Tunable Hydrogen Separation in sp–sp2 Hybridized Carbon

Article pubs.acs.org/JPCC

Tunable Hydrogen Separation in sp−sp2 Hybridized Carbon Membranes: A First-Principles Prediction Hongyu Zhang,† Xiujie He,‡ Mingwen Zhao,*,‡ Meng Zhang,† Lixia Zhao,† Xiaojuan Feng,† and Youhua Luo*,† †

Department of Physics, East China University of Science and Technology, Shanghai 200237, China School of Physics and State Key Laboratory of Crystal Materials, Shandong University, Jinan 250100, Shandong, China

‡

ABSTRACT: First-principles calculations are carried out to investigate the hydrogen separation characteristics of two-dimensional carbon allotropes consisting of sp- and sp2-hybridized carbon atoms, i.e., graphyne, graphdiyne, and rhombic-graphyne. The selectivities for H2 over several gas molecules, including CO, N2, and CH4, are found to be sensitive to the pore sizes and shapes. The penetration barriers generally decrease exponentially with the pore sizes. Our results reveal that graphyne with small pores is unsuitable for the purpose of hydrogen separation. Graphdiyne, with larger pores, exhibits a high selectivity (109) for hydrogen over large gas molecules such as CH4, but a relatively low selectivity (103) over small molecules such as CO and N2. The large differences in diffusion barriers for molecules penetration through a rhombic-graphyne monolayer, which possesses pore size in between that of graphyne and graphdiyne, lead to a high selectivity (>1016) for hydrogen separation from the others. The results suggest that the abundant pores of different sizes in these carbon allotropes make them ideal molecular sieves for gas separation applications directed toward different separation needs and objectives.

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graphene sheet is impermeable to gases as small as He,14,15 it is necessary to create pores in graphene to achieve gas permeability by experimental techniques, such as electron beam treatment and heavy ion bombardment.16,17 However, a cost-effective method of preparing graphene with precisely controlled pore structure is yet to come. Therefore, to achieve high efficiency and separation performance, the exploration of new membrane materials with intrinsic and synthetically defined pore structures, as an alternative route, is highly desirable. Similarly to purely sp2-hybridized graphene network, a wide range of planar carbon allotropes with one-atom thickness containing sp- and sp2-hybridized carbon atoms has been proposed theoretically.18 For instance, graphyne can be constructed by replacing one-third of carbon−carbon bonds in graphene with acetylene linkages (−CC−),19 encircling natural pores larger than densely packed honeycomb lattice in graphene, as shown in Figure 1a. Extension of linear chains between carbon hexagons by an additional acetylenic linkage generates another sp-sp2 hybridized carbon allotrope called graphdiyne,20,21 as shown in Figure 1b. Moreover, the extra alkyne unit increases the pore size of the network. Excitingly, large-area graphdiyne has recently been successfully fabricated on the surface of copper via a cross-coupling reaction, paving

INTRODUCTION Nowadays, the depletion of fossil fuel and increased environmental problems are triggering the search for clean and renewable energy. Hydrogen has been identified as a particularly attractive alternative energy source and carrier because of its efficiency, natural abundance, and environmental friendliness.1 Currently, hydrogen can be produced through steam re-forming of methane, partial oxidation of hydrocarbon fuels, gasification of coal, water electrolysis, etc.2 Regardless of production methods, there are many byproducts associated with the manufacture of hydrogen.3 Therefore, it is obligatory to separate hydrogen from other undesirable species through a cost-effective and efficient way. Common techniques employed for hydrogen separation include pressure swing adsorption (PSA), fractional/cryogenic distillation, and membrane separation. 4 Among the various technologies for hydrogen purification, membrane separation is considered to be most promising, which mainly stems from the small footprint, easy operation, high energy efficiency, and low investment cost compared to the other conventional counterparts.5,6 Although diverse membranes, such as polymers,6 metals,7 zeolite,8 and silica,9 have been studied and applied in industries, the graphene-based membranes are of particular interest and great potential for hydrogen separation because of its oneatom thickness, and consequently high efficiency.10,11 According to the mechanism of separation behaviors in many cases, the control of the pore size is an indispensable characteristic of a good membrane.12,13 In view of the fact that a perfect © 2012 American Chemical Society

Received: May 21, 2012 Revised: July 14, 2012 Published: July 15, 2012 16634

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Figure 1. Top view of (a) graphyne, (b) graphdiyne, (c) rhombic-graphyne, and (d) square-octagon layer. Blue balls indicate the inscribed circles of the pores, and the numbers are the corresponding diameters in Å.

the way for its practical applications.22 Inspired by this great progress, considerable theoretical efforts have been devoted to studying the unique properties of this novel carbon allotrope family, as well as to designing new layered carbon materials consisting of sp-sp2 hybridized carbon atoms.23−28 As shown in Figure 1c, replacement of two-thirds of carbon−carbon bonds by acetylene linkages leads to a new layered structure, here termed as rhombic-graphyne for convenience as it has rhombus-like pores.18,29 These planar allotropes with unique properties, such as highly diversified structures, large range of pore sizes, and high surface areas, may open up exciting opportunities for construction of molecular sieve membranes to meet different separation needs and objectives. In this contribution, on the basis of first-principles calculations within density functional theory (DFT),30−35 we presented systematic computational investigations on the membrane separation capability of these porous sp−sp2 hybridized carbon allotropes with different pore sizes for molecular gases (H2 versus CO, N2, and CH4). Our calculations show that the hydrogen permeability and selectivity over other gas molecules is mostly governed by the pore sizes and shapes. Consequently, for different gas mixtures, the hydrogen permeability and selectivity could be optimized by choosing the type of monolayer carbon membranes, as well as the size and shape of the pores.

subsequent calculations of the potential energy profiles (PEP) for molecular gases penetrating the membrane pores, the carbon atoms surrounding the penetrated pores were fully relaxed while the z coordinates of the other carbon atoms were kept fixed. The convergence tolerance of the energy was set to 10−5 Ha (1 Ha = 27.2114 eV), and the maximum allowed force and displacement were 0.002 Ha/Å and 0.005 Å, respectively. For a crosscheck, parts of the diffusion barrier calculations have been repeated with VASP code by using the climbing-image nudged elastic band method (cNEB).33−35 It was found that the diffusion energy barriers obtained from both codes are in good agreement. All the results presented herein were obtained with the DMol3 code.

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RESULTS AND DISCUSSION We first investigated the penetration of H2 through a triangularlike pore of a graphyne monolayer. Figure 1a gives the optimized structure of a two-dimensional graphyne layer in a 2 × 2 supercell, with the pore size characterized as the diameter of the inscribed circle. The optimized lattice constants are a = b = 6.83 Å, in good agreement with other DFT calculations.19,27 Due to the existence of sp-hybridized carbon atoms in graphyne, it is energetically more unfavorable than graphene by about 0.73 eV/atom. However, our results indicate that graphyne is more stable than the already-synthesized graphdiyne by about 0.16 eV/atom, implying its high synthetic feasibility. We examined several configurations for H2 molecule adsorption on top of the pore. We have verified that the configuration with the H2 axis aligned perpendicular to the graphyne plane is slightly more stable than the parallel adsorption configurations by about 0.023 eV. In addition, it can be intuitively speculated that this vertical orientation is favored for the H2 molecule to minimize the energy barrier during the penetration process. However, the energy barrier for H2 penetrating the pore of graphyne is still as high as 1.98 eV, making graphyne unsuitable for the purpose of H2 separation under normal experimental conditions.

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METHODS AND COMPUTATIONAL DETAILS All the calculations were performed by using the DMol3 package.30,31 The local density approximation (LDA) with Perdew−Wang (PWC) exchange−correlation functional32 was employed for the spin-unrestricted calculations. Our calculations were carried out using 2 × 2 supercells to simulate infinite planar sheets. A vacuum region of 20 Å was applied in the z direction to ensure negligible interaction between adjacent layers. In the preliminary search and optimization, the equilibrium adsorption configurations for molecular gases were fully relaxed without any symmetric constraints. In the 16635

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We next focused on the capability of graphdiyne with a much larger pore for H2 separation from several gas molecules, including CO, N2, and CH4. As shown in Figure 1b, the optimized lattice constants of graphdiyne are a = b = 9.39 Å, in good agreement with previous theoretical results.28,36 The energetically stable adsorption configurations for different gas molecules are presented in Figure 2. In comparison with the

Figure 3. Energy profiles for H2, CO, N2, and CH4 passing through the pores of (a) graphdiyne and (b) rhombic-graphyne as a function of adsorption height. The energies of respective equilibrium adsorption configurations are set to zero.

SH2 /gas = Figure 2. Top view and side view of (a) H2, (b) CO, (c) N2, and (d) CH4 adsorption above the pore of graphdiyne. The gray, red, blue, and pink spheres represent C, O, N, and H atoms, respectively.

DH 2 Dgas

=

A H2 e−EH2 / RT Agas e−Egas / RT

where D is the diffusion rate, A is the diffusion prefactor, and E is the diffusion barrier. Assuming that the prefactors of these four gases are identical (AH2/Agas = 1)13 and temperature T is 300 K, we obtained a selectivity of about 103, 103, and 109 for H2/CO, H2/N2, and H2/CH4, respectively. With a relatively low selectivity for H2 over CO and N2, graphdiyne exhibits no obvious advantage for separating H2 from small gas molecules. Nevertheless, compared to other classical membranes like polymer and silica,4,37 which usually have the selectivity for H2/ CH4 ranging from 10 to 103, the present porous structure has a significantly higher selectivity for H2/CH4. Therefore, graphdiyne can be applied for efficient separation of H2 from mixtures of large molecules in many industrial applications, including the separation of H2/organic gases and organic gas mixtures such as n-C4H10/i-C4H10, benzene/cyclohexane, and propylene/propane.39,40 From the above results, we can clearly see that the diffusion barriers for gas molecules passing through the membranes sensitively depend on the pore sizes and shapes. Considering that the pore of graphyne appears to be too small, whereas that of graphdiyne is relatively large for separation of H2 from small molecular gases, such as CO and N2, we investigated a planar rhombic-graphyne layer, which possesses a pore size between that of graphyne and graphdiyne, as shown in Figure 1c. The fully relaxed lattice constants are a = 6.91 Å and b = 6.84 Å. The binding energy of rhombic-graphyne with respect to isolated C atoms is 7.71 eV/atom from the present calculations, which is comparable to that of graphdiyne (7.76 eV/atom).

case of graphyne, the energy barrier for H2 passing through the pore of graphdiyne decreases drastically to 0.03 eV, indicating a high H2 permeability (Figure 3a). This can be mostly attributed to the small size of H2 (kinetic diameter: 2.89 Å)37,38 relative to the pore size (5.42 Å), as shown in Figure 1b. The energy maximum corresponds to the H2 molecule sitting in the middle of the pore, with two H atoms distributing on both sides of the graphdiyne plane. Similar configurations have also been found for CO and N2 passing through the pore of graphdiyne. It is worth pointing out that in the equilibrium configuration for CH4 adsorption, one H atom of CH4 points toward the center of the pore, while the other three H atoms point toward the three carbon hexagons surrounding the pore of graphdiyne. Moreover, this orientation is maintained during the penetration process. The carbon ring encircling the pore buckles outward from the gas molecules when the CO/N2/CH4 is in the pore center, in accordance with other theoretical results.26 The diffusion barriers for CO, N2, and CH4 passing through the pore were calculated to be 0.221, 0.216, and 0.58 eV, respectively (Figure 3a). On the basis of computed diffusion barriers, the pore selectivity for H2 over other gas molecules can be quantitatively estimated according to the Arrhenius equation: 16636

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Our results agree well with other theoretical results as well.18,29 To further confirm the stability of rhombic-graphyne, we also performed ab initio molecular dynamics (MD) simulations on rhombic-graphyne at 300 K for 1 ps. It was found that rhombicgraphyne remains stable without significant deformation. For gas molecule adsorption, similar equilibrium configurations were obtained. In the succeeding diffusion processes, the molecular reorientations were allowed at each step to minimize the energy of the system. In contrast to the case of graphdiyne, the orientation of CH4 changes during the diffusion process, resulting in symmetric configurations above and below the plane, as shown in Figure 4. The diffusion energy barrier for H2

To quantitatively characterize the membrane permeability, the permeance, which represents the productivity of a membrane, was calculated by the expression: Q = (N/Δp), where Q is the permeance (mol m−2 s−1 Pa−1), N is the molar flux (mol m−2 s−1) of molecular gases, and Δp is the partial pressure difference (Pa) across the membrane.8 Within the kinetic theory of gases, the number of gas particles colliding with the wall is given by Γ = (p/(2πmkBT)1/2), with p, m, kB and T denoting the pressure, the mass of the molecules, Boltzmann constant, and the temperature, respectively.41 The probability that a particle has the velocity to diffuse through the pore is given by f = ∫ ∞ vB (f(v) dv), where f(v) represents the Maxwell velocity distribution and vB represents the velocity corresponding to the diffusion energy barrier.11 Thus, the flux N is obtained by N = Γ·f. Assuming an incoming pressure of p = 3 bar and a pressure drop of Δp = 1 bar across the pore, we obtained H2 permeance of rhombic-graphyne on the order of 10−9 mol m−2 s−1 Pa−1 at T = 300 K, comparable to the industrially acceptable permeance for gas separation.42 Further improvement in permeance can be achieved by increasing temperature properly.11 Therefore, with an extremely high selectivity and a reasonable H2 permeance, this porous planar structure can efficiently separate H2 from all other analyzed gas molecules, which may find broad technological applications in the development of hydrogen separation membranes. As intuitively expected, the diffusion barrier decreases with increasing pore size. To obtain a more quantitative relationship between the energy barrier and the pore size characterized as the diameter of the inscribed circle, another carbon allotrope composed of equal numbers of squares and octagons29 was examined, as shown in Figure 1d. For a specific gas mixture (H2, CO, and N2), the diffusion barrier as a function of pore size is shown in Figure 5. Generally, to a very good

Figure 4. Representative configurations for CH4 located (a) above and (b) below the rhombic-graphyne layer. The key atoms involved in the reorientation process are labeled by different colors.

was calculated to be 0.54 eV, lower than that in porous graphene (0.61 eV).10 This moderate energy barrier can be easily overcome by H2 under experimental conditions. Similarly, the diffusion barriers for CO, N2, and CH4 passing through the pore of rhombic-graphyne were computed to be 1.55, 1.73, and 3.00 eV, respectively (Figure 3b). It is noteworthy that the diffusion barriers do not follow the order of the kinetic diameters of gas molecules. For instance, CO has a larger kinetic diameter (3.76 Å) than that of N2 (3.64 Å),37,38 but the diffusion barrier for the former is lower than that for the latter. This result highlights the different chemical and physical interactions between the molecules and the pore in determining the diffusion barriers. A similar relationship has also been reported for interaction of CO and N2 with porous graphene.11 Using the calculated diffusion barriers and the Arrhenius equation, the selectivities of this new pore were estimated to be 1016, 1019, and 1041 for H2/CO, H2/N2, and H2/CH4 at room temperature, respectively. Obviously, as compared to graphdiyne, the present membrane demonstrates significantly improved selectivity between H2 and all other analyzed molecules.

Figure 5. Diffusion energy barrier as a function of pore size. The solid 2

lines are the fit to Eb = A·e−(d + bd)/t. The fitting parameters A, b, and t are 0.143, −5.199, and 1.886 for H2, 40820.874, −18.588, and −6.271 for CO, and 90941.314, −16.383, and −4.927 for N2, respectively.

approximation, the diffusion barrier decreases exponentially with the pore size but the magnitudes are different for different gas molecules. Our result is qualitatively consistent with the case of a He atom penetration through perfect and defective graphene, where the size of the defects is expressed by the number of carbon atoms included in the formation of the defects.15 Therefore, the energy barriers for H2, CO, and N2 passing through a carbon atomic membrane with a sp−sp2 hybridized carbon network can be predicted from this simple relationship, which provides a guideline for tailoring porosity of 16637

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(14) 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. (15) Leenaerts, O.; Partoens, B.; Peeters, F. M. Appl. Phys. Lett. 2008, 93, 193107. (16) Fischbein, M. D.; Drndić, M. Appl. Phys. Lett. 2008, 93, 113107. (17) Compagnini, G.; Giannazzo, F.; Sonde, S.; Raineri, V.; Rimini, E. Carbon 2009, 47, 3201. (18) Baughman, R. H.; Eckhardt, H.; Kertesz, M. J. Chem. Phys. 1987, 87, 6687. (19) Narita, N.; Nagai, S.; Suzuki, S.; Nakao, K. Phys. Rev. B 1998, 58, 11009. (20) Haley, M. M.; Brand, S. C.; Pak, J. J. Angew. Chem., Int. Ed. Engl. 1997, 36, 836. (21) Haley, M. M. Pure Appl. Chem. 2008, 80, 519. (22) Li, G.; Li, Y.; Liu, H.; Guo, Y.; Li, Y.; Zhu, D. Chem. Commun. 2010, 46, 3256. (23) Zhou, J.; Lv, K.; Wang, Q.; Chen, X. S.; Sun, Q.; Jena, P. J. Chem. Phys. 2011, 134, 174701. (24) Long, M.; Tang, L.; Wang, D.; Li, Y.; Shuai, Z. ACS Nano 2011, 5, 2593. (25) Malko, D.; Neiss, C.; Viñes, F.; Görling, A. Phys. Rev. Lett. 2012, 108, 086804. (26) Jiao, Y.; Du, A.; Hankel, M.; Zhu, Z.; Rudolph, V.; Smith, S. C. Chem. Commun. 2011, 47, 11843. (27) Zhang, H.; Zhao, M.; He, X.; Wang, Z.; Zhang, X.; Liu, X. J. Phys. Chem. C 2011, 115, 8845. (28) Bu, H.; Zhao, M.; Zhang, H.; Wang, X.; Xi, Y.; Wang, Z. J. Phys. Chem. A 2012, 116, 3934. (29) Enyashin, A. N.; Ivanovskii, A. L. Phys. Status Solidi B 2011, 248, 1879. (30) Delley, B. J. Chem. Phys. 1990, 92, 508. (31) Delley, B. J. Chem. Phys. 2000, 113, 7756. (32) Perdew, J. P.; Wang, Y. Phys. Rev. B 1992, 45, 13244. (33) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169. (34) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15. (35) Henkelman, G.; Uberuaga, B. P.; Jónsson, H. J. Chem. Phys. 2000, 113, 9901. (36) Pan, L. D.; Zhang, L. Z.; Song, B. Q.; Du, S. X.; Gao, H.-J. Appl. Phys. Lett. 2011, 98, 173102. (37) de Vos, R. M.; Verweij, H. Science 1998, 279, 1710. (38) Oyama, S. T.; Lee, D.; Hacarlioglu, P.; Saraf, R. F. J. Membr. Sci. 2004, 244, 45. (39) Lee, H. R.; Shibata, T.; Kanezashi, M.; Mizumo, T.; Ohshita, J.; Tsuru, T. J. Membr. Sci. 2011, 383, 152. (40) Lee, H. R.; Kanezashi, M.; Shimomura, Y.; Yoshioka, T.; Tsuru, T. AIChE J. 2011, 57, 2755. (41) Hauser, A. W.; Schrier, J.; Schwerdtfeger, P. J. Phys. Chem. C 2012, 116, 10819. (42) Zhu, Z. J. Membr. Sci. 2006, 281, 754.

carbon membranes to achieve desired permeability and selectivity. It is noteworthy that with the decrease of pore size, the permeability and selectivity of these atomic carbon membranes changes in opposite directions. An ideal molecular sieve should have a good balance between permeability and selectivity, and an optimized pore size is therefore quite crucial.

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CONCLUSIONS In summary, we performed first-principles study on the capability of different sp-sp2 hybridized carbon allotropes with natural pores for separating H2 from several gas molecules, including CO, N2, and CH4. Our calculations show that the permeability and selectivity are closely correlated to the pore sizes and shapes of membrane, and the penetration barriers generally decrease exponentially with the pore sizes. The pore size of graphyne appears to be too small for H2 separation due to its high diffusion barrier (1.98 eV). With a selectivity of 109 for the H2/CH4 separation, graphdiyne exhibits remarkably good performance in H2 separation from mixtures of large molecules, whereas the pore structure is slightly too large to achieve ideal H2 separation from small molecules such as CO and N2. For rhombic-graphyne, the large differences in energy barriers for gas molecules penetration through this membrane (0.54, 1.55, 1.73, and 3.00 eV for H2, CO, N2, and CH4, respectively) allow highly selective H2 separation (>1016), while maintaining a reasonable H2 permeability. The excellent selectivity combined with acceptable permeability makes graphdiyne and rhombic-graphyne promising materials for the construction of molecular sieve membranes targeted for H2 separation and purification from different gas mixtures.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: M.Z., [email protected]; Y.L., [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Basic Research Program of China (No. 2012CB932302), the National Natural Science Foundation of China (No. 10974119).

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