Heptazine-based graphitic carbon nitride as an effective hydrogen purification membrane

Abstract

The purification of H₂ from other gases (CH₄, CO, CO₂, N₂, and H₂O) is a vital step for its safe usage. By using first-principles calculations and molecular dynamics simulations, we find that the porous graphitic carbon nitride (g-C₃N₄) monolayer works as an efficient and highly selective hydrogen purification membrane. In the DFT calculations, the transition state theory is used to search the lowest diffusion barrier (0.55 eV) for H₂ to go through the well-ordered intrinsic holes. Meanwhile, the excellent selectivity between H₂ and other gases shows that the g-C₃N₄ nanosheet is specific for diffusion of H₂. The MD simulations exhibit the whole dynamic purification process and confirm our previous DFT results. Our results indicate that the g-C₃N₄ nanosheet has great potential in separating H₂ from undesirable gases.

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1. Introduction

Hydrogen, as an environment-friendly, sustainable and high-energy-density resource, is regarded as one of the most efficient substitutes of fossil fuels to address the issue of the shortage of energy in the future.^1,2 However, a technical challenge in hydrogen production, storage, transportation and usage is the existence of undesirable gases, which may result in security risks. For example, a mixture of H₂, CO, and CH₄ is produced through the steam-methane reforming in current hydrogen production methods.³ The purification of H₂ from undesirable gases (CH₄, CO, CO₂, N₂, and H₂O) is, therefore, regarded as an important step in the hydrogen production process. Compared with traditional gas separation techniques (e.g. pressure swing adsorption or cryogenic distillation), two-dimensional (2D) materials with single-atom thickness seem more promising because of their distinct advantages in low energy consumption and recycling through physical interactions at the atomic scale.^4,5

The search and design of appropriate porous 2D materials have attracted wide attention both by theoretical calculations and experimental investigations.^6–9 In general, a suitable H₂ purification membrane should possess two characteristics: (a) no/little interaction between H₂ and membrane materials; (b) a certain diffusion barrier to differentiate migration between H₂ and other gases migration. Correspondingly, the permeance and selectivity are two important factors to evaluate the performance of purification membrane.¹⁰ Organic 2D materials including carbon-based,^11,12 polymer¹³ and h-BN membranes^14,15 and inorganic materials¹⁶ containing metallic, silica¹⁷ and zeolite¹⁸ membranes are current well-known membrane materials. Notably, Jiang et al.¹⁹ demonstrated that porous graphene with hydrogenated and nitrogen-functionalized at the edge of pores can facilitate H₂/CH₄ separation and reduce the barrier for H₂ diffusion. Meanwhile, the doping of nitrogen atom will not modify the hydrogen adsorption ability. Thus, it is straightforward for us to consider 2D carbon nitride material as a natural membrane in the H₂ purification and filtering.

Graphitic carbon nitride (g-C₃N₄) is similar to graphene with a sp² π-conjugated system through van der Waals interaction between layers, which has been applied in the field of energy and materials science.^2,20–24 Free-standing g-C₃N₄ monolayer is chemically and thermally stable. It can be synthesized by the thermal polycondensation process² and has shown huge potentials in the spintronic devices²⁵ and photocatalysis fields.^26,27 The single layer g-C₃N₄ is a direct band gap of about 2.4 eV at the gamma point, rendering them promising as metal-free water-splitting materials. At the same time, the intrinsic vacancies surrounded with nitrogen atoms in g-C₃N₄ nanosheet provide natural pathways for gases to diffuse compared to the extra/man-made pores or defects in other 2D materials, which makes them promising for H₂ purification.

In this context, we report that the g-C₃N₄ nanosheet may serve as an effective and highly selective H₂ separation membrane via the first-principles calculations. The target mixtures include H₂/(CH₄, CO) from the steam-methane reforming, H₂/H₂O from water splitting. The size of the intrinsic hole in g-C₃N₄ is appropriate, well-ordered and exhibits a higher permeability and selectivity for H₂ rather than H₂O, N₂, CO, CO₂, and CH₄. The combination of g-C₃N₄ in catalytic water splitting and H₂ purification will greatly extend the practical applications of g-C₃N₄ materials.

2. Computational details

First, all of the first principles calculations were carried out by the Vienna Ab-initio Simulation Package (VASP).²⁸ The Perdew–Burke–Ernzerhof (PBE)²⁹ functional with van der Waals correction (DFT-D2)³⁰ was chosen to consider the interaction between the gas molecules and g-C₃N₄. The climbing image nudged elastic band (CI-NEB) method³¹ was used to search the minimum energy pathway (MEP) when gases diffuse through the porous g-C₃N₄. The cut-off energy was set to 500 eV and the surface Brillouin zone was sampled with 5 × 5 × 1 Monkhorst–Pack k-point grids. A vacuum thickness of 20 Å with periodic boundary conditions was set to avoid the interactions between periodically-repeated layers. All of the structural relaxations are accomplished until the energy change is less than 10⁻⁴ eV and force change is less than 0.001 eV Å⁻¹. The adsorption energy (E_a) between gases and g-C₃N₄ is defined as

E_a = E_gas@g-C3N4 − (E_gas + E_g-C3N4)

where E_gas@g-C3N4, E_gas and E_g-C3N4 are the total energy of a gas molecule adsorbed on g-C₃N₄, a single gas molecule and g-C₃N₄ respectively. It should be noted that specific adopted functional plays a role on the calculation of gas permeation barriers because of the effect of short/long-range^32,33 force at the quantitative level, but it will not influence the qualitative permeation trend.³⁴

Then the MD simulations of H₂, N₂, H₂O, CO, CO₂ and CH₄ permeation were implemented by Forcite module available in Materials Studio software package. Similar as previous work,^12,14,35 gas molecules were interspersed between the g-C₃N₄ membranes and the initial conditions were 300 K with a total time of 1000 ps. The constant-volume and constant-temperature (NVT) ensemble and COMPASS³⁶ forcefield were employed during the simulation with a time step of 1 fs. The electrostatic interaction and van der Waals interaction were calculated using the atom based method.

3. Results and discussion

The geometric structure of g-C₃N₄ is determined first. Unlike the planar graphene, the single layered g-C₃N₄ forms two configurations – planar and buckled structures, containing 6 carbon and 8 nitrogen atoms in the primitive unit cell, as shown in Fig. 1. The optimized lattice constant of the planar g-C₃N₄ is 7.13 Å, in good agreement with the previous investigation² and the lattice constant of the buckled one is calculated to be 7.05 Å. When gas molecules adsorb on the surface of planar g-C₃N₄, the planar one transforms into the buckled one and this transformation is irreversible. Moreover, the buckled unit cell is 0.50 eV per unit cell more stable than the planar one, indicating a higher stability. This agrees well with previous reports.³⁷ The more stable buckled structure is, therefore, adopted for the following studies. Our buckled configuration is more stable than the reported planar graphitic carbon nitride,³⁸ which has a better H₂ purification performance.

Fig. 1 Schematic illustrations of 2 × 2 g-C₃N₄ (top view and side view) supercells: (a) the planar g-C₃N₄ and (b) the buckled g-C₃N₄. The nitrogen and carbon atoms are represented by the blue beads and grey beads, respectively.

Then various gas molecules (containing H₂, H₂O, N₂, CO, CO₂, and CH₄) adsorbed on the g-C₃N₄ with different adsorption configurations are investigated. Our simulations demonstrate that the adsorption sites of H₂, H₂O, N₂, CO, and CO₂ are at the intrinsic vacancy of g-C₃N₄ while the CH₄ prefers to adsorb above the hexagonal ring (the equilibrium adsorption configurations are presented in Fig. 2). The equilibrium adsorption heights and energies are summarized in Table 1. As listed in Table 1, the calculated equilibrium distance between molecules and substrate is mostly within 2–3 Å. The adsorption energies of most gas molecules are smaller than 0.3 eV, which indicates that the common adsorption mode is physisorption through weak van der Waals (vdW) interaction. H₂O molecule is an exception because of the orbital hybridization between H₂O and g-C₃N₄ nanosheet, which results in a much higher adsorption energy (the comparison between the density of state of H₂O absorbed g-C₃N₄ and pure buckled g-C₃N₄ is shown in Fig. S1 of ESI data†). It is worth noting that the adsorption configuration of H₂ here is similar with the pristine and nitrogen-doped graphdiyne,^9,39 confirming that the nitrogen atoms negligibly affect the adsorption properties.

Fig. 2 The equilibrium adsorption configuration of H₂, N₂, H₂O, CO, CO₂ and CH₄. The blue beads, grey, white and red beads represent the nitrogen, carbon, hydrogen, and oxygen atoms respectively (top view and side view).

Table 1 The equilibrium adsorption heights (D₀), adsorption energies (E_a) and diffusion barriers (E_b) of H₂, H₂O, N₂, CO, CO₂, and CH₄ molecules

	D0 (Å)	Ea (eV)	Eb (eV)
H2	2.68	−0.078	0.55
H2O	1.07	−0.513	1.59
N2	2.87	−0.117	1.95
CO	2.03	−0.155	1.80
CO2	2.93	−0.226	1.50
CH4	2.31	−0.163	3.36

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Next, in order to investigate the process of gas molecules passing through a g-C₃N₄ nanosheet, the initial state (IS) of the H₂ molecule is set as that the H–H axis is perpendicular to the plane with a distance of nearly 5 Å between H₂ and the centre of a vacancy in g-C₃N₄ nanosheet. The diffusion energy barrier is given by

E_b = E_TS − E_SS

where E_TS and E_SS represent the total energy of the transition state (TS) and the most stable state (SS) of H₂ when permeates through the porous g-C₃N₄ nanosheet. The energy profiles of diffusion pathways for different gas molecules are plotted in Fig. 3 and the diffusion energy barriers (E_b) are listed in Table 1. The H₂ diffusion barrier is about 0.55 eV, which is significantly higher than that of nitrogen-doped graphdiyne (0.08 eV)³⁹ and silicene with 585-divacancy (0.34 eV)⁴⁰ but is sufficiently surmountable at moderate temperature and pressure. Meanwhile, the calculated diffusion energy barriers are 1.50 eV, 1.59 eV, 1.80 eV, and 1.95 eV for CO₂, H₂O, CO and N₂, respectively. Obviously, the high E_a for H₂O molecule makes it difficult to pass through the g-C₃N₄ nanosheet. At the same time, it is worth noting that the diffusion energy barrier for CH₄ is 3.36 eV, showing that it is extremely difficult for CH₄ to permeate the intrinsic vacancy of g-C₃N₄ nanosheet. Therefore, it is predicted that the g-C₃N₄ can work as an ideal hydrogen purification membrane with high selectivity, especially for separation of H₂/CH₄ mixture.

Fig. 3 Minimum energy pathways for H₂, H₂O, N₂, CO, CO₂, and CH₄ molecules passing through g-C₃N₄.

Based on the MEP and diffusion energy barriers, we calculated the selectivity S and permeance P of various gas molecules to elucidate the properties of gas separation and diffusion for g-C₃N₄ nanosheet. For the selectivity of H₂ with other gas molecules, it is calculated by using the following equation:^40,41

where A is the ideal gas diffusion prefactor, E_Gas is the diffusion energy barrier for different gas molecules (as listed in Table 1), k_B is the Boltzmann constant and T is the temperature. Here we assumed that the diffusion prefactors of H₂, H₂O, N₂, CO, CO₂, and CH₄ have the same value, the temperature-dependent selectivity are illustrated in Fig. 4(a). The g-C₃N₄ nanosheet exhibits an excellent selectivity of H₂/CH₄ with 10⁴⁶ at the room temperature (300 K), much higher than those of H₂/H₂O (10¹⁷), H₂/CO (10²⁰), H₂/CO₂ (10¹⁵) and H₂/N₂ (10²³), showing an enormous advantage in H₂/CH₄ purification. This property is significantly superior to the similar 2D materials (shown at the Table 2). Then the classical permeance of gas molecules through membrane, defined as the ratio of the measured gases molar flux F (mol m⁻² s⁻¹) to the difference of partial pressure Δp (Pa), is estimated by the following formula:^14,41
where p, N_A, m, k_B and T represent the pressure, Avogadro constant, mass of molecule, Boltzmann constant and temperature, respectively. f(v) denotes the Maxwell distribution, and the kinetic energy at v_B can overcome the barrier. Here we adopt an approximation that the feed gas on one side is at 1 bar and the other side of the membrane is filled with any other gas at 2 bar pressure as previous works.⁴¹ Fig. 4(b) shows that the permeance of different gas molecules increased with the temperature. The calculated permeance of H₂ across the g-C₃N₄ nanosheet at 300 K is 10⁻⁷, which is acceptable for the industrial separation.⁴² Thus our DFT results provide a solid proof that the g-C₃N₄ with well-ordered pores is a potential H₂ purification membrane at the ambient atmosphere.

Fig. 4 (a) Selectivity and (b) permeance for H₂, H₂O, N₂, CO, CO₂, and CH₄ molecules passing through g-C₃N₄ nanosheet as a function of adsorption height or temperature. The horizontal line in the panel (b) is the industrial standard for gas permeation.⁴²

Table 2 The diameter of the pore, the calculated H₂ adsorption energy, permeation barrier and selectivity of g-C₃N₄, H-graphene, graphdiyne and silicene

Membrane	g-C3N4	H-graphene	Graphdiyne	Silicene
Dc (Å)	1.70	2.5	2.24	4.7
Ea (eV)	−0.078	−0.05	−0.07	−0.06
Eb (eV)	0.55	0.22	0.01	0.34
S(H2/CH4)	10^46	10^23	10^10	10^22

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The N atoms at the edge of porous graphene can increase the electrostatic interaction compared to no edge-modified graphene, resulting in a better selectivity and permeability for gas molecules.^43,44 To investigate the origin of such selectivity, we plotted the electron density distribution of different gas molecules permeating through the g-C₃N₄ at the transitional state structures in Fig. 5. The distribution of electron density gives a way to describe the interaction between the gas molecules and the substrate. Our results show that there is little electron density overlapping at the TS of H₂ diffusion compared with other TS configurations, suggesting that the electrostatic interaction plays a vital role during the permeation process. The electrostatic interaction will limit the permeation of other gas molecules due to the larger atomic sizes. Meanwhile, we plotted the vdW surface of g-C₃N₄ and gas molecules as shown in Fig. 6. The pore size of the g-C₃N₄ (unoccupied by vdW surface) as well as the diameters of cross section (D_c, vdW occupied) of different gas molecules is also evaluated (the values are listed in Table 3). The diameter of g-C₃N₄ pore is about 1.70 Å, significantly smaller than that of N-graphdiyne (2.24 Å), while the D_c (2.44 Å) of H₂ presents more overlapping with the vdW surface of g-C₃N₄ pore. The comparison between the sizes of vdW surface well explains why g-C₃N₄ presents higher diffusion energy barrier and better selectivity for H₂. Moreover, the overlapping between the vdW surface of g-C₃N₄ and other gases seems too much for gas molecules to permeate. Therefore, the suitable size of intrinsic vacancy in g-C₃N₄ is not only favourable for H₂ diffusion but also helpful to hinder the permeation of other gas molecules. The N atoms at the rim of pores bring a strong electrostatic interaction and vdW interaction, resulting into excellent gas selectivity, which is consistent to previous analysis.⁴³ Additionally, different from the traditional pores or defects caused by dangling bonds, the nitrogen atoms at the rim of intrinsic vacancy of g-C₃N₄ are covalent bond with the nearby carbon atoms, which provides a more stable permeation environment for the gases diffusion.^19,40 The good permeation of H₂ as well as the hindrance to other gases makes it feasible for application of g-C₃N₄ nanosheet in H₂ purification.

Fig. 5 Electron density of (a) H₂ (b) H₂O (c) N₂ (d) CO (e) CO₂ and (f) CH₄ at their corresponding transition states. Isosurface value is 0.002 e Å⁻³.

Fig. 6 Geometric structure and van der Waals (vdW) surface of (a) g-C₃N₄ (b) N-graphdiyne³⁹ (c) H₂ (d) N₂ (e) H₂O (f) CO (g) CO₂ and (h) CH₄. The blue, grey, white and red beads represent the nitrogen, carbon, hydrogen, and oxygen atoms respectively.

Table 3 The vdW occupied a volume of H₂, N₂, H₂O, CO, CO₂ and CH₄ and their corresponding diameters of the cross section (D_c) of our sphere models

	vdW occupied volume (Å^−3)	Diameter of cross section (Å)
H2	10.87	2.44
N2	23.76	3.20
H2O	19.48	3.34
CO	26.90	3.46
CO2	33.71	3.44
CH4	28.41	3.78

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In addition, we perform molecular dynamics (MD) simulations under the realistic condition to reproduce the dynamic process of H₂ and other gas molecules to diffuse through g-C₃N₄ nanosheet. A single component of 80 gas molecules and mixtures of 20 H₂, 20 N₂, 20 CO, 20 CO₂, 20 CH₄ and 20 H₂O gas molecules are put between the g-C₃N₄ nanosheets with a 1000 ps MD simulation. The snapshot of pure 80 H₂ molecules and mixtures of 120 gas molecules at 0 ps, 500 ps, 1000 ps are given in Fig. 7 (single components of N₂, CO, CO₂, CH₄ and H₂O gas molecules is shown in the Fig. S2†). Therefore, we found that nearly 9 H₂ molecules diffuse through the g-C₃N₄ after 1000 ps MD simulation at the mixture system of 120 gas molecules. Meanwhile, it is difficult for other gas molecules to pass through the membrane at room temperature, which is consistent with our former DFT results and the mixtures of gas molecules do not influence the performance of H₂ purification. Other gas molecules are trapped between the membranes. The MD simulations reveal that the H₂ can escape from the intrinsic vacancies of g-C₃N₄ at the room temperature while other gases will be trapped on the one side of g-C₃N₄, which further confirms the reliability of our results from the first-principles calculations. Although it is difficult for the experimenters to synthesize large-scale g-C₃N₄ nanosheets with well-order pores, it is still promising to be applied in small-size purification devices with the development of technology.

Fig. 7 Snapshots of (a) H₂ (b) gas mixture permeating through g-C₃N₄ nanosheet in the 0–1000 ps MD simulation at 300 K. The blue, grey, white and red beads represent the nitrogen, carbon, hydrogen, and oxygen atoms respectively.

4. Conclusions

We have performed the feasibility analysis on g-C₃N₄ as H₂ purification membrane. The graphitic carbon nitride with well-ordered sized intrinsic vacancies offers potential diffusion pathways for hydrogen diffusion, which is superior to the graphene or silicene with extra/man-made pores and defects. The minimum energy pathways determined by the first-principles calculations suggest that H₂ permeates the porous g-C₃N₄ with a surmountable diffusion barrier of 0.55 eV. Meanwhile, g-C₃N₄ exhibits a high selectivity between H₂ and other gases with the order of 10⁴⁶ (H₂/CH₄) at the room temperature. Considering the good permeation of H₂ as well as the hindrance to other gases, we report that g-C₃N₄ may serve as a promising filtration membrane for H₂ purification. Our theoretical simulations provide an extra approach for the application of g-C₃N₄ in addition to catalyzing water splitting into hydrogen.

Acknowledgements

The authors thank Dr Yadong Zhang and Dr Ruifeng Lu for valuable discussions and helps. The work is supported by the National Basic Research Program of China (973 Program, Grant No. 2012CB932400), the National Natural Science Foundation of China (Grant No. 21273158 and 21303112), the Natural Science Foundation of Jiangsu Province (Grant BK20130291), a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD). This is also a project supported by the Fund for Innovative Research Teams of Jiangsu Higher Education Institutions, Collaborative Innovation Center of Suzhou Nano Science and Technology.

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/c6ra06425f

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