Zilong Liu, Ge Zhao, Xiao Zhang, Lei Gao,*, Junqing Chen, Weichao Sun, Guanggang Zhou,Guiwu Lu,*

1 Beijing Key Laboratory of Optical Detection Technology for Oil and Gas, College of Science, China University of Petroleum (Beijing), Beijing 102249, China

2 Nano-Science Center, Department of Chemistry, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark

Keywords:Helium separation g-C9N7 membrane Selectivity Permeability Molecular simulation

ABSTRACT Increasing helium (He) demand in fundamental research, medical, and industrial processes necessitates efficient He purification from natural gas.However,most theoretically available membranes focus on the separation of two or three kinds of gas molecules with He and the underlying separation mechanism is not yet well understood.Using molecular dynamic(MD)and first-principle density function theory(DFT)simulations, we systematically demonstrated a novel porous carbon nitride membrane (g-C9N7) with superior performance for He separation from natural gas.The structure of g-C9N7 monolayer was optimized first,and the calculated cohesive energy confirmed its structural stability.Increasing temperature from 200 to 500 K,the g-C9N7 membrane revealed high He permeability,as high as 1.48×107 GPU(gas permeation unit,1 GPU=3.35×10-10 mol·s-1·Pa-1·m-2)at 298 K,and also exhibited high selectivity for He over other gases(Ar,N2,CO2,CH4,and H2S).Then,the selectivity of He over Ne was found to decrease with increasing the total number of He and Ne molecules,and to increase with increasing He to Ne ratio.More interestingly, a tunable He separation performance can be achieved by introducing strain during membrane separation.Under the condition of 7.5% compressive strain, the g-C9N7 membrane reached the highest He over Ne selectivity of 9.41 × 102.It can be attributed to the low energy barrier for He,but increased energy barrier for other gases passing through the membrane,which was subject to a compressive strain.These results offer important insights into He purification using g-C9N7 membrane and opened a promising avenue for the screening of industrial grade gas separation with strain engineering.

1.Introduction

Helium(He)is an extraordinary noble gas and has been widely used in a variety of industrial and scientific fields,such as cryogenics, arc welding, oil and gas detectors, silicon-wafer manufacture,the nuclear industry, and medical applications [1-5].However,with the growing demand for He, He resource is becoming very limited on earth.In the current stage,natural gas is still the richest and most accessible source of He.Thus, exploring effective technologies to separate high-purity He from natural gas, including alkane (CH4), carbon dioxide (CO2), nitrogen (N2), inert gases (Ne and Ar), and trace acid gas (H2S), is of great significance and an urgent task for practical applications [6-8].Compared to traditional technologies employed for He separation (low temperature distillation, pressure swing adsorption) [9-12], membrane technology is highly noticeable for its high efficiency, low energy consumption, simplicity in operation, ease of scale up, and no secondary pollution [13-15].The key of this technology lies in the appropriate selection of membrane material.Among various polymers, zeolites, metal-organic frameworks based membranes[16-18], a mutual restriction (trade-off) issue on gas permeability and selectivity seriously affects its development and industrialization [19,20].Therefore, it is necessary to find and develop a more efficient membrane for He separation.

Since the gas permeability is inversely proportional to membrane thickness[21],a good membrane should be as thin as possible to achieve maximum flux,mechanically robust to avoid rupture and also provided with well-defined pore size to increase gas selectivity.Because of its atomic thickness,two-dimensional(2D)materials could break the ‘‘trade-off” effect and greatly increase permeability.In the meanwhile, the gas separation mechanism of 2D materials is different to the polymer based membrane, and it can also maintain high selectivity under atomic thickness [22,23].In addition, 2D materials have excellent mechanical stability and chemical corrosion resistance,and are suitable for industrial applications.Therefore, 2D materials have become the mainstream of gas separation membrane research.Regarding the selectivity and permeability of the gas separation membrane, the pore size of the materials is also one of the influencing factors.For intrinsic graphene, silicon, and germanium membranes do not penetrate any molecules, which are required various methods to fabricate pores for gas separation [24-26].Although porous graphene can be obtained by applying electron beam treatment or ultravioletinduced oxidative etching, it is difficult to acquire well-controlled pore size and this process is also unprofitable and technically challenging in industrial processes.

Recently, 2D porous membranes with uniform pore size have attracted much attention in gas separation, such as g-C10N9, g-C2N, pc-C3N2, g-C3N3and P2C3[27-31].These research mainly focus on the purification of CO2, N2, H2, and some progresses have also been made in the separation of He.For example, Zhu et al.[32,33]studied the separation of g-C2N, g-C2O membranes to He using density function theory (DFT) and molecular dynamic (MD)simulations.It was found that the energy barrier of He passing through g-C2N, g-C2O membrane was 0.15 and 0.04 eV, respectively, and the permeability of the membrane to He reached 1 × 107and 1.03 × 107GPU (gas permeation unit, 1 GPU = 3.35×10-10mol·s-1·Pa-1·m-2),which were much larger than the value of 20 GPU in industry.Li et al.[34]found that the alreadysynthesized graphitic carbon nitride (g-C3N4) possessed excellent He separation efficiency over many natural and noble gas molecules and the selectivity of He and H2reach as high as 107at room temperature.Rao et al.[35]demonstrated that applying compressive strain to the CN membrane separated effectively He from Ar and Ne.Under 6% compressive strain, the energy barrier of He passing through the CN membrane was decreased to 0.11 eV.To the best of our knowledge,most theoretically available membranes focus on the separation of two or three kinds of gas molecules with He and the continuous gas separation under controlled strains remains less explored.

In this study,we have systematically explored a novel graphitic carbon nitride (g-C9N7) with regular and uniformly distributed pores for He separation using DFT and MD simulations.It was firstly calculated that the effective pore size of the g-C9N7membrane was 0.333 nm,which is slightly larger than the kinetic diameter of He (0.260 nm).Therefore, g-C9N7was expected to be a promising candidate for He separation.Significantly, it has been showed that g-C9N7monolayer possesses the high cohesive energy to maintain its structural integrity.Then,the separation behaviors of the gas mixture of He, Ne, CO2, Ar, N2, CO, and CH4through a monolayer g-C9N7membrane were investigated under various temperatures conditions.It was demonstrated outstandingly high selectivity in favor of He over other natural gas, especially for gas molecules of small size, such as Ne, which is difficult for other membranes.More interestingly, a tunable He separation performance can be achieved by introducing strain during membrane separation.Under the condition of 7.5% compressive strain, the g-C9N7membrane reached the highest He over Ne selectivity.The selectivity and permeability were also analyzed to evaluate the separation capacity of the g-C9N7monolayer, as well as the microscopic permeation process of seven gases in terms of their energy barriers.

2.Computational Methods

2.1.Molecular dynamics simulations

MD simulations are used to investigate the selectivity and permeability of He through the 2D porous g-C9N7membrane.The atomic interactions are described by the condensed-phase optimized molecular potential for atomistic simulation studies (COMPASS) force-field [36], which is a general all-atom force field for atomistic simulation of organic molecules, polymers and small gas molecules.The simulations were conducted in canonical(NVT, the volume and the temperature were constant) ensemble[37].The Andersen method was applied in the thermostat to control the thermodynamic temperature and generate the correct statistical ensemble.As a temperature control, the thermodynamic temperature was kept constant by allowing the simulated system to exchange energy with a ‘‘heat bath’’.The cut off distance of van der Waals interactions and electrostatic interactions was 1.25 nm.The time step was 1 fs and data were recorded every 1 ps.The total simulation time was fixed at 5 ns, which was long enough to detect several cycles of thermal vibration and to collect the full-precision trajectory of permeating molecules in the system.The model system consists of fixed helium wall and g-C9N7membrane, whose size is 4.834 nm × 4.836 nm that is typically used in the simulations [27,33,34].

2.2.Density functional theory calculations

The first-principles DFT calculations were performed with the DMol3module[38-40]in Materials Studio software.It was carried out to optimize the structure of the porous g-C9N7membrane and calculate the energy barriers of gases to pass through the porous g-C9N7membrane.The generalized gradient approximation(GGA)[41]with Perdew-Burke-Ernzerhof(PBE),which to deal with the exchange correlation of electrons.The van der Waals interaction has an important influence on the thermodynamic properties of the model system,so the Grimme method is used to correct the dispersion interactions in the calculation.The valence electrons of the system are expanded by the double numerical with polarization function (DNP), which has a computational precision being comparable to the Gaussian split-valence basis set 6-31g [42].Moreover, self-consistent field calculations were carried out with a convergence criterion of 10-6Ha(1 Ha=27.2114 eV)on the total energy.To obtain high-quality results, a real-space global orbital cut off radius as high as 0.60 nm and a smearing point of 0.002 Ha were chosen in all calculations.Monkhorst-Pack special kpoints of 6 × 6 × 1 grids were utilized to represent the Brillouin zone for all slab models.A vacuum thickness of 2.0 nm was built along the z direction of the g-C9N7monolayer,which was sufficient to avoid spurious interactions from neighboring molecules.

3.Results and Discussion

3.1.Structure and stability of g-C9N7 membrane

Fig.1(a) presents a top view of a fully optimized monolayer structure of(2×2)g-C9N7supercell.The pores on g-C9N7are naturally and uniformly distributed with the same shape and dimension.The atomic charges of porous g-C9N7are shown in Fig.S1(Supplementary Material).The optimized crystal lattice constant of g-C9N7consisting of tri-s-triazine rings is calculated to be 0.806 nm, which is in good agreement with previous theoretical predictions [43].The bond lengths of two C-N bonds in the pentagons and C-N bond connected to the s-triazines are 0.133,0.138, and 0.145 nm, respectively.The calculated results are also consistent with previous studies of g-C9N7in Table S1 [43].The electron density isosurface of the g-C9N7membrane has been plotted, as shown in Fig.1(b).The effectivepore size of the g-C9N7membrane (0.333 nm) is slightly larger than the kinetic diameter of He (0.26 nm), and comparable to those of Ne (0.32 nm), CO2(0.33 nm), Ar (0.34 nm), and N2(0.364 nm), but smaller than that of CH4(0.38 nm).This property would be suitable to separate He in accordance with the size sieving effect.

Fig.1.(a)The optimized geometry of the g-C9N7 monolayer in a 2×2 supercell.(b)The electron density isosurface of the porous g-C9N7 monolayer.Gray and blue spheres represent C and N atoms, respectively.

To make the best use of newly emerged 2D membrane, high structural stability is the prerequisite.The cohesive energy,namely, energy of decomposing the membrane into individual atoms, is usually used to characterize the structure stability.Hence, the cohesive energy (Ecoh) of the g-C9N7membrane can be calculated by the following equation:

where EC,EN,Eεare expressed as the energy of single C atom,single N atom,total g-C9N7membrane,respectively;n1and n2denote the numbers of C and N atoms in g-C9N7membrane, respectively.The unit of cohesive energy is eV.It was found that the cohesive energy of the g-C9N7membrane was calculated to be 6.25 eV, which was much higher than that of silicene (3.71 eV) and of bulk silicone(4.62 eV) [44,45].The obtained result indicated the high energetic stability of the g-C9N7monolayer structure.Since silicene is a stable enough for gas separation [46], the g-C9N7membrane can be also sufficiently stable for He separation.

3.2.Temperature effect on gas mixtures

Since natural gas is the main source for He, seven gases of He,Ne, Ar, CH4, CO2, N2, and H2S as the main composition of nature gas have been investigated.We firstly explored the separation behaviors of the gas mixture of these seven gases through a monolayer g-C9N7membrane with varying temperatures.In the initial model system, the number of molecules of He, CH4, CO2, N2, H2S,Ne and Ar are 80, 120, 30, 30, 10, 10, and 10, which are based on their molecular ratios in the natural gas.Fig.2 shows the final separation performance of the g-C9N7membrane at a temperature of 200 to 500 K after a MD simulation time of 5 ns.It can be observed that large numbers of He molecules can penetrate the g-C9N7membrane and kept at the permeate side (right side) of the membrane.As the temperature was increased to 298 K, Ne began to pass through the g-C9N7membrane.However,the number of penetrated Ne was far less than He, even when the temperature was up to 500 K.CO2was also found to pass through the membrane at 400 K.Moreover, the total number of gases passing through the g-C9N7membrane was gradually increased (26, 35, 37, 42,44), with increasing temperature from 200 to 400 K.It can be attributed to the relatively high kinetic energy of gas molecules,contributing to the penetration of the g-C9N7membrane.At 500 K, the total number of penetrated gas molecules was almost unchanged.

In order to more specifically explore the influence of temperature, the permeability F (mol·s-1·Pa-1·m-2) of the g-C9N7membrane was calculated as a function of temperature, with the following equation [47]:

where N and S represent the moles of gas molecules in the permeate side(mol)and the area of the g-C9N7membrane(m2),respectively.T is the time duration (s), and the pressure drop is set to 100 kPa across the pore[35].Using Eq.(2),the permeation curve of He permeating through the g-C9N7membrane at different temperatures was plotted in Fig.3.It can be found that the permeability of He increased gradually from 1.1 × 107to 1.74 × 107GPU when the temperature increased from 200 to 350 K.Then, the permeability of He decreased to 1.36×107GPU at 500 K.The value of He permeability reached as high as 1.48 × 107GPU at room temperature(298 K).Compared to the He permeability of porous g-C2N(1 × 107GPU) [32]and porous g-C2O (1.03 × 107GPU) [33], the g-C9N7membrane obtained the good permeability, which showed great potential application in He separation.

As Ne has passed through the g-C9N7membrane to the permeate side at 298 K(Fig.2(c)),it also needs to know whether other gas molecules will pass through the g-C9N7membrane.Thus, the separation performances of the g-C9N7membrane for He/Ne, He/Ar,He/CH4, He/CO2, He/H2S and He/N2six gas groups were further investigated.The total number of gases was 300 and the ratio of two gases in each group was 1:1 in the model system.Fig.4 exhibits the snapshots of the six groups of He/Ne, He/Ar, He/CH4, He/CO2, He/N2, He/H2S through g-C9N7membrane after a MD simulation time of 5 ns, respectively.It can be found from Fig.4(b)-(f)that Ar, CH4, CO2, N2, H2S molecules cannot pass through the g-C9N7membrane.While, only Ne passed through the g-C9N7membrane in Fig.4(a), which was consistent with their kinetic diameters compared to the pore size of g-C9N7.We come now to the general conclusion that the g-C9N7membrane has an outstanding He separation performance for the other five gas groups except He/Ne.In addition, a very interesting phenomenon is also found that the polar molecules CO2and H2S were aggregated together near the surface of membrane, indicating that the g-C9N7membrane could have unexpected ability for the adsorption of these two kinds of gases.

3.3.Selectivity and permeability of He/Ne separation

We have found that the separation of He among natural gases exhibited good separation performance using g-C9N7membrane in Section 3.2.However, this was not the case of the He/Ne mixture.To better understand the separation performance of He/Ne,we have investigated firstly the He/Ne mixture with a fixed gas ratio of 1:1 and varied number of gas molecules from 100 to 600,to see any change of the selectivity and permeability of He g-C9N7membrane.The final separations of the He/Ne mixture with the total gas number from 100 to 400 are shown in Fig.5 after a MD simulation time of 5 ns.It can be observed that as the total number of He/Ne increases, the number of He and Ne molecules entering the permeate side through the g-C9N7membrane increases from 20 to 89 and from 2 to 26,respectively.The permeation value of g-C9N7membrane for He was calculated by Eq.(2),while the selectivity (S) was calculated for He with MD simulations, using the following equation [27]:

Fig.2.Final configurations of the gas mixture permeating the g-C9N7 membrane at a temperature of(a)200 K,(b)250 K,(c)298 K,(d)350 K,(e)400 K,and(f)500 K after a MD simulation time of 5 ns.The gray, blue, white, light blue, red, yellow, earth-yellow, purplespheres represent C, N, H, He, O, S, Ne, Ar atoms, respectively.

Fig.3.The permeability of He permeating the g-C9N7 membrane as a function of temperature.

where x and y represent the number of the gas molecules in the permeate side and feed side, respectively.Fig.6(a) shows the selectivity (red) and permeability (blue) of He permeating through the g-C9N7membrane.Increasing the total number of He and Ne molecules, the selectivity of He over Ne was found to decrease from 10 to 3, while the permeability shows inverse trend to the selectivity.The maximum permeability of 3.78 × 107GPU can be achieved at the total number of He and Ne molecules of 400, then the value of permeability slightly drops down with increasing the total molecules to 600.This phenomenon can be attributed to the increased gas density (the pressure of the system) with the increasing the number of total molecules.With increasing the system pressure,it endows relatively high kinetic energy for both He and Ne, giving rise to a higher permeability.However,Ne has more possibility than He to pass through the g-C9N7membrane to the permeate side,thus the selectivity of He/Ne decreased.

Fig.4.Snapshots of the six groups of(a)He/Ne,(b)He/Ar,(c)He/CH4,(d)He/CO2,(e)He/H2S,(f)He/N2 through g-C9N7 membrane after a MD simulation time of 5 ns.Gray,blue, white, light blue, red, yellow, earth-yellow, and purplespheres represent C, N, H, He, O, S, Ne, and Ar atoms, respectively.

Fig.5.The snapshots of the He/Ne mixture permeating through the g-C9N7 membrane after a MD simulation time of 5 ns when the He/Ne ratio remains 1:1 and the total gas number is (a) 100, (b) 200, (c) 300, and (d) 400.The gray, blue, light blue, and earth-yellow spheres represent C, N, He, and Ne atoms, respectively.

Fig.6.The selectivity (red) and permeability (blue) of gas molecules permeating through the g-C9N7 membrane at (a) a constant He/Ne ratio of 1:1, with varying the total number of He and Ne gas molecules; (b) a constant number of 300 gas molecules, with varying the He/Ne ratio.

Secondly,we have kept the total number of gas molecules fixed at 300 and varied the He/Ne ratio from 1:3 to 3:1.The final separations of He/Ne gas mixture are shown in Fig.S2.It can be seen that with the decrease of the proportion of Ne, the number of Ne passing through the g-C9N7membrane decreased significantly from 22 to 6, and the number of He increased significantly from 28 to 98.The selectivity(red)and permeability(blue)of He permeating through the g-C9N7membrane were also calculated by Eqs.(2) and (3), as shown in Fig.6(b).It can be observed that the He selectivity of the g-C9N7membrane varied between 3 and 7, and the maximum selectivity for He was obtained at the He/Ne ratio of 2:1.This phenomenon can be influenced by the initial number and penetrated number of He and Ne.Besides, different He/Ne ratios (concentrations) give rise to pressure differences at a fixed gas volume, which could also influence the selectivity of the g-C9N7membrane.To evaluate the separation performance of g-C9N7membrane, the permeability should also be considered.Increasing the He/Ne ratio from 1:3 to 3:1, the permeability of g-C9N7membrane increased from 1.19×107to 4.16×107GPU.This is because when the total number of He/Ne in the system is fixed,the number of He in the model system increased with increasing the ratio of He/Ne.Therefore, there are more He permeating through the g-C9N7membrane, thus the permeability of the g-C9N7membrane to He increased.

3.4.Strain effect on He/Ne separation

In order to improve the separation performance of He/Ne,compressive and tensile strains were introduced to during membrane separation.Prior to investigating strain effects on He/Ne separation performance, it is a key issue to understand the stability of the g-C9N7membrane under tension and compression.The biaxial compressive/tensile strain (ε) is defined as [48]:

where a and Δa represents the original and strained lattice lengths of the monolayer,respectively.The change of the structural parameters of the g-C9N7membrane after applied compressive or tensile strain is shown in Table S2, including the bond length d1-d4(as shown in Fig.S3)and lattice parameters.When a compressive strain of 0 to 7.5% was applied to the membrane, the lattice constant would decrease from 1.610 to 1.489 nm,and the effective pore size was compressed from 0.333 to 0.290 nm.However, when the tensile strain of 0 to 7.5%was applied to the g-C9N7membrane,the lattice constant and the effective pore size can be both enlarged from 1.600 to 1.731 nm and from 0.333 to 0.376 nm, respectively.The cohesive energy of g-C9N7membrane under different strains were calculated by using Eq.(1) to determine the stability of the g-C9N7membrane.The cohesive energy curve of the g-C9N7membrane under different strains was plotted in Fig.S4.When the compressive strain and tensile strain applied to g-C9N7membrane were 7.5%, the cohesive energy were 5.83 and 5.98 eV, respectively,which were still much larger than the cohesive energy of silicene(3.71 eV) [49].It indicates that the g-C9N7membrane still kept a stable structure when applied with different compressive or tensile strains.

Table 1 The kinetic diameter (D0) of the gas molecules, the adsorption height (Had) of stable state between gas molecules and the pore center of g-C9N7 membrane with corresponding adsorption energy (Ead) and energy barrier (Ebarrier) of the gas molecules passing through g-C9N7 membrane.

Fig.7 shows snapshots of the separation performance of He/Ne mixture with applied compressive strain to the g-C9N7membrane.The quantities of He and Ne were both 150 in the model system and the simulation time was 5 ns.It can be observed that increasing the applied compressive strain from 0 to 6%,the number of He penetrating the g-C9N7membrane was 56, 61, 64, 51, 54, and 51,whereas the number of penetrated Ne was decreased considerably from 13 to 1.At an applied compressive strain of 7.5%, Ne atoms can no longer penetrate the g-C9N7membrane.This is because the effective pore size (0.290 nm) of the g-C9N7membrane is too small for Ne (0.320 nm) to pass through the g-C9N7membrane under the strain of 7.5%.A simple conclusion can be drawn that increasing the compressive strain,a better separation performance of He can be achieved, until only He can penetrate the g-C9N7membrane.

Next,the compressive strain was switched to the tensile strain.The snapshots of the He/Ne mixture permeating through the g-C9N7membrane suffered with tensile strains were shown in Fig.8.It can be clearly seen that as the tensile strain increased from 0 to 7.5%, the total number of He/Ne passing through the g-C9N7membrane into the permeate side increased from 69 to 119 correspondingly.Since the tensile strain applied to the g-C9N7membrane increased, the pore size of the g-C9N7membrane also became larger.Thus, Ne can pass through the g-C9N7membrane more easily.The selectivity and permeability of He permeating through g-C9N7membrane under the applied compressive and tensile strains were calculated using Eqs.(2) and (3), as shown in Fig.9.The negative sign in the figure represents the compressive strain applied to the g-C9N7membrane, while positive sign represents tensile strain.It can be observed that the permeability of the g-C9N7membrane to He varied from 2.16×107to 3.23×107GPU with the applied compression and tensile strain.The selectivity of the g-C9N7membrane to He decreased significantly when the compressive strain was shifted to the tensile strain.At the compressive strain of 7.5%,Ne did not pass through the g-C9N7membrane to the permeation side any more, thus the largest selectivity was obtained.This is because with increasing the compressive strain,the pore size of the g-C9N7membrane was too small for Ne to enter the permeation side, but it has a negligible effect on He entering the permeation side.In this way, a tunable He separation performance can be achieved by introducing strain.

Fig.9.The selectivity(red)and permeability(blue)of gas molecules through the g-C9N7 membrane as a function of strain.The negative strain represents the compressive strain applied to the g-C9N7 membrane, whereas the positive strain represents the tensile strain.

3.5.Selectivity and energy barriers of g-C9N7 membrane

The microscopic permeation processes of He and other natural gases (CH4, CO2, N2, H2S, Ne, Ar) were simulated by using DFT methodsin terms of their energy barriers.The kinetic diameter(D0) of the natural gas molecules, the adsorption height (Had) of stable state between gas molecules and the pore center of g-C9N7membrane with corresponding adsorption energy(Ead),and energy barrier(Ebarrier)of the gas molecules passing through g-C9N7membrane were summarized in Table 1 and the energy curve for gas molecules interacting with g-C9N7membrane was shown in Fig.S5.Here, the energy barrier of gas molecules passing through the g-C9N7membrane is defined as: Ebarrier= ETS- ESS.The Hadis the shortest distance between the gas molecule and the center of the g-C9N7membrane pore in the most stable state.It can be observed that the shortest height between gas and the g-C9N7membrane are in the range of 0.16-0.22 nm and the maximum adsorption energy varied from-0.38 to-1.07 eV.The weak adsorption between gas molecules and g-C9N7membrane is mainly attributed to van der Waals interaction, which is conducive to gas separation since the interruption of chemical reaction can be ignored [29].The energy barrier that gas molecules need to overcome to penetrate the g-C9N7membrane is closely related to the kinetic diameter of the gas molecules.Compared with other gas molecules, He, with the smallest the kinetic diameter, only needs to overcome the lowest energy barrier of 0.04 eV to pass through the g-C9N7membrane.It is noteworthy that the kinetic diameter of N2is larger than that of Ar,but its energy barrier is much smaller than that of Ar.That is because N2is a linear molecule, which is easier to pass through the g-C9N7membrane than Ar spherical gas.Based on these calculations, we use the Arrhenius formula to calculate the He selectivity of the g-C9N7membrane relative to other gases at room temperature (T = 298 K), which is defined as[50,51]:

Fig.7.Final configurations of the He/Ne gas mixture permeating through the g-C9N7 membrane under(a)0%,(b)1.5%,(c)3%,(d)4.5%,(e)6%,and(f)7.5%compressive strains.The quantities of He and Ne are both 150 in the model system.The gray, blue, light blue, and earth-yellow spheres represent C, N, He, and Ne atoms, respectively.

Fig.8.Final configurations of the He/Ne gas mixture permeating through the g-C9N7 membrane under(a)0%,(b)1.5%,(c)3%,(d)4.5%,(e)6%,and(f)7.5%tensile strains.The gray, blue, light blue, and earth-yellow spheres represent C, N, He, and Ne atoms, respectively.

where r is the diffusion rate of gas molecules,A is the diffusion prefactor.Note that A is taken as a constant A = 1011s-1in this work[52].E is the energy barrier for gas molecules passing throughg-C9N7membrane.The values of selectivity for He/Ne, He/Ar, He/CH4, He/CO2, He/N2, He/H2S are 4.7, 5.01 × 109, 1.98 × 1016,3.5 × 105, 1.08 × 104, 1.18 × 109, respectively.But when applied 7.5% compressive strain to the membrane, the value of selectivity for He/Ne and He/CH4increase considerably from 4.7 to 9.41× 102, and from 1.98× 1016to1.49×1037,respectively.Compared with typical 2D membranes used for He separation, such as the porous g-C2N [32], polyphenylene [52], graphdiyne [53], and g-C2O [33](Table S3), g-C9N7membrane possesses higher He/Ne and He/CH4selectivity.These obtained results indicated that the g-C9N7membrane has unexpected separation ability for He.

4.Conclusions

Combining MD and DFT simulations, we demonstrated a novel g-C9N7membrane with superior performance for He separation from natural gas.The effective pore size of g-C9N7membrane is 0.333 nm and it would be suitable to separate He among natural gas in accordance with the size sieving effect.Then, the stability of g-C9N7monolayer was confirmed by calculating its cohesive energy, showing high energetic stability in the presence and absence of tensile and compressive strains.With increasing temperature from 200 to 500 K, the g-C9N7membrane has an unexpected He separation performance among He, CH4, CO2, N2, H2S,Ne and Ar gas mixtures.In particular, the He permeability of g-C9N7membrane reaches as high as 1.48 × 107GPU at room temperature (298 K), which is larger than the value of 1 × 107GPU of g-C2N and g-C2O membranes.It is also consistent with the separation performance for six gas groups of He/Ne, He/Ar, He/CH4,He/CO2, He/N2, and He/H2S.

Since the difference of kinetic diameters of He and Ne is small,the separation performance of He/Ne mixtures were systematically investigated.Firstly, increasing the number of gas molecules from 100 to 600, the selectivity of He over Ne was found to decrease from 10 to 3.Whereas the permeability shows inverse trend to the selectivity, and the maximum permeability of 3.77 × 107GPU can be achieved at the total gas molecules of 400.Secondly,increasing the He/Ne ratio from 1:3 to 3:1, the selectivity of He over Ne increased from 3 to 7, while the permeability increased from 1.19 × 107to 4.16 × 107GPU.Introducing strain during He/Ne separation is found to be an excellent strategy for achieving controllable separation performance.Under the condition of 7.5%compressive strain, the g-C9N7membrane reached the highest He over Ne selectivity of 9.41 × 102based on DFT calculations.The superior He separation performance can be attributed to the low energy barrier for He, but increased energy barrier for other gases passing through the membrane, which was subject to a compressive strain.The obtained results provide a better understanding of He purification among natural gas using low-dimensional materials,and reveals a promising strategy for designing and screening industrial grade gas separation membranes with strain engineering.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors thank Dr.Xiao Chang, Dr.Xiaofang Li, and Dr.Lei Zhu (China University of Petroleum, Qingdao) for their active discussions and valuable suggestions.The computations were performed on Materials Studio at Shenzhen Supercomputing Center.This work was supported by the Science Foundation of China University of Petroleum,Beijing(2462020BJRC007,2462020YXZZ003,2462020BJRC005) and Major Science and Technology Project of Shanxi Province (20181101013, 20201102002).

Supplementary Material

Supplementary data to this article can be found online at https://doi.org/10.1016/j.cjche.2021.05.001.