Sayyed Jalil Mahdizadeh*ab and
Elaheh K. Goharshadib
aDepartment of Chemistry and Molecular Biology, University of Gothenburg, 405 30 Göteborg, Sweden. E-mail: sayyed.jalil.mahdizadeh@gu.se
bDepartment of Chemistry, Ferdowsi University of Mashhad, Mashhad 9177948974, Iran
First published on 25th June 2020
Multicomponent gas separation and purification is an important pre- or post-processing step in industry. Herein, we employed a multiscale computational approach to investigate the possibility of multicomponent low-weight gas (H2, O2, N2, CO2, CH4) separation and purification using novel porous 2D carbonaceous nanomaterials, namely Graphdiyne (GD), Graphenylene (GN), and Rhombic-Graphyne (RG). The dispersion-corrected plane-wave density functional theory (DFT) calculation combined with the Climbing Image Nudged Elastic Band (CI-NEB) method was employed to study the gas/membrane interaction energy and diffusion barrier of different gases passing through the geometrically optimized membranes. The results from CI-NEB calculations were then fitted to the Morse potential function to construct a bridge between quantum mechanics calculations and non-equilibrium molecular dynamics (NEMD) simulation. The selectivity of each membrane for all binary mixtures was calculated using the estimated diffusion energy barriers based on the Arrhenius equation. Finally, a series of extensive NEMD simulations were carried out to evaluate the real word and time dependent separation process. According to the results, CH4 molecules can be completely separated from the other gases using a GD membrane, O2 molecules from CH4, N2, and CO2 by a GN membrane, and H2 molecules from all other gases using a RG membrane.
Among various gas separation methods, membrane technique provides several advantages such as high energy efficiency, facile operation, easy maintenance, and low investment cost.7 The membrane separation is typically referred to separation technology based on a semipermeable or selective membrane.2,8 The membrane performance in a gas separation process is basically determined with two parameters, selectivity and permeability. Selectivity is the capability of a membrane to selectively separate a desired molecule from a mixture. Whereas, permeability shows the membrane's productivity per unit time.9 An ideal membrane, for gas separation purposes, should have a low diffusion barrier for a specific type of molecule (permeability) and high diffusion barrier for other components within the gas mixture (selectivity). Apparently, a membrane with high selectivity usually suffers from low permeability, and vice versa.10 Therefore, there is always an intercommunication between selectivity and permeability of a membrane.
Traditional membranes for gas separation, like polymers,11 metals,12 zeolites,13 silica,14 and metal organic frameworks15 do not possess both high permeability and selectivity. Carbonaceous materials can be considered as very promising membranes in gas separation processes, since carbon is an abundant element and its allotrope's production techniques have been widely evaluated.9 It has been proven that the membrane permeability inversely correlates with its thickness.16 Therefore, porous 2D graphene-based nanomaterials, with one-atom thickness, have fascinated a great attention as efficient membranes for gas and liquid separation and purification processes.17–21
The pristine graphene is totally impermeable to any kind of gases even tiny He molecules.22 Hence, making in-plane pores in graphene sheets is necessary to attain molecular permeability. However, carving perfect and precise nanopores at large density level on a graphene sheet is extremely tricky and needs advanced breakthroughs in nano-scale manufacturing technologies.23 Therefore, finding novel 2D membranes with intrinsic uniform nanopores with specific architecture is essential as an alternative route. Graphenylene is an interesting allotrope of graphene with all the sp2-hybridized carbon atoms which was firstly suggested by Balaban et al.24 Graphenylene has attracted a great attention because of its thermal and mechanical stability and especially periodic unique pore architecture.25–27 Recently, some research groups could successfully synthesize graphenylene.3,28 Similar to graphene and graphenylene with purely sp2-hybridized network, other advanced 2D carbonaceous nanomaterials with successive sp2- sp-hybridized carbon atoms have been hypothesized theoretically.29 For example, the graphyne family can be built by replacing 1/3 of C–C bonds in graphene with n-acetylene linkages (–CC–) (n = 1, 2, 3, …) which would produce graphyne, graphyne-2 (graphdiyne), graphyne-3, etc., respectively.30 Interestingly, some experimental techniques have been employed to successfully produce graphynes family.31–33 On the other hand, replacement of 2/3 of C–C bonds in graphene with acetylene linkage will produce a new 2D layered carbon allotrope called rhombic-graphyne.34
Due to the precise and uniform pore structure of these 2D nanomaterials, they are considered as promising ideal membrane for gas separation and purification.35 Jiao et al.36 evaluated the potential application of graphdiyne as membrane to separate H2 from syngas. According to their findings, graphdiyne shows a H2 permeability about 104 times greater than that of porous graphene. Zhao et al.37 investigated the selective separation of different light gases by H-, O-, and F-substituted graphdiyne using computational approaches. They found that O- and F-substituted graphdiyne could efficiently separate CH4 and N2 gases. Cranford et al.38 estimated the flux of H2 passing through the graphdiyne membrane to be 7–10 g cm−2 s−1 from a gas mixture containing CH4 and CO molecules. Employing the first principle calculations, Zhang35 studied the H2 separation features of graphynes family over light gas molecules (e.g. CH4, N2, CO). According to their results, graphyne was not a suitable membrane for H2 separation because of its small pore size. However, graphdiyne demonstrated a high selectivity for H2 molecules (109) over bigger molecules like CH4 but relatively low selectivity (103) over smaller molecules. In addition, they showed that rhombo-graphyne has an extremely high selectivity for H2 molecules (1016) over other light gases. Zhang et al.39 showed that some graphyne derivatives, with pore sizes of 7 × 8 Å, could effectively blocks both di-branched and mono-branched pentane isomers. Using the dispersion-corrected DFT calculations, Zhu et al.1 estimated the separation performance of light gas mixtures via strained-control graphenylene. Their results indicated that applying lateral strain has a notable impact on the separation performance and selectivity of graphenylene membrane.
Herein, using dispersion corrected DFT calculations (DFT-D3) and non-equilibrium molecular dynamics simulation (NEMD), we have evaluated the selective separation performance of Graphdiyne (GD), Graphenylene (GN), and Rhombo-Graphyne (RG) for multicomponent mixture of light gases including H2, N2, O2, CO2, and CH4 molecules.
The Climbing Image Nudged Elastic Band (CI-NEB) method45 was used with dispersion-corrected DFT calculations (DFT-D3),46 as implemented in the Quantum ESPRESSO package, to investigate the minimum energy pathways (MEPs) of various gas molecules passing through the different membranes and to extract the interaction potential function parameters. The path threshold for CI-NEB calculations was set to 0.05 eV Å−1 and 20 points were defined to discretize the path.
All NEMD simulations were carried out by LAMMPS package.48 The velocity Verlet scheme was employed with time step of 0.5 fs to integrate the equation of atomic motions. The periodic boundary conditions were also applied in X and Y directions. The simulation box was first fully equilibrated for 2 ns in the NVT ensemble (Nose–Hoover thermostat) with a fixed 1 atm pressure exerted on both pistons along the Z direction. Afterwards, the production run was lunched in the NEMD scheme along with applying 100–700 MPa pressure on the feed's piston (Fig. 3). In NEMD scheme, exerting much higher pressure than that practically applied is utterly prevalent to elevate the signal-to-noise ratio and minimize thermal noises within a short timescale.49 To apply pressure (P), defined amount of force (F) was exerted on every individual atoms of the piston based on the equation, F = (P × A)/n, where A and n are the piston area and the number of atoms, respectively. Both pistons were free to move along the Z direction to reach the desired pressure.
The interaction energy between gas molecules and different membranes were extracted from quantum mechanics calculations and modeled using the Morse potential function as will discuss in the next section. The COMPASS force field50,51 was employed to describe both bonded and non-bonded interactions of gas molecules with 15 Å cutoff for van der Waals forces. Coulomb's law was employed for short-range coulombic interactions within a cutoff radius of 15 Å, while, PPPM technique52 was considered for long-range coulombic interaction.
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Fig. 1 The optimized structure of (a) Graphdiyne (GD), (b) Graphenylene (GN), and (c) Rhombo-Graphyne (RG). The dashed area confined between two lattice vectors ![]() ![]() |
Afterwards, CI-NEB calculations were employed to investigate the MEPs of various gas molecules passing through the different membranes (Fig. 2) and to extract the interaction potential function parameters. The interaction energy between membrane surface and gas molecules, E, were calculated for 20 points which were used to discretize the MEP. Then, chi-square minimization technique was used to fit these points into the Morse potential (eqn (1)) by generalized reduced gradient algorithm.54
E = D0[e−2α(r−r0)−2e−α(r−r0)] | (1) |
Fig. 2 shows the interaction energy of various gas molecules permeating through the different membranes calculated using CI-NEB and those fitted to the Morse potential. As this figure shows, the Morse potential fits very good at both attraction and repulsion regions. Table 2 compares the energy barriers for different gas molecules calculated using CI-NEB and those predicted from Morse potential. As one can see from Table 2, the difference between two energy barriers is less than 2% for all diffusing gas molecules. According to these results, the Morse potential could precisely reproduce the interaction energies and could be considered as a perfect bridge between quantum mechanics calculations and molecular dynamics simulation in this work. It has been approved that Morse potential can accurately describe the non-bonded interactions calculated by high level quantum mechanics techniques.55 The Morse potential parameters for interaction between various gas molecules and different membranes are shown in Table S1.†
GD | GN | RG | |||||||
---|---|---|---|---|---|---|---|---|---|
Morse | QM | Rel. (%) | Morse | QM | Rel. (%) | Morse | QM | Rel. (%) | |
CH4 | 1.240 | 1.235 | 0.4 | 2.781 | 2.754 | 1.0 | 5.475 | 5.451 | 0.4 |
CO2 | 0.231 | 0.230 | 0.4 | 0.784 | 0.782 | 0.3 | 2.232 | 2.240 | 0.3 |
N2 | 0.494 | 0.494 | 0.0 | 0.880 | 0.872 | 0.9 | 2.838 | 2.864 | 0.9 |
O2 | 0.218 | 0.221 | 1.4 | 0.412 | 0.415 | 0.7 | 1.855 | 1.888 | 1.7 |
H2 | 0.061 | 0.061 | 0.0 | 0.115 | 0.113 | 1.8 | 0.801 | 0.812 | 1.3 |
The membrane selectivity for one gas (Gas1) over other gases (Gas2) can be estimated based on the Arrhenius equation:52
![]() | (2) |
GD | GN | RG | |
---|---|---|---|
H2/CH4 | 5 × 1019 | 2 × 1044 | 9 × 1077 |
H2/CO2 | 7 × 102 | 2 × 1011 | 1 × 1024 |
H2/N2 | 2 × 107 | 6 × 1012 | 3 × 1034 |
H2/O2 | 5 × 102 | 1 × 105 | 1 × 1018 |
O2/CH4 | 1 × 1017 | 2 × 1039 | 7 × 1059 |
O2/CO2 | 1.4 | 1 × 106 | 8 × 105 |
O2/N2 | 4 × 104 | 5 × 107 | 2 × 1016 |
CO2/CH4 | 8 × 1016 | 1 × 1033 | 9 × 1053 |
CO2/N2 | 3 × 104 | 32.5 | 3 × 1010 |
N2/CH4 | 3 × 1012 | 4 × 1031 | 3 × 1043 |
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Fig. 3 Snapshot of the simulation box after the initial 2 ns equilibrium stage. Two pistons and membrane are illustrated in grey and blue, respectively. |
Fig. 4 shows the number of gas molecules (Ngas, gas = N2 and CO2) passing through the GD as a function of applied pressure (P) and time (t). While both NN2 and NCO2 increase almost linearly with time, the rates of increase, at constant pressure, is much higher for CO2 gas. For example, at 500 MPa, NN2 and NCO2 reach to 200 after 26 and 5.5 ns, respectively. In addition, Fig. 4 illustrates the gas flux (Fgas, gas = N2 and CO2) as a function of applied pressure. As one can see, there is also a linear correlation between gas flux and applied pressure. Hence, the gas permeability can be estimated from the slope of the linear plot Fgas vs. P. The gas permeability values of GD membrane for CO2 and N2 gases were calculated to be 25.1 and 5.5 L h−1 cm−2 MPa−1 (at STP), respectively.
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Fig. 4 Number of N2 and CO2 molecules (Ngas) passing through the GD a function of time (t), and gas flux (Fgas) as a function of exerted pressure (P). |
According to the NEMD simulation results, oxygen molecules are able to diffuse through the GD and GN membranes but not RG. Fig. 5 shows the NO2 and FO2 values of GD and GN membranes as a function of applied pressure and time. The number of oxygen molecules passing through both GD and GN membranes increases almost linearly with time. However, at the constant pressure, NO2 for GD is much higher than that of GN. For instance, at 500 MPa, NO2 reaches to 300 after 5.4 and 25 ns for GD and GN membranes, respectively. The O2 gas permeability values were estimated to 29.3 and 9.8 L h−1 cm−2 MPa−1 (at STP) for GD and GN membranes, respectively.
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Fig. 5 Number of O2 molecules (NO2) passing through the GD and GN membranes as a function of time (t) and, and O2 flux (FO2) as a function of exerted pressure (P). |
Hydrogen molecules, due to the smallest size, can pass through all different types of membranes. Fig. 6 shows the NH2 and FH2 values of GD, GN, and RG membranes. NEMD simulations show that, at the constant applied pressure, the number of H2 molecules diffusing through the RG is significantly lower than those of GD and GN membranes. For example, at 300 MPa, the time elapsed for NH2 to reach 1000 was 0.15, 0.26, and 2.0 ns for GD, GN, and RG membranes respectively. The calculated H2 gas permeability values were calculated to be 2180.1, 1070.5, and 160.2 L h−1 cm−2 MPa−1 (at STP) for GD, GN, and RG membranes, respectively.
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Fig. 6 Number of H2 molecules (NH2) passing through the GD, GN, and RG membranes as a function of time, and H2 flux (FH2) as a function of exerted pressure (P). |
The NEMD simulation results gave us the following insights: (1) methane molecules can be separated from the other gases (i.e. H2, O2, CO2, N2) using the GD as membrane (2) none of the membranes can completely separate CO2 and N2 molecules. However, the permeability of CO2 molecules through the GD membrane is ∼5 times greater than that of N2 molecules. (3) O2 and H2 can be separated from other gases by means of GN membrane. (4) H2 and O2 molecules can be separated perfectly using RG membrane. (5) the NEMD simulation results are generally consistent with the selectivity data calculated from Arrhenius equation. However, after analyzing the NEMD data and comparing the results with Arrhenius selectivity values, the limitation of the Arrhenius equation for prediction of the true selectivity was clearly revealed. For example, RG membrane is totally impermeable for all gases except H2, but Arrhenius predicts a very high selectivity for O2/CH4 (∼1060), CO2/CH4 (∼1054), and N2/CH4 (∼1043). It is because the selectivity value based on the Arrhenius equation depends on the difference between the diffusion barrier energies of each gas and not the absolute values. Therefore, a membrane can be impermeable for both gases (with very different barrier energies) while the Arrhenius shows a very high selectivity.
Footnote |
† Electronic supplementary information (ESI) available: The Morse potential parameters for interaction between various gas molecules and different membranes, optimized unit cell of different membranes, and .xyz file format of graphdiyne, graphenylene, and rhombic-graphyne membranes. See DOI: 10.1039/d0ra04286b |
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