Porous Graphene as the Ultimate Membrane for Gas Separation

NANO LETTERS

Porous Graphene as the Ultimate Membrane for Gas Separation

2009 Vol. 9, No. 12 4019-4024

De-en Jiang,*,† Valentino R. Cooper,*,‡ and Sheng Dai† Chemical Sciences DiVision and Materials Science and Technology DiVision, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831 Received July 9, 2009; Revised Manuscript Received September 8, 2009

ABSTRACT We investigate the permeability and selectivity of graphene sheets with designed subnanometer pores using first principles density functional theory calculations. We find high selectivity on the order of 108 for H2/CH4 with a high H2 permeance for a nitrogen-functionalized pore. We find extremely high selectivity on the order of 1023 for H2/CH4 for an all-hydrogen passivated pore whose small width (at 2.5 Å) presents a formidable barrier (1.6 eV) for CH4 but easily surmountable for H2 (0.22 eV). These results suggest that these pores are far superior to traditional polymer and silica membranes, where bulk solubility and diffusivity dominate the transport of gas molecules through the material. Recent experimental investigations, using either electron beams or bottom-up synthesis to create pores in graphene, suggest that it may be possible to employ such techniques to engineer variable-sized, graphene nanopores to tune selectivity and molecular diffusivity. Hence, we propose using porous graphene sheets as one-atom-thin, highly efficient, and highly selective membranes for gas separation. Such a pore could have widespread impact on numerous energy and technological applications; including carbon sequestration, fuel cells, and gas sensors.

“Carbon has this genius of making a chemically stable twodimensional, one-atom-thick membrane in a three-dimensional world. And that, I believe, is going to be very important in the future of chemistry and technology in general.” This remark by the late Richard E. Smalley in his 1996 Nobel lecture predicted the exploding interest in graphene. Since its successful isolation in 2004,1 waves of discoveries in fundamental physics, materials science, device applications, and the chemistry of graphene have been reported.2-6 The isolation of a free-standing graphene sheet was a remarkable feat in that it allowed researchers to study a truly one-atom-thin two-dimensional system. The relative inertness of the graphene π-system coupled with its mechanical strength opens up many potential opportunities for materials applications. One such potential application is the use of graphene sheets as membranes for gas separation. Membrane separation of gases is desirable due to its low energy cost.7 For example, the purification and production of H2 by the most common route of methane reforming requires separating H2 from other gases.8 As such, various membranes have been developed for hydrogen separation, including metallic, silica, zeolite, carbon-based, and polymer membranes. These membranes range from tens of nanometers to several micrometers in thickness. However, since the permeance of a membrane is inversely proportional to the thickness of the membrane,9 * To whom correspondence should be addressed, [email protected] and [email protected]. † Chemical Sciences Division. ‡ Materials Science and Technology Division. 10.1021/nl9021946 CCC: $40.75 Published on Web 09/23/2009

 2009 American Chemical Society

these membranes may be limited in their overall efficiency/ productivity. The exciting feature of the graphene sheet is its one-atom thickness, therefore being the ultimate membrane. Understanding molecular and atomic transport through such a truly two-dimensional membrane is not only fundamentally interesting but may be useful in a number of applications such as proton exchange membranes in fuel cells, separating gases to increase the sensitivity of chemical sensors, and the separation of carbon dioxide from the exhaust gases of industrial/power plants. The perfect graphene sheet, however, is impermeable to gases as small as He.10 This is due to the fact that the electron density of its aromatic rings is substantial enough to repel atoms and molecules trying to pass through these rings. Therefore, to achieve gas permeability it is necessary to “drill holes” in the graphene sheet. Recently, the electron beam of a transmission electron microscope has been employed to punch closely spaced nanopores within suspended graphene sheets.11 Alternatively, molecular building blocks have been assembled to create porous two-dimensional sheets.12 Improvements in these techniques may be fruitful for creating ordered subnanometer-sized pores within graphene sheets which may then be used as two-dimensional molecular-sieve membranes for gas separation. Previously, Sint et al.13 used classical molecular dynamics (MD) simulations to study the diffusion rates of solvated ions (Na+, K+, Cl-, and Br-) passing through graphene nanopores driven by an external electric field. These studies highlighted the viability of graphene as ion separation membranes as they were able to simulate pores that exhibited

selectivity either toward cations or anions. The charges on the graphene sheet and their responses to the passing-through ions/molecules are not straightforward to deal with in classical MD simulations but would be automatically accounted for within the framework of first principles density functional theory (DFT). More importantly, gas separation, which is paramount to the chemical industry and subject to huge potential saving of energy, has not been explored for similar graphene membranes. In this paper, we computationally demonstrate the membrane separation capability of a porous graphene sheet for molecular gases (H2 versus CH4) by designing subnanometer-sized pores and modeling their selective diffusion of gas molecules with first principles methods. Density functional theory calculations with planewave bases and periodic boundary conditions were employed to explore the potential energy surface and dynamics of hydrogen and methane molecules passing through subnanometer pores created in a graphene sheet. Initial static calculations were performed using both the Perdew, Burke, and Erzenhoff (PBE14) functional form of the generalizedgradient approximation (GGA) and the Rutgers-Chalmers van der Waals density functional (vdW-DF) for exchange and correlation.15,16 Dispersion interactions should be important for the interaction of neutral, nonpolar molecules such as H2 and CH4 with the aromatic rings of the graphene sheet and therefore we employ the vdW-DF in order to evaluate the strength of these interactions. The vdW-DF has been extensively tested on numerous systems;17 including the physisorption of small molecules to graphene sheets18,19 and the adsorption of H2 within metal-organic framework materials.20 Here, the recently developed self-consistent vdWDF15 as implemented in a modified version of the Abinit21 planewave code was employed. Norm-conserving pseudopotentials and a kinetic-energy cutoff of 680 eV for planewaves were used. Given the large unit cell required to model the porous graphene, only the Γ-point was used for sampling the Brillouin zone. First principles MD (FPMD) simulations were performed using the Vienna ab initio simulation package22,23 and the all-electron projector-augmented wave method24,25 within the frozen core approximation to describe the electron-core interaction, thus requiring a lower kineticenergy cutoff (300 eV in this case).25 For the FPMD simulations, 15 H2 or CH4 molecules were placed within a hexagonal cell with the porous graphene in the ab-plane and a c-dimension of 12 Å. Constant-temperature simulations with a time step of 1 fs at 600 K were performed. Figure 1a illustrates the creation of a pore which displays high H2/CH4 selectivity. We, first, removed two neighboring rings from a graphene sheet with a 6 × 6 hexagonal lattice which has a periodicity of 1.47 nm (see Figure 1b) based on the PBE-optimized lattice parameter for graphene (2.45 Å). Next, four unsaturated carbon atoms were passivated with hydrogen atoms while the remaining four were substituted with nitrogen atoms (Figure 1a). Figure 2 depicts the electron density isosurface of the graphene pore at a rather low value of 0.02 e/Å3. Here, the pore can be seen to be approximately rectangular in shape with dimensions of 3.0 Å × 3.8 Å. 4020

Figure 1. (a) Creation of a nitrogen-functionalized pore within a graphene sheet: The carbon atoms in the dotted circle are removed, and four dangling bonds are saturated by hydrogen, while the other four dangling bonds together with their carbon atoms are replaced by nitrogen atoms. (b) The hexagonally ordered porous graphene. The dotted lines indicate the unit cell of the porous graphene. Color code: C, black; N, green; H, cyan.

Figure 2. Pore electron density isosurface of the nitrogenfunctionalized porous graphene (isovalue of 0.02 e/Å3).

Certainly, an experimental realization of this porous graphene may be challenging; however, we propose two promising approaches based on recent experimental efforts. In the first approach, an electron beam can be used to punch holes in the graphene sheet11 and the dangling bonds can then be passivated by nitrogen doping with ammonia.26 A second approach is to synthesize a building block similar to the one enclosed in the dotted lines in Figure 1b and then assemble the building blocks into a larger sheet of porous graphene. This approach was successfully applied to construct a two-dimensional framework from building blocks created via the trimerizaton of terephthalonitrile.12 The Nano Lett., Vol. 9, No. 12, 2009

Figure 3. Interaction energy between H2 and the nitrogenfunctionalized porous graphene as a function of adsorption height. Insets show the definition of adsorption height and orientation of H2 in the pore. Legends: red squares, solid lines, vdW-DF; black circles, dashed lines, PBE.

resulting porous material consisted of 1.5 nm channels, featuring many pyridinic N atoms around the pore rim.12 While refinements in these techniques will be necessary to create well-ordered, appropriately sized pores, these successes offer potential pathways to synthesizing the porous graphene proposed in Figure 1. We examined several adsorption configurations for H2 placed at the center of the pore. Energetics from PBE calculations show that both the out-of-plane orientation and the in-plane orientation with the H2 bond axis pointing toward the passivating H atoms are slightly repulsive, while the inplane orientation with the H2 bond axis pointing toward N atoms is slightly attractive (we denote this orientation as XYZH2; see Figure 3 inset). vdW-DF yields the same energetic ordering for the three orientations. The favorable interaction of H2 at the XYZH2 configuration can be attributed to attraction between H2 and the N atoms. We next explored the potential energy surface (PES) for displacing the H2 molecule from the XYZH2 position perpendicularly out of the graphene plane. Figure 3 shows the PES for both PBE and vdW-DF. Both methods indicate that the PES is relatively flat (with barriers of 0.025 and 0.04 eV for PBE and vdW-DF, respectively) for H2 moving in and out of the pore. Including the vdW interaction shifts the PBE PES down by about 0.05 eV, though not uniformly. vdW-DF shows that H2 interacts most strongly at ∼1.6 Å above the pore. It should be noted that the true adsorption height may be 0.25-0.35 Å smaller as vdW-DF has a tendency to overestimate separation distances.27 At room temperature (RT) which corresponds to an energy of 0.025 eV, we expect that the H2 molecule would be able to overcome the barrier to passing through this pore. This result is consistent with the fact that the kinetic radius of H2 (2.89 Å)28 is smaller than the width of the pore (3.0 Å). To investigate the selectivity of the pore for the diffusion of H2 relative to CH4, we also explored the PES for CH4 passing through the pore. Similar to the H2 calculations, we examined several configurations of CH4 adsorbed in the pore Nano Lett., Vol. 9, No. 12, 2009

Figure 4. Interaction energy between CH4 and the nitrogenfunctionalized porous graphene as a function of adsorption height. Insets show the definition of adsorption height and orientation of CH4 in the pore. Legends: red squares, solid lines, vdW-DF; black circles, dashed lines, PBE.

center and found that in the most stable orientation, the four H atoms of CH4 point toward the four corners of the rectangular pore (see inset of Figure 4). In this configuration, PBE shows a repulsive interaction of 0.41 eV. The inclusion of vdW interactions gives a slightly less repulsive energy of 0.33 eV. The PES for displacing the CH4 molecule out of the pore shows a parabolic decrease in the repulsive interaction which, after an inflection point at ∼1 Å, reaches a shallow attractive well at larger separation distances, for both PBE and vdW-DF. In the latter case, the well is deeper with a depth of -0.18 eV around 2.5 Å, while for the former, the well is very shallow with a depth of -0.03 eV around 2.75 Å. Incorporation of vdW interactions shifts the PES curve down by an average 0.1 eV, and one can consider the PBE curve to sufficiently approximate the shape of the vdWDF PES. This barrier is also consistent with the larger kinetic radius of CH4 (at 3.8 Å)28 relative to the pore width. On the basis of molecular diffusion barriers, the pore selectivity of H2/CH4 can be easily estimated. In contrast with traditional membranes for H2 separation such as silica and polymers where selectivity is a product of diffusivity and solubility ratios,29 the concepts of solubility and free volume are not applicable for the one-atom-thin graphene membrane. Here, the diffusivity ratio alone determines the selectivity of the gas molecule passing through the pore. Assuming that the diffusion rates follow the Arrhenius rate equation and that the prefactor is of the same magnitude for both gases,30 the vdW-DF diffusion barriers of 0.04 and 0.51 eV for H2 and CH4, respectively, yield a selectivity of 108 for H2/CH4 (see the Supporting Information for details). This is a remarkably high selectivity, considering that both polymer and silica membranes usually have a selectivity for H2/CH4 ranging from 10 to 103 (ref 8). Although metallic membranes have similarly high H2/CH4 selectivity as the proposed porous graphenesdue to the dissociation of H2 molecules at the membrane surface which facilitates faster diffusion of atomic hydrogen species8sthey are unfavorable as they are expensive and susceptible to H-induced degradation.8 4021

Figure 5. Snapshots of H2 diffusing through the nitrogen-functionalized pore from first principles molecular dynamics simulations at 600 K. The passing-through H2 molecule is highlighted in dark gray.

The low diffusion barrier of the H2 molecule through the pore should allow us to observe passing-through events with FPMD simulations. Given that PBE and vdW-DF give similar PES for H2 interacting with the pore and that the vdW-DF method has yet to be incorporated within an MD simulation code, we used the PBE method for the MD simulations. We performed an NVT simulation at 600 K. We chose the high temperature to accelerate the dynamics, in order to observe passing-through events within a reasonable simulation time. During a 36 ps run, we observed an H2 passing through rate of 0.1 molecules/ps. This relatively fast rate is simply a reflection of the relatively low potential energy barrier for H2 passing through the pore as indicated by the PES. Figure 5 shows snapshots of a passing-through event. At 244 fs, the H2 molecule enters the pore in an XYZH2 position, as predicted by the geometry optimization discussed above, and then stays there for about 180 fs. At 424 fs, the H2 molecule begins to diffuse out of the pore. Similar MD simulations for the CH4 molecule were performed, but no passing-through events were observed for the same time frame. Hence, the FPMD simulations further illustrate the high permselectivity of the porous graphene for H2/CH4 separation. Using our MD simulation for H2 passing through the pore, we give a crude estimate of the H2 flux through the porous graphene membrane. Averaging the number of passingthrough events (4) over the simulation time (36 ps) and taking into account the area of the membrane (187 Å2), yield a flux of 10 mol H2 cm-2s-1. Assuming a pressure drop of 1 bar across the membrane, we arrive at an H2 permeance of 1 mol m-2 s-1 Pa-1. If we take into account the underestimate (by ∼0.015 eV) of the diffusion barrier by PBE, the permeance would be lowered by a factor of only 1.3 at 600 K. For comparison, a 30-nm-thick silica membrane has an H2 permeance of 5 × 10-7 mol m-2 s-1 Pa-1 at 673 K,28 and a similarly thick silica-alumina membrane has an H2 permeance of 2-3 × 10-7 mol m-2 s-1 Pa-1 at 873 K.31 Polymeric membranes tend to have even lower H2 permeance32 than oxide-based membranes. We attribute the porous graphene’s high permeance to its one-atom thickness, as the permeance of a membrane (namely, the productivity 4022

Figure 6. An all-hydrogen passivated pore in graphene (a) and the pore electron-density isosurface (b). Isovalue is at 0.02 e/Å3.

of a membrane33) is inversely proportional to the membrane thickness.9 The high selectivity of the pore for H2/CH4 separation relies on the precise control of the pore size, which is determined by how the pore is created and how the dangling bonds are passivated. The exact placement of N atoms and H atoms as shown in Figure 1 probably requires the bottomup organic synthesis, as the hole-punching by electron beam followed by NH3 treatment is unlikely to offer such a precise control. To alleviate this difficulty of N functionalization but still maintain the high H2/CH4 selectivity, one can create an all-hydrogen passivated pore as shown in Figure 6a. In this case, the eight dangling σ-bonds are saturated with H, rather than substituting four carbon atoms with N. The width of the pore is narrowed to 2.5 Å due to the additional H atoms, while the length of the pore remains at ∼3.8 Å (Figure 6b). This smaller pore size does have an effect on the diffusion barriers: we found that the vdW-DF barrier for H2 and CH4 increases to 0.22 and 1.60 eV, respectively (Figures 7 and 8).34 Since the selectivity is dictated by the ratio of the two diffusion barriers, the dramatically increased CH4 diffusion barrier coupled with the small change in the H2 diffusion barriers translates into a drastic increase in the H2/CH4 selectivity in the all-H pore relative to that of the Nfunctionalized pore. Again, by use of the Arrhenius equation to estimate the selectivity, this new pore will have a Nano Lett., Vol. 9, No. 12, 2009

Figure 7. Interaction energy between H2 and the all-hydrogen passivated porous graphene as a function of adsorption height. Insets show the definition of adsorption height and orientation of H2 in the pore. Legends: red squares, solid lines, vdW-DF; black circles, dashed lines, PBE.

Figure 8. Interaction energy between CH4 and the all-hydrogen passivated porous graphene as a function of adsorption height. Insets show the definition of adsorption height and orientation of CH4 in the pore. Legends: red squares, solid lines, vdW-DF; black circles, dashed lines, PBE.

selectivity of H2/CH4 at ∼1023 at room temperature. We also note that the 0.22 eV barrier for H2 passing through the pore can be overcome quite frequently at room temperature: assuming a prefactor of 1013 s-1, we estimate a passingthrough frequency of 109 per second at room temperature. Due to its simpler chemical construction, this all-H pore is even more promising for separating H2 from CH4 than the N-functionalized pore. The absence of dangling bonds and the fact that no chemical reactions occur during H2/CH4 separations at typical moderate operating temperatures8 suggest that the porous graphene membrane will be stable during the separation process. A porous graphene membrane, like other membranes for gas separation, will be susceptible to short-circuit by largesize pore defects. To assess this effect, we first examined two larger pore sizes to determine at what size the pore will lose its H2/CH4 selectivity. Using DFT-PBE calculations, we found that H2 can pass through the two larger pores without Nano Lett., Vol. 9, No. 12, 2009

a barrier (Figures S1 and S2 and Table S1 in the Supporting Information), while the diffusion barrier for CH4 decreases to a negligible 0.02 eV for the medium-sized pore (width at 3.8 Å) and to zero for the largest pore (5.0 Å). For pores greater than 3.8 Å (which is roughly the kinetic radius of CH4), both H2 and CH4 diffuse through without a barrier. We then analyzed the graphene membrane’s selectivity as a function of the concentration of larger-pore defects, assuming a simple two-pore-sized model where the smaller pore is highly selective for H2/CH4 while the larger pore allows both gases to pass without a barrier. We found that for a given temperature, there is a critical concentration of larger-pore defects for a desired selectivity (Figure S3 in the Supporting Information). Furthermore, increasing temperature can be used to suppress the effect of defects. (See Supporting Information section 4 for further details.) This analysis is useful for understanding the capacity of porous graphene for gas separation, given the reality of imperfect manufacturing techniques. For separation of small gas molecules, the key parameter demonstrated here is the pore width with respect to the kinetic radii of the target molecules. Although the two types of pores examined in Figures 1 and 6 are similar in structure, they have different widths (2.5 Å versus 3.0 Å) which make a big difference in separating H2 (kinetic radius 2.9 Å) from CH4 (kinetic radius 3.8 Å). On the basis of these calculations, we conclude that for a given separation, the design principle is to construct a pore with the size close to or slightly smaller than that of the smaller molecule of the gas mixture. To finetune the pore size, one can consider different passivating groups for the pore rim (such as hydrogen versus nitrogen). It is certainly challenging to make subnanometer pores in graphene, as the smallest pores achieved experimentally so far are still in the range of several nanometers.11,12 However, we hope that our work will stimulate experimentalists to take up this challenge. In conclusion, we have designed two one-atom-thin porous membranes for gas separation. These membranes are derived from a graphene sheet with ordered, appropriately passivated holes in it. The first pore features nitrogen functionalization together with hydrogen passivation and an isosurface plot of the electron density indicates that the pore is approximately rectangular in shape with dimensions of 3.0 Å × 3.8 Å. The second pore has all-H passivation and dimensions of 2.5 Å × 3.8 Å. An exploration of the potential energy surface and molecular dynamics simulations highlight the selectivity of the pores for H2 over CH4. Using our computed diffusion barriers, we estimate H2/CH4 selectivities on the order of 108 and 1023 for the N-functionalized and the all-H pores, respectively. First principles molecular dynamics simulations indicate a high flux of H2 through the N-functionalized pore in the graphene membrane which is in accord with the relatively low H2 diffusion barriers. Our work here represents a first effort to demonstrate the possibility of using porous graphene for gas separation. Such one-atom-thin molecular sieves may be useful for separating carbon dioxide in carbon sequestration applications and as membranes in fuel cells and gas sensors. Furthermore, our 4023

vdW-DF results could be useful for the accurate parametrization of empirical force fields for large scale simulations of the interactions of gases with the porous graphene at realistic pressures and temperatures. Acknowledgment. D.J. and S.D. were supported by the Division of Chemical Sciences, Geosciences, and Biosciences, and V.R.C. was supported by the Division of Materials Sciences and Engineering, Office of Basic Energy Sciences, U.S. Department of Energy under Contract No. DE-AC05-00OR22725 with UT-Battelle, LLC. This research used resources of the National Energy Research Scientific Computing Center, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. Supporting Information Available: Estimate of membrane selectivity using the Arrhenius equation for the diffusion, estimate of diffusion prefactors using the transition state theory, studies of two additional pore sizes for H2/CH4 separation, and estimate of selectivity by a graphene membrane with mixed pore sizes. This material is available free of charge via the Internet at http://pubs.acs.org/. References (1) Novoselov, K. S.; Geim, A. K.; Morozov, S. V.; Jiang, D.; Zhang, Y.; Dubonos, S. V.; Grigorieva, I. V.; Firsov, A. A. Science 2004, 306, 666. (2) Avouris, P.; Chen, Z. H.; Perebeinos, V. Nat. Nanotechnol. 2007, 2, 605. (3) Geim, A. K.; Novoselov, K. S. Nat. Mater. 2007, 6, 183. (4) Beenakker, C. W. J. ReV. Mod. Phys. 2008, 80, 1337. (5) Neto, A. H. C.; Guinea, F.; Peres, N. M. R.; Novoselov, K. S.; Geim, A. K. ReV. Mod. Phys. 2009, 81, 109. (6) Park, S.; Ruoff, R. S. Nat. Nanotechnol. 2009, 4, 217. (7) Freemantle, M. Chem. Eng. News 2005, 83, 49. (8) Ockwig, N. W.; Nenoff, T. M. Chem. ReV. 2007, 107, 4078. (9) Oyama, S. T.; Lee, D.; Hacarlioglu, P.; Saraf, R. F. J. Membr. Sci. 2004, 244, 45. (10) Bunch, J. S.; Verbridge, S. S.; Alden, J. S.; van der Zande, A. M.; Parpia, J. M.; Craighead, H. G.; McEuen, P. L. Nano Lett. 2008, 8, 2458. (11) Fischbein, M. D.; Drndic, M. Appl. Phys. Lett. 2008, 93, 113107. (12) Kuhn, P.; Forget, A.; Su, D. S.; Thomas, A.; Antonietti, M. J. Am. Chem. Soc. 2008, 130, 13333. (13) Sint, K.; Wang, B.; Kral, P. J. Am. Chem. Soc. 2008, 130, 16448. (14) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. ReV. Lett. 1996, 77, 3865.

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NL9021946

Nano Lett., Vol. 9, No. 12, 2009