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Efficient helium separation of graphitic carbon nitride membrane
Accepted Manuscript Efficient Helium Separation of Graphitic Carbon Nitride Membrane Feng Li, Yuanyuan Qu, Mingwen Zhao PII:
S0008-6223(15)30132-9
DOI:
10.1016/j.carbon.2015.08.013
Reference:
CARBON 10178
To appear in:
Carbon
Received Date: 4 June 2015 Revised Date:
5 August 2015
Accepted Date: 6 August 2015
Please cite this article as: F. Li, Y. Qu, M. Zhao, Efficient Helium Separation of Graphitic Carbon Nitride Membrane, Carbon (2015), doi: 10.1016/j.carbon.2015.08.013. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Nitride Membrane
a
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Feng Li ab, Yuanyuan Qua*, Mingwen Zhaoa*
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Efficient Helium Separation of Graphitic Carbon
School of Physics, Shandong University, Jinan, Shandong, 250100, People’s Republic of
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China; b School of Physics and Technology, University of Jinan, Jinan, Shandong, 250022, People’s Republic of China
ABSTRACT
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An efficient membrane for helium separation from natural gas is quite crucial for cryogenic industries. However, most experimentally available membranes fail in separating helium from small molecules in natural gas, such as H2, as well as in 3He/4He isotopes separation. Using first-
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principles calculations, we theoretically demonstrated that the already-synthesized graphitic
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carbon nitride (g-C3N4) has high efficiency in helium separation from the gas molecules (H2, N2, CO and CH4) in natural gas and the noble gas molecules (Ne and Ar). The selectivity of He over H2 molecule at room temperature is calculated to be as high as 107. More interestingly, the gC3N4membrane can also serve as a quantum sieving membrane for 3He/4He separation with a predicted transmission ratio of 18 at 49 K, thus offers a combined means of both He and 3He isotope separation.
* Correspondence authors. Tel: +86 531 88364655. Email: [email protected]. (Mingwen Zhao) or Tel: +86 531 88363350 Email: [email protected]. (Yuanyuan Qu)
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1. Introduction As an extraordinary noble gas, helium has wide application in advanced technologies, such as
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cryogenics, arc welding, space rockets and silicon-wafer manufacture [1]. However, helium resource is very limited on earth. Natural gas remains the richest and most accessible source of helium, which makes helium purification an inevitable stage for its storage and utilization [2-5]. Among various technologies employed for helium separation [6], membrane technology stands
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out for its high efficiency, small footprint, simplicity in operation, ease of scale up and environmental friendliness [7]. Membrane is the key of this technology, as it defines selective
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barriers for gas molecules. An ideal membrane should be as thin as possible to maximize flux, mechanically robust to prevent rupture and have well-defined pore size to increase selectivity [8].
Graphene-based membranes offer competitive candidates for such molecular-sieving
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membranes, owing to its atomic thickness, superior stiffness and natural porous structure. However, both experimental and theoretical works indicate that a perfect graphene sheet is impermeable to gases, even as small as helium, because of its densely packed honeycomb lattice
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structure [9,10]. Consequently, pores with well-defined sizes should be created in graphene (porous graphene) as channels for gas separation. Porous graphene can be achieved via top-down
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approach by utilizing electron beam treatment or ultraviolet-induced oxidative etching to create pores [11-14]. Subsequently, many theoretical studies have shown that graphene and graphene analogues with appropriate pore sizes are implementable for gas purification or isotopes separation [15-29]. However, these strategies face the same difficulty that the pore size should be well-controlled, which remains a technical challenge for porous graphene. The broad distribution of the pore size in porous graphene would reduce the selectivity of the membrane.
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Besides porous graphene, there are other kinds of two-dimensional (2D) porous membranes with regular and uniformly distributed subnanometer pores, such as polyphenylene [30], graphdiyne [31] and graphitic carbon nitride (g-C3N4) [32]. These porous membranes can act as
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natural molecular sieves, and have great potential for future industrial applications, such as hydrogen [33-40], isotope [41-44], and other gas separation and purification [45]. Among these porous structures, g-C3N4 has attracted considerable attention owing to its potential applications
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in solar energy conversion [46-48], spintronics devices [49,50], energy storage [51] etc. The framework of g-C3N4 consisting of tri-s-triazine (heptazine) rings was demonstrated to be the
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most stable allotrope among various 2D carbon nitrides under ambient conditions [52]. More importantly, the multi-layer g-C3N4material has already been successfully synthesized by a variety of methods [53-55], which have paved the way for producing single-layer free-standing g-C3N4 membrane, in the light of producing graphene from graphite [56]. Moreover, the
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excellent thermal, mechanical and chemical stabilities of g-C3N4 [57] are quite promising for gas purification under arbitrary conditions.
In this contribution, using first-principles calculations, we demonstrated that the already-
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synthesized g-C3N4 material exhibits remarkably high selectivity in favor of He over other
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natural gas, especially for the small-sized gas molecules, such as H2, which is difficult for other membranes. The selectivity of He over H2 molecule at room temperature can be as high as 107. This membrane can also be utilized for He separation from other noble gas molecules with the selectivities of 1010 for Ne and 1051 for Ar. More interestingly, our quantum sieving analysis indicates that it might be used for 3He/4He isotope separation due to the quantum tunneling effect, offering a combined means of both He and 3He isotope separation.
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2. Computational Methods The first-principles calculations have been performed within the density functional theory (DFT)
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using the plane-wave pseudopotential approach as implemented in the Vienna Ab initio Simulation Package (VASP) [58-60]. The electron-electron interactions are treated within a generalized gradient approximation (GGA) in the form of Perdew-Burke-Ernzerhof (PBE) for the exchange-correlation functional [61]. The van der Waals (vdW) interactions were included
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explicitly by using the empirical correction scheme of Grimme (DFT+D2) [62]. The electron wavefunctions were expanded using the plane-waves with the energy cutoff of 500 eV. The
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atomic coordinates were fully relaxed using a conjugate gradient scheme without any symmetry restrictions until the maximum force on each atom was smaller than 0.01eV/Å. Vacuum space larger than 15 Å was used to avoid the interaction between adjacent images. The MonkhorstPack meshes of 7×7×1 were used in sampling the Brillouin zone for the 2×2 supercells of g-C3N4
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[63]. For the transition state calculations, we have performed minimum energy path profiling using the climbing image nudged elastic band method (CNEB) as implemented in the VASP transition state tools [64,65]. The structural convergence criteria were similar to that used in the
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above-mentioned structure optimization. In the subsequent calculations of the potential energy profiles for gas molecules penetrating the membrane pores, the nearest-neighbor atoms
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surrounding the penetrated pores were fully relaxed while the z-coordinates of the other atoms were kept fixed. The steered molecular dynamics simulation was performed by GROMACS package [66] using the universal force field (UFF) [67]. More details can be found in the Supplementary Materials (Supplementary Method).
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3. Results and Discussions 3.1 Efficient helium separation from natural gas molecules
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The lattice constant of g-C3N4consisting of tri-s-triazine rings is calculated to be 7.13 Å, consistent with previous literatures [48,68]. Fig. 1a presents a top view of a fully relaxed (2×2) g-C3N4 supercell. The pores on g-C3N4 are naturally and uniformly distributed with the same shape and dimension. According to the electron counting role, the N atoms at the edges of the
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pores are doubly bonded without the needs of hydrogen passivation. The pore size is characterized by the diameter of the inscribed circle, 4.76 Å, which is suitable for He or H2
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separation from other gas molecules [17,18].
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Fig. 1 (a) Top view of (2×2)g-C3N4 supercell. The brown and blue balls represent the C and N atoms, respectively. The yellow circles indicate the inscribed circles of the pores. (b) Energy profiles for He, H2, Ne, CO, N2, Ar and CH4 passing through the pore of the g-C3N4 membrane. Different colors indicate different gas molecules. Colored points indicate the results obtained by first-principles calculations, and the curves show the numerically interpolated potentials. The insert graphs show the side views of the transition states of He and H2 passing through the pore respectively.
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The energetically most favorable configuration of a gas molecule on the g-C3N4membrane was determined by structural optimization. It was found that gas molecules prefer to reside right
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above a pore at different heights depending on the species of gas molecules, as listed in Table 1.
Table 1. The equilibrium height (h0) between the gas molecules (He, H2, Ne, CO, N2, Ar and CH4) and the g-C3N4 membrane, the adsorption energies (Ea) of the gases on the g-C3N4
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membrane, the energy barriers (Eb) of gases penetrating the pore and the selectivities (S, at
gas
h0(Å)
He
2.489
H2
2.283
Ne
2.491
CO
3.329
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T=300 K) of He over the other gases. Ea(eV)
Eb(eV)
S(He/gas)
0.017
0.354
1
0.091
0.747
107
0.052
0.937
1010
0.036
2.087
1030
2.848
0.128
2.348
1034
Ar
2.463
0.099
3.376
1051
CH4
2.951
0.147
4.216
1065
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N2
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The adsorption energy (Ea) was defined as: Ea = E g −C3 N 4 + E gas − Esas
(1)
where Esas is the total energies of g-C3N4 with an adsorbed gas molecule at the most stable adsorption state, Egas and E g −C3 N 4 represent the energy of an isolated gas molecules and the pristine g-C3N4, respectively.―The adsorption energies and the equilibrium heights are in the range of 0.017~0.147eV and 2.283~3.329 Å, respectively, as listed in Table 1, suggesting the interaction between gas molecules and g-C3N4 is dominated by weak van der Waals interactions.
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Helium molecule has the weakest interaction with the g-C3N4, which is lower than that of CH4 by almost one order. This feature may facilitate the separation of He atom from other gas molecules.
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The energy barrier for a gas molecule passing through a pore of g-C3N4 was then determined from first-principles. In order to get the initial states (IS) and the final states (FS) for transition state searching, the gas molecules were placed on either side of theg-C3N4 surface with a
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distance larger than 5 Å. Then the energy profiles of the gas molecule passing through the pore were sequentially scanned using the CNEB strategy as shown in Fig. 1b. The energy barrier (Eb)
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of a gas molecule penetrating through the pore is calculated from the energy difference between the transition state (TS) and equilibrium adsorbing state (EAS), Eb = ETS
EEAS. The energy
barriers for He, H2, Ne, CO, N2, Ar, and CH4 passing through a pore of g-C3N4 are listed in Table 1. The energy barrier strongly depends on the kinetic diameter of the molecule, i.e.
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molecules with larger kinetic diameter would induce stronger repulsive interaction that leads to huge barriers when penetrating the pore. He has the lowest energy barrier (0.354 eV) which is lower than that of CH4 by one order and only half of the second lowest one (0.747 eV for H2).
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This clearly indicates that using the g-C3N4 membrane, He can be separated from other gas molecules with high efficiency, as these molecules are in principle blocked by the relatively
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higher energy barriers.
Separating He from H2 is a big challenge in He purification, because they have very close kinetic diameters (2.60 Å for He and 2.89 Å for H2 [69,70]). Most of the membranes, such as the porous silicene [17,18], polyphenylene [33,34,43] or graphdiyne [36,37,44], fail to separate He from H2, as the energy barriers of H2 and He passing through these membranes are almost equal, as shown in Table 2. It is interesting to see that for the g-C3N4 membrane, the energy barrier of
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H2 is twice that of He, suggesting efficient He separation behavior. A more intriguing finding lies in the fact that the pore size of the g-C3N4 membrane (4.76Å) is almost the same as that of the porous silicene (4.7 Å) [17,18], but the latter one fails to separate He from H2. We argue that
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this discrepancy may due to the polarity of the atoms along the pore edge, as the negatively polarized N atom surrounds the pores for the g-C3N4 membrane while the neutral Si atom resides
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around the pores for the porous silicene.
Table 2. Comparison results on energy barrier Eb (eV) and selectivity (S, at T=300 K) between
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porous membranes. g-C3N4
silicene
polyphenylene
graphdiyne
Eb (He)
0.354
0.33(a)
0.523(g), 0.43(c)
0.033(h)
Eb (H2)
0.747
0.34(b)
0.37(c),0.61(d)
0.03(e),0.1(f)
Eb (Ne)
0.937
0.53(a)
1.245(g)
--
S (He/H2)
107
--
--
--
S (He/Ne)
1010
6×102(c)
--
2×103(a)
Ref. 17(b)Ref. 18(c)Ref. 33(d)Ref. 34(e)Ref. 36(f)Ref. 37(g)Ref. 43(h)Ref. 44
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(a)
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membranes
To study the He separation efficiency of the g-C3N4 membrane, the selectivity (S) for He over
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other gas molecules was calculated based on the Arrhenius equation [71,72]:
S He / gas =
rHe A e − EHe / RT = He − Egas / RT rgas Agas e
(2)
where r is the diffusion rate, A is the interaction (diffusion) prefactor, and E is the diffusion barrier. Here we assumed that the prefactors of gases are identical (AHe= Agas=1011 s-1) for simplification [33]. The temperature-dependent diffusion rates and selectivities are depicted in
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Fig. 2. The selectivities for He over other gas molecules at room temperature (300 K) are also listed in Table 1. It is clearly shown that the g-C3N4 membrane exhibits higher permeability and selectivity for He. Moreover, compared to other porous membranes (porous silicene,
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polyphenylene and graphdiyne) as shown in Table 2, the g-C3N4 membrane distinguishes itself by a selectivity enhancement around 107 times for He over H2 or Ne. Similar results can also be obtained by using a local density approximation (LDA) functional, showing He has better
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selectivity compared with other gas molecules (see Supplementary Table S1).
Fig. 2 The transmission rate (a) and the selectivity (b) of gas molecules passing through the pore
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molecules.
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on g-C3N4 membrane as a function of temperature. Different colors indicate different gas
To further understand the improved He purification behavior of the g-C3N4 membrane, we plotted the electron density isosurfaces for the transition states of He, H2, Ne, and CH4 molecules passing through the g-C3N4 membrane in Fig. 3. The repulsive interaction between gas molecule and g-C3N4 membrane is related to their electron density overlap due to the close-shell feature of the gas molecule and the semiconducting feature of the membrane. Intuitively, large electron density overlap would lead to strong repulsion which hinders the diffusion of the gas molecules
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passing through the pore. From Fig. 3, we can see that there is no obvious overlap between the electron density isosurfaces of He and the membrane at an isovalue of 0.015 e/Å3. However, the electron density overlap at the same isovalue increases gradually for H2, Ne and CH4, among
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which CH4 has the most pronounced electron density overlap with the membrane, and thus the
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highest energy barrier.
Fig. 3 Electron-density isosurfaces for (a) He, (b) H2, (c) Ne, and (d) CH4 passing through the pore of g-C3N4membrane at the transition states. The isovalue is 0.015 e/Å3. It is noteworthy that when the membrane is utilized in gas separation, the pressure difference between two sides of the membrane will cause global burden to the 2D system, therefore may induce local enlargement of the pore size. To reveal this effect on the gas separation efficiency, we have applied a biaxial tensile strain of 1% to the g-C3N4 supercell (see Supplementary Fig.
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S1a), which enlarges pore size to 4.83 Å compared with one without tensile strain (4.76 Å). Our first-principles calculations indicated that the energy barriers for He and H2 passing through the pore of the stretched g-C3N4 are 0.311 and 0.672 eV, respectively, which are slightly smaller
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than the corresponding values (0.354 and 0.747 eV) of the unstretched membrane (see Supplementary Fig. S1b). The selectivity (~106) of He over H2 at 300 K remains very high in this stretched g-C3N4 membrane. Therefore, the global burden in principle may not change the
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to pass through the g-C3N4 membrane under burden.
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property of separation, which means that compared with other molecules, He still has the priority
3.2 Steered Molecular Dynamics Simulation of Separating He from H2
The steered molecular dynamic simulation was also performed to investigate the separation efficiency between He and H2. In our system, two sheets of g-C3N4 membrane are placed in a
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box of dimension of 3.5657 nm×3.088 nm×50 nm, with a distance of 6 nm. At the initial state, 140 He and 140 H2 molecules are placed randomly in between the two sheets, as shown in Fig.
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4a. A pulling force was applied to these two sheets by connecting them with a hypothetical zerolength spring with a spring constant of 27 pN/nm.
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A total of 4 ns simulation was performed for each trajectory and the simulation results are shown in Fig. 4b. As can be seen, more than 95% of the He molecules have escaped out of the two layers within 1 ns, however, none of the H2 molecule has passed through the g-C3N4 membrane. These results are in good agreement with our first-principles calculations, which suggest He has a 107 of selectivity over H2 molecule. During the pulling, the equilibrium pressure reduced to 11 Bar after 0.5 ns, indicating that separating He from H2 do not require high pressure condition. Similar results were obtained when using a spring with a spring constant of
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83 pN/nm (See Supplementary Fig. S2). More trajectory snapshots can be found in the
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Supplementary Fig. S3.
Fig. 4 (a) Snapshots of the initial state. The He molecule are highlighted in orange and the H2 molecule are highlighted in yellow. (b) Fraction of transmission of He and H2 (upper panel) and
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the pressure changes during pulling (lower panel).
3.3 Separating 3He from 4He
Separating He isotopes (3He and 4He) is quite necessary for cryogenic industries, because they
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have different thermal properties. We therefore examined whether the g-C3N4 membrane is
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implementable for separating 3He from 4He. It is noteworthy that these two He isotopes have the same energy profile as passing through the g-C3N4 membrane (black curve in Fig. 1b), because they have the same number of electrons and protons. However, different masses of the two isotopes would give rise different probabilities when they pass through the membrane via quantum tunneling. On the basis of the energy profile obtained from first-principles calculations, we performed one-dimensional (1D) finite difference calculations [73] of the quantum tunneling probability t(E) as a function of kinetic energy E as shown in Fig. 5. It can be seen that 3He
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transmission is preferred at low kinetic energy regime (<0.337 eV) while 4He transmission becomes more likely at high kinetic energy regime (>0.337 eV). The equivalent transmission probability occurs when the kinetic energy of a particle equals the height of the energy barrier
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(0.337 eV). Therefore, it is reasonable to keep the gas at a low temperature (where particles with lower kinetic energy) to enhance the selectivity of 3He from 4He. It should be noticed that although different exchange functional forms may give different kinetic crossovers
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(Supplementary Table 1S), the overall trend of the tunneling probability maintains
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(Supplementary Fig. S4).
Fig. 5 Quantum-mechanical and classical transmission probability of He passing through the pore of g-C3N4as a function of kinetic energy. The black solid line represents the classical transmission, the blue solid line represents the quantum-mechanical transmission of 3He isotope and the red dashed line represents that of 4He isotope.
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Based on t(E), the thermally weighted transmission probability p(T) can be calculated by taking the integral of the product of t(E) and p(E,T), the kinetic energy distribution in one dimension for a given temperature T:
p( E , T ) =
1 e − E / k BT 4πk B TE
(3)
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p(T ) = ∫ p( E , T )t ( E )dE
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This result is derived from the Gaussian distribution of velocities in one dimension, and the E-1/2 appearing in p(E,T) is due to the substitution of the integral variable of dv by dE. Here, we
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assumed a classical Boltzmann distribution for the velocities of both 3He and 4He as suggested by previous studies [19,20,22,43,44]. This strategy not only provides a more conservative estimation of 3He/4He selectivity, but also avoids the complexity of dealing with a mixed nonideal quantum gas composed of fermionic 3He and bosonic 4He. The thermally weighted results
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at low temperature regime (49-65 K) are summarized in Fig. 6, including (a) the thermally weighted transmission probability of 3He and 4He; (b) the ratio of quantum-mechanical to classical transmission; (c) the 3He/4He transmission ratio. As can be seen in Fig. 6a, the
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transmission probabilities of both 3He and 4He isotopes deviate largely from the classical case, due to the quantum tunneling effect of helium atom, leading to huge values for the ratio of
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quantum-mechanical to classical transmission for both 3He and 4He isotopes shown in Fig. 6b. The 3He/4He transmission ratio plotted in Fig. 6c exhibits an exponentially decrease from 18 to 1.8 as temperature increases from 49 to 65 K, indicating a strong preference for 3He transmission at a lower temperature.
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Fig. 6 (a) Thermally weighted transmission of classical helium (black solid line), 3He (blue solid line) and 4He (red dashed line); (b) ratio of quantum-mechanical to classical transmission
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probability; (c) 3He/4He transmission ratio.
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Although the g-C3N4 membrane exhibits great selectivity of 3He at low temperature, the transmission probability is 10-34 at 49 K (Fig. 6a), corresponding to a quite low helium flux around 10-34 moles cm-2 s-1 at a pressure of one bar (collision rate approximately 1024 cm-2s-1 [19]), which remains very low for industrial application. However, the g-C3N4 membrane is still predicted to have better performance on both selectivity and flux compared to the predicted hydrogen-passivated porous graphene [43], which has a predicted 3He/4He transmission ratio of
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3 at 77 K with a total helium flux below 10-36 moles cm-2s-1 at the same pressure condition. Several strategies can be used to increase this impractical flux, such as imposing high pressure. Moreover, taking advantage of the excellent mechanical properties of the g-C3N4 membrane, one
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can enlarge the pore size by applying tensile stress on the membrane, and thereby lower the penetration barrier and improve the transmission flux. Additionally, carbon nitrides have abundant 2D nanostructures with various size of pores [74,75], which can be used to optimize
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the 3He transmission with good selectivity and an industrially acceptable flux. Nevertheless, due to the part per million level of concentration of helium in the natural resource, and even less of He isotope, it has never been an easy task to purify 3He isotope out of the natural gas. However,
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our present work offers a promising family of membranes for separating He from other gas molecules, as well as separating 3He from 4He.
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4. Conclusions
Using first-principles calculations, we theoretically demonstrated that the already-synthesized gC3N4 membrane has high selectivity for separating He from other gas molecules (H2, N2, CO and
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CH4) in natural gas, as well as from noble gas molecules, such as Ne and Ar. The energy barrier for He molecule passing through the g-C3N4 membrane is calculated to be 0.354 eV, but the
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selectivity over H2 molecule at room temperature is predicted to be as high as 107. More interestingly, the g-C3N4 can serve as an efficient quantum sieving membrane for 3He/4He separation with a predicted transmission ratio of 18 at 49 K. Our results offer a promising membrane for separating 3He from natural gas which is quite crucial for cryogenic industries.
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SUPPLEMENTARY MATERIALS Supplementary Method, Supplementary Table and Supplementary Figures can be found in
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Supplementary Materials online.
ACKNOWLEDGMENT
This work is supported by the National Basic Research Program of China (No.2012CB932302),
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the National Natural Science Foundation of China (Nos.91221101, 21433006), the 111 project (No. B13029), the Technological Development Program in Shandong Province Education
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Department (Grant No. J14LJ03), the Fundamental Research Funds of Shandong University (Grant No. 2015HW012), and the National Super Computing Centre in Jinan.
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Supplementary Materials for
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Efficient Helium Separation of Graphitic Carbon Nitride Membrane
a
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Feng Li ab, Yuanyuan Qua*, Mingwen Zhaoa*
School of Physics, Shandong University, Jinan, Shandong, 250100, People’s Republic of China;
b
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School of Physics and Technology, University of Jinan, Jinan, Shandong,250022, People’s Republic of China
Supplementary Method
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Steered molecular dynamics simulation
The steered molecular dynamics simulation was performed by GROMACS package[1],
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using the universal force field (UFF)[2]. The electrostatic potential (ESP) charges of the g-C3N4 lattice was calculated by Gaussian 09[3]. In our system, two sheets of g-C3N4 membrane were
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placed in a box of dimension of 3.5657 nm×3.088 nm×50 nm, with a distance of 6 nm. At the initial state, 140 He and 140 H2 molecules are placed in between the two sheets. After energy minimization, the system was then fully relaxed for 200 ps at 298 K. Following that, a pulling force was applied to the two sheets by connecting them with a hypothetical zero-length spring with a spring constant of 27 pN/nm or 83 pN/nm. A total of 4 ns simulation was performed for each trajectories, and the fraction of transmission of both He and H2 were recorded.
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Supplementary Table
Table S1: The energy barriers (Eb) of gases penetrating the pore and the selectivities (S, at
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T=300 K) of He over the other gases calculated by LDA, GGA with or without van der Waal’s corrected dispersion term. GGA Gas
GGA+vdW
LDA
LDA+vdW
S (He/gas)
Eb (eV)
S (He/gas)
Eb (eV)
S (He/gas)
Eb (eV)
S (He/gas)
He
0.405
1
0.354
1
0.193
1
0.184
1
H2
0.873
108
0.747
107
0.493
105
0.435
104
Ne
0.990
1010
0.937
1010
0.584
107
0.567
106
CO
2.232
1031
2.087
1030
1.557
1023
1.543
1023
N2
2.565
1036
2.348
1034
1.839
1028
1.755
1026
Ar
3.419
1051
3.376
1051
2.761
1043
2.760
1043
CH4
4.545
1069
4.216
1065
3.810
1061
3.700
1059
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Eb (eV)
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Supplementary Figures
Figure S1. (a) The g-C3N4 structure under 1% tensile strain, where a1 , a2 represent two primitive vectors. (b) Energy barriers of He (black) and H2 (red) passing through the free g-C3N4 membrane (solid lines) and under-tensile g-C3N4 membrane (dashed lines).
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Figure S2. Fraction of transmission of He and H2 (upper panel) and the pressure changes during
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pulling (lower panel) under a spring constant of 83 pN/nm.
Figure S3. Trajectory snapshots during simulation under a spring constant of 27 pN/nm.
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Figure S4. Quantum-mechanical and classical transmission probability of He passing through the pore of g-C3N4 as a function of kinetic energy based on the energy barrier calculated by the LDA functional (with vdW corrected dispersion term), where kinetic crossover is 0.08 eV (with 0.104 eV adsorption energy). The black solid line represents the classical transmission, the blue solid line represents the quantum-mechanical transmission of 3He isotope and the red dashed line
Supplementary Reference
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represents that of 4He isotope.
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1. Pronk, S.;Páll, S.;Schulz, R.;Larsson, P.;Bjelkmar, P.;Apostolov, R., et al., GROMACS 4.5: a high-throughput and highly parallel open source molecular simulation toolkit. Bioinformatics 2013, 29 (7), 845-854. 2. Garberoglio, G., OBGMX: a web-based generator of GROMACS topologies for molecular and periodic systems using the universal force field. Journal of computational chemistry 2012, 33 (27), 22042208. 3. Frisch, M. J.;Trucks, G. W.;Schlegel, H. B.;Scuseria, G. E.;Robb, M. A.;Cheeseman, J. R., et al. Gaussian 09, Gaussian, Inc.: Wallingford, CT, USA, 2009.
S0008-6223(15)30132-9
DOI:
10.1016/j.carbon.2015.08.013
Reference:
CARBON 10178
To appear in:
Carbon
Received Date: 4 June 2015 Revised Date:
5 August 2015
Accepted Date: 6 August 2015
Please cite this article as: F. Li, Y. Qu, M. Zhao, Efficient Helium Separation of Graphitic Carbon Nitride Membrane, Carbon (2015), doi: 10.1016/j.carbon.2015.08.013. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
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Nitride Membrane
a
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Feng Li ab, Yuanyuan Qua*, Mingwen Zhaoa*
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Efficient Helium Separation of Graphitic Carbon
School of Physics, Shandong University, Jinan, Shandong, 250100, People’s Republic of
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China; b School of Physics and Technology, University of Jinan, Jinan, Shandong, 250022, People’s Republic of China
ABSTRACT
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An efficient membrane for helium separation from natural gas is quite crucial for cryogenic industries. However, most experimentally available membranes fail in separating helium from small molecules in natural gas, such as H2, as well as in 3He/4He isotopes separation. Using first-
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principles calculations, we theoretically demonstrated that the already-synthesized graphitic
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carbon nitride (g-C3N4) has high efficiency in helium separation from the gas molecules (H2, N2, CO and CH4) in natural gas and the noble gas molecules (Ne and Ar). The selectivity of He over H2 molecule at room temperature is calculated to be as high as 107. More interestingly, the gC3N4membrane can also serve as a quantum sieving membrane for 3He/4He separation with a predicted transmission ratio of 18 at 49 K, thus offers a combined means of both He and 3He isotope separation.
* Correspondence authors. Tel: +86 531 88364655. Email: [email protected]. (Mingwen Zhao) or Tel: +86 531 88363350 Email: [email protected]. (Yuanyuan Qu)
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1. Introduction As an extraordinary noble gas, helium has wide application in advanced technologies, such as
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cryogenics, arc welding, space rockets and silicon-wafer manufacture [1]. However, helium resource is very limited on earth. Natural gas remains the richest and most accessible source of helium, which makes helium purification an inevitable stage for its storage and utilization [2-5]. Among various technologies employed for helium separation [6], membrane technology stands
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out for its high efficiency, small footprint, simplicity in operation, ease of scale up and environmental friendliness [7]. Membrane is the key of this technology, as it defines selective
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barriers for gas molecules. An ideal membrane should be as thin as possible to maximize flux, mechanically robust to prevent rupture and have well-defined pore size to increase selectivity [8].
Graphene-based membranes offer competitive candidates for such molecular-sieving
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membranes, owing to its atomic thickness, superior stiffness and natural porous structure. However, both experimental and theoretical works indicate that a perfect graphene sheet is impermeable to gases, even as small as helium, because of its densely packed honeycomb lattice
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structure [9,10]. Consequently, pores with well-defined sizes should be created in graphene (porous graphene) as channels for gas separation. Porous graphene can be achieved via top-down
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approach by utilizing electron beam treatment or ultraviolet-induced oxidative etching to create pores [11-14]. Subsequently, many theoretical studies have shown that graphene and graphene analogues with appropriate pore sizes are implementable for gas purification or isotopes separation [15-29]. However, these strategies face the same difficulty that the pore size should be well-controlled, which remains a technical challenge for porous graphene. The broad distribution of the pore size in porous graphene would reduce the selectivity of the membrane.
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Besides porous graphene, there are other kinds of two-dimensional (2D) porous membranes with regular and uniformly distributed subnanometer pores, such as polyphenylene [30], graphdiyne [31] and graphitic carbon nitride (g-C3N4) [32]. These porous membranes can act as
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natural molecular sieves, and have great potential for future industrial applications, such as hydrogen [33-40], isotope [41-44], and other gas separation and purification [45]. Among these porous structures, g-C3N4 has attracted considerable attention owing to its potential applications
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in solar energy conversion [46-48], spintronics devices [49,50], energy storage [51] etc. The framework of g-C3N4 consisting of tri-s-triazine (heptazine) rings was demonstrated to be the
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most stable allotrope among various 2D carbon nitrides under ambient conditions [52]. More importantly, the multi-layer g-C3N4material has already been successfully synthesized by a variety of methods [53-55], which have paved the way for producing single-layer free-standing g-C3N4 membrane, in the light of producing graphene from graphite [56]. Moreover, the
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excellent thermal, mechanical and chemical stabilities of g-C3N4 [57] are quite promising for gas purification under arbitrary conditions.
In this contribution, using first-principles calculations, we demonstrated that the already-
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synthesized g-C3N4 material exhibits remarkably high selectivity in favor of He over other
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natural gas, especially for the small-sized gas molecules, such as H2, which is difficult for other membranes. The selectivity of He over H2 molecule at room temperature can be as high as 107. This membrane can also be utilized for He separation from other noble gas molecules with the selectivities of 1010 for Ne and 1051 for Ar. More interestingly, our quantum sieving analysis indicates that it might be used for 3He/4He isotope separation due to the quantum tunneling effect, offering a combined means of both He and 3He isotope separation.
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2. Computational Methods The first-principles calculations have been performed within the density functional theory (DFT)
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using the plane-wave pseudopotential approach as implemented in the Vienna Ab initio Simulation Package (VASP) [58-60]. The electron-electron interactions are treated within a generalized gradient approximation (GGA) in the form of Perdew-Burke-Ernzerhof (PBE) for the exchange-correlation functional [61]. The van der Waals (vdW) interactions were included
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explicitly by using the empirical correction scheme of Grimme (DFT+D2) [62]. The electron wavefunctions were expanded using the plane-waves with the energy cutoff of 500 eV. The
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atomic coordinates were fully relaxed using a conjugate gradient scheme without any symmetry restrictions until the maximum force on each atom was smaller than 0.01eV/Å. Vacuum space larger than 15 Å was used to avoid the interaction between adjacent images. The MonkhorstPack meshes of 7×7×1 were used in sampling the Brillouin zone for the 2×2 supercells of g-C3N4
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[63]. For the transition state calculations, we have performed minimum energy path profiling using the climbing image nudged elastic band method (CNEB) as implemented in the VASP transition state tools [64,65]. The structural convergence criteria were similar to that used in the
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above-mentioned structure optimization. In the subsequent calculations of the potential energy profiles for gas molecules penetrating the membrane pores, the nearest-neighbor atoms
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surrounding the penetrated pores were fully relaxed while the z-coordinates of the other atoms were kept fixed. The steered molecular dynamics simulation was performed by GROMACS package [66] using the universal force field (UFF) [67]. More details can be found in the Supplementary Materials (Supplementary Method).
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3. Results and Discussions 3.1 Efficient helium separation from natural gas molecules
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The lattice constant of g-C3N4consisting of tri-s-triazine rings is calculated to be 7.13 Å, consistent with previous literatures [48,68]. Fig. 1a presents a top view of a fully relaxed (2×2) g-C3N4 supercell. The pores on g-C3N4 are naturally and uniformly distributed with the same shape and dimension. According to the electron counting role, the N atoms at the edges of the
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pores are doubly bonded without the needs of hydrogen passivation. The pore size is characterized by the diameter of the inscribed circle, 4.76 Å, which is suitable for He or H2
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separation from other gas molecules [17,18].
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Fig. 1 (a) Top view of (2×2)g-C3N4 supercell. The brown and blue balls represent the C and N atoms, respectively. The yellow circles indicate the inscribed circles of the pores. (b) Energy profiles for He, H2, Ne, CO, N2, Ar and CH4 passing through the pore of the g-C3N4 membrane. Different colors indicate different gas molecules. Colored points indicate the results obtained by first-principles calculations, and the curves show the numerically interpolated potentials. The insert graphs show the side views of the transition states of He and H2 passing through the pore respectively.
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The energetically most favorable configuration of a gas molecule on the g-C3N4membrane was determined by structural optimization. It was found that gas molecules prefer to reside right
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above a pore at different heights depending on the species of gas molecules, as listed in Table 1.
Table 1. The equilibrium height (h0) between the gas molecules (He, H2, Ne, CO, N2, Ar and CH4) and the g-C3N4 membrane, the adsorption energies (Ea) of the gases on the g-C3N4
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membrane, the energy barriers (Eb) of gases penetrating the pore and the selectivities (S, at
gas
h0(Å)
He
2.489
H2
2.283
Ne
2.491
CO
3.329
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T=300 K) of He over the other gases. Ea(eV)
Eb(eV)
S(He/gas)
0.017
0.354
1
0.091
0.747
107
0.052
0.937
1010
0.036
2.087
1030
2.848
0.128
2.348
1034
Ar
2.463
0.099
3.376
1051
CH4
2.951
0.147
4.216
1065
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N2
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The adsorption energy (Ea) was defined as: Ea = E g −C3 N 4 + E gas − Esas
(1)
where Esas is the total energies of g-C3N4 with an adsorbed gas molecule at the most stable adsorption state, Egas and E g −C3 N 4 represent the energy of an isolated gas molecules and the pristine g-C3N4, respectively.―The adsorption energies and the equilibrium heights are in the range of 0.017~0.147eV and 2.283~3.329 Å, respectively, as listed in Table 1, suggesting the interaction between gas molecules and g-C3N4 is dominated by weak van der Waals interactions.
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Helium molecule has the weakest interaction with the g-C3N4, which is lower than that of CH4 by almost one order. This feature may facilitate the separation of He atom from other gas molecules.
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The energy barrier for a gas molecule passing through a pore of g-C3N4 was then determined from first-principles. In order to get the initial states (IS) and the final states (FS) for transition state searching, the gas molecules were placed on either side of theg-C3N4 surface with a
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distance larger than 5 Å. Then the energy profiles of the gas molecule passing through the pore were sequentially scanned using the CNEB strategy as shown in Fig. 1b. The energy barrier (Eb)
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of a gas molecule penetrating through the pore is calculated from the energy difference between the transition state (TS) and equilibrium adsorbing state (EAS), Eb = ETS
EEAS. The energy
barriers for He, H2, Ne, CO, N2, Ar, and CH4 passing through a pore of g-C3N4 are listed in Table 1. The energy barrier strongly depends on the kinetic diameter of the molecule, i.e.
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molecules with larger kinetic diameter would induce stronger repulsive interaction that leads to huge barriers when penetrating the pore. He has the lowest energy barrier (0.354 eV) which is lower than that of CH4 by one order and only half of the second lowest one (0.747 eV for H2).
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This clearly indicates that using the g-C3N4 membrane, He can be separated from other gas molecules with high efficiency, as these molecules are in principle blocked by the relatively
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higher energy barriers.
Separating He from H2 is a big challenge in He purification, because they have very close kinetic diameters (2.60 Å for He and 2.89 Å for H2 [69,70]). Most of the membranes, such as the porous silicene [17,18], polyphenylene [33,34,43] or graphdiyne [36,37,44], fail to separate He from H2, as the energy barriers of H2 and He passing through these membranes are almost equal, as shown in Table 2. It is interesting to see that for the g-C3N4 membrane, the energy barrier of
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H2 is twice that of He, suggesting efficient He separation behavior. A more intriguing finding lies in the fact that the pore size of the g-C3N4 membrane (4.76Å) is almost the same as that of the porous silicene (4.7 Å) [17,18], but the latter one fails to separate He from H2. We argue that
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this discrepancy may due to the polarity of the atoms along the pore edge, as the negatively polarized N atom surrounds the pores for the g-C3N4 membrane while the neutral Si atom resides
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around the pores for the porous silicene.
Table 2. Comparison results on energy barrier Eb (eV) and selectivity (S, at T=300 K) between
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porous membranes. g-C3N4
silicene
polyphenylene
graphdiyne
Eb (He)
0.354
0.33(a)
0.523(g), 0.43(c)
0.033(h)
Eb (H2)
0.747
0.34(b)
0.37(c),0.61(d)
0.03(e),0.1(f)
Eb (Ne)
0.937
0.53(a)
1.245(g)
--
S (He/H2)
107
--
--
--
S (He/Ne)
1010
6×102(c)
--
2×103(a)
Ref. 17(b)Ref. 18(c)Ref. 33(d)Ref. 34(e)Ref. 36(f)Ref. 37(g)Ref. 43(h)Ref. 44
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(a)
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membranes
To study the He separation efficiency of the g-C3N4 membrane, the selectivity (S) for He over
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other gas molecules was calculated based on the Arrhenius equation [71,72]:
S He / gas =
rHe A e − EHe / RT = He − Egas / RT rgas Agas e
(2)
where r is the diffusion rate, A is the interaction (diffusion) prefactor, and E is the diffusion barrier. Here we assumed that the prefactors of gases are identical (AHe= Agas=1011 s-1) for simplification [33]. The temperature-dependent diffusion rates and selectivities are depicted in
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Fig. 2. The selectivities for He over other gas molecules at room temperature (300 K) are also listed in Table 1. It is clearly shown that the g-C3N4 membrane exhibits higher permeability and selectivity for He. Moreover, compared to other porous membranes (porous silicene,
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polyphenylene and graphdiyne) as shown in Table 2, the g-C3N4 membrane distinguishes itself by a selectivity enhancement around 107 times for He over H2 or Ne. Similar results can also be obtained by using a local density approximation (LDA) functional, showing He has better
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selectivity compared with other gas molecules (see Supplementary Table S1).
Fig. 2 The transmission rate (a) and the selectivity (b) of gas molecules passing through the pore
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molecules.
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on g-C3N4 membrane as a function of temperature. Different colors indicate different gas
To further understand the improved He purification behavior of the g-C3N4 membrane, we plotted the electron density isosurfaces for the transition states of He, H2, Ne, and CH4 molecules passing through the g-C3N4 membrane in Fig. 3. The repulsive interaction between gas molecule and g-C3N4 membrane is related to their electron density overlap due to the close-shell feature of the gas molecule and the semiconducting feature of the membrane. Intuitively, large electron density overlap would lead to strong repulsion which hinders the diffusion of the gas molecules
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passing through the pore. From Fig. 3, we can see that there is no obvious overlap between the electron density isosurfaces of He and the membrane at an isovalue of 0.015 e/Å3. However, the electron density overlap at the same isovalue increases gradually for H2, Ne and CH4, among
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which CH4 has the most pronounced electron density overlap with the membrane, and thus the
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highest energy barrier.
Fig. 3 Electron-density isosurfaces for (a) He, (b) H2, (c) Ne, and (d) CH4 passing through the pore of g-C3N4membrane at the transition states. The isovalue is 0.015 e/Å3. It is noteworthy that when the membrane is utilized in gas separation, the pressure difference between two sides of the membrane will cause global burden to the 2D system, therefore may induce local enlargement of the pore size. To reveal this effect on the gas separation efficiency, we have applied a biaxial tensile strain of 1% to the g-C3N4 supercell (see Supplementary Fig.
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S1a), which enlarges pore size to 4.83 Å compared with one without tensile strain (4.76 Å). Our first-principles calculations indicated that the energy barriers for He and H2 passing through the pore of the stretched g-C3N4 are 0.311 and 0.672 eV, respectively, which are slightly smaller
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than the corresponding values (0.354 and 0.747 eV) of the unstretched membrane (see Supplementary Fig. S1b). The selectivity (~106) of He over H2 at 300 K remains very high in this stretched g-C3N4 membrane. Therefore, the global burden in principle may not change the
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to pass through the g-C3N4 membrane under burden.
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property of separation, which means that compared with other molecules, He still has the priority
3.2 Steered Molecular Dynamics Simulation of Separating He from H2
The steered molecular dynamic simulation was also performed to investigate the separation efficiency between He and H2. In our system, two sheets of g-C3N4 membrane are placed in a
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box of dimension of 3.5657 nm×3.088 nm×50 nm, with a distance of 6 nm. At the initial state, 140 He and 140 H2 molecules are placed randomly in between the two sheets, as shown in Fig.
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4a. A pulling force was applied to these two sheets by connecting them with a hypothetical zerolength spring with a spring constant of 27 pN/nm.
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A total of 4 ns simulation was performed for each trajectory and the simulation results are shown in Fig. 4b. As can be seen, more than 95% of the He molecules have escaped out of the two layers within 1 ns, however, none of the H2 molecule has passed through the g-C3N4 membrane. These results are in good agreement with our first-principles calculations, which suggest He has a 107 of selectivity over H2 molecule. During the pulling, the equilibrium pressure reduced to 11 Bar after 0.5 ns, indicating that separating He from H2 do not require high pressure condition. Similar results were obtained when using a spring with a spring constant of
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83 pN/nm (See Supplementary Fig. S2). More trajectory snapshots can be found in the
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Supplementary Fig. S3.
Fig. 4 (a) Snapshots of the initial state. The He molecule are highlighted in orange and the H2 molecule are highlighted in yellow. (b) Fraction of transmission of He and H2 (upper panel) and
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the pressure changes during pulling (lower panel).
3.3 Separating 3He from 4He
Separating He isotopes (3He and 4He) is quite necessary for cryogenic industries, because they
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have different thermal properties. We therefore examined whether the g-C3N4 membrane is
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implementable for separating 3He from 4He. It is noteworthy that these two He isotopes have the same energy profile as passing through the g-C3N4 membrane (black curve in Fig. 1b), because they have the same number of electrons and protons. However, different masses of the two isotopes would give rise different probabilities when they pass through the membrane via quantum tunneling. On the basis of the energy profile obtained from first-principles calculations, we performed one-dimensional (1D) finite difference calculations [73] of the quantum tunneling probability t(E) as a function of kinetic energy E as shown in Fig. 5. It can be seen that 3He
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transmission is preferred at low kinetic energy regime (<0.337 eV) while 4He transmission becomes more likely at high kinetic energy regime (>0.337 eV). The equivalent transmission probability occurs when the kinetic energy of a particle equals the height of the energy barrier
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(0.337 eV). Therefore, it is reasonable to keep the gas at a low temperature (where particles with lower kinetic energy) to enhance the selectivity of 3He from 4He. It should be noticed that although different exchange functional forms may give different kinetic crossovers
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(Supplementary Table 1S), the overall trend of the tunneling probability maintains
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(Supplementary Fig. S4).
Fig. 5 Quantum-mechanical and classical transmission probability of He passing through the pore of g-C3N4as a function of kinetic energy. The black solid line represents the classical transmission, the blue solid line represents the quantum-mechanical transmission of 3He isotope and the red dashed line represents that of 4He isotope.
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Based on t(E), the thermally weighted transmission probability p(T) can be calculated by taking the integral of the product of t(E) and p(E,T), the kinetic energy distribution in one dimension for a given temperature T:
p( E , T ) =
1 e − E / k BT 4πk B TE
(3)
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p(T ) = ∫ p( E , T )t ( E )dE
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This result is derived from the Gaussian distribution of velocities in one dimension, and the E-1/2 appearing in p(E,T) is due to the substitution of the integral variable of dv by dE. Here, we
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assumed a classical Boltzmann distribution for the velocities of both 3He and 4He as suggested by previous studies [19,20,22,43,44]. This strategy not only provides a more conservative estimation of 3He/4He selectivity, but also avoids the complexity of dealing with a mixed nonideal quantum gas composed of fermionic 3He and bosonic 4He. The thermally weighted results
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at low temperature regime (49-65 K) are summarized in Fig. 6, including (a) the thermally weighted transmission probability of 3He and 4He; (b) the ratio of quantum-mechanical to classical transmission; (c) the 3He/4He transmission ratio. As can be seen in Fig. 6a, the
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transmission probabilities of both 3He and 4He isotopes deviate largely from the classical case, due to the quantum tunneling effect of helium atom, leading to huge values for the ratio of
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quantum-mechanical to classical transmission for both 3He and 4He isotopes shown in Fig. 6b. The 3He/4He transmission ratio plotted in Fig. 6c exhibits an exponentially decrease from 18 to 1.8 as temperature increases from 49 to 65 K, indicating a strong preference for 3He transmission at a lower temperature.
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Fig. 6 (a) Thermally weighted transmission of classical helium (black solid line), 3He (blue solid line) and 4He (red dashed line); (b) ratio of quantum-mechanical to classical transmission
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probability; (c) 3He/4He transmission ratio.
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Although the g-C3N4 membrane exhibits great selectivity of 3He at low temperature, the transmission probability is 10-34 at 49 K (Fig. 6a), corresponding to a quite low helium flux around 10-34 moles cm-2 s-1 at a pressure of one bar (collision rate approximately 1024 cm-2s-1 [19]), which remains very low for industrial application. However, the g-C3N4 membrane is still predicted to have better performance on both selectivity and flux compared to the predicted hydrogen-passivated porous graphene [43], which has a predicted 3He/4He transmission ratio of
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3 at 77 K with a total helium flux below 10-36 moles cm-2s-1 at the same pressure condition. Several strategies can be used to increase this impractical flux, such as imposing high pressure. Moreover, taking advantage of the excellent mechanical properties of the g-C3N4 membrane, one
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can enlarge the pore size by applying tensile stress on the membrane, and thereby lower the penetration barrier and improve the transmission flux. Additionally, carbon nitrides have abundant 2D nanostructures with various size of pores [74,75], which can be used to optimize
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the 3He transmission with good selectivity and an industrially acceptable flux. Nevertheless, due to the part per million level of concentration of helium in the natural resource, and even less of He isotope, it has never been an easy task to purify 3He isotope out of the natural gas. However,
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our present work offers a promising family of membranes for separating He from other gas molecules, as well as separating 3He from 4He.
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4. Conclusions
Using first-principles calculations, we theoretically demonstrated that the already-synthesized gC3N4 membrane has high selectivity for separating He from other gas molecules (H2, N2, CO and
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CH4) in natural gas, as well as from noble gas molecules, such as Ne and Ar. The energy barrier for He molecule passing through the g-C3N4 membrane is calculated to be 0.354 eV, but the
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selectivity over H2 molecule at room temperature is predicted to be as high as 107. More interestingly, the g-C3N4 can serve as an efficient quantum sieving membrane for 3He/4He separation with a predicted transmission ratio of 18 at 49 K. Our results offer a promising membrane for separating 3He from natural gas which is quite crucial for cryogenic industries.
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SUPPLEMENTARY MATERIALS Supplementary Method, Supplementary Table and Supplementary Figures can be found in
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Supplementary Materials online.
ACKNOWLEDGMENT
This work is supported by the National Basic Research Program of China (No.2012CB932302),
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the National Natural Science Foundation of China (Nos.91221101, 21433006), the 111 project (No. B13029), the Technological Development Program in Shandong Province Education
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Department (Grant No. J14LJ03), the Fundamental Research Funds of Shandong University (Grant No. 2015HW012), and the National Super Computing Centre in Jinan.
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Supplementary Materials for
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Efficient Helium Separation of Graphitic Carbon Nitride Membrane
a
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Feng Li ab, Yuanyuan Qua*, Mingwen Zhaoa*
School of Physics, Shandong University, Jinan, Shandong, 250100, People’s Republic of China;
b
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School of Physics and Technology, University of Jinan, Jinan, Shandong,250022, People’s Republic of China
Supplementary Method
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Steered molecular dynamics simulation
The steered molecular dynamics simulation was performed by GROMACS package[1],
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using the universal force field (UFF)[2]. The electrostatic potential (ESP) charges of the g-C3N4 lattice was calculated by Gaussian 09[3]. In our system, two sheets of g-C3N4 membrane were
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placed in a box of dimension of 3.5657 nm×3.088 nm×50 nm, with a distance of 6 nm. At the initial state, 140 He and 140 H2 molecules are placed in between the two sheets. After energy minimization, the system was then fully relaxed for 200 ps at 298 K. Following that, a pulling force was applied to the two sheets by connecting them with a hypothetical zero-length spring with a spring constant of 27 pN/nm or 83 pN/nm. A total of 4 ns simulation was performed for each trajectories, and the fraction of transmission of both He and H2 were recorded.
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Supplementary Table
Table S1: The energy barriers (Eb) of gases penetrating the pore and the selectivities (S, at
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T=300 K) of He over the other gases calculated by LDA, GGA with or without van der Waal’s corrected dispersion term. GGA Gas
GGA+vdW
LDA
LDA+vdW
S (He/gas)
Eb (eV)
S (He/gas)
Eb (eV)
S (He/gas)
Eb (eV)
S (He/gas)
He
0.405
1
0.354
1
0.193
1
0.184
1
H2
0.873
108
0.747
107
0.493
105
0.435
104
Ne
0.990
1010
0.937
1010
0.584
107
0.567
106
CO
2.232
1031
2.087
1030
1.557
1023
1.543
1023
N2
2.565
1036
2.348
1034
1.839
1028
1.755
1026
Ar
3.419
1051
3.376
1051
2.761
1043
2.760
1043
CH4
4.545
1069
4.216
1065
3.810
1061
3.700
1059
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Eb (eV)
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Supplementary Figures
Figure S1. (a) The g-C3N4 structure under 1% tensile strain, where a1 , a2 represent two primitive vectors. (b) Energy barriers of He (black) and H2 (red) passing through the free g-C3N4 membrane (solid lines) and under-tensile g-C3N4 membrane (dashed lines).
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Figure S2. Fraction of transmission of He and H2 (upper panel) and the pressure changes during
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pulling (lower panel) under a spring constant of 83 pN/nm.
Figure S3. Trajectory snapshots during simulation under a spring constant of 27 pN/nm.
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Figure S4. Quantum-mechanical and classical transmission probability of He passing through the pore of g-C3N4 as a function of kinetic energy based on the energy barrier calculated by the LDA functional (with vdW corrected dispersion term), where kinetic crossover is 0.08 eV (with 0.104 eV adsorption energy). The black solid line represents the classical transmission, the blue solid line represents the quantum-mechanical transmission of 3He isotope and the red dashed line
Supplementary Reference
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represents that of 4He isotope.
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