Separation of Hydrogen Gas from Coal Gas by Graphene Nanopores

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Separation of Hydrogen Gas from Coal Gas by Graphene Nanopore Debing Li, Wei Hu, Junqiao Zhang, Hui Shi, Qu Chen, Tianyang Sun, Lijun Liang, and Qi Wang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.5b06165 • Publication Date (Web): 12 Oct 2015 Downloaded from http://pubs.acs.org on October 14, 2015

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The Journal of Physical Chemistry

Separation of Hydrogen Gas from Coal Gas by Graphene Nanopores Debing Li†, §, Wei Hu‡, §, Junqiao Zhang†, Hui Shi╨, Qu Chen┴, Tianyang Sun†, Lijun Liang†, ±,*, Qi Wang†,* †

Department of Chemistry and Soft Matter Research Center, Zhejiang University, Hangzhou

310027, People’s Republic of China ‡

Division of Theoretical Chemistry and Biology, School of Biotechnology, KTH Royal

Institute of Technology, SE-10691 Stockholm, Sweden ╨

State Key Laboratory of Coal Conversion, Institute of Coal Chemistry, Chinese Academy of

Sciences, Taiyuan 030001, People’s Republic of China ┴

School of Biological and Chemical Engineering, Zhejiang University of Science and

Technology, Hangzhou, 310023, People’s Republic of China ±

Department of Polymer Science and Engineering, Zhejiang University, Hangzhou 310027,

People’s Republic of China §

These authors contributed equally to this work

* Corresponding authors. Fax: +86 571 87951895. E-mail addresses: [email protected] (Q. Wang) [email protected] (L. Liang)

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Abstract We designed a series of porous graphene as the separation membrane for hydrogen gas in coal gas. The permeation process of different gas molecules (H2, CO, CH4, and H2S) in porous graphene was evaluated under the atmospheric pressure and high pressure conditions. Our results indicate the hydrogen permeability and selectivity could be tuned by the size and the shape of the porous graphene. For graphene with bigger pores, the selectivity for hydrogen gas could decrease. In the porous graphene with same pore area, the hydrogen gas selectivity could be affected by the shape of the pore. The potential of mean force (PMF) of different gases to pass through a good separation candidate was calculated. The order of PMF for different gases to pass through the good separation candidate is H2 < CO < CH4 ≈ H2S, which is also confirmed by the first-principle density function theory (DFT) calculation. Keywords: Gas separation, hydrogen gas, nanoporous graphene, permeability, selectivity


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1. Introduction Gas separation is a significantly important issue due to its wide range of applications, such as cleaning air and recycling hydrogen gas1-2. Hydrogen separation from the coal gas (primarily composed of CO, CH4, H2S and H2) is significant for a new clean technology

3-4

.

Compared with traditional gas separation technology, membrane separation technology is considered as low-cost, environment friendly and highly efficient5-7. Based on its different composition, membrane could be mainly divided into organic membrane8-10, inorganic membrane11-12 and hybrid membrane13-15. The organic membrane made from polymer is usually inappropriate for hydrogen gas separation since the gas permeation through the organic membrane is very low16. In addition, the polymeric membrane could not be used in such a long time due to the aging and plasticization problems17. Inorganic membrane made from carbon molecular sieve is proven to effectively separate different gas molecules but the membrane is too fragile for industrial applications18. Recently, the single layer thick membrane, made from graphene, has attracted many attentions due to its unique electronic and mechanical properties19-21. In addition, porous graphene can also be synthesized by creating pores in the pristine graphene sheet using electron beam sculpting22, oxidative etching23, ion bombardment24, or graphene oxide reduction25. What is more, the porous graphene with specific geometry has been successfully synthesized by a crosscoupling method26-27. More interestingly, graphene nanopores fabricated from graphene sheets are shown to be extremely thin and structurally robust. It has been extensively studied on potential applications over a wide range from ion-selectivity10, 28, water desalination29-30, to DNA sequencing31-33. Meanwhile, some experimental and theoretical investigations have suggested that porous graphene membrane is a good option for gas separation34-38. Kim et al. pointed out that high CO2/N2 selectivity could be achieved by well-interlocked graphene and graphene oxide membrane35. High selectivity on the order of 108 for H2/CH4 was found in a nitrogen-functionalized graphene pore by computational study34. The results from Du’s work show that hydrogen gas could be separated by a small graphene nanopore36. All these results indicate that hydrogen gas could be separated by modified porous graphene. However, the effect of pore shape especially with the same area of porous graphene was not considered in these studies. In addition, the permeation mechanism of hydrogen gas through porous graphene was poorly understood. The molecular mechanical simulations combined with first-principles DFT calculations have been successfully applied to investigate the gas separation by membranes34, 39. Herein, a combination of molecular simulations and first-principles DFT calculations were used to investigate the hydrogen gas selectivity from coal gas by porous graphene. We designed a series of porous graphene with different pore sizes and shapes for hydrogen separation. The



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main components of coal gas including H2, CO, H2S and CH4 were selected as separation gas molecules. The permeation process of four different types of gas molecules through porous graphene was investigated under atmospheric and high pressure conditions. The free energy profile for four different types of gas molecules to permeate porous graphene was calculated by potential of mean force (PMF) method in molecular dynamics (MD) simulation. The results were confirmed by DFT calculation, and the permeation mechanism of four different types of gas molecules to pass through nanoporous graphene was investigated.

2. Computational Details 2.1 Molecular Dynamics Simulations All MD simulations were carried out by GROMACS 4.5.2 software package40-42. Force field parameters for graphene (σCC = 3.85 Å, εCC= 0.439 kJ·mol-1) were taken from our previous work43-44, and all atoms in graphene nanopores were set to be neutral. The parameters of the Lennard-Jones potential for cross-interactions (graphene–gas) between nonbonded atoms were obtained from Lorentz-Berthelot combination rules. The parameters of different gas molecules are listed in the Supporting Information (Table S1 – Table S4)45-49. In order to study the effect of pressure on gas permeability and separation selectivity, we put a biased pressure to the system by applying external force to each atom of gas molecules in the z axis direction as set in reference50. The applied force on an individual atom was given by f=PA/N, where P is the biased pressure, A is the area of the membrane, and N is the total number of atoms for gas molecules. The details about applying biased pressure are present in Supporting Information. The length of the simulation box is 6.93 nm, 6.87 nm and 20.00 nm in x, y, and z dimensions, respectively. The box was divided into two phase including gas phase and vacuum phase in the simulation initial state. A pristine graphene was fixed at z=0 nm, and the porous graphene membrane was placed at z=5 nm. In porous graphene membrane，all carbon atoms except for those at the pore edge were frozen during the simulations. After the initial equilibration to minimize the energy, we performed a constant volume and temperature dynamics (NVT) simulation at 300 K controlled by the Nosé-Hoover thermostat method, and a fixed time step of 1 fs was used. Periodic boundary conditions were applied in all three dimensions. The free energy difference between these two states was calculated by Equation 1:

∆G = −

1

β

ln

Z( ξ ) 1 ρ( ξ ) = − ln ′ Z( ξ ) β ρ( ξ ′)

⑴

where ρ(ξ) is the distribution function in the ξ state. Herein, the potential of mean force (PMF)51 of different types of gas to pass through porous graphene was calculated by umbrella samplings and Weighted Histogram Analysis Method (WHAM). We sampled the distances between center-of-mass of gas molecular and the porous graphene from -1.0 nm to 1.0 nm along the z-axis with the same spacing (0.02 nm).


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2.2 First-Principles DFT Calculations All DFT calculations were performed using the spin-polarized DFT implemented in the Vienna ab initio simulation package (VASP)52. The electron-ion interaction was described by the projector augmented wave (PAW) pseudopotentials53 and the energy cutoff for the planewave basis set was set at 400 eV. The exchange-correlation interactions were described by generalized gradient approximation of Perdew, Burke, and Ernzerhof (GGA-PBE)54. The gas molecule was put aside of ca. 1.7 nm × 1.7 nm porous graphene, and the system was optimized. The optimized geometry was considered to be the initial state. Then a rough geometry obtained by translating gas molecules to the other side of membrane in the initial state was optimized. This optimized geometry represented the final state. Then the climbing image nudged elastic band (CI-NEB) method55 was performed to obtain the minimum energy pathway for the gas molecules passing through the graphene with different nanopores. At last, the DFT-D method was used to confirm the effects of van der Waals (vdW) to the energy barrier of gas molecules to pass through porous graphene.

Figure 1. Structure of porous graphene nanopore models: (a) g-1, (b) g-2, (c) g-3, (d) g-3a, (e) g-3b, (f) g-4. The number is named by the drilled number of benzene ring. g-1 means only one benzene ring is drilled. In the three geometries, the drilled benzene rings of g-3, g-3a and g-3b are the same but the shapes of the drilled district are different. The blue ball means the hydrogen atoms, and the graphene is represented by the green licorice model.



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Figure 2. Initial structure of system with the g-3 porous model and coal gas including H2, CO, CH4, and H2S (left: top view; right: side view). Blue ball represents the hydrogen atom, the gas is represented by the licorice model and graphene plane is represented by the green licorice model. The bias pressure varied from 0 to 200 MPa was used to drive the gas to pass through the nanopores.

3. Results and discussion The pore area from different porous graphene was estimated based on the drilled area of the benzene rings, and the sequence of pore area is g-1 < g-2 < g-3 < g-4. The permeation ratio is used to characterize permeability. The permeation ratio of gas molecule A is defined as follows PA=nA/NA, where nA is the molecules number of A permeating through the membrane and NA is the total molecules number of A. As shown in Figure 3, gas molecules spontaneously permeate from the gas phase to the vacuum phase without applied bias pressure. In all four different types of porous graphene, the hydrogen gas can permeate through membrane and the permeation ratio are ca. 1%, ca. 40%, ca. 75% and ca. 75% in g-1, g-2, g-3 and g-4, respectively. The permeation ratio for hydrogen gas in g-1 is really low. It shows that g-1 couldn’t be an ideal hydrogen gas separation. As the process is spontaneous, 75% hydrogen permeation ratio in g-3 and g-4 is really very high. However, all the gas can permeate through the g-4 membrane, which leads to the separation failure of hydrogen gas. The results suggest that the porous graphene of g-4 is too big to separate the hydrogen gas from the coal gas. Based on the data from Figure 3, g-3 membrane is found to be a good candidate to separate hydrogen gas from coal gas with high separation efficiency. To further investigate permeability quantitatively, the molecular flow is adopted to demonstrate the permeation velocity of hydrogen gas. The molecular flow defined as F=N/(TS), where N refers to the mole of the molecules permeating through the membrane, T is the simulation time and S is the area of membrane. The molecular flow of hydrogen gas in g-3 is as high as 8722 mol/(m2 ·s), which makes it considerable proper for hydrogen gas separation. The results that graphene nanopore with suitable pore size has a good separation efficiency for hydrogen separation are in good agreement with the results from other groups34, 36. 6 ACS Paragon Plus Environment

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Figure 3. Permeation ratio of different types of gas to pass through different porous without applied bias pressure: (a) g-1; (b) g-2; (c) g-3; (d) g-4. To study the effect of gas adsorption on the separation property of graphene membrane, the distributions of gas molecules along z direction were calculated. The z-axis is perpendicular to the plane of the porous graphene membrane and the porous graphene membrane is placed at z=5 nm. As shown in Figure 4, carbon monoxide, hydrogen sulfide and methane molecules tend to distribute within the region of 0.5 nm around the porous graphene membrane because of the strong vdW interactions between gas molecules and the membrane. However, the hydrogen molecules prefer to uniformly distribute. In some cases, the gas molecules that have significant adsorption with the porous graphene membrane can more effectively find the pore by diffusing onto the membrane. However, the phenomenon is not observed in the system. This indicates that the pore size is a key factor affecting separation efficiency and the effect of adsorption is feeble for the system. When the pore size is big enough for gas molecules to pass through, the adsorption on the graphene membrane may become a most important factor to affect the separation efficiency56-57.



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Figure 4. Distribution of gas molecule of the final configurations (t = 10 ns) along the Z direction: (a) g-1; (b) g-2; (c) g-3; (d) g-4.

Figure 5. Permeation ratio of different types of gas to pass through porous membrane with the same area of g-3 but different geometries: (a) g-3a; (b) g-3b. To investigate the effect of the geometry of porous membrane on the hydrogen gas separation, the different geometries with the same porous area based on g-3 were designed and named as g-3a and g-3b since g-3 shows an excellent hydrogen gas separation from the coal gas. From the data of Figure 5, the permeation ratios of all four different types of gas to pass through g-3a are much higher than these of g-3b. It shows us it is much easier for all the types of gas to pass through g-3a than g-3b. The permeation ratio for H2 is ca. 73%, 60% for CO and CH4, and 20% for H2S to pass through the g-3a in 10 ns simulation. The pore geometries of g-3a are more round than other porous graphene membranes (g-3, g-3b). The CH4 molecule prefers to pass thought circular pore due to the structure of methane when the 8 ACS Paragon Plus Environment

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pore area is the same. Therefore, it is much easier for CH4 to pass through g-3a but not g-3b. It shows us the pore geometry is very important for the hydrogen separation. The permeation ratio of hydrogen gas to pass through g-3b is only ca. 15%, which is much lower than that of g-3. The geometry difference is that the largest part of g-3 in the middle of porous membrane is a little bigger than that of g-3b. From the animation trajectories (data not shown), the process of the H2 molecule to pass through the small porous membrane (g-3 and g-3b) was observed. The hydrogen molecule tends to pass through the porous graphene membrane with the orthogonal configuration, which has also been confirmed in DFT calculation37-38. The small differences of the geometry between g-3 and g-3b in the largest part could lead H2 to pass through g-3 much easier than that of g-3b. Based on the effects of different sizes and geometries of porous graphene membrane on the gas separation, g-3 shows us the excellent hydrogen gas separation performance from coal gas. To further confirm the performance of hydrogen gas separation by g-3, the simulations with different applied pressures varied from 20 MPa to 200 MPa were performed. As shown in the Figure 6, all the permeation ratios of hydrogen gas are 100% in 10 ns simulation under three different biased applied pressures varying from 20 MPa to 200 MPa. It shows that it is very easy for H2 to pass through the g-3 porous membrane due to the imposed pressure, but it is still difficult for H2 to pass through the g-1 porous membrane as shown in Figure S1. However, the separation effects of hydrogen gas and other gas from coal gas could be affected under a much higher biased pressure. CO can also permeate through g-3 under the applied pressure higher than 50 MPa. It shows that the selected biased pressure should not be over high to ensure the separation effects. The free energy profile of different types of gas molecules to pass through the g-3 was calculated along the reaction coordination. As shown in the Figure 7, the free energy barrier is ca. 16.07 kJ·mol-1 for hydrogen molecule to pass through g-3 porous membrane. It is very easy for hydrogen molecule to pass through the g-3 porous membrane due to the relatively small free energy barrier. However, the free energy barrier is ca. 37.32 kJ·mol-1 for CO, 70.62 kJ·mol-1 for H2S and 63.14 kJ·mol-1 for CH4 to pass through the g-3 porous membrane. Using the Arrhenius equation, one can estimate that the separation selectivity for different types of gases to pass through g-3 could be as high as 3.6×103, 3.1×109 and 1.6×108 for H2/CO, H2/H2S and H2/CH4, respectively. Consequently, the g-3 is a good hydrogen gas separation membrane since the separation of hydrogen gas from the coal gas is significantly high.



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Figure 6. Permeation ratio of hydrogen gas to pass through g-3 under different applied bias pressure: (a) 20 MPa; (b) 50 MPa; (c) 200 MPa.

Figure 7. Potential of mean force of different gases to pass through g-3 porous graphene membrane. To confirm our results from the simulation and understand the separation mechanism much better, the DFT method was used to calculate the minimum energy pathway (Figure S2) and energy barrier for different types of gas molecule to pass through the graphene with different 10 ACS Paragon Plus Environment

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nanopores. The Table 1 shows the energy barriers for H2, CO, H2S and CH4 molecule pass through the graphene with different nanopores. The vdW many body and screening effects are important for accurately calculating interaction energy in extended systems like graphene58-61. However, the purpose of this work has achieved without vdW many body and screening effects. Meanwhile, we find that the difference between the energy barriers with and without DFT-D is very small. So only normal pairwise treatment of vdW contributions were tested in the present work due to the limitation of computational resources. To better understand the contributions of energy and entropy to the free energy, the entropy change could be calculated by equation -T∆S=∆A-∆U, where ∆A is free energy calculated above, and ∆U is approximated at energy barrier. The calculated thermodynamic functions for gas molecules pass through g-3 porous graphene membrane are presented in Table 2. The values of -T∆S for all gases are positive, and ∆S are negative. It suggests that it hinders gases to pass through porous graphene. The number of possible conformations has a sharp decrease when the gas molecule approaches the pore. For H2 as an example, the value of -T∆S is much greater than that of ∆U, whereas for other gas molecules the values of -T∆S are smaller than those of ∆U. Thus, the determining factor that gases pass thought g-3 porous graphene membrane is entropy change for H2 and energy change for other gas molecules. Two interesting phenomena could be found from our calculations. Firstly, the smaller the nanopore is, the harder the molecules could pass through. For instance, the g-1 structure provides a very high energy barrier for the all gas molecules except H2. As a result, g-1 could not be used in the future to separate the hydrogen gas. When the nanopore is large, it is easy for all molecules to pass through. For example, the energy barriers for the four gas molecules to pass through the g-4 structure are -10.62, 6.76, 10.62 and 4.83 kJ·mol-1, respectively. The second interesting phenomenon is the performance of different gas molecules on passing through the porous graphene. We could see that H2 is the easiest to pass through and H2S is the hardest. This could be attributed to the scale of the molecule, and we could conclude that it is harder for bigger molecules to pass than for smaller ones, and the results were confirmed by the results from MD simulations and PMF calculations. Table 1. Energy barrier of gas molecules for passing different porous graphene / kJ·mol-1 H2

CO

H2S

CH4

g-1

57.92

250.98

405.42

337.85

g-2

12.55

65.64

126.45

106.18

g-3

2.90

28.96

50.20

47.30

g-4

-10.62

6.76

10.62

4.83

g-3a

-9.65

15.44

22.20

21.24

g-3b

23.17

96.53

115.83

96.53



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Table 2. Calculated thermodynamic functions for gas molecules pass through g-3 porous graphene membrane / kJ·mol-1 H2

CO

H2S

CH4

16.07

37.32

70.62

63.14

∆U

2.90

28.96

50.20

47.30

-T∆S

13.17

8.36

20.42

15.84

∆A a

a

∆U was approximated at energy barrier

4. Conclusion Porous graphene could be used as the separation membrane for hydrogen gas in coal gas. The combined MD and DFT methods were used to design a good hydrogen gas separation membrane and explore the mechanism of hydrogen separation from the coal gas. Our results indicate that the hydrogen permeability and selectivity could be tuned by the size and the shape of the porous graphene. For graphene with a bigger pore, the selectivity for hydrogen gas could decrease. The g-3 is found to be a good candidate membrane for hydrogen separation. In the porous graphene with the same pore area, the hydrogen gas selectivity could be affected by the shape of the pore. Exerted by a high pressure (20 MPa), all the hydrogen gas could be separated by g-3 membrane. In addition, the order of PMF for different gases to pass through a good separation candidate is H2 < CO < CH4 ≈ H2S, which is also confirmed by DFT calculations.

Acknowledgements This work was financially supported by the National Natural Science Foundation of China (Grant Nos. 21273200, 21503186 and J1210042).

Supporting Information Method of applying biased pressure, force field parameters for gas molecules, permeation ratio of hydrogen gas to pass through g-1 under different applied bias pressure, minimum energy pathway for the different gas molecules pass through the graphene with different nanopores.


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Figure 1. Structure of porous graphene nanopore models: (a) g-1, (b) g-2, (c) g-3, (d) g-3a, (e) g-3b, (f) g4. The number is named by the drilled number of benzene ring. g-1 means only one benzene ring is drilled. In the three geometries, the drilled benzene rings of g-3, g-3a and g-3b are the same but the shapes of the drilled district are different. The blue ball means the hydrogen atoms, and the graphene is represented by the green licorice model.

99x68mm (300 x 300 DPI)

ACS Paragon Plus Environment


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Figure 2. Initial structure of system with the g-3 porous model and coal gas including H2, CO, CH4, and H2S (left: top view; right: side view). Blue ball represents the hydrogen atom, the gas is represented by the licorice model and graphene plane is represented by the green licorice model. The bias pressure varied from 0 to 200 MPa was used to drive the gas to pass through the nanopores. 49x20mm (300 x 300 DPI)


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Figure 3. Permeation ratio of different types of gas to pass through different porous without applied bias pressure: (a) g-1; (b) g-2; (c) g-3; (d) g-4. 120x90mm (300 x 300 DPI)



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Figure 4. Distribution of gas molecule of the final configurations (t = 10 ns) along the Z direction: (a) g-1; (b) g-2; (c) g-3; (d) g-4. 121x92mm (300 x 300 DPI)


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Figure 5. Permeation ratio of different types of gas to pass through porous membrane with the same area of g-3 but different geometries: (a) g-3a; (b) g-3b. 57x20mm (300 x 300 DPI)



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Figure 6. Permeation ratio of hydrogen gas to pass through g-3 under different applied bias pressure: (a) 20 MPa 59x45mm (600 x 600 DPI)


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Figure 6. Permeation ratio of hydrogen gas to pass through g-3 under different applied bias pressure: (b) 50 MPa; 64x52mm (600 x 600 DPI)



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Figure 6. Permeation ratio of hydrogen gas to pass through g-3 under different applied bias pressure: (c) 200 MPa. 65x53mm (600 x 600 DPI)


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Figure 7. Potential of mean force of different gases to pass through g-3 porous graphene membrane 82x68mm (300 x 300 DPI)



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Table of Contents 45x33mm (300 x 300 DPI)


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Separation of Hydrogen Gas from Coal Gas by Graphene Nanopores

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