Theoretical study of helium separation performance of crown ether-graphane membranes

Tong Zan; Yang Yin-Li; Xu Jing; Liu Wei; Chen Liang

doi:10.7498/aps.72.20222183

Abstract

Helium (He) is widely used in many scientific and industrial fields, and the shortage of He resources and the growing demand make He separation extremely important. In this work, the He separation performances of a series of graphanes containing crown ether nanopores (crown ether graphane, CG-n, n = 3, 4, 5, 6) are studied by first-principles calculations. At first, the minimum energy paths of He and other 10 gas molecules (Ne, Ar, H₂, CO, NO, NO₂, N₂, CO₂, SO₂ and CH₄) passing through CG-n membranes are calculated, and the factors affecting the energy barriers are also investigated. The calculated results show that He is the easiest to pass through all the four CG-n membranes with energy barriers of 4.55, 1.05, 0.53 and 0.01 eV, respectively. He can be separated by CG-5 and CG-6 with very low energy barriers, and the energy barrier of He passing through CG-6 is the lowest, so far as we know. Moreover, all gas molecules can pass through CG-6 with low energy barriers, including many molecules with large kinetic diameters, such as CO (0.13 eV) and N₂ (0.16 eV). Therefore, CG-6 is also expected to be used in the screening field of other gas molecules. In addition, it is found that the energy barriers of gas molecules passing through CG-n are synergistically affected by the size of the crown ether nanopore, the kinetic diameter and the type of the gas molecules. Secondly, the diffusion rates of gas molecules passing through CG-5 and CG-6 and the He selectivity towards other 10 gases of CG-5 and CG-6 at different temperatures are calculated. It is found that CG-5 exhibits extremely high He selectivity in a wide temperature range (0–600 K). In summary, the crown ether graphanes CG-5 and CG-6 can serve as excellent He separation membranes with high He selectivity. This work is expected to inspire one to develop other graphene-based two-dimensional separation membranes for separating He and other gas molecules.

Keywords:

Authors and contacts

1.
College of Optical, Mechanical and Electrical Engineering, Zhejiang A & F University, Hangzhou 311300, China
2.
School of Physical Science and Technology, Ningbo University, Ningbo 315211, China

Corresponding author: Xu Jing, jingxu@zafu.edu.cn ; Liu Wei, weiliu@zafu.edu.cn ;

Funds: Project supported by the Natural Science Foundation of Zhejiang Province, China (Grant No. LQ20B030002), the National Natural Science Foundation of China (Grant Nos. 12075211, 11975206, 11875236, 12074341), and the Scientific Research Foundation of Zhejiang A&F University, China (Gant Nos. 2019FR005, 2019FR006).

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References

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Cited By

图 1 CG-n的优化结构和孔径值(单位: Å)　(a) CG-3; (b) CG-4; (c) CG-5; (d) CG-6. 黑色、红色和橙色的球分别代表碳原子、氧原子和氢原子

Figure 1. Optimized structures and pore size (unit: Å) of CG-n: (a) CG-3; (b) CG-4; (c) CG-5; (d) CG-6. The black, red, and orange balls represent carbon, oxygen, and hydrogen atoms, respectively.

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图 2 气体分子通过CG-n膜的最低能量路径　(a) CG-3; (b) CG-4; (c) CG-5; (d) CG-6

Figure 2. The minimum energy paths of gas molecules passing through CG-n membranes: (a) CG-3; (b) CG-4; (c) CG-5; (d) CG-6.

DownLoad: Full-Size Img PowerPoint

图 3 气体分子通过CG-5膜时的静电势等值面图　(a) He; (b) H₂; (c) Ne; (d) CO₂; (e) NO₂; (f) NO; (g) CO; (h) N₂; (i) SO₂; (j) Ar; (k) CH₄

Figure 3. Electrostatic potential isosurfaces of (a) He, (b) H₂, (c) Ne, (d) CO₂, (e) NO₂, (f) NO, (g) CO, (h) N₂, (i) SO₂, (j) Ar and (k) CH₄ molecules passing through CG-5 membrane.

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图 4 气体分子通过(a) CG-5膜和(c) CG-6膜的扩散速率-温度曲线; (b) CG-5膜和(d) CG-6膜的He选择性-温度曲线

Figure 4. Diffusion rate-temperature curves of gas molecules through (a) CG-5 and (c) CG-6; He selectivity-temperature curves of (b) CG-5 and (d) CG-6.

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表 1 气体分子在CG-n上稳定吸附时的吸附能E_ad 和吸附高度H

Table 1. Adsorption energies E_ad and the adsorption heights H of gas molecules adsorbed stably on CG-n.

	CG-3		CG-4		CG-5		CG-6
	E_ad/eV	H/Å	E_ad/eV	H/Å	E_ad/eV	H/Å	E_ad/eV	H/Å
He	–0.15	2.89	–0.10	2.00	–0.12	2.40	–0.11	2.00
Ne	–0.22	3.11	–0.17	2.82	–0.11	2.00	–0.14	2.00
Ar	–0.18	4.00	–0.16	4.00	–0.15	4.00	–0.22	2.00
CH₄	—	—	–0.37	2.40	–0.36	2.30	–0.29	1.79
H₂	–0.24	2.70	–0.23	2.50	–0.14	2.00	–0.18	2.00
CO₂	—	—	–0.15	3.70	–0.15	3.70	–0.53	0.00
NO	—	—	–0.49	2.90	–0.22	3.10	–0.27	1.80
CO	—	—	–0.25	3.00	–0.23	2.90	–0.22	2.00
N₂	–0.33	3.10	–0.24	3.20	–0.22	3.10	–0.24	1.90
NO₂	—	—	–0.40	3.10	–0.11	3.60	–0.29	0.00
SO₂	—	—	—	—	–0.20	3.60	–0.27	0.00

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表 2 气体分子的动力学直径 (D) 和通过CG-n膜时的能垒 E_barrier. D值来自文献[37]

Table 2. Kinetic diameters (D) of the gas molecules, and energy barriers E_barrier for gas molecules passing through each CG-n membrane. D values from literature [37].

	D/Å	E_barrier/eV
	D/Å	CG-3	CG-4	CG-5	CG-6
He	2.60	4.55	1.05	0.53	0.01
Ne	2.82	12.07	2.80	1.44	0.05
Ar	3.54	22.80	8.90	4.86	0.42
CH₄	3.80	—	10.81	6.07	0.80
H₂	2.89	6.23	1.91	1.00	0.12
CO₂	3.30	—	3.45	1.76	0.53
NO	3.17	—	5.12	2.50	0.10
CO	3.69	—	5.48	2.83	0.13
N₂	3.64	15.56	5.95	3.15	0.16
NO₂	—	—	5.42	2.15	0.29
SO₂	4.12	—	—	3.40	0.27

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表 3 室温(300 K) 下, 多孔膜材料对He (相对于其他气体)的选择性 (S)

Table 3. Selectivity (S) of porous membrane materials for He (over other gases) at room temperature (300 K).

Type	CG-5^a	CG-6^a	IGP^b	CTF-0^c	C₂N^d	g-C₃N₄^e	g-C₂O^f	PG^g
S(He/Ne)	1.63×10¹⁵	4.66	1×10⁶	4×10⁶	3×10³	1×10¹⁰	30	2×10⁷
S(He/CH₄)	4.03×10⁹²	1.32×10¹³	7×10³¹	6×10³⁸	7×10³¹	1×10⁶⁵	1.15×10²⁸	8×10³⁷
S(He/Ar)	2.39×10⁷²	5.24×10⁶	6×10²¹	5×10³⁵	4×10¹⁸	1×10⁵¹	1.68×10¹⁴	6×10³⁶
S(He/N₂)	6.24×10⁴³	3.09×10²	1×10¹²	2×10²⁷	3×10¹²	1×10³⁴	1.54×10⁶	6×10²⁷
S(He/CO)	2.79×10³⁸	80.5	1×10¹¹	5×10²⁴	—	1×10³⁰	6.72×10⁴	6×10²⁴
S(He/CO₂)	3.63×10²⁰	4.22×10⁸	3×10⁸	4×10¹⁶	8×10¹⁸	—	5.82×10²	—
S(He/H₂)	7.18×10⁷	52.7	—	—	—	—	—	—
S(He/NO)	8.51×10³²	29.6	—	—	—	—	—	—
S(He/NO₂)	1.20×10²⁷	4.11×10⁴	—	—	—	—	—	—
S(He/SO₂)	9.42×10⁴⁷	1.90×10⁴	—	—	—	—	—	—
注: ^a本工作, ^b文献[13], ^c文献[23], ^d文献[41], ^e文献[38], ^f文献[21], ^g文献[6].

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[1]	Cho A 2009 Science 326 778 Google Scholar
[2]	杨初平, 耿屹南, 王捷, 刘兴南, 时振刚 2021 物理学报 70 135102 Google Scholar Yang C P, Geng Y N, Wang J, Liu X N, Shi Z G 2021 Acta Phys. Sin. 70 135102 Google Scholar
[3]	Fatemi S M, Abbasi Z, Rajabzadeh H, Hashemizadeh S A, Deldar A N 2017 Eur. Phys. J. D 71 194 Google Scholar
[4]	Dai Z, Deng J, He X, Scholes C A, Jiang X, Wang B, Guo H, Ma Y, Deng L 2021 Sep. Purif. Technol. 274 119044 Google Scholar
[5]	王倩, 赵江山, 范元媛, 郭馨, 周翊 2020 物理学报 69 174207 Google Scholar Wang Q, Zhao J S, Fan Y Y, Guo X, Zhou Y 2020 Acta Phys. Sin. 69 174207 Google Scholar
[6]	Wei S, Zhou S, Wu Z, Wang M, Wang Z, Guo W, Lu X 2018 Appl. Surf. Sci. 441 631 Google Scholar
[7]	Rufford T E, Chan K I, Huang S H, May E F 2014 Adsorpt. Sci. Technol. 32 49 Google Scholar
[8]	Stern S A, Sinclair T F, Gareis P J, Vahldieck N P, Mohr P H 1965 Ind. Eng. Chem. 57 49
[9]	Yao B, Mandrà S, Curry J O, Shaikhutdinov S, Freund H J, Schrier J 2017 ACS Appl. Mater. Interfaces 9 43061 Google Scholar
[10]	Pakdel S, Erfan-Niya H, Azamat J 2022 J. Mol. Graphics Modell. 115 108211 Google Scholar
[11]	Mirzaei M, Karimi-Sabet J, Nikkho S, Towfighi-Darian J 2022 ACS Appl. Nano Mater. 5 1745 Google Scholar
[12]	Schrier J 2010 J. Phys. Chem. Lett. 1 2284 Google Scholar
[13]	Andrews N L P, Fan J Z, Forward R L, Chen M C, Loock H P 2017 Phys. Chem. Chem. Phys. 19 73 Google Scholar
[14]	Malekian F, Ghafourian H, Zare K, Sharif A A, Zamani Y 2019 Eur. Phys. J. Plus 134 212 Google Scholar
[15]	Liu M, Gurr P A, Fu Q, Webley P A, Qiao G G 2018 J. Mater. Chem. A 6 23169 Google Scholar
[16]	Koenig S P, Wang L, Pellegrino J, Bunch J S 2012 Nat. Nanotechnol. 7 728 Google Scholar
[17]	Peng Y, Li Y, Ban Y, Jin H, Jiao W, Liu X, Yang W 2014 Science 346 1356 Google Scholar
[18]	Oyama S, Lee D, Hacarlioglu P, Saraf R 2004 J. Membr. Sci. 244 45 Google Scholar
[19]	Kim H W, Yoon H W, Yoon S M, Yoo B M, Ahn B K, Cho Y H, Shin H J, Yang H, Paik U, Kwon S, Choi J Y, Park H B 2013 Science 342 91 Google Scholar
[20]	Sun W 2021 Nat. Nanotechnol. 16 1054 Google Scholar
[21]	Liu X, Chang X, Zhu L, Li X 2019 Comput. Mater. Sci. 157 1 Google Scholar
[22]	Chen X, Zhang S, Hou D, Duan H, Deng B, Zeng Z, Liu B, Sun L, Song R, Du J, Gao P, Peng H, Liu Z, Wang L 2021 ACS Appl. Mater. Interfaces 13 29926 Google Scholar
[23]	Wang Y, Li J, Yang Q, Zhong C 2016 ACS Appl. Mater. Interfaces 8 8694 Google Scholar
[24]	Boutilier M S H, Sun C, O’Hern S C, Au H, Hadjiconstantinou N G, Karnik R 2014 ACS Nano 8 841 Google Scholar
[25]	Hu W, Wu X, Li Z, Yang J 2013 Nanoscale 5 9062 Google Scholar
[26]	Sluiter M H F, Kawazoe Y 2003 Phys. Rev. B 68 085410 Google Scholar
[27]	Elias D C, Nair R R, Mohiuddin T M G, Morozov S V, Blake P, Halsall M P, Ferrari A C, Boukhvalov D W, Katsnelson M I, Geim A K, Novoselov K S 2009 Science 323 610 Google Scholar
[28]	Pumera M, Wong C H A 2013 Chem. Soc. Rev. 42 5987 Google Scholar
[29]	Guo K, Liu S, Tu H, Wang Z, Chen L, Lin H, Miao M, Xu J, Liu W 2021 Phys. Chem. Chem. Phys. 23 18983 Google Scholar
[30]	Kresse G, Furthmüller J 1996 Comput. Mater. Sci. 6 15 Google Scholar
[31]	Blöchl P E 1994 Phys. Rev. B 50 17953 Google Scholar
[32]	Perdew J P, Burke K, Ernzerhof M 1996 Phys. Rev. Lett. 77 3865 Google Scholar
[33]	Grimme S, Antony J, Ehrlich S, Krieg H 2010 J. Chem. Phys. 132 154104 Google Scholar
[34]	Chadi D J 1977 Phys. Rev. B 16 1746 Google Scholar
[35]	Henkelman G, Uberuaga B P, Jónsson H 2000 J. Chem. Phys. 113 9901 Google Scholar
[36]	Li X, Guo T, Zhu L, Ling C, Xue Q, Xing W 2018 Chem. Eng. J. 338 92 Google Scholar
[37]	Li J R, Kuppler R J, Zhou H C 2009 Chem. Soc. Rev. 38 1477 Google Scholar
[38]	Li F, Qu Y, Zhao M 2015 Carbon 95 51 Google Scholar
[39]	Zhu L, Jin Y, Xue Q, Li X, Zheng H, Wu T, Ling C 2016 J. Mater. Chem. A 4 15015 Google Scholar
[40]	Blankenburg S, Bieri M, Fasel R, Müllen K, Pignedoli C A, Passerone D 2010 Small 6 2266 Google Scholar
[41]	Zhu L, Xue Q, Li X, Wu T, Jin Y, Xing W 2015 J. Mater. Chem. A 3 21351 Google Scholar
[42]	Zhu Z 2006 J. Membr. Sci. 281 754 Google Scholar

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