Theoretical Prediction of Hydrogen Separation Performance of Two

Dec 3, 2015 - The DFT calculations demonstrate that the fused pentagon network with proper pore sizes presents a surmountable energy barrier (0.18 eV)...
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Theoretical Prediction of Hydrogen Separation Performance of TwoDimensional Carbon Network of Fused Pentagon Lei Zhu,†,‡ Qingzhong Xue,*,†,‡ Xiaofang Li,‡ Yakang Jin,‡ Haixia Zheng,‡ Tiantian Wu,‡ and Qikai Guo‡ †

State Key Laboratory of Heavy Oil Processing and ‡College of Science, China University of Petroleum, Qingdao 266580, Shandong P. R. China ABSTRACT: Using the van-der-Waals-corrected density functional theory (DFT) and molecular dynamic (MD) simulations, we theoretically predict the H2 separation performance of a new two-dimensional sp2 carbon allotropes-fused pentagon network. The DFT calculations demonstrate that the fused pentagon network with proper pore sizes presents a surmountable energy barrier (0.18 eV) for H 2 molecule passing through. Furthermore, the fused pentagon network shows an exceptionally high selectivity for H2/gas (CO, CH4, CO2, N2, et al.) at 300 and 450 K. Besides, using MD simulations we demonstrate that the fused pentagon network exhibits a H2 permeance of 4 × 107 GPU at 450 K, which is much higher than the value (20 GPU) in the current industrial applications. With high selectivity and excellent permeability, the fused pentagon network should be an excellent candidate for H2 separation. KEYWORDS: hydrogen separation, two-dimensional carbon network, DFT, molecular dynamics, energy barrier, size restriction

1. INTRODUCTION Because of the energy crisis and environmental pollution, it is essential to exploit clean energy sources instead of fossil fuels. As an energy carrier, hydrogen possesses the highest energy density,1 produces only water after oxidation, and its energy conversion efficiency is much higher than that of fossil fuels, so it is the most promising alternative energy source in the future.2−4 Currently, steam reforming gas (CH4+H2O → CO(CO2)+H2) is the dominant technology for hydrogen production.5 The product usually has the impurities of CO, CH4, CO2, N2, H2O, and so on.6 As these impurities can severely cause fuel-cell catalyst poisoning when hydrogen is used as fuel-cell,7 the separation of hydrogen is of crucial importance. Compared with the traditional H2 separation technologies, such as pressure swing absorption and cryogenic distillation, membrane separation technology has been widely used in H2 separation because of its easy operation and low energy cost.8,9 In the past, traditional membranes, such as metal, polymer, and zeolite membranes have been widely used for H2 separation.10−14 Hosseini et al. identified that the miscible polymer blends with interpenetration networks significantly enhanced the selectivity of H2/CO2.11 Yilmaz and his coworks assessed the performance of zeolite imidazolate framework (ZIF) based mixed matrix membranes (MMMs) for H2/CH4 and H2/CO2 separation and found that ZIF-90 could enhance the H2/CH4 selectivity.14 For all types of membranes, there is a trade-off between selectivity and permeability, and the permeance of a membrane is inversely proportional to its thickness.15 However, all these membranes © 2015 American Chemical Society

range from tens of nanometers to several micrometers in thickness, and the permeance of these membranes are seriously affected by their thickness. Hence, a one-atom thin membrane may be a good candidate for H2 separation. Fortunately, graphene, a single atomic layer with two-dimensional array of planar hexagonal units of sp2-hybrdized carbon atoms, has been demonstrated the thinnest sheet (0.34 nm) with extraordinary chemical and mechanical stability.16−20 However, the perfect graphene sheet is impermeable to gases as small as He, due to the substantial electron density of its aromatic rings.21 To conquer the problem, “drill holes” in perfect graphene sheet to achieve gas permeability has been realized in recently.22,23 A focused electron beam of the transmission electron microscope has been successfully used to punch nanopores in graphene by Michael D. Fischbein.22 Lehtinen and his coworks have also employed heavy ion bombardment to punch nanopores in graphene sheets, which defect size can be tuned by ion energy.23 However, the precise control of pore size and pore density remains a formidable technology challenge, and these methods inevitably increase the cost and complexity. In addition, the edged carbon atoms of pores in porous graphene should be passivated, because of the dangling bonds with high chemical activity.24−26 To conquer these obstacles, some carbon allotropes monolayer membranes with periodically distributed uniform pores have been put forward for hydrogen Received: October 11, 2015 Accepted: December 3, 2015 Published: December 3, 2015 28502

DOI: 10.1021/acsami.5b09648 ACS Appl. Mater. Interfaces 2015, 7, 28502−28507

Research Article

ACS Applied Materials & Interfaces separation such as graphyne,27 graphdiyne,8,9,28 graphenylene.29 Luo et al. performed first-principles calculations to determine the H2 separation characteristics of graphdiyne, and they found that rhombic-graphyne has a high H2 selectivity toward CO, N2, and CH4.27 Buehler and his coworks predicted that graphdiyne monolayer has a mass flux of H2 molecules on the order of 7− 10 g cm−2 s−1, allowing the separation of CO and CH4 molecules.28 Zhi et al. theoretically predicted that the H2 selectivity of graphenylene toward CO, CO2, N2, and CH4 can reach 1 × 1012, 1 × 1013, 1 × 1014, and 1 × 1034, respectively.29 These carbon allotropes monolayer membranes possess of many excellences, including periodically distributed uniform pores and extraordinary chemical and mechanical stability. Whether there are other carbon allotropes with such characteristics has aroused people’s intensive interest. Recently, a new 2D sp2 carbon allotrope-fused pentagon network has been theoretically explored.30,31 Maruyama et al. proposed that this carbon allotrope can be obtained from the fused pentagon trimers (acepentalene structure32) sharing three edges with three adjacent pentagon trimers.30 First-principles total-energy calculations demonstrated that the fused pentagon network has a slightly higher total energy than C60 and retains its planar structure up to 1000 K, which means that the fused pentagon network is stable.30 Meanwhile, the fused pentagon network has periodically distributed uniform pores, so can this carbon allotrope monolayer be a promising candidate for H2 separation? The question has never been discussed before. In this paper, we use the van-der-Waals-corrected density functional theory (DFT) and molecular dynamic (MD) simulations to study the performance of the fused pentagon network on H2 separation. First, the energy barriers of gas permeating through this membrane are calculated using the DFT to investigate the selectivity of this membrane. Then, we explain the origin of the H2 selectivity of the fused pentagon network from both structural and electronic prospects. Finally, we use the MD simulations to study the permeance of this monolayer.

(NVT), carried out at temperatures from 300 to 600 K. The temperature of the system is controlled by the Andersen thermostat method, with a fixed time step of 1 fs, and the collision ratio is set as 1.0. Data was collected every 5 ps, and full-precision trajectory was then recorded. Van der Waals interactions and Ewald electrostatic interactions were applied with a cutoff distance of 9.5 Å. Periodic boundary conditions were applied in all three dimensions. The DFT calculation and MD simulations were carried out using DMol3 and Discover codes embedded in the Material Studio software, respectively.

3. RESULTS AND DISCUSSION First, we optimize the lattice structure of the fused pentagon network in a 2 × 2 supercell, as presented in Figure 1a. The

Figure 1. (a) Fully optimized 2 × 2 supercell of FPN sheet. (b) Pore electron density isosurface of the fused pentagon network is also displayed (isovalue of 0.08 e/Å3).

Table 1. Optimized Lattice Parameters of This Work, and the Lattice Parameters Comparison with That of the Previously Theoretical Calculation d1 (Å) d2 (Å) d3 (Å) θv (deg) θs (deg)

2. MODELS AND METHODS In this paper, first principle calculations were performed to calculate the energy barriers of gas permeating through this membrane. The Perdew−Burke−Ernzerhof (PBE) functional under the generalized gradient approximation (GGA), which interprets the nonhomogeneity of the true electron density using the gradient of charge density, for exchange-correlation functional, was employed to calculate the spinunrestricted all-electron DFT calculations. Due to the dispersion interactions is important for the interaction of neutral, nonpolar molecules such as H2, N2, and CH4 molecule with the fused pentagon network,17 we use a semiempirical dispersion correction approach proposed by Grimme33 to correct the noncovalent forces. The double numerical plus polarization (DNP) basis set is used to expand electronic wave function. The convergence criterias are of 1 × 10−5 Ha (1 Ha = 27.2114 eV) in energy, 0.002 Ha/Å in maximum, 0.005 Å in maximum displacement.34,35 A 20 Å vacuum thickness is used to prevent the interaction between two sheets. The Brillouin zone is expressed using a 6 × 6 × 1 Monkhorst−Pack meshes. In addition, we use MD simulations to study the permeance of fused pentagon network on H2 separation. An approximately square sheet of the fused pentagon network (71.4 Å × 74.2 Å) serves as a monoatomistic membrane. The “gas reservoir” consists of 100 H2 molecules, 20 CH4 molecules, 10 CO molecules, 10 CO2 molecules, 10 N2 molecules, and 10 H2O molecules. A condensed-phase optimized molecular potential for atomistic simulation studies (COMPASS) is used for describing the interatomic interactions.36 All full atomistic simulations are subject to a canonical ensemble

this work

ref 31

1.41 1.43 1.56 120 108

1.40 1.42 1.54 120 108

optimized lattice parameter is 6.77 Å, in good agreement with previous theoretical predictions.30,31 Three different kinds of carbon bonds and two different kinds of bond angles shown in Figure 1a are also unanimous agreement with previous work,31 as shown in Table 1. The diameter of the pore is 3.0 Å, which is larger than the kinetic diameter of H2 (2.89 Å),37 whereas smaller than those of the other gas molecules (3.30 Å for CO2, 3.64 Å for N2, 3.76 Å for CO, 3.8 Å for CH4, and 3.28 Å for H2O). This implies that the two-dimension fused pentagon network may be severed as two-dimensional molecular-sieve membranes for H2 separation. Next, we explore the H2 selectivity of the fused pentagon network toward the other gas molecules. Before determining the transition states (TS) and energy barriers of gas molecules passing through this sheet, we calculate the interaction energy between a gas molecule and the fused pentagon network to confirm the most stable state (SS), in which the gas molecule absorbs on the surface of the fused pentagon network. The 28503

DOI: 10.1021/acsami.5b09648 ACS Appl. Mater. Interfaces 2015, 7, 28502−28507

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Figure 2. Top view and side view of (a) H2, (b) N2, (c) CO, (d) CO2, (e) CH4, and (f) H2O adsorption above the pore of the fused pentagon network. The gray, green, blue, and red spheres represent C, H, N, and O atoms, respectively. Figure 3. Electron-density isosurfaces for (a) H2, (b) CO2, (c) CO, (d) N2, (e) H2O, and (f) CH4 molecules passing through the pore of fused pentagon network. (isovalue of 0.1 e/Å3).

Table 2. Adsorption height (Had) between Gas Molecules and the Pore Center of Fused Pentagon Network with Corresponding Adsorption Energy (Ead) and the Energy Barrier (Ebarrier) for Gas Molecules Passing through the Fused Pentagon Network Had (Å) Ead (eV) Ebarrier(eV)

H2

N2

CO

CO2

CH4

H2O

1.6 −0.20 0.18

2.2 −0.26 0.70

2.4 −0.21 0.62

2.8 −0.22 0.60

2.6 −0.25 2.05

1.8 −0.37 0.61

network with corresponding adsorption energy are also summarized in Table 2. The calculated adsorption energy shows that the gas molecules are all physically adsorbed on the fused pentagon network by weak van der Waals interaction. Thus, the fused pentagon network shows great advantages for H2 separation over previously porous graphene, which need additional hydrogen atoms or nitrogen atoms to passivate the edged carbon atoms with dangling bonds.39 For the adsorption height of SS between the gas molecules and the center of the pore in the fused pentagon network, H2 molecule is closer to the pore center in the fused pentagon network so that it more easily passes through. We then search the transition state (TS) of gas molecules penetrating through the membrane and calculate the energy barrier for gas molecules passing through the fused pentagon network. The energy barrier for gas molecule passing through the membrane is defined as

Table 3. Calculated H2 Selectivity (S) toward the Other Gas Molecules Passing through the Fused Pentagon Network (FPN) at Room Temperature (T = 300 K), and the Selectivity Comparison with That of the Previously Proposed Porous Structure membrane

FPN

ref S (H2/CO2) S (H2/CO) S (H2/N2) S (H2/CH4) S (H2/H2O)

this work 1 × 107 1 × 107 1 × 108 1 × 1031 107

graphdiyne ref 9a

silica ref 13 10

1 × 103 1 × 1010

1 × 102 1 × 103

g-C3N3 ref 41 1 × 104 1 × 106 1 × 1026

E barrier = E TS‐ESS

a

Reference 9 considers the effect of frequencies in the form of partition function.

where ETS and ESS represent the interaction energies between gas molecules and fused pentagon network at TS and SS, respectively. The energy barriers of gas molecules passing through the fused pentagon network are summarized in Table 2. Compared with the energy barriers of the other gas passing through the monolayer, H2 molecule shows an unexpectedly low energy barrier (0.18 eV). Thus, H2 molecule can penetrate through the fused pentagon network at moderate condition. Note that the threshold energy barrier for gas penetration is about 0.5 eV.40 On the basis of the calculated energy barriers of gas molecules penetrating through the fused pentagon network, we use the Arrhenius equation38 to estimate the H2 selectivity of fused pentagon network toward the other gas quantitatively. The Arrhenius equation is defined as follows

interaction energy between the gas molecule and fused pentagon network are computed by the equation E int = Egas + sheet − Egas − Esheet

where Egas+sheet is the total energy of the gas molecule and the fused pentagon network, Egas is the energy of isolated gas molecule, and Esheet is the energy of pure fused pentagon network. The minimum energy pathways (MEP) for the gas molecule penetrating through the fused pentagon network are searched by transition state confirmation based on nudged elastic band method (NEB).8,38 We examine the adsorption behaviors of gas molecules on the fused pentagon network. The configuration of SS can be found in Figure 2. The adsorption height of SS between the gas molecules and the center of the pore in the fused pentagon

SH2 /gas = 28504

rH2 rgas

=

A H2 exp( − E H2 /RT ) Agasexp( − Egas /RT ) DOI: 10.1021/acsami.5b09648 ACS Appl. Mater. Interfaces 2015, 7, 28502−28507

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Figure 4. Final configurations of the mixture gases permeating through the fused pentagon network at (a) 300, (b) 350, (c) 400, (d) 450, (e) 500, (f) 550, and (g) 600 K.

for N2, 3.76 Å for CO, 3.8 Å for CH4, and 3.28 Å for H2O) are larger than the diameter of the pore; hence they must overcome a higher energy barrier for penetrating through the sheet. Note that the energy barrier of gas molecules passing a membrane has intensive relationship with its kinetic diameter. Therefore, the remarkably high H2 selectivity of the fused pentagon network toward the other molecules is mainly determined by the diameter of the pore. For deeper understanding the influence of energy barrier of gas molecules passing through the fused pentagon network, we plot the electron density isosurfaces of gas molecules interacting with the fused pentagon network, as shown in Figure 3. Obviously, there are no electron overlap between H2 molecule and the pore of fused pentagon network, while CO2, N2, CO and H2O molecules have a pronounced electron overlap with the fused pentagon network, resulting in a higher energy barrier than that of H2 molecule. As described in Figure 3, there is an entire electron density overlapping between CH4 molecule and the edge atoms of pore in the fused pentagon network, resulting in a great energy barrier. Intrinsically, it is the electron density of the edge atoms of pore in the fused pentagon network that hinders the gas molecules passing through the membrane. The performance of a H2 separation membrane is not only determined by selectivity but also the permeance−flux. Using the MD simulations, we investigate the process of H2 molecule passing through the fused pentagon network, and estimate the H2 permeance at temperature from 300 to 600 K. In the process of simulations, the permeation can be divided into three steps. First, gas molecules adsorb on the membrane surface by the van der Waals interaction. Then, they linger on the surface for a few picoseconds before successfully crossing the membrane due to the gas concentration difference between the “gas reservoir” and the vacuum space. Finally, the gas molecules cross the sheet and reach the other side of the membrane. After 1 ns simulation, the final configurations of MD simulations at different temperatures are shown in Figure 4. We confirm that there are 33, 36, 45, 46, 47, 48, and 48 H2 molecules passing through the fused pentagon network to the vacuum space at 300, 350, 400, 450, 500, 550, and 600 K, respectively, whereas the other molecules cannot penetrate through this monolayer. Considering the H2 number of passing

Figure 5. Permeance of H2 molecules as a function of temperature.

where r is the diffusion rate, A is the diffusion prefactor, and E is the diffusion energy barrier. Assuming A of the gas molecules are a constant.41 We calculate H2 selectivity of the fused pentagon network toward the other gas at 300 K, and compare the H2 selectivity with other two-dimensional monolayer, as shown in Table 3. Compared with traditional silica,13 carbon allotrope-graphdiyne,9 and the g-C3N3,42 the fused pentagon network exhibits remarkably high selectivity for H2 over the other gas molecules, including N2, CO, CO2, H2O, and CH4 molecules. We also calculate the H2 selectivity of the fused pentagon network toward the other gas at the temperature of 450 K, which is the low limit temperature of methane reforming,6 and the selectivities of H2/CO2, H2/H2O, H2/ CO, H2/N2, and H2/CH4 are 1 × 104, 1 × 105, 1 × 106, 1 × 106, and 1 × 1021, respectively. Although the selectivity of H2/ CO2 is relatively smaller, the value is still superior for effective separation.9,43 Note that the calculated H2 selectivity of the fused pentagon network is an ideal theoretical result. We explain the origin of the high H2 selectivity of the fused pentagon network from both structural and electronic prospects. According to discussion above, the pore diameter of this monolayer is 3.0 Å, which is larger than the kinetic diameter of H2 (2.89 Å) molecule. This is why the H2 molecule can pass through the monolayer freely. However, all the kinetic diameters of the other gas molecules (3.30 Å for CO2, 3.64 Å 28505

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15CX08009A), Graduate Innovation Fund of China University of Petroleum (27R1510047A, YCX2014070, YCX2015057).

through the fused pentagon network over the simulation time (1 ns) and taking into account the area of the membrane (71.4 Å × 74.2 Å), and assuming a pressure drop of Δp = 1 bar across the pore, we calculate the H2 permeance of fused pentagon network at different temperatures, as shown in Figure 5. It can be seen that the permeance of H2 molecule increases with increasing temperature, but the growth rate decreases gradually with increasing temperature. Accounting for the kinetic energy of H2 molecule and the relation between temperature and kinetic energy, the kinetic energy of H2 molecule can be written as E = 3kBT/2. Apparently, at a higher temperature, the kinetic energy of H2 molecule is larger so that it more easily overcomes the energy barrier and permeates through the membrane. However, the influence of energy barrier on gas molecule penetration gets lower with the kinetic energy of H2 molecule increased. Specially, the H2 permeance of fused pentagon network is about 4 × 107 GPU (gas permeation unit; 1GPU = 3.3 × 10−9 mol cm−2 s−1 bar−1) at 450 K, which is 4 times higher than that of C2N membrane reported by Xu.44 As noted, the H2 permeance of the fused pentagon network is much higher than the industrially acceptable permeance (20 GPU) for gas separation.45 The high permeance of this sheet could be attributed to its one-atom thickness, as the permeance of a membrane is inversely proportional to its thickness. On the basis of our simulation results, we can find that the fused pentagon network only allows H2 molecule to pass through and inhibits the other molecules passing through even at the temperature as high as 600 K. Meanwhile, the H2 permeance of this monolayer is also undoubtedly higher than other membranes.44 Therefore, the fused pentagon network should be an excellent candidate for H2 separation, because of its high selectivity and excellent permeability.

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4. CONCLUSIONS In summary, we use the van-der-Waals-corrected DFT computation and MD simulations to investigate the H2 separation performance of the fused pentagon network. The DFT calculated results show that H2 molecule can pass through the membrane easily with a surmountable energy barrier (0.18 eV). Furthermore, the fused pentagon network shows an exceptionally high selectivity for H2/gas (CO, CH4, CO2, et al.) at 300 and 450 K. In addition, using MD simulations we demonstrate that the fused pentagon network exhibits a high H2 permeance of 4 × 107 GPU at 450 K, which is much higher than the value in the current industrial applications. The fused pentagon network monolayer is far superior to the current industrial applications and has great potential application in H2 separation.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Tel: 86-053286981169. Fax: 86-0532-86981169. Notes

The authors declare no competing financial interest.

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REFERENCES

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ACKNOWLEDGMENTS

This work is supported by the Natural Science Foundation of China (11374372, 41330313), Taishan Scholar Foundation (ts20130929), the Fundamental Research Funds for the Central Universities (13CX05009A, 14CX05013A, 28506

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DOI: 10.1021/acsami.5b09648 ACS Appl. Mater. Interfaces 2015, 7, 28502−28507