Ultimate Permeation Across Atomically Thin Porous Graphene

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Science  18 Apr 2014:
Vol. 344, Issue 6181, pp. 289-292
DOI: 10.1126/science.1249097

Thin and Selective Outpourings

When using a membrane to separate materials, the efficiency of the separation is limited by how fast the gas or liquid passes through the membrane and by how selective it is. Thinner membranes usually allow for faster flow rates but are usually less selective. Attempting to maintain selectivity, Celebi et al. (p. 289) developed a sophisticated way to drill holes of controlled diameter in a graphene sheet about two layers thick. For such a thin membrane, the primary barriers to separation come from entrance and exit from the holes and not from the motion through the membrane.


A two-dimensional (2D) porous layer can make an ideal membrane for separation of chemical mixtures because its infinitesimal thickness promises ultimate permeation. Graphene—with great mechanical strength, chemical stability, and inherent impermeability—offers a unique 2D system with which to realize this membrane and study the mass transport, if perforated precisely. We report highly efficient mass transfer across physically perforated double-layer graphene, having up to a few million pores with narrowly distributed diameters between less than 10 nanometers and 1 micrometer. The measured transport rates are in agreement with predictions of 2D transport theories. Attributed to its atomic thicknesses, these porous graphene membranes show permeances of gas, liquid, and water vapor far in excess of those shown by finite-thickness membranes, highlighting the ultimate permeation these 2D membranes can provide.

Recent advances in graphene synthesis and processing (13) have enabled demonstrations of atomically thin two-dimensional (2D) membranes showing mechanical sturdiness and hermetic sealing (4, 5). Initial attempts to endow mass permeability to the otherwise impermeable graphene have been based on formation of a single aperture (6) and randomly etched or defect-originated pores (7, 8). However, the macroscopic quantification of mass transport through such 2D pores is extremely challenging because the task demands a large number of pores with controlled dimensions.

We have developed a facile and reliable method for making 2D membranes (Fig. 1, A to G). This process uses chemical vapor deposition (CVD) optimized to grow graphene with minimal defects and good grain connectivity in order to prevent undesirable crack formation (9). A clean transfer process places two layers of graphene consecutively onto a SiNx frame punctured with 49 pores each of 4 μm in diameter (Fig. 1D), forming freestanding graphene layers that are thinner than 1 nm. This double transfer strengthens the freestanding graphene and keeps it from leakage through random defects (10, 11). Cleanliness and quality of graphene are found to be crucial during this graphene transfer process because grain boundary defects, polymer residues, or dust particles can induce crack formation while perforating the graphene. Scanning electron microscope (SEM) images (Fig. 1E and fig. S1) support that our transfer process produces crack-free graphene over the length scale of the entire frame. The freestanding film of double-layer graphene remains impermeable to gases and water. Nanopores were then drilled with a focused ion beam (FIB) to produce porous membranes (Fig. 1, F and G). We used Ga-based FIB to perforate apertures between 14 nm and 1 μm in diameter and He-based FIB for <10-nm-pore drilling. Low exposure doses (5 × 10−6 to 5 × 10−5 pA/nm2 for Ga+ ions and 6 × 10−3 pA/nm2 for He+ ions) enabled fast and precise drilling, resulting in well-defined pore diameter distributions (Fig. 1, H to K).

Fig. 1 Membrane fabrication and diameter distribution.

(A) Schematic of the porous graphene fabrication process. Step 1: freestanding SiNx membrane formation (by means of KOH etching). Step 2: microscale pore formation through the SiNx membrane (by means of photolithography and reactive ion etching). Step 3: graphene transfer. Step 4: graphene surface cleanup. Step 5: physical perforation of graphene (by means of Ga- and He-based FIB drilling). (B) Photograph (bottom view) of a full membrane structure. (C) Bottom view SEM image of the SiNx membrane. (D to G) Top view SEM images of (D) porous freestanding SiNx window before graphene transfer, (E) freestanding graphene transferred on one of the 4-μm-wide SiNx open pores, (F) 50-nm-wide apertures FIB-drilled on the freestanding graphene (Ga FIB) (scale bar, 500 nm), and (G) 7.6-nm-wide apertures perforated in the similar way (He FIB) (scale bar, 100 nm). (H to K) Aperture size distributions of the (H) 7.6-nm-, (I) 16-nm-, (J) 50-nm-, and (K) 100-nm-perforated graphene membranes.

The large number of pores (~103 to 106 per membrane) allows gas flows detectable with conventional mass flow meters. The membranes are mechanically sturdy enough to stand pressure differences of up to 2 bar (higher pressure not tested). N2 flow shows linear pressure dependence (figs. S2 and S3), resulting in pressure-independent permeance. N2 flux displays diameter dependence characterized by two asymptotic theories: free molecular transport (effusion) and modified Sampson’s model (12, 13) for small- and large-size apertures, respectively (Fig. 2A). For apertures smaller than 50 nm, the mean free path (λ) becomes larger than the aperture diameter (d), and the probability of having intermolecular collisions in the vicinity of the aperture decreases. Here, the transport enters the molecular flow regime featured by effusion for small apertures. Knudsen numbers (λ/d) for membranes (7.6 nm < d < 50 nm) are between 1 and 10, which is well within the molecular flow regime, and so the flow can be explained by the effusion mechanism, which is purely dependent on the probability of a molecule hitting the aperture. This can be quantified by the effusion flux, Embedded Image, where n is the gas number density, Embedded Image is the mean molecular speed, P is the pressure, kB is the Boltzmann constant, T is the temperature, and m is the molecular weight. As the pore diameter enlarges, more molecules interact with one another near the aperture, causing a transition from effusion to a more collective flow. However, collective flow models based on pore wall interactions (the Hagen-Poiseuille model) are not suitable to explain the flow behavior for atomically thin membranes. Such flows through an array of infinitely thin orifices can be modeled by a modified Sampson’s formula (12, 13) Embedded Image (1)where QS is the orifice flux, di is the diameter of aperture i on the graphene, μ is the dynamic viscosity of the gas species, and κ is the porosity based on the graphene area. The narrow pore diameter distributions allow us to predict that QS is linearly correlated with the diameter. Indeed, the permeance asymptotically approaches the QS prediction as the diameter gets larger than the mean free path (λ) (Fig. 2A). A more comprehensive quantification of gas permeance can be performed with respect to the Knudsen number (Kn = λ/d). The gas permeances for different pore size and gas variations are shown collectively in Fig. 2B, spanning a Kn range of 0.03 to 15. Here, the permeances are normalized by the effusion prediction for the corresponding species. For gas diffusion in a long capillary, it is known that there exists a minimum in the flux-Kn diagram at Kn of O(1), stemming from molecule-wall interaction and drift-to-diffusion shift (1416). However, investigators have observed no such minimum for relatively short capillaries that limit this interaction. Indeed, the gas permeation data of our extremely thin membrane confirms the omission of Knudsen’s minimum, which underscores that Knudsen’s minimum is primarily the result of the molecule-wall interaction. In the absence of the continuous radial confinement of gas transport, the effusion sets the asymptote in both the transition and molecular flow regimes, thus eliminating any minimum in the permeance.

Fig. 2 Characterization of gas transport through the membranes.

(A) N2 permeance per pore through different-diameter apertures (red circles) in comparison with predictions of the free molecular flow (effusion) theory (horizontal dashed line) and the modified Sampson’s model (dashed curve). (B) Permeance normalized with the free molecular flow prediction versus Knudsen number, with the Knudsen minimum undetected. (C) Gas permselectivity (defined as the permeances of H2, He, CH4, N2, CO2, or SF6 normalized by N2 permeance) for graphene membranes with different pore diameters (7.6 to 1000 nm) presented with respect to molecular weight. The solid line represents a power-law fit of the data, showing an exponent of –0.49, indicating an inverse square root mass dependence. (D) H2/CO2 gas separation factors versus pore diameter. The permeate composition was determined with mass spectroscopy for calculation of the separation factors. The solid line is drawn for visual guidance.

Because effusion is directly proportional to the average thermal speed of the molecules, it is expected that the effusive permeance would be directly proportional with m–1/2 following Graham’s law of effusion. Moreover, when the flow deviates from the effusive to collective behavior, gas viscosity also scales with m1/2, leading to the same mass scaling. These predictions are confirmed in Fig. 2C for all pore diameters, showing a permselectivity proportional to m–1/2. The origin of gas separation lies in the absence of linear momentum transfer between different molecular species (17). When intermolecular collisions exist during the permeation, the linear momentum is transferred from lighter molecules to heavier ones, causing a collective flow, thus reducing the separation. For single-component gas flows, there is no such momentum transfer even if there are molecular collisions, but when a gas mixture is permeating through graphene pores, these collisions must be eliminated. Therefore, apertures with diameters smaller than λ can have better separation efficiencies.

Selectivity for gas mixtures deviates from the permselectivity estimation for single gas permeance comparison. We measured mixed gas selectivity under cross flow conditions (fig. S4A). Gas mixtures with well-defined compositions were partially permeated through each graphene membrane, and the permeate gas compositions were determined by means of mass spectroscopy. The separation factor is defined asEmbedded Image (2)where α is the separation factor and γi and ϕi denote the mole fractions of species i in the permeate and the feed sides, respectively. The pore size dependence of α is shown in Fig. 2D for equally mixed H2 and CO2 gases. As predicted, the smallest pores can separate the best, close to the theoretical maximum predicted by the effusion theory for H2/CO2max = 4.69), whereas a clear decay in α is seen as the diameter increases, approaching the no-separation limit. This approach is correlated with the increased role of the collective flow, as explained above. The separation factor as we measured does not change much over the molar ratios of the feed mixture (fig. S4B).

Our atomically thin graphene membranes also permeated water and vapor at rates in excess of the conventional ultrafiltration and transpiration membranes, respectively. Onset of the water permeation is unfavorable for the membrane if only one side is wet because of capillarity, provided that the continuum theory holds true. Assuming that a mean free path for liquids can be comparable with the molecule’s own sizes, we took the water molecule size (~0.3 nm) as the displacement between molecular interactions and compared it with the pore aperture diameters. The equivalent Kn for water lies well below 0.01, placing the transport in the continuum flow regime. Therefore, it is not surprising that even a few bars of applied pressure could not initiate water flows because the capillary force at the graphene opening is high enough to equilibrate the driving pressure. On the contrary, water vapor permeated easily. Our measurements (fig. S5), based on the upright cup method (18), yielded many-orders-of-magnitude-higher water vapor transmission rate in comparison with that of breathable textiles (19). In order to eliminate the air-water-graphene interface and instigate water flow, we connected water from both sides of the membrane by prewetting the permeate side (micropit). This prewetting process helped initiate water permeation through the membrane even at a slight pressure difference of 250 mbar. After initial flow stabilization for ~5 min, a constant rate of water permeation through the membrane was established (fig. S6). The measured water permeance for the 50-nm pore membranes is five- to sevenfold higher than for conventional ultrafiltration membranes. We attribute these enhancements in water and vapor transport to the atomic thickness and the hydrophobic nature of graphene.

Our observed water flux is on the order of magnitude comparable with a theoretical prediction (Eq. 1) that accounts for the effect of water entrance to an infinitesimally thin porous membrane (Fig. 3) (13). The major obstacle in the data acquisition is that graphene could peel off during the water flux measurement (20). The water flow funneled toward graphene pores could shear off the stripped graphene from the membrane area and eventually break the membrane. To suppress membrane disintegration, we cut and glued the edge of the active membrane area to the underlying SiNx support by means of direct Pt deposition using FIB (Fig. 3, inset). The Pt enclosure successfully protected the membranes from peeling.

Fig. 3 Water permeation data.

Water flow rates per graphene pore for three graphene membranes with different pore sizes, in comparison with the modified Sampson’s model prediction (dashed line). (Inset) SEM image of the Pt enclosure surrounding the entire membrane area to prevent membrane disintegration (scale bar, 10 μm).

Permeance and selectivity provide a figure of merit for membrane performance in practical applications. As shown in Fig. 4A, the gas permeance of the porous graphene membrane is orders of magnitude superior to other polymeric (21), inorganic (2224), graphene oxide (10, 11), and composite membranes. The selectivity is comparable with some conventional polymer or carbon molecular sieve (CMS) membranes (2527). For certain applications, permeance becomes more crucial than selectivity, in which large amounts of gases with comparable molar ratios are separated (for example, CO2 removal from natural gas) (28, 29). Effusion-based selectivity is also important for separation of gases with large mass differences, such as removal of high carbons from natural gas, flavor selection, and organic solvent separation (30).

Fig. 4 Membrane figures of merit and comparisons.

(A) Comparison of H2/CO2 gas-separation performances of the porous graphene membranes (7.6-nm pore diameter, with 4.0% porosity) and other membranes: graphene oxide (GO) (10, 11), poly(1-trimethylsilyl-1-propyne) (PMSP) (25), polyetherimide (PEI) (26) carbon molecular sieve (CMS) (27), zeolite (22, 23), silica (24), metal-organic framework (MOF) (34), and SiC (35). (B) Water permeance values for porous graphene (50-nm pores, with 4.7% porosity) and other ultrafiltration membranes [acrylic (31, 32), cellulosics, and polysulfone (31, 33)]. (C) Comparison of water vapor transmission rate for porous graphene membranes (five 400-nm-pore membrane samples, with porosity ranging from 3.6 to 11.5%) and waterproof-yet-breathable textile membranes [data taken from (18, 19)]. All porous graphene permeance values are based on the total graphene membrane area.

Our porous graphene membranes also permeate water several times faster than do ultrafiltration membranes such as acrylic (31, 32), cellulosics, and polysulfone (31, 33), reducing the pressure requirements proportionally (Fig. 4B). Despite this high water permeance, when air is present on the other side of the graphene we have not observed any water flow, even up to a few bars of pressure difference. Our porous graphene membrane thus might be an efficient waterproof membrane material, while being highly breathable owing to observed ultrahigh vapor permeances. Indeed, the comparison of the water vapor transmission rate of our graphene membranes with commercial waterproof membranes (18, 19) confirms up to 4 orders of enhancement in breathability (Fig. 4C).

We have engineered large-scale physical perforation of free-standing graphene having controlled pore sizes ranging from <10 nm to 1 μm. Such membranes enable quantitative analysis of mass transport phenomena, such as atmospheric pressure effusion, through atomically thin apertures, revealing distinct effusive, transition, and collective flow regimes. Orders-of-magnitude enhancements are observed for gas, water, and water vapor permeances, compared with the state-of-the-art membranes.

Supplementary Materials

Materials and Methods

Figs. S1 to S11

References (3645)

References and Notes

  1. Acknowledgments: We appreciate the support from Binnig Rohrer Nanotechnology Center of ETH Zurich and IBM Zurich. J.B. and H.G.P. thank Swiss National Science Foundation for financial support (200021–137964). This work was partially supported by LG Electronics Advanced Research Institute, for which K.C., R.M.W. and H.G.P. are grateful. I.S. is thankful to Swiss National Science Foundation for support in equipment procurement (REquip 206021_133823). H.G.P. appreciates P. Jenny at ETH Zurich for his discussion on Knudsen’s minimum. J. Patscheider and L. Bernard at Laboratory for Nanoscale Materials Science of EMPA (Swiss Federal Laboratories for Materials Science and Technology), Switzerland, performed x-ray photoelectron spectroscopy and time-of-flight secondary ion mass spectrometry analyses, and C. Bae and H. Shin at the Department of Energy Science of Sungkyunkwan University, Korea, took high-resolution transmission electron microscope images, for which we are grateful.
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