CH4 Gas Separation by Variation in Pore Geometry of Nanoporous

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H/CH Gas Separation by Variation in Pore Geometry of Nanoporous Graphene Bharath Raghavan, and Tribikram Gupta J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b08662 • Publication Date (Web): 30 Dec 2016 Downloaded from http://pubs.acs.org on January 3, 2017

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The Journal of Physical Chemistry

H2/CH4 Gas Separation by Variation in Pore Geometry of Nanoporous Graphene Bharath Raghavan† and Tribikram Gupta∗,‡ †Department of Chemical Engineering, R. V. College of Engieering, Bangalore ‡Department of Physics, R. V. College of Engineering, Bangalore E-mail: [email protected]

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Abstract We studied the behavior of H2 and CH4 flowing through various pore geometries of nanoporous graphene using molecular dynamics method. Ten different geometries of pore-18, with different eccentricities were prepared. It was found that the gas permeance and adsorption layer were heavily influenced by the eccentricity of the pores. On further investigation, it was also found that the jaggedness of the pore geometry played a role as well. It was also noted that at specific eccentricities, pore-18 exhibited hydrogen selective behavior, which was found to extend to pore-12, 14, 16, 20, 24 and 30 as well. Furthermore, it was shown that the H2 permeance of these pores can reach 9 times the value of that of pore-10 (which was previously found to be the only selective pore). Hence, these pores show H2 selectivity with high H2 yields. Thus, this study demonstrates the exciting possibility of creating highly efficient H2 separators by pore geometry variation. Recent experimental studies, which involve an atom-byatom removal technique to create nanopores, point to the possibility of obtaining these geometries in the lab.

Introduction Gas separation using membranes has gained wider acceptance in the industry due to their many advantages over conventional methods. 1,2 They are especially useful in obtaining pure hydrogen gas, which is crucial if the concept of “hydrogen economy” is to be fully realized. 3 It has been shown by many studies that graphene drilled with nanopores, known as nanoporous graphene (NPG), is an excellent material for gas separation. 4,5 Graphene is a two dimensional sheet of sp2 -hybridized carbon system, well known for possessing exceptional mechanical, thermal and electrical properties. 6–8 Pure graphene has been shown to be impenetrable to most gases molecules, including helium. 9,10 However, by virtue of nanopores present in the graphene sheet, it has been experimentally shown that it can be used to transmit gas molecules selectively. 11–13 2 ACS Paragon Plus Environment

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Koeing et al. experimentally generated sub-nanometer level pores using UV oxidative etching. 11 Pores were made in a micrometer sized graphene sheet, and it was shown that these pores had the ability to separate H2 from CH4 . Specifically, H2 and CO2 were shown to pass through the pore while CH4 and Ar were blocked. Pores of larger sizes were also generated, and they were shown to block SF6 , but allow H2 , CO2 , N2 and CH4 . Recently many computer simulations have been undertaken to study the possibility of using carbon allotropes, including NPG, as membranes for gas separation. 14 Jian et al. was the first to study gas separation using nanoporous graphene. 15 Blankenburg et al. 16 calculated diffusion barriers for H2 , He and other gas molecules (Ne, O2 , N2 , CO, CO2 , NH3 and Ar) penetrating through the graphene membrane pores passivated by hydrogen atoms and found that the barrier for the passage of H2 or He was much smaller than other gases. Recently, Ambrosetti et al. 17 evaluated the permeation barriers and adsorption energies for H2 O, CH4 , CO, CO2 , O2 , H2 and Ar using DFT method. Selectivity trends of different gases were studied by H Liu et al. 18 using MD, and it was found that selectivity is a function of the kinetic diameter of the molecules. A W Hauser et al. estimated the selectivities of CH4 over N2 , CO2 , O2 , and H2 . 19 Effective separation of CO2 -N2 gas mixture using NPG has also been demonstrated. 20 There are many factors that affect the permeation of gas molecules through NPG. One of the main factors is the adsorption layer, which is the layer formed due to adsorption of gas molecules on to the graphene surface. This adsorption layer was first observed by Du et al. for H2 -N2 separation. 21 It was then clearly studied by Drahushuk et al. where they presented a five step model for gas permeation. 22 The contribution of the adsorption layer to the total flux has also been investigated in detail by Sun et al. 23 They spilt the gas flux into direct flux (flux due to gas molecules coming from the bulk phase) and surface flux (flux due to molecules coming from the adsorption layer), and showed that the surface flux contributes more to the total flux for molecules such as CH4 and N2 as compared to H2 and He. In addition, other factors such as pore functionalization have also been investigated. Shan et al. have shown



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that pore CO2 -N2 separation can be greatly improved by functionalization of the pore with a polar atom such as nitrogen. 24 Recently, positive charges have shown significant effect on the permeability and selectivity in graphdiyne for hydrogen purification. 25 Although many studies have investigated various factors that affect gas permeance through NPG, not many studies have concentrated on the behavior of gas flux with respect to change in pore geometry for a constant pore area. Some studies, such as the one carried out by Du et al. 21 have touched on the subject. While studying the effect of pore area on hydrogen and nitrogen separation, two pores of same area but different eccentricities were also taken, and it was found that they produced different gas permeances. But, this issue was not investigated in greater detail. In addition, Wen et al. 26 noted that an elliptically shaped pore-13 has a unique characteristic of hindering the permeation of methane molecules. This behavior is not exhibited by a circular shaped pore-13. Thus, it can be seen that the amount of deviation of the pore from a circular shape affects the permeance. Since, eccentricity is a common way to quantify this deviation, it is important to study the effect of pore eccentricity on gas permeation. Thus, in this paper, a systematic study of the effect of variation of pore eccentricity on gas permeance has been carried out. We used molecular dynamics (MD) simulations to investigate the way in which the pore eccentricity affects the behavior of hydrogen and methane permeance. The possibility of obtaining hydrogen selective pores by variation in pore eccentricity was also investigated. We also detailed an experimental procedure that could be used to obtain these geometries.

Methods We investigated the behavior of a H2 /CH4 gas mixture through NPG with respect to variation of pore eccentricity using MD simulations. The MD simulations were carried out using the LAMMPS 27,28 software package. The C-C, C-H and H-H interaction were modeled using the AIREBO potential. 29 The simulations were run for 2.5 × 107 timesteps with a timestep of


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0.0002 ps, resulting in a simulation time of 5 ns. The data was collected every 4000 steps. The models were kept at the NVT ensemble, and were held at a constant temperature of 300 K by using Nos´e-Hoover thermostat.

Figure 1: (a) The simulation box used in this study. (b-k) The different pore-18 geometries employed in this study. The simulation box (shown in Figure 1) was 42 ˚ A × 42 ˚ A × 300 ˚ A with the periodic boundary condition applied across the x and y direction and the reflective boundary condition was applied in the z direction. A graphene sheet of 4 nm × 4 nm was placed at the center. The coordinates for the carbon atoms of graphene were generated using VMD. 30 The four corners of the graphene sheet were fixed so as to avoid vertical displacement. However, the rest of the sheet was free to move. The gas molecules can be either placed only on one side of the graphene sheet, 24 or on both sides. 23 In our simulations, the molecules were placed only on one side of the graphene sheet. Although this leads to a non-equilibrium system, it was done as it is an easier way to study the separation process. The feed was made up of 100 molecules of hydrogen and methane each (200 molecules in total). The gas molecules were placed in random positions above the graphene sheet. The area below the graphene 5 ACS Paragon Plus Environment


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sheet was left empty. Pores were created in the graphene membrane by removing or drilling carbon atoms from the sheet. The pore area of each pore was characterized by the pore number, or the number of carbon hexagons removed when creating the pore. It is easier to study the effect of pore eccentricity using larger pore sizes, because it is easier to obtain a greater variation of geometries for these larger pores. On the other hand, the pore size cannot be too large as we anticipate that the effect of geometry will diminish as the pore size increase. Considering these two conditions, pore-18 was taken as the ideal pore to be used for this study. 10 different geometries for pore-18 were created in order to study the behavior of gas permeance with respect to change in pore geometry. The different geometries are shown in Figure 1b-k. Although these geometries are not expected to be intrinsically stable, they can be made stable by the method of Lee et al. 31 They have shown that fabricated pores with different geometries can be robustly passivated by Si atoms. As mentioned earlier, the adsorption layer is an important factor in the determining the gas permeance. The adsorption layer is the layer formed due to adsorption of gas molecules on to the graphene sheet upto 6 ˚ A above and below the graphene sheet. 23 In our study, the strength or concentration of the adsorption layer was measured by the average number of adsorbed molecules. This was calculated by counting the number of gas molecules (H2 and CH4 ) present in the adsorption layer at each timestep, and then averaging over the number of timesteps. The eccentricity of the pore geometry is a measure of how far the geometry is from a regular circle. We can expect that the more elongated a geometry is, the lesser will be the number of gas molecules permeating through it. The eccentricity is calculated by fitting an ellipse to the edge atoms of the pore by the method of Fitzgibbon et al., 32 and then finding the eccentricity of that ellipse. This method is discussed in more detail in the Supporting Information. The eccentricities obtained for the pore-18 geometries used in the study are shown in Table 1.


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Table 1: Eccentricity values for the different geometries of pore-18. The naming convention of the geometries is as per Figure 1. (b) 0.906007

(c) 0.266359

(d) (e) 0.733573 0.499404

(f) 0.719692

(g) 0.645524

(h) 0.742729

(i) 0.703635

(k) 0.798408

(j) 0.88743

The permeance was calculated by the method of Sun et al., 23 the details of which are given in the Supporting Information. The gas permeances obtained from simulations were plotted against the eccentricity values of the different pores.

Results and Discussions 10 different geometries of pore-18, with different eccentricities, were taken and 5 ns simulations were carried out for each. Gas permeances calculated from the simulations were obtained by averaging over 4 separate runs starting from different initial gas configurations. The plots of gas permeance with respect to eccentricity are shown in Figure 2a. The first observation that can be made is that gas permeance varies greatly with the eccentricity of the pore geometries, even though the pore areas of all the pores are the same. This shows that gas permeance through NPG is not only a function of pore area, but is dependent on the pore geometry as well. Secondly, it can be observed that the nature of the dependence of gas permeance on eccentricity is complicated. One would expect that the gas permeance should decrease with increase in eccentricity. However, two points with eccentricities of 0.703635 and 0.733573 exhibit a sharp increase in permeance for both CH4 and H2 . This is despite their high eccentricity values. The pore with eccentricity 0.906007 shows low CH4 permeance as expected, but shows a sharp increase in H2 permeance. Thus, these exceptional pore geometries require further investigation.


H2 CH4

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H2 CH4

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Figure 2: (a)Behavior of H2 and CH4 permeance with change in eccentricity of pore-18. (b) Average number of H2 and CH4 molecules in the adsorption layer. Due to the way in which carbon atoms are drilled out of the hexagonal graphene sheet to create the pores, we postulate that different geometries may not just have differences in elongation, they also have differences in their irregularity or the “jaggedness” as well. This can be seen in the case of the pores geometries shown in Figure 1g and Figure 1i. The pore geometry depicted in 1i is quite “regular”, and almost resembles a parallelogram. It does not have many sharp edges, and is a smooth shape. However, the pore geometry depicted in 1g is quite “irregular”, and does not resemble any particular shape. It possesses many sharp edges and is highly “jagged”. We hypothesize that this variation in jaggedness for different pore geometries will contribute to the fluctuations in gas permeances. It is important to note that eccentricity and jaggedness are not quantities that can be varied independently at will. If the pore number and eccentricity of a pore is fixed, it also automatically fixes the jaggedness. In order to test this hypothesis, we propose a method to quantify the jaggedness. It is calculated by finding the convex hull of the geometry by the method of Jarvis et al. 33 and then calculating, by Monte Carlo method, the area of the region lying inside the convex hull but outside the pore geometry itself. This method is discussed in more detail in the 8 ACS Paragon Plus Environment

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Supporting Information. The jaggedness and their corresponding eccentricity values for all simulated geometries of pore-18 are shown in Table 2. Table 2: Jaggedness values for the different geometries of pore-18. The naming convention of the geometries is as per Figure 1. (b) 12.2346

(c) 15.5886

(d) 11.2687

(e) 17.3148

(f) 21.8009

(g) 19.1449

(h) 22.7281

(i) 10.4021

(j) 19.1743

(k) 31.2797

Interestingly, it can be seen from Table 2 that three anomalous eccentricity values of 0.703635 (geometry i), 0.733573 (geometry d) and 0.906007 (geometry b) show very low jagged areas of around 10 to 12. This might explain their behavior. Non-jagged geometries will provide more space for molecules to permeate through as compared to jagged geometries, even if they are not circular. Given this behavior, it can be inferred that jaggedness plays a role only for pores with very low jaggedness values, and loses its significance for more jagged pores. For higher jagged pores, the eccentricity becomes the main parameter in determining the permeance. Thus, it is argued that jaggedness should not be treated as a fundamental quantity that directly dictates the gas permeance. Rather, its function is only to cause few pore geometries to exhibit anomalously high gas permeances. An important observation can be made by looking at the behavior of the average number of adsorbed molecules for different geometries. As shown in Figure 2b, the adsorption layer varies significantly with respect to geometry. Furthermore, the nature of this dependence is also interesting. The plot for CH4 is almost the inverse of the Figure 2a. The pores that exhibit high CH4 permeance have low average concentration of CH4 in the adsorption layer. Likewise, when the pore exhibits low CH4 permeance, a high average concentration of CH4 in the adsorption layer is found. H2 does not exhibit this phenomenon as strongly as CH4 . This is because H2 has a weak adsorption layer. 23 By looking at Figure 2a, an interesting phenomenon can be observed. Three pores having an eccentricity of 0.719692, 0.742729 and 0.906007 have high hydrogen permeance 9 ACS Paragon Plus Environment


but negligible methane permeance. In our 5 ns simulations, only 2-6 methane molecules were observed to pass through these pores. Thus, these pores are H2 selective. Furthermore, these pores also exhibit high H2 permeance, which means the throughput or yield of hydrogen from these pores is also high. It is important to note that all three selective geometries show approximately the same H2 permeance, pointing to the fact that all three are equally effective for H2 separation. To extend this geometry induced selectivity to other pore numbers as well, we have simulated pore-10, 12, 14, 16, 20, 24 and 30. The highly elongated geometry of pore-18 with an eccentricity of 0.906007 (see Figure 1b) was found to be the easiest to replicate in other pore numbers due to its simple shape. This was taken as the prototype shape, and all the other pore numbers were simulated with this geometry (see Figure S1 in the Supporting information). Since the geometrical configuration of pore-18 possessing this shape was found to be selective, it is expected that the other pores will exhibit a similar selective behavior. Unlike pore-18, the other pore numbers were not averaged over 4 configurations as we were only looking for a rough confirmation of the selective behavior. The resultant permeances from the 5 ns simulations are shown in Figure 3a. 1.5

H2 CH4

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Figure 3: (a) Behavior of gas permeance for different pore numbers at elongated geometries. (b) Ratio between H2 permeances of higher pore numbers with that of pore-10. 10 ACS Paragon Plus Environment

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It can be seen that, similar to the case of pore-18, the pores operated at these specific geometry numbers show large H2 permeance and low CH4 permeance. Thus, other pore numbers also exhibit H2 selective phenomenon. Furthermore, as the pore number increases, the hydrogen permeance increases while the methane permeance exhibits only a marginal increase. This means that the selectivity as well as hydrogen yield increase as the pore number is increased. Therefore, high pore sized configurations, if designed with the right eccentricity, can be used as excellent gas separators. Thus, even high pore numbers can function as good hydrogen selective sieves. This is especially interesting given the fact that previous studies, which did not look into the geometry factor, have shown that only pore 10 is hydrogen selective. 21,23 As shown in Figure 3b, the H2 permeance of the selective geometries of pore-18 is around 3 times greater than that of pore-10. Also, the H2 permeance of higher pore numbers are several times greater, with pore-30 having a permeance 9 times greater than pore-10. Thus, not only can higher pore numbers be made selective, it can also produce hydrogen at high yields. Hence, pores of nanoporous graphene made at the correct pore eccentricities can be used to selectively sieve H2 gas from a H2 -CH4 mixture at higher yields that pore-10. On observing Figure 3a, it can be seen that the H2 permenace does not exhibit a linear increase. There is only a small increase in permeance from pore-10 to pore-14. Then from, pore-16 to pore-20 there is an abrupt increase in the permeance. After pore-20, the permeance continues to increase but at a smaller rate. This phenomenon can be explained as follows. Pores-10, 12 and 14 are small in size and hence, both the pore geometry and the presences of CH4 molecules effectively block the H2 molecules from permeating. However, as the pore size increases, there is enough space for the H2 molecules to permeate despite the blocking by methane. Given this explanation, it would be expected that as the pore number increases, the H2 permeance would increase at an even greater rate. However, it should be noted that as the pore number reaches a critical point (in our simulation it is pore-24) the area is so large



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that more CH4 molecules are able to permeate through the pore. This produces additional blocking, not present in pores-16 to 20, which hinders the H2 permeance. Based on the above discussion, pore-20 with an elliptical geometry would be the pore that would behave as the most efficient H2 separator. This is because, after pore-20 the CH4 permeance starts to increase, reducing the selectivity. Although Figure 3a has been plotted for elliptical geometries, a similar is expected to be shown the above pore numbers were made in other selective geometries as well. Thus, pore-20 designed at any selective geometry would be exhibit the above behavior, and will be the most ideal pore for gas separation. The experimental implementation of these specific pore geometries is certainly challenging, especially given the fact that not many previous experimental studies have looked into the creation of non-circular pores. However, we propose an approach, based on previous experimental studies. Russo et al. demonstrated an atom-by-atom removal technique to generate pores in graphene. 34 They were able to obtain pores with a radius of 3 ˚ A, which is sufficient for H2 -CH4 separation. The method involved a nucleation phase where nucleation sites, with 1–2 carbon atoms removed, were generated by bombardment with 3 keV Argon ions. Subsequently, by application of a uniform defocused electron beam of 80 keV, the nanopores nucleation sites were opened using atom-by-atom removal technique. This method allows for creation of pores with atomic level precision, which would be very beneficial in creating pores with non-circular geometries. We hypothesize that by creating pores using this atom-by-atom removal technique, it could be possible to generated highly elongated or jagged geometries required for selectivity. This is because, the removal of atoms one at a time would allow for a greater control over the shape or geometry of the pore. However, this technique will require refinement so that geometry induced selectivity in NPG can be experimentally demonstrated.


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Conclusion We studied the behavior of H2 and CH4 permeance with respect in pore geometry, specifically the eccentricity. It was found that variation in pore eccentricity of NPG significantly affects the gas permeance. It was expected that the gas permeance will decrease as the eccentricity increase. However, this was not found to be the case as three geometries with eccentricities 0.703635, 0.733573 and 0.906007 exhibited anomalously high permeances. This was explained by introducing the concept of pore “jaggedness”. It was found that the three anomalous points all had very low jaggedness values, which accounted for their anomalous behavior. In addition to this, the adsorption layer was also found to change significantly with geometry. The concentration of the CH4 and H2 molecules in the adsorption layer was greater if the permeance of that pore geometry was less. Also, it was found that the pores with eccentricities 0.719692, 0.742729 and 0.906007 exhibit high H2 selectivity. Thus, H2 selectivity was observed for pores as large as pore-18. Furthermore, it was showed that this behavior extends to pores with pore numbers 14, 16, 20 and 24 as well. Thus, geometry induced selectivity is observed in NPG. This is especially interesting given the fact that previous studies, which did not look into the geometry factor, have found that pores above pore-10 do not exhibit selectivity. However, this study shows that it is possible to obtain hydrogen selective pores at much larger pore numbers. Furthermore, these pores exhibit 9 times the hydrogen permeance (or yield) of than pore-10. Thus, by considering geometric effects, highly efficient H2 sieves can be obtained. We also proposed that the atom-by-atom growth of nanopores described by Russo et al. as a suitable method that could be used to generate the pore geometries necessary for selectivity.



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Supporting Information Available The images of pore-10 to 30 used in the study, as well as the method of calculation of gas permeance are included. A description of the ellipse fitting and jaggedness calculation algorithms is also included. This material is available free of charge via the Internet at http://pubs.acs.org/.

Acknowledgement The authors thank Dr. M. A. Lourdu Antony Raj, Head of Chemical Engineering Department R. V. College of Engineering, for providing us with the computational facilities to carry out this work. They also thank Dr. Vinod Kallur and Dr. Hemanth K. Billihali for providing their valuable inputs and useful discussions. The authors declare than no financial support from any organization or institute was provided to carry out this work.

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CH4 Gas Separation by Variation in Pore Geometry of Nanoporous

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