ARTICLE pubs.acs.org/JPCC
Separation of Hydrogen and Nitrogen Gases with Porous Graphene Membrane Huailiang Du,†,‡ Jingyuan Li,† Jing Zhang,‡ Gang Su,§ Xiaoyi Li,*,†,‡ and Yuliang Zhao*,† †
Key Laboratory for Biomedical Effects of Nanomaterials & Nanosafety, National Center for Nanosciences and Technology of China, Institute of High Energy Physics, Chinese Academy of Sciences, Beijing 100049, China ‡ College of Materials Science and Optoelectronics Technology, Graduate University of Chinese Academy of Sciences, Beijing 100049, China § College of Physical Sciences, Graduate University of Chinese Academy of Sciences, Beijing 100049, China ABSTRACT: We designed a series of porous graphene as the separation membrane of H2/N2. The selectivity and permeability could be controlled by drilling various nanopores with different shapes and sizes. The mechanisms of hydrogen and nitrogen to permeate through the porous graphene are different. The small nanopore (pore-11) can only allow the hydrogen molecules to permeate due to the size restriction. In the systems of bigger nanopores (e.g., pore-13, pore-14, etc.), where the pore size is big enough to allow nitrogen molecules to permeate without any restriction, we observed more permeation events of nitrogen than that of hydrogen molecules. The reason is that the van der Waals interactions with the graphene membrane make the nitrogen molecules accumulate on the surface of graphene. When the pore size further increases, the flow of hydrogen molecules exhibits the linear dependence on the pore area, while there is no obvious correlation between the flow of nitrogen molecules and the pore area.
’ INTRODUCTION Gas separation such as hydrogen separation is very important for the study of a new clean energy technique.1 A lot of materials have been developed to pursue the gas separation.2,3 Traditional systems for gas separation in industry consume a significant energy cost4 and cause environmental problems. The use of the membrane system5 as an efficient separation for the gas mixtures without any phase change obviously reduces the energy cost compared to traditional systems, so it may become a powerful material for the gas separation. Separation membranes6,7 could be divided into organic membranes, which are made of polymers; inorganic membranes that comprise membranes made of carbon, glass, metal, ceramics (including zeolites), and the hybrid membranes such as inorganic polymeric membranes (PDMS); and organicinorganic hybrid membranes. Glassy polymeric membranes exhibit good selectivity of different gas molecules8 and greatly improve the gas separation techniques but are often criticized because of their low gas permeability9 in room temperature. Meanwhile, the selectivity of rubbery polymeric membranes6 is mainly influenced by differences in the condensability of the gas species. In order to improve the performance of polymeric membranes, a lot of new compound materials have been developed. The silicone rubber/ poly(4-vinylpyridine)/polyetherimide10 composite hollow fibers were found to have high permeability and selectivity among H2, CO2, O2, N2, and CH4. The miscible polymer blends with r 2011 American Chemical Society
interpenetration networks were gained and behaved well on the selectivity of H2/CO2.11 One of the challenges of developing polymeric membranes is to achieve good gas selectivity without sacrificing any gas permeability.12 Another shortage of polymeric membranes is that the structure will gradually change due to aging and plasticization so that the second challenge of polymeric membranes is to achieve the long-lived gas separation performance. Carbon molecular sieve (CMS)13,14 as one of the porous inorganic membranes for gas separation has been developed with great efforts to provide better selectivity and thermal and chemical stability. It has been proven that CMS can separate the mixtures of gas molecules with minor differences among them.15 CMS is mechanically much stronger than polymeric membranes with excellent thermal and chemical stabilities.16,17 However, CMS is so brittle and fragile that it requires careful preparation.18 According to the mechanism of separation behaviors in many cases, the control of the pore size is an indispensable characteristic of a good membrane.19 The good separation membrane should have controllable pore size, stable structure, and efficient permeability. Graphene, the single-atom-thick planar membrane20,21 and the strongest structure22 that exists so Received: July 2, 2011 Revised: October 23, 2011 Published: October 27, 2011 23261
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Table 1. Lennard-Jones Interaction Parameters
Figure 1. Full view of the system: the graphene sheet is represented by a yellow plane with white points referring to carbon atoms, and the pore shape is colored by red; hydrogen and nitrogen molecules are colored by green and blue, respectively.
Figure 2. Structure of porous graphene models: (a) pore-10, (b) pore11, (c) pore-12, (d) pore-13, (e) pore 16, (f) pore-19, (g) pore-22, (h) pore-27, and (i) pore-32; each model is named according to the number of drilled atoms from the graphene sheet. Graphene is represented by yellow hexagons, and the pore shape is colored red; the drilled carbon atoms of graphene are shown by transparent gray balls.
far in the earth, becomes attractive for its potential applications to be a good membrane. Actually, graphene is impermeable for any atoms even as small as helium.23 In 2008, Michael D. Fischbein et al. successfully punched nanopores in graphene using a focused electron beam of the transmission electron microscope (TEM) and demonstrated that porous graphene is very stable.24 From then on, many achievements based on a porous graphene membrane have been reported. K. Sint et al. observed the ion selectivity through porous graphene composed by the functionalized graphene nanopores.25 The porous graphene was also found to allow the DNA to pass through the nanopores and may have the potential to conduct rapid sequencing of DNA.26 Recently, porous graphene as the gas separation membrane has been investigated by quantum mechanical calculations. J. Schrier proposed that porous graphene can act as the economical means of separating helium from other noble gases.27 De-en Jiang et al. used the porous graphene to separate H2 and CH4.28 The previous investigations of porous graphene as the gas separation membrane were based on quantum mechanical calculations. It will be very interesting to study the process of gas separation, especially the effect of pore size on the penetration
atom
σ (nm)
ε/kb (K)
hydrogen35
0.2960
34.2
nitrogen36
0.3798
71.4
carbon37
0.3400
28.0
kinetic of different gas molecules using molecular dynamics simulation. We designed a series of porous graphene with different pore sizes and shapes as the separation membrane for H2/N2. We found that both the selectivity and permeability could be controlled by adjusting the pore size and shape. The mechanisms of the hydrogen and nitrogen molecules to permeate through the porous graphene are different. The selectivity largely results from the different penetration mechanism of these molecules.
’ MODEL DESIGN The full view of the porous graphene model is shown in Figure 1. In order to gain a series of pore sizes, we drilled carbon atoms from the graphene and named the porous graphene model according to the number of drilled atoms, i.e., pore-11, pore-12, pore-13, etc., as shown in Figure 2. All molecular dynamics (MD) simulations are carried out by the NAMD29 (version 2.6) package with a CHARMM30 force field. VMD31 is used for molecular modeling and representation. The van der Waals (VDW) interactions were calculated within a cutoff distance of 12 Å, and the parameters of the Lennard-Jones potential were listed in Table 1. There are 142 hydrogen and 142 nitrogen molecules in the simulation system with the dimension of 42 Å 45 Å 100 Å. Periodic boundary conditions were applied in all three dimensions. The porous graphene membrane was placed in the middle of the box. Every model was simulated under 298 K for a 5 ns MD simulation after equilibration, and data were collected at each 20 fs. As we mentioned above, we used the L-J potential to measure the VDW interactions, which can be defined as " 6 # σ 12 σ ð1Þ ULJ ðrÞ ¼ 4ε r r ’ RESULTS AND DISCUSSION Pore size of those models was characterized as the average of the shortest and largest inner distances within the pore. Pore area was estimated according to the area of benzene rings drilled out of the graphene surface, shown as the gray part surrounded by the red line in Figure 2. In most cases, the permeation process could be divided into three steps. First, the gas molecule moves close to the membrane pore. Then, it moves back and forth across the pore for a few picoseconds. Finally, it goes to the other side of the membrane. The average duration time of hydrogen molecules around the membrane pore is longer than that of nitrogen molecules. Since there is no pressure gradient or the chemical potential difference in the simulation system, the number of permeation of gas molecules across the membrane to the left side is almost equivalent to that to the right side. We counted the permeation events in both directions. As shown in Table 2, there is no 23262
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Table 2. Pore Size, Pore Area, and the Number of Passing Gas Molecules through a Porous Graphene Membranea panel
a
(a)
(b)
(c)
(d)
(e)
(f)
(g)
(h)
(i)
name
pore-10
pore-11
pore-12
size (Å)
3.725
4.135
4.46
pore-13
pore-16
pore-19
pore-22
pore-27
pore-32
4.48
6.525
6.73
7.265
8.12
area (Å2)
46.84
51.53
56.21
56.21
8.645
65.58
74.95
84.32
98.37
112.42
H2-passage
10
9
22
45
39
68
92
121
178
N2-passage
0
1
9
129
255
223
243
214
241
Panel designations are from Figure 2.
Figure 3. Permeation ratio H2/N2 and N2/H2 against the number of drilled atoms in the graphene membrane.
Figure 4. Gas distributions along the x, y, and z axes.
nitrogen molecule observed to permeate through pore-10 during a 5 ns simulation, while 10 hydrogen molecules go through the pore. This is completely due to the pore size restriction. The VDW diameters of hydrogen and nitrogen atoms were around 2.64 Å and 3.7 Å, respectively, and the corresponding kinetic diameters are 2.89 Å32 and 3.64 Å.33,34 The size of pore-10 (3.725 Å) is too small for nitrogen to get through, while barely large enough for hydrogen to permeate. In this way, hydrogen
molecules can be completely separated from nitrogen molecules by model pore-10. When the pore size increases to 4.135 Å (pore-11), there is only one nitrogen molecule that permeates through the pore during a 5 ns simulation, and the corresponding number of hydrogen molecules is nine. When the pore size further increases to 4.46 Å (pore-12), there are still less nitrogen molecules that permeate through the porous graphene. As shown in Figure 2, 23263
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The Journal of Physical Chemistry C pore-11 and pore-12 can only allow the nitrogen molecules to permeate with some specific orientations. The restriction of the molecular orientation largely prohibits the permeation of nitrogen molecules. When nitrogen molecules are not blocked by the pores (e.g., pore-13), there are more nitrogen molecules that permeate through the porous graphene membrane than hydrogen molecules. It should be pointed out that although the pore areas of pore-13 and pore-12 are equal, nitrogen molecules could permeate through pore-13 without the orientation restriction as in the case of pore-12 (Figure 2). In this way, the number of permeating nitrogen molecules through pore-13 increases dramatically and is more than that of the hydrogen molecules. When the pore size further increases, there are still more nitrogen molecules that permeate through the nanopores. The permeation ratio, defined as the ratio of the numbers of permeation events of the two types of gas molecules, could be used to describe the selectivity of the membrane. The permeation ratio is presented in two ways, permeation ratio N2/H2 (blue line in Figure 3) and permeation ratio H2/N2 (red line in Figure 3). The higher permeation ratio means better selectivity of the membrane. If the permeation ratio is equal to one, there is no selectivity. There is a minimum in the curve of the permeation ratio H2/N2 against the pore size. The H2/N2 ratio decreases as the pore size increases until pore-16, where a maximum N2/H2 permeation ratio is observed. In other words, the number of permeations of nitrogen molecules is much less than that of hydrogen molecules when the pore is small, while it turns into the opposite tendency when the pore becomes larger. It is the restriction of size and shape that blocks nitrogen from getting through the relatively smaller pore. However, why do nitrogen molecules permeate through the nanopores more effectively than
Figure 5. Snapshot of gas distributions: nitrogen and hydrogen molecules are represented by green and blue balls, respectively; the graphene sheet placed in the center of the box at z = 0; and the plane is colored by yellow.
ARTICLE
hydrogen molecules in the systems of pore-13, -16, -19, -22, -27 and -32? In order to study the phenomena of better permeation of nitrogen molecules through these porous graphene models, we first calculated the distributions of the N2 and H2 molecules along the x, y, and z directions, as shown in Figure 4. The z axis is perpendicular to the plane of the graphene membrane. Hydrogen molecules uniformly distribute along the x, y, and z directions, and nitrogen molecules also uniformly distribute along the x and y directions. However, nitrogen molecules show great tendency to stay within the region of (5 Å around the graphene membrane, as can be viewed in Figure 5. Then, the van der Waals interactions between gas molecules and the graphene membrane along the z direction are also calculated. As shown in Figure 6, the graphene membrane exhibits great adsorption to nitrogen. It is the van der Waals interactions with the graphene membrane that make nitrogen molecules distribute within a single molecule layer to the graphene surface. In this way, the significant adsorption of nitrogen molecules makes it much more effective for nitrogen molecules to find the pore by diffusing onto the two-dimensional (2-D) surface; however, hydrogen molecules have to find the pore in a three-dimensional (3-D) space. This results in more permeation events of nitrogen through porous graphene than that of hydrogen. When the pore size further increases, the difference between the 2-D and 3-D diffusion becomes less significant. The permeation ratio N2/H2 decreases. The flow is used to characterize the membrane permeability quantitatively, which is defined as F ¼
NðmolÞ Sðm2 ÞTðsÞ
ð2Þ
where N is the moles of gas molecules that permeated through the membrane in both directions, S refers to the area of membrane in total, and T is the time duration. Since there is no pressure gradient or chemical potential difference across the membrane, we did not observe the net flow in any direction of gas molecule transportation. We calculated the flow of N2 and H2 in various membrane models, as shown in Figure 7. There is a prodigious increase of the flow of nitrogen molecules at around 57 Å2 of the pore area, where the restriction of the size and shape to the nitrogen permeation begins to vanish. After that, the flow of nitrogen molecules exhibits no correlation with the area of pores. In the case of the hydrogen molecules, there is only a small increase of the flow of hydrogen molecules at 57 Å2, which is due to the different shape of pore-12 and pore-13.
Figure 6. VDW energy between the gas molecule and graphene membrane along the z-axis. The graphene membrane is located at z = 0. 23264
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Figure 7. Flow of gas molecules passing through the porous graphene membranes at different pore areas.
After that, the hydrogen flow increases as the pore area increases. It exhibits a linear relationship between the hydrogen flow and the pore area.
’ CONCLUSIONS We found that the porous graphene membrane could be used to separate hydrogen and nitrogen molecules. The selectivity and permeability could be controlled by drilling different shapes and sizes of pores on a graphene membrane. One hundred percent of the separation of hydrogen from nitrogen could be achieved by using pore-10 with the pore size barely bigger than the hydrogen molecule and smaller than the nitrogen molecule. However, when the pore size increases to 6.525 Å (pore-16), the best selectivity of nitrogen from hydrogen is achieved. The van der Waals interactions with a graphene membrane can make nitrogen molecules distribute within a single molecule layer around the graphene surface, which induces more nitrogen permeation events through porous graphene than that of hydrogen when the pore is bigger than pore-13. The flow of nitrogen molecules increases prodigiously when the pore area is around 57 Å2, where the restriction of the size and shape to nitrogen permeation begins to vanish. Over this area, the flow of nitrogen molecules exhibits no correlation to the pore area. It is totally different in the case of hydrogen. The hydrogen flow exhibits a linear relationship to the pore area in the whole range. ’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected] (X.L.);
[email protected] (Z.Y.).
’ ACKNOWLEDGMENT This work was supported by the 973 program (2011CB933400 and 2012CB932901), the National Natural Science Foundation of China (project 21144001, 10934008, and 90922033), the Knowledge Innovation Program of Chinese Academy of Sciences, and the China Postdoctoral Science Foundation (grant 119103S139). We would like to express our thanks to Professor Miao Bing for very useful discussions. ’ REFERENCES (1) Sedigh, M. G.; Onstot, W. J.; Xu, L.; Peng, W. L.; Tsotsis, T. T.; Sahimi, M. J. Phys. Chem. A 1998, 102, 8580–8589. (2) Williams, J. J.; Wiersum, A. D.; Seaton, N. A.; D€uren, T. J. Phys. Chem. C 2010, 114, 18538–18547.
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