 s, which may be attributed to coalescing of smaller pores upon additional etching or greater polymer contamination on the 50 s sample. Nevertheless, the density of pores above 1 nm was higher for 50 s, consistent with the hypothesis that extended plasma etching is capable of enlarging the pores. Since larger pores in PCTE transfer are less likely to be covered by contamination, its largest pores suggest the maximum size that can be found in the actual graphene−

PCTE membranes. Therefore, it was assumed that pores were below 2 nm during transport measurements up to 50 s etching time and a few larger pores (Figure S1) were consequently discarded from the direct transfer pore size distribution and not included in theoretical modeling. The measured pore diameters were further adjusted to account for effective pore area by treating each carbon atom as a van der Waals (vdw) sphere18 (see Supporting Information, Section 2). Upon discarding pores with negative diameters, for the vertically ion-bombarded graphene, the pore density decreased to 50−70% and 60−90% of the original value for direct and PCTE transfer, respectively (Figure 4a). The density of water-permeable pores that would permit forward osmosis was estimated as pores with diameters E

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Figure 4. Analytical modeling and analysis of transport across nanoporous graphene. (a) Carbon vdw-adjusted pore diameter distribution from direct (top) and PCTE (bottom) transfer. For each bin, theoretical water permeance of graphene from no-slip hydrodynamics was estimated from all water-permeable vdw-adjusted pores. Density of water-permeable pores is indicated in blue, and their fraction compared to all vdw-adjusted pores is indicated in parentheses. Bottom left panel compares theoretical water permeance of graphene to that of entire membrane (graphene + PCTE) subject to concentration polarization at ΠDraw = 22.6 atm. (b) Comparison of experiments to analytical models with pores from direct (circle-dotted) and PCTE (square-dotted) transfer. Dotted lines enveloping the experimentally measured values represent the upper and lower bounds corresponding to different fractions (40% and 57%) of PCTE pores that are not sealed by IP. Left: Osmotic water flux predicted by model using no-slip hydrodynamics and internal concentration polarization. Right: KCl and Allura Red diffusive permeance predicted by continuum diffusion theory. (c) Comparison of this work to reported molecular dynamics simulations and experiments. Water permeation coefficients estimated from experimental measurements and theoretical predictions based on pore size distributions from direct and PCTE transfer, are shown. PCTE transfer pore size distribution is not available for the 10 s plasma etch data point. For all distributions and transport data points, vertical ion bombardment was performed at a density of ∼6 × 1013 cm−2.

between that of the water molecule and draw solute (dwater ≤ dpore ≤ dglycerol, see Table 1). Compared to the previous report18 of water-permeable pore density of (1.5−1.7) × 1011 cm−2

corresponding to only 6−7% of the pores, ion bombardment and oxygen plasma etching were capable of introducing a F

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their contributions were 68% and 27% for 30 and 50 s etch time in the case of PCTE transfer. Therefore, the increase in water permeance is attributed not only to the higher density of pores, but also to the emergence of a few large pores after extended etching that contribute disproportionately to the transport. This trend is expected in viscous flow across filters with a distribution of pore sizes where more flow is diverted to larger pores.34 We hypothesized that diffusive leakage of the draw solute through large pores compromises the osmotic pressure difference (ΔΠ) driving water across nanoporous graphene on support pores (see Figure S4). Thus, solute concentration on the feed side of the graphene was solved self-consistently to calculate the effective driving potential, ΔΠeff. Continuum diffusion with steric exclusion and Nernst−Planck equations were used to describe draw solute transport through permeable graphene pores (dpore ≥ dglycerol ≈ 1.2 nm) and PCTE pores, respectively, redefining u and solute concentration on the feed side of graphene, CF,i as

higher density of water-permeable pores that constituted a greater fraction of the total number of pores (Table 1). Table 1. Pore Density from Direct Transfer and PCTE Transfer Samples pore density (cm−2)

sample type

before vdw correction

after vdw correction

water permeable pore density (cm−2)

direct, 10 s direct, 30 s direct, 50 s PCTE, 30 s PCTE, 30 s

0.39 × 1013

0.21 × 1013

0.038 × 1013

18.18

1.59 × 1013

0.82 × 1013

0.151 × 1013

18.45

1.64 × 1013

1.12 × 1013

0.151 × 1013

13.48

0.12 × 1013

0.11 × 1013

0.048 × 1013

45.24

0.098 × 1013

0.06 × 1013

0.026 × 1013

42.86

water permeable pore fraction (%)

graphene graphene u = K water (ΠD,m − ΠF, i) = K water (ΠD, m − f (C F, i))

Theoretical Modeling of Transport across Graphene Membranes. To elucidate the relationship between the size distribution of the created pores and the resulting transport properties, an analytical model was constructed for a simple system comprised of monolayer nanoporous graphene on a 200 nm cylindrical PCTE pore.18 Transport was modeled as onedimensional and steady state, and solute concentrations were considered uniform over each side of the graphene. To compare the transport measured across graphene to theoretical models, the graphene permeance was calculated accounting for the fact that not all of the PCTE pores are available for transport due to the nylon plugs. The water flux, solute permeance, and water permeation coefficients per single pore were estimated for a range of the fraction of PCTE pores actually available for transport, estimated as 40−57% based on experiments (see Supporting Information, Section 3), which corresponds to 4−5.7% of total graphene membrane area. To theoretically estimate water transport across permeable graphene nanopores, no-slip hydrodynamics through a pore in a plane with finite thickness was adopted.14,18,33,34 This model is simple, without any fitting parameters, and agrees with molecular dynamics simulations to within an order of magnitude.14 Assuming no draw solute leakage across the pores, volumetric water flux u (which also equals the water flow velocity) driven by osmotic pressure difference ΔΠ is

(2)

C F, i =

graphene Kdiff C D,m(1 − e(u / D)LPCTE) − uC F,m

graphene (1 − e(u / D)LPCTE) − u e(u / D)LPCTE Kdiff D graphene Kdiff = ∑ 2(ri − rglycerol) APCTE ri ≥ rglycerol

,

(3)

where osmotic pressures on draw and feed sides of the graphene Π D,m and Π F,i are functions of the solute concentrations CD,m and CF,i, respectively, CF,m is the solute concentration in the feed reservoir, D and Kgraphene denote diff solute diffusivity and diffusive permeance, and LPCTE is the PCTE pore length (see Supporting Information, Section 3 for derivation and each property). This approach accounts for internal concentration polarization that negatively impacts performance of asymmetric membranes with porous supports.35 With draw solute leakage and the resulting internal concentration polarization within the support pores for the overall membrane (graphene + PCTE) incorporated, the model predicted almost no or small concentration polarization effects for pore size distributions in PCTE transfer at the osmotic pressure of 22.6 atm (Figure 4a, bottom left panel). However, the overall membrane permeance was lower than that of the nanoporous graphene by 49% and 78% in the case of direct transfer for 30 and 50 s plasma etch time, respectively, indicating that the concentration polarization from large leaky pores can significantly compromise the water flux. This phenomenon is well-known in forward osmosis35 and may partly explain the differences in permeance in experiments involving forward osmosis versus pressure-driven flow.19 Water flux predicted from direct transfer pore size distributions increased with plasma etch time from 10 to 50 s and provided an upper bound on the experimentally measured flux (Figure 4b, left panel). PCTE transfer exhibited a similar progression from 30 to 50 s, with lower flux due to its lower pore density. To understand diffusive transport of solutes across the membrane in the absence of water flow, we considered diffusion of KCl and Allura Red across graphene suspended across a single PCTE pore using continuum diffusion theory

⎡ π ∑i ri 4 1 ⎤⎥ graphene ΔΠ = K water ΔΠ u=⎢ ⎢⎣ μ(3π ∑i ri + 8Lgraphene) APCTE ⎥⎦ (1)

for any pore with radius ri larger than water molecules but smaller than the draw solute, where Kgraphene is graphene water permeance to water (m3 m−2 Pa−1 s−1) from no-slip hydrodynamics, μ is water viscosity, Lgraphene is graphene thickness, and APCTE is single PCTE pore area. Nanoporous graphene permeance (water flux normalized by osmotic pressure of draw solution, ΔΠ = ΠD,m) to water estimated with no-slip hydrodynamics revealed that the contribution of the larger pores occurring at a low density becomes increasingly significant with increasing plasma etch time (Figure 4a). For direct transfer, pores smaller than 1 nm were responsible for 100%, 65%, and 28% of the total permeance for 10, 30, and 50 s of plasma etching time, while G

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∑

2(ri − rsolute)

ri ≥ rsolute

1 APCTE

compares within an order of magnitude to predictions of molecular dynamics and hydrodynamics incorporating slip, although it tends to predict a lower flux.14 The good agreement between our simple analytical model and experimental measurements suggests that continuum hydrodynamics is useful for estimating transport properties of membranes comprising a nanoporous atomically thin layer suspended over a porous substrate with finite thickness. The model shows that large pores contribute disproportionately to transport, especially in the case of water flow that scales more strongly with pore size, compared to solute diffusion. Furthermore, large pores lead to draw solute leakage in forward osmosis and induce concentration polarization, which is difficult to measure experimentally since the solute concentration in the feed side remains negligibly low even when it is significant within the PCTE pore. The polarization intensifies with increasing draw solution osmotic pressure within the typical range for seawater,38 especially at longer etch time as large pores emerge (see Figure S5). This implies that fabricating monodisperse pores is pivotal to designing graphene membranes that are less subject to draw solute leakage. It is notable that the measured solute and water transport decreased until 10 and 20 s of plasma etching, respectively. The initial reduction in water flux could arise from strong interactions between water molecules and oxygen plasmainduced functional groups on the pore edges, which may impede the flow of water molecules.29 Similarly, negatively charged functional groups at graphene pores can retard solute diffusion due to electrostatic repulsion.25,39,40 These intermolecular or Donnan-type interactions are expected to be more prominent when pores are small. However, since transport is always dominated by the larger pores in the pore size distribution, it is difficult to experimentally deduce the contribution of the smaller pores to water and solute transport. After the initial decline, the KCl diffusion experienced its steepest 3-fold rise from 20 to 30 s of plasma etch time, while the highest surge in the water flux occurred later between 30 and 40 s. This increase in KCl diffusion preceding an increase in water permeance may be due to the emergence of pores larger than the draw solute during the etching process. To verify the hypothesis, a very low density (∼1010 cm−2) of large pores (∼0.05 nm larger than glycerol ethoxylate) was added to the pore size distribution of direct transfer at 10 s. For water transport under forward osmosis, our model predicts that this heterogeneity only intensifies the solute concentration polarization and reduces the membrane permeance to water by ∼20% (see Figure S6). However, the large pores present pathways for K+ and Cl− transport and enhance solute diffusion by ∼80%. Although the effects of pore functionalization at short plasma etching or graphene surface interactions are not captured by the model, this analysis suggests that the emerging heterogeneity in the pore size distribution could explain the faster increase in KCl diffusion with plasma etch time compared to water flux. The model overestimated water and solute transport for smaller pores (10 and 30 s of plasma etching), especially for direct transfer (Figure 4b). As noted previously, interactions between the functional groups on graphene pores and water or solutes may account for this discrepancy. Another possibility is that the measured pore size distribution does not accurately represent the actual membranes. Since as-grown graphene was directly transferred prior to pore creation, the direct transfer samples are less subject to contamination, setting an upper

(C F,m − C P, i) (4)

A

C P, i =

C F,m ∑i 2(ri − rsolute) + C P,m L PCTE PCTE

∑i 2(ri − rsolute) +

APCTE L PCTE

(5)

for any pore with radius ri larger than the solute radius rsolute, where CF,m denotes concentration on feed side of graphene, CP,m is permeate solution concentration, and D is solute diffusivity (see Supporting Information, Section 3). The graphene membrane permeance to KCl and Allura Red was estimated by normalizing the flux with feed solution concentration. Model predictions based on direct transfer pore size distribution provided upper limits on the experimentally measured permeance to both solutes at all plasma etching times except for Allura Red at 10 s, where no pores larger than 1 nm were found (Figure 4b, right panel). Predictions based on PCTE transfer exhibited consistently lower permeance, which agreed better with experiments and showed a rising trend with etch time. While transport was measured and modeled across a high density of pores in this work, molecular dynamics simulations typically estimate transport across a single graphene pore. To compare this work with predictions from literature, we calculated water permeation coefficients for a single graphene pore (ns−1 Pa−1) based on the estimated pore size and density. The weighted pore diameter was defined as the representative size that would yield the same permeance to water as the original distribution (see Supporting Information, Section 4). For both direct and PCTE transfer, the weighted diameters were approximately 0.60 and 0.83 nm at 30 and 50 s of plasma etch time, respectively. From the measured water permeance, permeation coefficients were calculated by dividing the permeance by pore density of water-permeable pores, with lower and upper limits provided by direct and PCTE transfer pore density and 57% and 40% of PCTE pores unplugged by nylon, respectively, and theoretical estimates were also calculated with no-slip hydrodynamics (see Supporting Information, Section 4). Concentration polarization was not considered in computing the experimental permeation coefficients. Both experimental and theoretical coefficients for 50 s plasma etch time were within the same order of magnitude and closely matched predictions in literature,14,27,37 but the experimentally measured coefficients at 10 and 30 s etch time were lower than predictions of continuum models as well as simulation results13,15 (Figure 4c). We note that the 10 s etch corresponds to the case where all pores are sub-nanometer. The greater discrepancy may be due to a combination of one or more of several factors including (1) actual pore geometry, functional groups, or pore charge being different than those in the models or simulations, (2) preferential blockage of smaller pores due to contamination, (3) strong interactions of water molecules with the functional groups in case of smaller pores, (4) inherent inaccuracies in the models or simulations, especially for sub-nanometer pores, or (5) limitations of the methods used to measure the pore size distributions. Discussion on Transport across Graphene Membranes. Recent studies have shown that water flow across a graphene nanopore estimated by no-slip hydrodynamics H

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For interfacial polymerization, hexamethylenediamine (98%, SigmaAldrich) in deionized water with sodium bicarbonate buffer and adipoyl chloride (98%, Sigma-Aldrich) dissolved in hexane (anhydrous, 95%, Sigma-Aldrich) were used. Glycerol ethoxylate (average Mn ≈ 1,000 with n = 6−7, Sigma-Aldrich) in deionized water was used as the draw solute in forward osmosis water flux measurement. For solute diffusion experiments, potassium chloride standard solution (1 M, Fluka) and Allura Red AC (≥98.0%, Sigma-Aldrich) were used with an in situ miniature dip-in conductivity electrode (ET915, eDAQ) and fiber optic probe connected to UV−vis spectrophotometer (Cary 60 UV−vis, Agilent Technologies) to measure the transport. QUANTIFOIL holey carbon film with an array of 1.2 μm diameter holes on 200 M Au grid (658-200-AU, Ted Pella, Inc.) was used to transfer graphene for STEM imaging, and chloroform (≥99.9%, Sigma-Aldrich) was used as a solvent to dissolve polycarbonate in the PCTE transfer process. Graphene Transfer to PCTE Membrane. Graphene was transferred to a PCTE membrane following the procedure by O’Hern et al.18,25,36 Prior to transfer, PCTE membranes were pretreated with didecylamine to enhance hydrophobicity, which prevents the copper etchant from wicking into the graphene−PCTE interface and improves transfer quality. After immersing them in didecylamine solution in ethanol (0.05 M) on a shaker plate for 60 min, each PCTE membrane was rinsed in triplicate for 10 min each in separate fresh ethanol dish to wash off residual didecylamine and then air-dried. CVD graphene on copper was cut into smaller square pieces of ∼1 cm2 and graphene on their back side was removed by floating them on APS-100 for 3.5 min. After 5 min of floating on three subsequent deionized water baths and rinsing in ethanol to completely remove graphene residues as well as APS-100, the didecylaminetreated PCTE membrane was gently placed on the top side of copper with graphene, with the stack sandwiched by weighing papers and then by glass slides as the outermost covers. Rolling a glass pipet tube on the top glass slide with light pressure allowed the pliable PCTE to conform to graphene, resulting in an adhered PCTE−graphene− copper stack. Then, the whole stack was floated on an APS-100 bath with the copper side down, which was etched in a nitrogen-filled chamber at 3.5 bar (gauge) for 45 min. The resulting graphene−PCTE membrane was then rinsed in seven deionized water baths for 5 min each, after which ethanol was added into the water and the membrane was taken out while in contact with 90% ethanol in water. After air drying, the membrane was then baked on a hot plate at 110 °C in air for 10 h to help PCTE adhere to graphene and completely dry any remaining liquid within PCTE pores or between graphene and PCTE. Interfacial Polymerization. Interfacial polymerization was performed as reported in our previous publication,18 immediately following the baking stage of graphene transfer process described above. Hexamethylenediamine solution, 5 mg/mL in deionized water, was introduced into the bottom piece of a Franz cell (Permegear Inc.) and filled to the brim. The membrane was then placed on it grapheneside down so that the graphene was in contact with the solution below through the 9 mm orifice of the bottom piece of the Franz cell. The membrane was then topped by the top piece of the cell which was clamped tightly with the bottom piece, and 5 mg/mL adipoyl chloride solution in hexane was carefully added to the top side compartment, with the membrane separating the two solutions. After nylon-6,6 formation for 60 min, the top side was rinsed by replacing the solution with hexane and then with ethanol, 7 times each. Then, the Franz cell was disassembled, and the nylon-sealed membrane was rinsed in three ethanol baths. Water Flux Measurements. Water flux measurements under forward osmosis were carried out in the custom-made diffusion cell shown in Figure 2a, using aqueous glycerol ethoxylate solution as the draw solution and deionized water as the feed solution. The concentration of glycerol ethoxylate solution was 26.46 wt %, which is equivalent to an osmotic pressure ΠDraw = 22.6 atm, as measured by an osmometer (Wescor 5500 vapor pressure osmometer), but 11.49 wt % (5.09 atm) solution was used for 60 and 75 s plasma etching time where severe internal concentration polarization was observed due to high water flux. The fabricated graphene membrane, protected by

bound on the pore density and the modeled transport. However, polycarbonate residues can cover the smaller pores during the PCTE transfer process, leading to underestimation of the pore density. Additionally, differences in the geometry and conductivity of substrates (TEM grid versus PCTE membrane) during pore creation may affect ion bombardment or plasma treatment, and it is possible that contamination on the actual membranes may shield the graphene from the plasma etch or occlude smaller pores during measurement.

CONCLUSIONS Control of pore size and density in nanometer or subnanometer range is critical to the function of nanoporous graphene membranes. We developed a facile method of ion bombardment and oxygen plasma etching to introduce a high density of nanopores in macroscopic monolayer graphene membranes. STEM imaging revealed the relationship between different pore creation parameters and the resulting pore size distribution. The role of ion bombardment was found to be crucial in nucleating defects to realize a higher density of pores, leading to enhanced membrane permeance. The realization of high water flux and size-selectivity at the sub-nanometer scale between salt (KCl) and small molecules (Allura Red) indicates that the transport properties are tunable by simply controlling the pore creation parameters. Plasma etching initially impeded water and solute transport when pores were small but consistently enlarged the pores to permit an order of magnitude higher permeance. However, in most cases, the pore size distributions showed a predominance of very small pores, and a sparse scattering of larger, more permeable pores with increasing etch time, suggesting that larger pores may grow more easily than smaller defects. More importantly, this work theoretically predicted water and solute transport that compared reasonably well to experimental results. The constructed multiscale analytical model connects transport across the distribution of pore sizes and within the support to estimate the overall transport properties of the membrane. The disproportionate effects of large pores on solute leakage show that it is imperative to further improve the pore generation process to achieve uniformly distributed sub-nanometer pores, especially to enhance water flux under osmosis by minimizing concentration polarization. A different oxidative etching process leading to self-limited pore growth25 or varying ion bombardment parameters including inclined irradiation with different kinds of ions or particles may help to narrow down the created pore size distribution. With experimental progress in tunable membrane performance and theoretical analysis correlating membrane transport properties to the measured pore size distribution, this work takes a step toward harnessing graphene in membrane applications including reverse osmosis, nanofiltration, or ultrafiltration.41 METHODS Materials. For all membranes for transport measurements and samples for STEM imaging, monolayer CVD graphene film grown on 18 μm thick substrate copper foil from Graphenea, Inc., was used for consistency. The graphene has grain size up to 10 μm, and its coverage is >95% (all the specifications provided from manufacturer’s product datasheet). Sterlitech’s PVP-free (hydrophobic) 25 mm diameter polycarbonate track etched (PCTE) membranes with 200 nm pores were modified with didecylamine18 (Sigma-Aldrich). APS-100 from Transene was used as ammonium persulfate etchant to etch copper. I

DOI: 10.1021/acsnano.7b04299 ACS Nano XXXX, XXX, XXX−XXX

Article

ACS Nano silicone gaskets (Grace Bio-Laboratories, Inc.), was mounted on the orifice region of the cell with graphene facing the syringe side of the cell and PCTE on the syringe-less side. Both sides of the cell were rinsed with 90% ethanol in water with magnetic stirrers for 10 min to ensure that the membrane is sufficiently wet and then thoroughly rinsed with degassed deionized water. Draw solution (7.4 mL) was placed on the graphene side of the cell, while 7.4 mL of deionized water was introduced to the PCTE side to minimize dilutive internal concentration polarization that would occur in the opposite configuration18,42 (see Supporting Information for details). After sealing the open port of the draw solution side with a rubber plug, stirring was commenced and osmotic pressure difference across the membrane was allowed to drive water from the feed to the draw side. The resulting increase in volume was reflected in the rise of liquid meniscus along the syringe, which was periodically recorded for 20 min using time-lapse photography. The water flux measurements were performed in triplicate with fresh solutions to minimize uncertainty. Solute Diffusion Measurements. Solute diffusion was measured in the same diffusion cell with 6.9 mL of feed solution on the graphene side and 6.9 mL of permeate solution on the PCTE side so that no hydrostatic head could be built. For KCl transport, diffusion of K+ and Cl− from 0.5 M KCl feed solution was measured with the conductivity probe in deionized water on the permeate side. Rise in conductivity resulting from the salt diffusion was periodically recorded for 15 min. Measurements were performed in triplicate. Using UV−vis spectrophotometer, Allura Red diffusion from 1 mM Allura Red AC in 0.5 M KCl feed solution was measured in 0.5 M KCl background on both feed and permeate sides to prevent electrokinetic effects from affecting the transport.36 Absorbance spectra were recorded for 40 min on the permeate side. The experiments were performed in triplicate. Graphene Transfer to TEM Grids from Measured Membranes. After the transport measurements, the measured membrane was cut into smaller pieces (∼2−3 mm) comparable to the size of TEM grids. A small piece was carefully placed on a TEM grid sitting on a glass slide so that graphene and amorphous carbon film side of the grids could come into contact. A small (∼5 μL) amount of ethanol was gently dropped on the stack using a micropipet, air-dried, and baked on a hot plate in air at 110 °C for 20 h to allow the membrane to conform to the carbon film of the TEM grid. Then, the stack was placed on the bottom of a clean glass Petri dish with the grid side down and was very slowly immersed in chloroform by slowly adding the chloroform (∼75 mL) to the dish with minimal disturbance using a glass pipet. After 5 min when chloroform had completely dissolved the polycarbonate, the chloroform was partially removed while ensuring that the stack was still immersed in it (∼15 mL remaining) to avoid tearing of graphene from drying due to surface tension (27.50 mN/m) (see Figure 3a). The Petri dish was refilled with fresh chloroform (∼60 mL) using a clean glass pipet and the partial removal and replenishment of chloroform were repeated five times in total to dilute the polycarbonate solution. The same repetitive procedure was carried out with ethanol, which has a lower surface tension (22.10 mN/m), with the stack never exposed to the air during the process. After replacing the chloroform with ethanol, the solution was carefully withdrawn, and the graphene-transferred TEM grids were baked on a hot plate at 110 °C for 60 min. Scanning Transmission Electron Microscopy. Scanning transmission electron microscopy (STEM) imaging of graphene pores was performed with an aberration-corrected Nion UltraSTEM 100 at Oak Ridge National Laboratory. The prepared graphene samples on TEM grids were baked at 160 °C for 9 h at pressure of 10−5 Torr to help remove surface contamination, cooled to room temperature, and then immediately loaded into the microscope. Imaging was performed at 60 keV, below the knock-on threshold for carbon atoms, to minimize damage on graphene using a semiconvergence angle of 30 mrad and an inner semiangle of 54 mrad for the annular dark field detector. For each sample, randomly selected areas with field of view of 16 nm × 16 nm were imaged to result in >10 images for each pore creation condition.

ASSOCIATED CONTENT S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsnano.7b04299. Pore creation procedure and parameters, complete pore size distributions, derivation of transport model, data analysis, and supplementary discussion (PDF)

AUTHOR INFORMATION Corresponding Author

*[email protected] ORCID

Rohit Karnik: 0000-0003-0588-9286 Notes

The authors declare no competing financial interest.

ACKNOWLEDGMENTS This work was supported in part by the King Fahd University of Petroleum and Minerals in Dhahran, Saudi Arabia through the Center for Clean Water and Clean Energy at MIT and KFUPM under project number R10-CW-09, and in part by the U.S. Department of Energy, Basic Energy Sciences, Award Number DE-SC0008059. D.J. acknowledges support from the Samsung Fellowship. STEM imaging was conducted at ORNL’s Center for Nanophase Materials Sciences (CNMS), which is a DOE Office of Science User Facility (J.C.I.). This work made use of the MRSEC Shared Experimental Facilities at MIT, supported by the National Science Foundation under Award Number DMR-1419807. REFERENCES (1) Shannon, M. A.; Bohn, P. W.; Elimelech, M.; Georgiadis, J. G.; Mariñas, B. J.; Mayes, A. M. Science and Technology for Water Purification in the Coming Decades. Nature 2008, 452, 301−310. (2) WWAP (United Nations World Water Assessment Programme). The United Nations World Water Development Report 2016: Water and Jobs; UNESCO: Paris, 2016. (3) Meyer, J. C.; Geim, A. K.; Katsnelson, M. I.; Novoselov, K. S.; Booth, T. J.; Roth, S. The Structure of Suspended Graphene Sheets. Nature 2007, 446, 60−63. (4) Geim, A. K. Graphene: Status and Prospects. Science 2009, 324, 1530−1534. (5) Bunch, J. S.; Verbridge, S. S.; Alden, J. S.; Van Der Zande, A. M.; Parpia, J. M.; Craighead, H. G.; McEuen, P. L. Impermeable Atomic Membranes from Graphene Sheets. Nano Lett. 2008, 8, 2458−2462. (6) Lee, C.; Wei, X.; Kysar, J. W.; Hone, J. Measurement of the Elastic Properties and Intrinsic Strength of Monolayer of Graphene. Science 2008, 321, 385−388. (7) Koenig, S. P.; Wang, L.; Pellegrino, J.; Bunch, J. S. Selective Molecular Sieving through Porous Graphene. Nat. Nanotechnol. 2012, 7, 728−732. (8) Cohen-Tanugi, D.; Grossman, J. C. Nanoporous Graphene as a Reverse Osmosis Membrane: Recent Insights from Theory and Simulation. Desalination 2015, 366, 59−70. (9) Geise, G. M.; Park, H. B.; Sagle, A. C.; Freeman, B. D.; McGrath, J. E. Water Permeability and Water/salt Selectivity Tradeoff in Polymers for Desalination. J. Membr. Sci. 2011, 369, 130−138. (10) Elimelech, M.; Phillip, W. A. The Future of Seawater Desalination: Energy, Technology, and the Environment. Science 2011, 333, 712−717. (11) Geise, G. M.; Lee, H.-S.; Miller, D. J.; Freeman, B. D.; McGrath, J. E.; Paul, D. R. Water Purification by Membranes: The Role of Polymer Science. J. Polym. Sci., Part B: Polym. Phys. 2010, 48, 1685− 1718. J

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DOI: 10.1021/acsnano.7b04299 ACS Nano XXXX, XXX, XXX−XXX