C2H6 Mixture Using Functionalized Nanoporous

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Separation of CH4/C2H6 mixture using functionalized nanoporous silicon carbide nanosheet Jafar Azamat, and Alireza R. Khataee Energy Fuels, Just Accepted Manuscript • DOI: 10.1021/acs.energyfuels.8b01433 • Publication Date (Web): 29 May 2018 Downloaded from http://pubs.acs.org on May 30, 2018

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Separation of CH4 from CH4/C2H6 mixture with N-pore in SiCNS membrane.

N-pore

Separation of CH 4 from CH4/C2H6 mixture with two layer SiCNS membrane with F-pore in its center.

F-pore

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Separation of CH4/C2H6 mixture using functionalized nanoporous silicon carbide nanosheet

Jafar Azamat,a Alireza Khataee a,* a

Research Laboratory of Advanced Water and Wastewater Treatment Processes, Department of Applied Chemistry,

Faculty of Chemistry, University of Tabriz, 51666-16471 Tabriz, Iran

*

Corresponding author: E–mail address: [email protected]

Tel.: +98 4133393165; Fax: +98 4133340191

1 ACS Paragon Plus Environment

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Abstract Gas separation process by 2D structure membranes has recently been considered. Some nanostructure membranes such as graphene have already been used extensively, but silicon carbide nanosheet (SiCNS) capabilities for gas separation have not been studied yet. Due to property and structure of this nanosheet, it can be used for gas separation with high permeability and selectivity. In this regard, the separation of alkane mixtures such as methane/ethane mixture is important due to their many industrial applications. Accordingly, we studied the capability of SiCNS membrane using molecular dynamics simulation technique for separation of CH4/C2H6 mixture. To separate gas mixture by SiCNS membrane, some engineered pores were created on the surface of the membrane. At the same time, some of these pores have become functionalized by appropriate chemical groups. The potential of the mean force of methane and ethane molecules was calculated in the path of the pores, and it showed that gas molecule (methane or ethane) with low potential of the mean force could easily pass through the pore. Also, the effect of the presence of multi SiCNS layers was investigated. The results showed that in some cases, with increasing the number of SiCNS layers, the selectivity of the system was increased.

Keywords: Methane; Ethane; Silicon carbide nanosheet; Gas separation; PMF; Density map.


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1. Introduction Alkanes are a homologs batch of hydrocarbons in the saturated form and have only carbon and hydrogen atoms, where they are linked together by single bonds. The difference between two consecutive alkanes is in a CH2 group. Crude oil and natural gas and are the most important source of alkanes. These saturated hydrocarbons are used as a source of heat, electricity generation, chemical feedstocks, paraffin wax, synthesis of polymers and serves as intermediate in the drugs synthesis. On the other hand, separation of different members of alkanes is one of the most important objectives in the petrochemical industries because they are feedstock in various chemical industries 1 and serve as raw materials in the synthetic chemistry 2 in many chemical reactions. The natural gas is composed of methane, and other hydrocarbons such as ethane and their separation are a bottleneck in practical production. The separation of CH4/C2H6 mixture is important due to their many industrial applications in the petroleum industry.3, 4 CH4 has the high energy level and can be used instead of gasoline fuels in transportation. Because of the similar chemical and physical properties of CH4 and C2H6 gases, it is challenging to find a new method that will do separation of CH4/C2H6 mixture with high selectivity. The conventional distillation methods are used for the separation of CH4/C2H6 mixture, and then, their mixture need excessive cooling to very low temperatures to separate each other, and then, the current separation method is associated with high energy consumption. Accordingly, the search for alternative ways to separate CH4/C2H6 mixture is imperative 5 to reduce the energy and equipment costs.6 Along with distillation methods, gas separation could be done with adsorptive membranes. This method is an effective method but to do it, an adsorbent with high


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selectivity and large capacity is needed. Some sorbents 7 with high selectivity have been used for gas separation at low pressures. Esrafili et al. study the N2O reduction by CO molecule over the surface of silicon carbide nanosheets (SiCNS) using DFT calculations. They obtained values of adsorption energies of CO and N2O molecules, and their results showed that the N2O molecule has a stronger interaction with the SiCNS surfaces. Accordingly, when CO/N2O mixture is injected on the surface of SiCNS as an adsorbent, the silicon atom of the membrane should be covered by N2O molecule.8 In other work, Gopalsamy et al. showed a new approach for the adsorption isotherms of gas mixtures. They calculated some thermodynamic properties of the adsorption process, such as the enthalpy, Gibbs free energy, and entropy for the adsorption process of CH4/C2H6 mixtures by various covalent organic frameworks (COF) including COF-102, COF-105, and COF- 108. They obtained the rank of selectivity of different COFs for CH4/C2H6 mixture and finally, it was reported that COF-102 was the best candidate for the separation CH4/C2H6 mixture at the room temperature.9 In other theoretical study, Pitakbunkate and co-workers investigated the behaviour of hydrocarbon mixture (CH4/C2H6) in confined spaces in nanoscale shale pores to model kerogen pores in shale reservoirs and study their effect on adsorption selectivity. They used a slit pore made of graphite walls. The separation between graphite layers was varied to observe the effect of confinement on the adsorption selectivity of CH4/C2H6 mixtures. Results showed that C2H6 is preferred over CH4 in the confined system.10 Gas separation process could also be accomplished by passing the gas molecules through an appropriate membrane with high selectivity and permeability.11 Li et al.

12

predicted metal

organic frameworks (MOF), due to their tunable structures, will display great potential in the gas


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separation process. He et al. 13 investigated the performances of 19 different MOFs for separation of CH4, C2H4, and C2H6. They showed that in MOFs with the high density of open metal sites had better performance in the gas separation than that of other MOFs and ZIFs (zeolitic imidazolate frameworks). In other work, Altintas et al. investigated the capability of different MOFs for separation of CH4/C2H6 and C2H4/C2H6 mixtures. Their results showed that some MOFs had higher adsorption selectivity than traditional zeolites under similar operating conditions. They showed that with increasing pressure, adsorption selectivity of MOFs was decreased and also as the limiting pore size increased, adsorption selectivity decreased. Generally, MOFs membranes can be introduced as alternatives to traditional membranes for the gas separation process.14 Guo and coworkers

15

accomplished Monte Carlo simulations to investigate adsorption and

separation process of methane/ethane mixtures in zeolites, isoreticular metal organic framework, and ZIFs. Two types of adsorption sites are in these membranes including sites with strong interactions with the adsorbent (at low pressure) and sites with strong interactions with surrounding adsorbates (at high pressure). In the CH4/C2H6 mixture, the C2H6 molecules limited the adsorption of CH4. On the other hand, selectivity of C2H6 was affected by temperature at the low pressure. In binary adsorption, C2H6 molecules favor sites with strong adsorbent interactions. Packing effects played an important role at the high pressures, and it became easy for CH4 molecules to access the sites. As a result, for zeolites and ZIFs, a low temperature could enhance C2H6 separation performance at the low pressures. In other theoretical work, Hauser et al.

16

studied the functionalized graphene nanosheet

capability for the separation of CH4 from other gas molecules using density functional theory method. They obtained the reaction barrier energies between some gas molecules and atoms of


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edge pore of graphene with various pore size. Their results showed that graphene, with appropriate pores, was capable of separating CH4 from the gas mixture at room temperature and above. In addition to the above cases, the performance of other new membranes for the separation of gases mixture should be investigated. But it's not possible to investigate all of the cases using experimental manners. Then, we can use molecular dynamics (MD) simulations method. MD simulations are carried out for investigation of microscopic interactions between atoms and molecules, for the solution of the equations of motion, in a specially designed system. In this method, the transport properties of many-body systems could be studied, and their results are compared with the results of conventional experimental methods. So, this method enables us to learn new things, something that cannot be found out in experimental techniques. In the gas separation process, the kinetic diameter of gas molecules and the interaction between membrane and gas molecules play an important role. Herein, using MD simulations, the ability of SiCNS was investigated for separation of the CH4/C2H6 gas mixture. SiCNS membrane, with a honeycomb structure, composed of silicon and carbon atoms

17

with sp2

hybridization. 18 2D nanostructure materials as a new category of materials have attracted a lot of studies.

19

Given its structure, SiCNS can be used as a nanostructure membrane for gas

separation with unique physicochemical properties such as high thermal and chemical stability20 and low chemical reactivity towards oxidation. 21 SiCNS has many similarities to graphene and boron nitride structures, with hexagonal structures in 2D structures and layer-stacking sequences

22

in 3D structures and covalent bonds

between their planes in 3D networks. Recently, the synthesis of SiCNS has been reported by


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Lin.23 Because of the thin thickness of one-atom-thick SiCNS, gas separation through it can be done effectively with high permeability. However, pristine SiCNS membrane, without any pore in its surface, due to the high electron density of aromatic rings, is impermeable to small gas molecules even helium similar to graphene membrane.24 Therefore, to design a suitable SiCNS membrane for gas separation, it is necessary to drill pores on the surface with proper diameter and also, in some cases it needs to some functional groups added to the edge atoms of pores. We believe that the present research can give an opportunity to use the SiCNS with appropriate pores on the surface for gas separation.

2. Computational method In this study, we focus on the separation of the CH4/C2H6 gas mixture using SiCNS membranes with variously engineered pores on the surface of the membrane with different functionalized groups including H, F, O, N, and S atoms (H-pore, F-pore, O-pore, N-pore, and Spore). Also, we used one case with a non-functionalized pore in the center of SiCNS membrane (SiC-pore). These pores are shown in Figure 1. Similar to other 2D structure nanosheets such as graphene,24 boron nitride,

25

and molybdenum disulfide

26

, the pristine SiCNS is also

impermeable to gas molecules. So, we created various pores on the surface of SiCNS to investigate the gas separation through them. For design pores, the Si and C atoms were removed from pristine SiCNS and then, the vacant positions were filled with desired atoms. The area of designed pores is listed in Figure 1 ranging from 31.0 Å2 to 10.49 Å2. Geometric optimization of functionalized SiCNS was done using density functional theory method to obtain their optimized


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structure and atomic charges. These calculations were done at the B3LYP level of theory using the 6-311G basis set by GAMESS package. 27 The MD simulation was performed in different temperatures under atmospheric pressure conditions. Previous studies have shown that SiCNS, as a single layer membrane, is attainable and stable in high pressure or temperature.18 All simulations were carried out by NAMD 2.12.28 As can be seen in Figure 2a, in the simulation box, the CH4/C2H6 gas mixture was placed uniformly between two SiCNS membranes in the central simulation cell as a gas phase with dimensional of 30×30×40 Å3. On the left and right of the central cell, two vacuum simulation cells made with the same size (the permeate sides). Also, in this work, we investigated the effect of multilayer SiCNS on the gas separation phenomenon (see Figure 2b). For calculation of permeated gas molecules, the number of permeate gas molecules from the gas phase to the permeate sides through pores of the membrane was monitored during the simulation. This model was used in the previous studies. 29-31 In each simulated system, there were 55 molecules for each CH4 and C2H6 gas molecules, totally 110 gas molecules. To avoid vertical displacement, SiCNS membrane was fixed during the simulation. Initially, the simulation cell was equilibrated to minimize the energy, and then, MD simulations were carried out for 20 ns at the various temperatures between 273.15 K and 373.15 K in a canonical ensemble. The Langevin dynamics method was used to control system temperature. For each investigated system, a set of 5-8 independently MD runs were done from various initial velocity distributions. In all three directions of the simulation cell, the periodic boundary conditions were applied. The required Lennard-Jones potential parameters for SiCNS membrane ware taken from reference

32

and for gas molecules, we used from CHARMM force

field parameters.33 The Lorentz–Berthelot mixing rules

34

were applied for cross-interactions


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between nonbonded atoms. PME (Particle Mesh Ewald) scheme

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35

was used for long-range

electrostatic interactions, and all analysis scripts were composed by VMD 1.9.3. 36 To figure out the permeation of gas molecules from the designed pores, the potential of the mean force (PMF) of gas molecules was calculated by umbrella sampling

37

method across the

designed pores. The sampling path was from 10 Å to 25 Å with the 0.5 Å spacing along the zaxis; so that the gas molecules were inserted in a distance of 10 Å, vertically aligned with the center of the pore. Then, the obtained data were analysis by WHAM

38

(weighted histogram

analysis method). Gas separation using nanostructure membranes has recently been considered in the industry. The gas permeation mechanism is justifiable with the pore-flow model. In this model, the gas molecules are passed across the pore of the membrane. Pore size, its shape and functional groups on the edge pore are important factors that they are effective in the gas separation process using membranes. We can use from computational techniques, such as MD simulations, to obtain microscopic information of systems and therefore we'll understand the mechanism of transport of gas molecules through membranes. Herein, we used from SiCNS membrane for separation of the CH4/C2H6 gas mixture in various temperatures with different functional groups on the created edge pore in the SiCNS membrane. In this way, we also used from PMF calculations to predict theoretically the ability of SiCNS membrane for gas permeation through designed pores before MD simulations.

3. Results and discussion We focus on the effect of pore size and some functional groups on the separation of alkane mixtures. In this way, some selected pores were not suitable, so that both of methane and ethane


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gas molecules passed through the selected pore or both of them were not able to pass the pore. For example, when we used S (sulfur) atom for functionalization of edge pore, in the large Spore, both of CH4 and C2H6 could pass easily through this large pore and then, their separation did not happen in this pore. On the other hand, in the case of small S-pore, gas molecules did not pass. It can be said that the appropriate pore size and functional groups have a vital role in the gas separation phenomenon and with excessive increasing the pore size, the selective gas separation process does not occur. In other studies, 39-41 similar results were reported. So that gas molecules could not pass through considered pores, owing to the space restriction or repulsive force between edge pore atoms and gas molecules.

3.1. PMF calculations The PMF calculations can be used to predict the permeation of gas molecules from specific path such as a pore of the membrane.42 Herein, for CH4 and C2H6 molecules in the various systems, PMF was calculated in the simulation systems before, after and inside the pore (from 10 Å to 25 Å along the z-axis of simulation box). Figure 3 shows the PMFs for CH4 and C2H6 in different pores. These gas molecules were allowed to permeate through pore when their PMF energy was low; but if the energy barrier was high, the permeation of gas molecules was not possible or slightly occurred.43 As can be seen in this Figure, in the all of cases, PMF for C2H6 was higher than that of CH4. Due to this trend, always the numbers of methane permeated through pores of SiCNS were higher than that of ethane molecules and when the amount of PMF energy was very high (such as for ethane in N-pore system), this gas molecule encountered with the large energy barrier and cannot pass through the pore. However, methane with lower PMF passed through this pore.


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Hence, based on the PMF results, it can be said that the trend of permeated gas molecules through the pores of SiCNS is consistent with their trend of PMF energy.44 In these gas mixtures, due to the large size of C2H6 relative to CH4, ethane molecules faced with large energy barrier when passing through the pore of the membrane, so that, in all investigated systems, the permeated number of methane molecules were greater than ethane molecules. However, in some pores both gas molecules permeated from them, so the gas separation did not occur. But in the case of N-pore, only methane molecules passed through the pore, and the separation of this mixture could be done.

3.2. Gas permeation and selectivity In the separation process of the CH4/C2H6 gas mixture in the various temperatures, the permeation ratio (PRG) and the selectivity of different pores was obtained by monitoring the permeative gas molecules during the simulation time. Variously functionalized pores of SiCNS showed different behaviors. PRG was described as:45

PR G =

the number of permeated gas the total number of gas molecules

(1)

As can be seen in Table 1, in the whole of CH4/C2H6 systems with different functional groups on the edge pore, methane gas molecules could pass through these pores. With increasing system temperature, PRG for methane was also increased, but this trend was accompanied by reducing pore selectivity. Therefore, a high PRG for a specific gas molecule in a mixture does not mean a good selectivity. 14 In our simulation box, gas molecules don’t distribute uniformly in the whole of the box, so that they approach onto the surface of SiCNS membrane. Of course, this phenomenon helps them to pass through the pores. We can observe this accumulation of gas molecules in Figure 4 using 11 ACS Paragon Plus Environment

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density map profiles of gas molecules in simulation box. This Figure shows the density map of methane and ethane at the low (298K) and the high (773K) temperatures in F-pore system. Other systems follow a similar trend. The distribution of gas molecules in the simulation box was not the same at the low and the high temperatures. In the 298 K, due to the van der Waals interactions between gas molecules and membrane atoms, gas molecules accumulated near the SiCNS surface, so that there is a high-density region of gas molecules as an adsorption layer near the membrane. On the other hand, in 773 K, gas molecules had little accumulation around the SiCNS membrane, and their distribution was almost uniformly in the whole simulation box. Also, the distribution of molecules in the simulation cell was different for methane and ethane molecules because of differences in the interaction energy of methane and ethane with SICNS membrane (Figure 5).

29

As can be seen in Figure 5, the interaction energy between gas

molecules and SiCNS membrane, for ethane is stronger than that of methane-SiCNS. This trend in this figure is for F-pore system in 298 K; however, in other systems, this trend was the same. So that the interaction energy for the C2H6-membrane was always stranger than that of the CH4membrane. This phenomenon causes ethane molecules to accumulate near the SiCNS membrane more than methane molecules which are also shown in Figure 4. Also, in the density maps (Figure 4), in the low temperature, both gas molecules often accumulated in a region around the SiCNS membrane. However, in the high temperature, accumulation of gas molecules around the SiCNS membrane did not occur, and they distributed in the whole simulation cell. This is due to increasing system temperature cause to the interaction between gas molecules, and SiCNS membrane became weaker; therefore, gas molecules were easily distributed throughout the simulation box.


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Figure 6 shows the number of methane and ethane permeated in CH4/C2H6 mixture systems through the various pores in different temperatures during the simulation time. We studied the effect of temperature rise on the gas separation phenomenon so that systems behavior was investigated in 273, 298, 323, 348 and 373 K. The gas molecules that can pass through the pore due to their low PMF, they come out of the gas phase spontaneously. In fact, no extra force was used in this work to separate gas molecules, and with the time during the simulation, gas molecules entered into the vacuum phase. As the system temperature rises, the number of gas molecules passing through the pores increased. On the other hands, with increasing temperature, the selectivity of SiCNS pores decreased (see Table 2). According to the PMF results, MD results confirmed that CH4 passed through the functionalized pores more than C2H6 at all studied temperatures. This phenomenon can also be due to the stronger adsorption intensity of ethane relative to methane on the surface of SiCNS membrane (see Figure 5). In the case of N-pore, even with increasing temperature, ethane molecules did not pass through this pore and accumulated on the surface of SiCNS. However, in the whole case of pores, all methane or ethane molecules weren’t entered into the vacuum phase, and some of them remain in the central box. In the research, the unit for gas permeation measurement used is Gas Permeation Unit (GPU), where 1 GPU =3.35×10-10 mol.m-2.s-1.Pa-1. These values are listed in Table 1. As can be seen, values of gas permeance in various pores and temperatures were different. In totally, gas permeance increased with increasing system temperature. Also, the highest amount of gas permeance is obtained for the SiC-pore. But this pore did not have good selectivity for CH4/C2H6 mixture; therefore, it cannot be a good pore for the separation of methane. However, the N-pore system with a 100% selectivity and good gas permeance (2.613×105 GPU in 298 K) can be the


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best pore for separation of methane from CH4/C2H6 mixture. This value for methane in SiCNS membrane is much higher than that of for conventional membranes such as polysulfone membrane (31.2 GPU). 46 In other work, Sun et al. 47 obtained the CH4 permeance approximately 6.52×104 GPU using neutral nanoporous graphene membranes. In investigated systems, functional groups on the edge pore played an important role in the gas separation process. For example, in a comparison between N-pore and SiC-pore, although the pore size of N-pore (14.23 Å2) was larger than that of SiC-pore (13.36 Å2), ethane molecules did not pass through N-pore, but these gas molecules were able to pass through the SiC-pore. This trend was also confirmed by the PMF diagrams in Figure 3 with low and large energy barrier for ethane molecule in SiC-pore and N-pore systems, respectively. In fact, the functional group on the edge pore of N-pore system has caused to this pore act as a selective pore for CH4/C2H6 mixture. Of course, as the results show, the size of pores also affects the gas permeation process, so that any gas molecule passed through the small S-pore (10.49 Å2). As is clear from the results of Table 1, all of the gas molecules could not get out of the gas box, and some of them remain in the central box. Hence, to completely gas separation, we increased the simulation time, so that systems were run 100 ns (that is a long-time simulation for our systems). During this long-time simulation, permeated gas molecules did not significantly change; for example, in the N-pore system, the permeation ratio of CH4 increased from PRCH4=54.54%

in 298K during 20 ns to PRCH4=61.5% in 298 K during 100 ns MD simulation. In fact,

due to the outflow of gas molecules from the gas phase, the pressure difference between both gas and vacuum phases is reduced, and thus the gas permeation is reduced. So, if necessary to the gas box will be empty, the additional pressure must be applied to this system.


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Another investigated parameter was the membrane selectivity (S) for each gas molecules in mixture system. This parameter is obtained from Equation (2) as follows: 48

y CH4

SCH4

= C2 H 6

where SCH4

y C2 H 6

x CH4

(2)

x C2 H 6

is methane selectivity, y is the mole fractions of the gas molecule in the vacuum C2 H 6

phase, and x is the mole fractions of the gas molecule in the gas phase. The selectivity results are given in Table 2. High selectivity of methane occurred in the low temperatures, but with temperature increasing, the pore selectivity was decreased. Furthermore, since in the case of Npore system, only methane passes through the pore, so, this membrane can be the best choice for separation of CH4/C2H6 mixture. Also, the long-time simulation (100 ns) showed that selectivity of SiCNS did not change with increasing simulation time.

3.3. Two-layer systems In our designing system, some systems could not separate the CH4/C2H6 mixture from each other. So that, except for the N-pore, both gas molecules passed through the pore in the rest of the systems. To overcome this problem, we designed new setup with using two-layer SiCNS as the membrane on each side of the box (see Figure 2b). In two-layer membrane systems, similar to the single-layer membrane system, methane and ethane gas molecules were able to permeate through the embedded pore in the first SiCNS membrane and enter the region between two layers; but, due to high van der Waals interaction between ethane molecules and SiCNS membrane, these gas molecules trapped in this region. However, methane molecules permeated through the embedded pore in the second SiCNS membrane. Of course, it should be noted that


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all of the methane molecules did not escape from the second region and some of them remained in this region. In fact, by using the second SiCNS layer, the selectivity of SiCNS pores significantly increased. In these systems, the performance of F-pore and O-pore systems was changed; so that these two systems were able to separate methane gas from CH4/C2H6 mixture due to the use of the second SiCNS membrane. Figure 7 shows the number of methane molecules permeated from the second SiCNS membrane. In two membrane systems, some gas molecules remained in the central box, and in some cases permeated from the first membrane and remained in the area between the two membranes and finally only methane molecules permeated through second membrane (in F-pore and O-pore systems), in the event that ethane molecules were not able to pass through the second membrane. The value of gas permeance in 298 K for methane molecule was 8.878×104 GPU in F-pore and 8.332×104 GPU in O-pore. However, with increasing system temperatures, these values also increased (up to 1.149×105 GPU for F-pore and 1.111×105 GPU for O-pore in 373 K). Figure 8 shows density map profiles for methane and ethane molecules in the two-layer Fpore system in 298 K which confirms this process. As can be seen in this Figure, methane molecules passed through both membranes (Figure 8a), but ethane molecules (Figure 8b) could not pass through the pore of the second membrane.

3.4. Gas permeation mechanisms During the simulations, the methane and ethane permeation was monitored to determine their passing event mechanism. After reaching equilibrium and distributing gas molecules in the central simulation box, methane or ethane molecules approached to the surface of SiCNS membrane. In this situation, due to the interactions between gas molecules and membrane, they spend more time near the surface of the membrane. This process occurred in all systems. After 16 ACS Paragon Plus Environment

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this, the gas molecules (methane or ethane) which were able to pass through the pores of SiCNS, passed through them and entered the vacuum phase. To better understand this process, z-position of one of methane and ethane molecules during the simulation was monitored as shown in Figure 9 in 298 K. In system setup, SiCNS membrane was placed at z = -20 Å and +20 Å in the simulation box (the z-axis was perpendicular to the surface of SiCNS). Figure 9 shows that gas molecules, especially ethane molecules, move toward the surface of SiCNS due to the interactions between them and membrane. In this process, gas molecules were located near the membrane until they pass through the pore (see Figure 9a). However, in some systems such as N-pore system in total simulation time (see Figure 9b), ethane molecules they were not able to permeate through the pore and stayed in the space between the two SiCNS membranes close to them. Of course, it should be noted that due to the stronger adsorption intensity between ethane-SiCNS compared to methane-SiCNS, ethane molecules spend more time near the membrane. Despite the fact that ethane molecules spend more time near the membrane, but due to their more PMF energy than methane, they permeated through the pore less than methane molecules. At the same time, after passing through the pore, ethane molecules do not spread in the simulation box, and they were still distributed around the membrane. As a mentioned, during the 20 ns simulation time, gas molecules move toward the surface of the membrane and were located near it until they pass through the pore. Then, some gas molecules passed through the pore of the membrane and entered into the vacuum phase. However, the time delay for each CH4 or C2H6 molecules was different. Also, in the different temperatures, this parameter was changed. So that the temperature increases, the time delay was decreased. For example, in Figure 9a, z-position of one of CH4 and C2H6 molecules was shown in 17 ACS Paragon Plus Environment

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F-pore system. Due to the stronger adsorption intensity between C2H6-membrane compared to CH4-membrane, C2H6 molecules spend more time near the surface of the membrane and therefore the time delay for C2H6 molecules was more than that of CH4 molecules. So that, at first, one of the CH4 molecules passed through the pore in 7.6th ns, and then one of the C2H6 molecules passed in 10th ns.

4. Conclusions In this research, we investigate the capability of the SiCNS membrane for separation of alkane mixtures. In this way, the CH4/C2H6 gas mixture was selected due to their many industrial applications in the petroleum industry. For separation of gas molecules using SiCNS membrane, some pores with different size were created on the surface of SiCNS, and then, the edge of pores was functionalized with various appropriated chemical groups including H, F, O, N, and S atoms. Also, in one case, a non-functionalized pore in the SiCNS was designed. For passing gas molecules through the desired pores, they first approached the membrane and attracted onto the membrane surface and then permeated through the pore. Although, in this process due to interaction energy between gas molecules and membrane atoms, gas molecules approached to SiCNS, however, designed pores played a more important role. In the results, we showed that among the systems examined, single layer N-pore system with an appropriate size had the best performance and was able to separate methane from CH4/C2H6 mixture with a 100% selectivity and good gas permeance (2.613×105 GPU in 298 K). In other systems which pores did not act selectable, we used multi-layer membrane technique to separate gas mixture from each other. In this case, F-pore and O-pore systems responded to this trick and selectivity of SiCNS pores significantly increased, so that these two systems were able to separate methane gas from CH4/C2H6 mixture. In these systems, ethane molecules remained in the central box or the area 18 ACS Paragon Plus Environment

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between the two membranes, but methane molecules were able to pass through the second pore. We also examined the effect of temperature rise, and the results showed that with increasing temperature, the selectivity of pores decreased, while the gas permeance increased.

Note The authors declare no competing financial interest.

Acknowledgments Authors thank the University of Tabriz for the support provided. Jafar Azamat as a postdoc researcher gratefully acknowledges use of the services and facilities of the University of Tabriz.

Conflict of interest We wish to confirm that there are no known conflicts of interest associated with this publication.


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Tables

Table 1. The permeation ratio of CH4 gas and its gas permeance in different temperatures for various one-layer systems. Temperature (K)

273

298

323

348

373

System

PRG×100 for CH4

Gas permeance (×105 GPU) for CH4

H-pore F-pore O-pore N-pore SiC-pore H-pore F-pore O-pore N-pore SiC-pore H-pore F-pore O-pore N-pore SiC-pore H-pore F-pore O-pore N-pore SiC-pore H-pore F-pore O-pore N-pore SiC-pore

63.64 60 54.54 50.90 49.09 65.45 65.45 60 54.54 54.54 70.90 70.90 63.63 58.18 56.36 74.54 72.72 67.27 61.81 60 76.36 80 70.90 69.09 63.63

1.399 1.723 1.666 2.438 2.504 1.439 1.880 1.833 2.613 2.783 1.559 2.037 1.944 2.787 2.875 1.639 2.089 2.055 2.961 3.061 1.679 2.298 2.166 3.309 3.247


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Table 2. The CH4 selectivity of various pores in different temperatures for one-layer systems.

System Temperature (K)

H-pore

SCH 4

C2 H 6

F-pore

SCH 4

O-pore

SCH 4

C2 H 6

C2 H 6

N-pore

SCH 4

C2 H 6

SiC-pore

SCH 4

C2 H 6

273

1.66

3

3.75

Only CH4 permeated

1.17

298

1.64

2.57

2.54

Only CH4 permeated

1.20

323

1.56

2.44

2.19

Only CH4 permeated

1.15

348

1.52

2.22

1.95

Only CH4 permeated

1.14

373

1.50

2.20

1.69

Only CH4 permeated

1.13


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Energy & Fuels

Figures H-pore

F-pore

O-pore

N-pore

SiC-pore

S-pore

Figure 1. Sketches of the all types of functionalized pores on the surface of SiCNS membrane. Area of each pore is: H-pore (31.0 Å2), F-pore (23.73 Å2), O-pore (22.31 Å2), N-pore (14.23 Å2), SiC-pore (13.36 Å2) and S-pore (10.49 Å2).


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 2. (a) Snapshut from simulation system via one layer SiCNS membrane with N-pore in its center (b) Snapshut from simulation system with two-layer SiCNS membrane with F-pore in its center. (red: methane; green: ethane; yellow: silicon; cyan: carbon; purple: nitrogen and pink: fluoride).


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50 H-pore

Ethane

45

Methane

40

PMF (kcal/mol)

35 30 25 20 15 10 5 0 10

15

Axial position (Å)

20

25

20

25

20

25

50 F-pore

Ethane

45

Methane

40

PMF (kcal/mol)

35 30 25 20 15 10 5 0 10

15 Axial position (Å)

50 O-pore

Ethane

45

Methane

40 35

PMF (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

30 25 20 15 10 5 0 10

15 Axial position (Å)


Energy & Fuels

50 N-pore

Ethane

45

Methane

PMF (kcal/mol)

40 35 30 25 20 15 10 5 0 10

15

20

25

20

25

Axial position (Å)

50 SiC-pore

Ethane

45

Methane

40 35

PMF (kcal/mol)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 30 of 37

30 25 20 15 10 5 0 10

15

Axial position (Å)

Figure 3. The potential of the mean force for CH4 and C2H6 molecules, were sampled from 10 Å to 25 Å along the z-axis of simulation box (SiCNS membranes were located inside this position, exactly in z= 20 Å).


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Figure 4. Density map for CH4 and C2H6 gas molecules in the F-pore system in the low and high temperatures: (a) CH4 in 298 K, (b) C2H6 in 298 K, (c) CH4 in 773 K, (d) C2H6 in 773 K (In the rest of the systems, there was the same trend).


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 5. Interaction energy between gas molecules with SiCNS membrane in the F-pore system during the simulation time in 298 K. With increasing temperature of system, the interaction between gas molecules and SiCNS membrane became weaker (data not shown).


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50

Number of gas permeation

H-pore

Methane

45

Ethane

40 35 30 25 20 15 10 5 0 260

280

300

320 340 Temperature (K)

360

380

360

380

360

380

50 Methane


45

F-pore

Ethane

40 35 30 25 20 15 10 5 0 260

280

300


50 O-pore

Methane

45


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

Ethane

40 35 30 25 20 15 10 5 0 260

280

300



Energy & Fuels

50


N-pore

Methane

45 40 35 30 25 20 15 10 5 0 260

280

300


360

380

360

380

50


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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45

Methane

40

Ethane

SiC-pore

35 30 25 20 15 10 5 0 260

280

300


Figure 6. The number of gas permeation through the various pores of SiCNS membrane in

different temperatures. Each data point represents the average of 5-8 sets of independently simulations from various initial velocity distributions.


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25 F-pore Number of permeate methane gas through second membrane

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Energy & Fuels

O-pore

20

15

10

5

0 260

280

300


360

380

Figure 7. The number of CH4 molecules permeation through the second SiCNS membrane in Fpore and O-pore systems in different temperatures. In these two systems, only CH4 molecules passed through the second membrane. Each data point shows the average of 5-8 sets of independently simulations from various initial velocity distributions.


Energy & Fuels 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Figure 8. Density map for (a) CH4, (b) C2H6, in two-layer F-pore system in 298 K. As can be seen, only CH4 molecules could pass through the second layer while C2H6 molecules could not pass through the second layer.


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Figure 9. Variations of the z-position of methane and ethane molecules during the simulation time; (a) in F-pore system, (b) in N-pore system (only methane molecules were able to pass the pore). (SiCNS membranes were located at positions z = +20 Å and -20 Å in the simulation box, which is indicated by the dash line).


C2H6 Mixture Using Functionalized Nanoporous

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