H₂ is an environmentally-friendly, sustainable and high-density-resource energy.^[1] It is regarded as one of the most probable substitutes of fossil fuels to deal with the shortage of energy in the future. With the fast development of science and technology, large-scale H₂ production is probable on a long timescale. However, an important problem in the H₂ production is the gas mixture.^[2] For example, the mixture of H₂, H₂O, CO, and CH₄ gases exists in the H₂ production course by the current steam-methane reforming method.^[3] The H₂ and Cl₂ mixed gases come from electrolysis saturated salt water in the chlor alkali industry.^[4] Ammonia waste gas produces H₂ and N₂ mixed gases.^[5] Therefore, effectively separating H₂ from these mixed gases (H₂, N₂, H₂O, CO, Cl₂, and CH₄) should be very important for environmental protection and energy development.

There are three kinds of traditional gas separation methods, that is: pressure swing adsorption, cryogenic distillation and membrane separation.^[6] The membrane separation method uses a two-dimensional (2D) nanomaterial with single-atom thickness to separate mixed gases, which has the advantages of low consumption and facile operation at room temperatures.^[7,8] So far, these kinds of membranes have been reported to separate mixed gases, such as zeolite,^[9] silica,^[10] and carbon-based polymers,^[11–14] and so on.

Generally, a suitable H₂ purification membrane should have three characteristics. (i) No/weak interaction between H₂ and membrane, which is reflected by small adsorption energy (E _ad). The physisorption by the van der Waals (vdW) interaction in the whole process^[15] should maintain E _ad smaller than 0.3 eV. (ii) There should be a big difference in diffusivity between H₂ and other kinds of gases reflected by the diffusion energy barrier (E _b) to differentiate the migration velocity between H₂ and other kinds of gases. For example, the E _b of H₂ through the monolayer porous graphene (PG) is 0.37 eV, but that of O₂, CO₂, and N₂ are all larger than 1.20 eV.^[16] The difference between E _b values of H₂ and other gases (N₂, CO, CO₂, and CH₄) is more than 0.8 eV through the divacancy defected 2D silicone,^[17] and that between E _b values of H₂ and CH₄ is 0.62 eV through graphdiyne.^[18] (iii) Permeance (P) and selectivity (S) are two important indicators to measure the H₂ purification effect for membrane.^[19] As reported, the S values of H₂/CH₄ are 10²², 10⁸, 10²³ for silicone^[20] and some graphene-based membranes, respectively.^[18]

In recent years, since the successful experimental isolation of graphene,^[21,22] it has been used for gas separation. However, the small pore of 2.80 Å for graphene is smaller than that of the H₂ molecule (2.90 Å)^[23,24] and thus induces more dense carbon atoms and restricts its application in H₂ purification.^[24,25] To be effectively used for gas separation, graphene with differently-sized pores has been designed.^[25,26] These pores are created by the electron beam punching method^[27] or chemical etching method.^[28–30] For example, Zhu et al.^[31] theoretically predicted the H₂ separation performance of a new two-dimensional sp² carbon allotropes-fused pentagon network. Du et al.^[32] explored whether the number of H₂ molecules permeating through the porous graphene (PG) increases as the pore size increases. However, when the pore size is much larger than the bond length of the H₂ molecule, more N₂ molecules will pass through the membrane, which will influence the selectivity of H₂/N₂. Therefore, too small holes and too large holes in the gas separation membrane will greatly reduce the P and reduce the S, respectively.

A potential membrane for H₂ purification should have a suitable hole that can effectively facilitate the separation of H₂ from mixed gases.^[33] It has been reported that the effective method to obtain suitable pores is the N doping. For example, Zhu et al.^[34] have proven the good performance of a newly synthesized porous C₂N monolayer for separating He, which had sufficient stability, high S and good P. Lu et al.^[35] found that the N doping of carbon nanomaterials could reduce the overlap of the electron density around the pores, which allows the gases to easily pass through the pore. Huang et al.^[36] explored whether the substitution of N for C in the PG could reduce the E _b values of the gases. As is well known, the new 2D graphitic carbon nitride (g-C₃N₄) membrane has been discovered in experiment^[37] and is stable.^[35–38] Its pore diameter (4.80 Å) is much larger than that of graphene (2.84 Å). Although the S by the monolayer g-C₃N₄ for H₂/CH₄ and H₂/CO (10⁵⁴ and 10²³ at 300 K)^[39] is bigger than that for nitrogen doped graphdiyne^[40] (H₂/CH₄ is 10¹² and H₂/CO is 10⁵ at 300 K) and PG^[17] (H₂/CO is 10²¹ at 300 K). However, the P of H₂ through the monolayer g-C₃N₄ membrane at 300 K (18.5 mol/m²sPa calculated by us) is much smaller than that for nitrogen doped graphdiyne ( ^[41]), but bigger than for PG ( ^[17]) at 300 K. Thus, the high S and low P of the monolayer g-C₃N₄ indicates that it is not ideal for isolating H₂ from the mixed gases. In addition, methods such as strain^[42] and charge control^[43] have been introduced to improve the gas separation performance of the membrane.

There is an interesting Robeson upper bound phenomenon^[44] of the membrane. The highest S at a given P lay near or on a line is called the upper bound.^[45,46] Higher P tends to have lower S, but larger holes often induce higher P.^[45,46] Therefore, the Robeson upper bound has the P–S trade-off. Thus, effectively reducing the pore size in the monolayer g-C₃N₄ membrane to further improve the S and P of H₂ from mixed gases (H₂, N₂, H₂O, CO, Cl₂, and CH₄) should be an urgent task.

Moreover, it has been discovered that the pore diameter can be adjusted by constructing a bilayer membrane because the upper and lower layer can be shifted or rotated, which can effectively reduce the pore size and improve the P and S of the H₂ from mixed gases because of the boundary overlapping.^[36,47,48] For example, Bartolomei et al.^[49] have confirmed that the three-layer graphene with an interlayer displacement of 1.6 Å can narrow the size of the hole, which can make it convenient for the H₂ and N₂ molecules to penetrate. Huang et al.^[36] built a quasi-2D new carbon allotrope, which is formed by the bilayer PG through the interlayer bonding and can simultaneously improve the P of H₂ and S of H₂/CH₄.

A review of the literature reveals that there has been no study of H₂ purification from mixed gases (H₂, N₂, H₂O, CO, Cl₂, and CH₄) with a bilayer g-C₃N₄ membrane. However, monolayer g-C₃N₄ has been successfully isolated experimentally.^[50,51] Moreover, the bilayer 2D membrane can be easily obtained, such as bilayer graphynes,^[49] bilayer polyphenylene,^[52] bilayer graphene,^[53] etc. Therefore, the bilayer g-C₃N₄ membrane can be easily obtained experimentally. Theoretically, the effective pore size of the bilayer g-C₃N₄ membrane with no interlayer shift in the horizontal direction is about 3.25 Å, which is a little larger than that for H₂ molecule(2.90 Å) and much smaller than that for other gas molecules (3.24 Å for H₂O, 3.64 Å for N₂, 3.46 Å for O₂, 3.74 Å for CO, 3.80 Å for CH₄, 3.14 Å for Cl₂). Therefore, the bilayer g-C₃N₄ membrane should be ideal for H₂ separation from impurity gases (H₂, N₂, H₂O, CO, Cl₂, and CH₄). In this paper, we will first describe the computational details in section 2. We then present our results and discussion in section 3. Finally, we draw our conclusions in section 4.

All of our structure and electronic calculations are carried out by the density functional theory (DFT) implemented in the DMol³ code.^[54] The Perdew–Burke–Ernzerhof (PBE)^[55] functional of the generalized gradient approximation (GGA)^[56] is employed for the exchange correlation potential.^[57] The double numerical basis sets with the polarization functionals basis sets (DNP) are used. The approximate semi-classical dispersion correction scheme DFT+D proposed by Grimme (PBE+D2) is employed in all the calculations to consider the van der Waals forces.^[36,58,59] The vacuum space of 20 Å is set in a 2×2×1 supercell, which is large enough to avoid the interaction of periodic image. During the geometric optimization, the convergence criteria are 2×10⁻⁵ Hartree (1 Hartree=4.3597×10⁻¹⁸ J) for energy, 4×10⁻³ Hartree/Å for Hellmann–Feynman force, and 5×10⁻³ Å for atomic displacement. The criterion of self-consistent field energy is 1×10⁻⁵ Hartree.

The accuracy of our method is first tested for the monolayer g-C₃N₄ membrane. The optimized average bond length of C–N is 1.34 Å, which is in good agreement with the value of 1.41 Å presented by other researchers.^[18,36,39] The calculated energy gap (E _g) between the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) is 1.28 eV, which close to that of the condensed graphitic carbon nitride obtained from its ultraviolet-visible spectrum by Zhang et al.^[51] Above all, the computational scheme used in this paper is reliable.

We first find out the most stable geometric structure of the bilayer g-C₃N₄ membrane. The 2 × 2 supercell is shown in Fig. 1(a). There are 48 carbon and 84 nitrogen atoms in total. The initial structure of the bilayer g-C₃N₄ with a diameter of ∼4.80 Å is directly constructed with the aligned C and N atoms in the upper and lower layer as shown Fig. 1(a). This is regarded as an AA-stacking style, which should be most stable structure for graphene^[53] and black phosphorous.^[60] We also consider four different low-energy isomers for bilayer g-C₃N₄ calculated by Wu et al.^[61] Obviously, the calculated energy of the AA-stacking structure is the lowest in the energy of all the structures, therefore, the AA-stacking structure is used for H₂ separation. However, the top layer in the optimized bilayer g-C₃N₄ structure with a diameter of ∼3.25 Å is shifted as shown Fig. 1(a). The total energy of the bilayer g-C₃N₄ with an interlayer distance from 2.4 Å to 5.0 Å is shown in Fig. 1(a). It can be seen in this figure that the bilayer g-C₃N₄ membrane with an interlayer distance of 3.4 Å has the lowest energy.

Fig. 1.

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Fig. 1. (a) Plot of relative energy versus interlayer distance of bilayer g-C3N4 membrane. (b) Relative energy for four different angle stacking styles (0°, 60°, 120°, and 180° clockwise) according to the lowest energy structure. (c) Top view of the four different stacking structures. (d) (upper) Temperature and (lower) energy versus time obtained from molecular dynamics simulation of the bilayer g-C3N4 membrane at 300 K.

Importantly, because of the overlap of the boundary, the effective diameter of the pore decreases from the ∼4.8 Å of the monolayer g-C₃N₄ membrane to about ∼3.25 Å of the bilayer g-C₃N₄ membrane, which is larger than that for H₂ molecule (2.90 Å) and smaller than that for other gas molecules (3.24 Å for H₂O, 3.64 Å for N₂, 3.46 Å for O₂, 3.74 Å for CO, 3.14 Å for Cl₂, 3.80 Å for CH₄). Therefore, the bilayer g-C₃N₄ membrane should be ideal for H₂ separation from impurity gases (H₂, N₂, H₂O, CO, Cl₂, and CH₄).

To contain the hole in the up and down layer in the bilayer g-C₃N₄ membrane, which are aligned (0°), and confirm the most stable bilayer g-C₃N₄ membrane, the upper layer is rotated 60°, 120°, and 180°clockwise, resulting in three different bilayer g-C₃N₄ membranes; as shown in Fig. 1(c). It can be seen from Fig. 1(b) that the aligned (0°) bilayer g-C₃N₄ membrane with an effective diameter of ∼3.25 Å has the lowest energy.

The most stable adsorption position of single gas molecule on the bilayer g-C₃N₄ membrane is discussed in the following. For the various adsorbed gases, the equilibrium adsorption height (D _ad) values between the adsorbed gases and the membrane, and also the adsorption energy (E _ad) values of the molecules on the membrane are listed in table 1. It can be seen from the table that the D _ad is within 2 Å∼3 Å after optimization. The E _ad of the gas on the bilayer g-C₃N₄ membrane is defined in the following:^[15] 1 where , and are the total energy of the single gas molecule, the bilayer g-C₃N₄ membrane, and one gas molecule adsorbed bilayer g-C₃N₄ membrane, respectively. There is a weak interaction between H₂ (N₂, O₂, Cl₂, and CH₄) and the bilayer g-C₃N₄ membrane, while the H₂O molecule strongly binds to the bilayer g-C₃N₄ membrane. Therefore, most of the gas molecules except for H₂O are physically adsorbed on the bilayer g-C₃N₄ membrane. This is in agreement with the conclusion given by Zhang et al.,^[51] the water can effectively exfoliate g-C₃N₄ into ultrathin nanosheets, thereby exploring why the H₂O molecule in the mixed gas cannot easily permeate the bilayer g-C₃N₄ membrane.

Table 1.

Table 1.

Table 1. Values of D ad, E ad and E b of H2, N2, H2O, O2, CO, Cl2, and CH4 gas molecules, and values of S of H2 over other gases and values of P when gases passing through membrane at 300 K. . H2 H2O N2 CO Cl2 CH4 Diameter 2.89 3.24 3.64 3.74 3.14 3.80 D ad/Å 2.26 1.97 2.72 2.59 2.45 2.44 E ad/eV 0.16 0.66 0.22 0.24 0.26 0.28 E b/eV 0.16 1.86 1.60 1.72 1.03 3.46 — 1.40×1028 3.43×1028 1.60×1026 4.30×1014 2.50×1055 P/( ) 13.00 6.80×10−28 2.07×10−24 2.01×10−26 2.44×10−15 3.15×10−55

Table 1. Values of D ad, E ad and E b of H2, N2, H2O, O2, CO, Cl2, and CH4 gas molecules, and values of S of H2 over other gases and values of P when gases passing through membrane at 300 K. .

To further examine the stability of the bilayer g-C₃N₄ membrane, the molecular dynamics simulation with a Nose-Hoover thermostat at 300 K is performed for the 2 × 2 supercell of the bilayer g-C₃N₄ membrane for 5 ps. The 5 ps has proved sufficient to simulate the whole dynamic course.^[62–64] The curve of energy versus time at 300 K is shown in Fig. 1(d). It can be seen in this figure that the bilayer g-C₃N₄ membrane is intact after 5 ps, which means that it is remarkably stable at room temperature.

The E_b for the penetration of the gas molecule from the pore of the bilayer g-C₃N₄ membrane listed in table 1 is calculated from the following equation:^[15] 2 Here, E _TS and E _SS are the total energy of the transition state (TS) and that of the most stable state (SS) of the gas molecules adsorbed membrane, respectively; E _b can describe the difficulty of the gas molecule penetrating through the membrane. Figure 2 shows the equilibrium adsorption configuration for each of H₂, N₂, H₂O, CO, CO₂, and CH₄ (top view and side view). These red molecules are different gas molecules. Figure 3 presents the energy profile for each of H₂, N₂, H₂O, CO, Cl₂, and CH₄ passing through the pore of the bilayer g-C₃N₄ membrane. It can be seen from this figure that the initial structure with H₂ about 4.0 Å distance to the center of the pore has the lowest energy. Thus, the IS should be the most stable state in the whole process. Meanwhile, when the gas molecules are located in the center of the hole of the first layer, the structure is called transition state (TS) and has a maximum energy. Finally, when the gas molecule comes downward to about 4 Å below the center of the pore of the second layer, the whole energy reaches the lowest point, which is called the final state (FS). To clearly show the site of the gas molecule, the penetration process of H₂ through the pore is shown as an example in Fig. 3(b).

Fig. 2.

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	Fig. 2. Equilibrium adsorption configuration of H2, N2, H2O, CO, CO2, and CH4 (top view and side view). The red molecules are different gas molecules.

Fig. 3.

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	Fig. 3. (a) Energy profile for H2, N2, H2O, CO, Cl2, and CH4 passing through the pores of bilayer g-C3N4 membrane. (b) Configuration of IS, TS, and FS of CH4 when their permeating through the bilayer g-C3N4 membrane.

Generally, if the E _b is smaller than 0.2 eV, then the penetration process can be realized at room temperature without additional pressure. In addition, the E_b is an important parameter for calculating S and P. It can found from table 1 that the E_b for H₂ is only 0.16 eV, while that for other kinds of gas molecules are all larger than 1 eV. This indicates that the bilayer g-C₃N₄ membrane can effectively prevent other five kinds of gases from shifting to the other side and thus realize the H₂ purification.

The S of the bilayer g-C₃N₄ membrane can indicate the purity of H₂ after separating H₂ from mixed gases. The S can be calculated from the Arrhenius equation^[17,18] as follows: 3 where r _gas is the rate constant, A is the ideal gas diffusion prefactor, is the diffusion energy barrier for different gas molecules, k _B is the Boltzmann constant, and T is the temperature. Blankenburg et al.^[17] have explored that the diffusion prefactors of all species gases are identical (10⁻¹¹/s), therefore, . The temperature-dependent S values of these gas molecules when penetrating the bilayer g-C₃N₄ membrane are shown in Fig. 4. It can be explored from table 1 that the bilayer g-C₃N₄ membrane exhibits an excellent S value of H₂/CH₄ at the room temperature (T = 300 K), which is bigger than that for H₂/other gas. Therefore, the possibility for purifying H₂ by the bilayer g-C₃N₄ membrane at room temperature is probable. Obviously, the S value of the bilayer g-C₃N₄ membrane is much larger than that of monolayer g-C₃N₄ membrane(10⁴⁶)^[39] and silicone (10²²).^[18] Therefore, the bilayer g-C₃N₄ membrane has higher S for the H₂ gas vs other five kinds of gases than those of many kinds of membranes.

Fig. 4.

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	Fig. 4. Plots of (a) selectivity and (b) permeance versus temperature for H2, O2, N2, Cl2, CO, CH4, H2O molecules passing through the bilayer g-C3N4.

The performance of a membrane lies on its P, which is defined as , where F is the molar flux ( ) of the gas, and the is the pressure difference across the membrane. First, the Fis determined by , where N and f represent the number of gas molecules colliding with the membrane and the probability for a gas molecule to diffuse through the pore at a given velocity. According to the kinetic theory of gases, . Here, p, A, m, k _B, and T are the pressure, Avogadro constant, mass of the molecule, Boltzmann constant, and temperature, respectively. The probability for a particle to diffuse through the pore at a given velocity is defined as, where f(v) is the Maxwell velocity distribution and v _B represents the velocity corresponding to the diffusion energy.^[17] The pressure p is set to be 3×10⁵ Pa and the pressure difference is 10⁵ Pa.^[15] The P values for the gases are exhibited in Fig. 4. We can find from the figure that there is an increasing tendency of P for the gases with temperature rising. Obviously, the P of H₂( ) is 10⁵⁶ times that for CH₄( ) at the room temperature. Therefore, the bilayer g-C₃N₄ membrane should be good for H₂ from the impurity gases (H₂, N₂, H₂O, CO, Cl₂, and CH₄). Moreover, the P of H₂ from the bilayer g-C₃N₄ ( ) is much superior to that from porous graphene ( .^[21] Thus, the bilayer g-C₃N₄ membrane has higher P for H₂ versus the other five kinds of gases than that of many kinds of membranes.

The charge density isosurfaces of the transition state structure for seven kinds of gas molecule penetration through the bilayer g-C₃N₄ membrane are shown in Figs. 5(a)–5(f), while the charge density isosurface of H₂ and CH₄ permeating from the monolayer g-C₃N₄ membrane are shown in Figs. 5(g) and 5(h). Clearly, the methane has the “most” electron overlaps with the neighboring atoms in the seven gas molecules. Except for H₂, the other six kinds of gases all have electron overlaps with neighboring atoms. The areas of electron overlaps are different, which can clearly explain why the E _b, S, and P have so great difference for H₂ and CH₄. Obviously, the smaller hole in the bilayer g-C₃N₄ structure than that in the monolayer g-C₃N₄ membrane induces the bigger repulsive forces between the other gases and the boundary.

Fig. 5.

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	Fig. 5. Electron density of bilayer g-C3N4 membrane with (a) H2, (b) CH4, (c) CO, (d) Cl2, (e) H2O, (f) N2, and (g) O2 at corresponding transition states, and that of the monolayer g-C3N4 membrane (g) H2, and (h) CH4. Isosurface is 0.2 a.u.

To explore the purification process of H₂ from the mixed gas at room temperature, the molecular dynamics simulation under the realistic condition is performed to reproduce the permeating process of mixed gases to pass through the bilayer g-C₃N₄ membrane. The initial pressure is set to be 50 atm (1 atm = 1.01325×10⁵ Pa) and the temperature is set to be 300 K. At the beginning of the MD simulation, the gas molecules are placed between two bilayer (5 × 5) g-C₃N₄ wall, and 120 gas molecules (20 H₂ molecules and 20 CH₄ molecules, 20 N₂ molecules, 20 Cl₂ molecules, 20 CO molecules, 20 H₂O molecules) are located on the left side of the wall. The simulated total time is set to be 5000 ps. The snapshots of mixture of 120 gas molecules at 0 ps, 500 ps, 1000 ps, and 5000 ps are shown in Fig. 6, the corresponding membranes are fixed in the whole simulation course.

Fig. 6.

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	Fig. 6. Snapshot of mixture permeating through (a) bilayer g-C3N4 membrane and (b) monolayer g-C3N4 membrane in the simulation for 0 ps, 500 ps, 1000 ps, and 5000 ps. White balls denote H2 molecules.

The molecular dynamics simulation reveals that 11 and 13 H₂ molecules are on the right-hand side of the bilayer g-C₃N₄ membrane after 1000 ps and 5000 ps at 300 K, while 13 H₂ molecules, 2 H₂O molecules, 1 N₂ molecule and 1 CO molecule permeate the monolayer g-C₃N₄ after 1000 ps, 13 H₂ molecules, 2 H₂O molecules, 3 N₂ molecule, 3 CO molecule, and 4 CH₄ permeate the monolayer g-C₃N₄ after 5000 ps at 300 K as shown in Fig. 6(b). Thus, the bilayer g-C₃N₄ will be a better H₂ separation membrane than the monolayer g-C₃N₄.

The bilayer porous graphitic carbon nitride (g-C₃N₄) membrane has suitable pores with a diameter of about 3.25 Å for H₂ purification from the impurity gases (H₂, N₂, H₂O, CO, Cl₂, and CH₄). The average adsorption energy reveals that most gas molecules except for H₂O are physically adsorbed on the bilayer g-C₃N₄ membrane. Compared with the monolayer g-C₃N₄ membrane, the bilayer g-C₃N₄ membrane can effectively reduce the diffusion energy barrier of H₂, which is of benefit to H₂ purification. The bilayer g-C₃N₄ membrane has high selectivity for H₂ over other kinds of gases (H₂/N₂ is 3.43×10²⁸; H₂/H₂O is 1.40×10²⁸; H₂/CO is 1.60×10²⁶; H₂/Cl₂ is 4.30×10¹⁴; H₂/CH₄ is 2.50×10⁵⁵) and the permeance of H₂ ( ) at 300 K, which should have great potential applications in energy and environmental research. The molecular dynamics simulation shows that the selectivity and permeability of the bilayer g-C₃N₄ membrane are larger than those of the monolayer g-C₃N₄ membrane. Therefore, the bilayer g-C₃N₄ membrane should be ideal for purifying H₂ from the impurity gases (H₂, N₂, H₂O, CO, Cl₂, and CH₄).