CH4 and

Article pubs.acs.org/JPCC

Porous Carbon Nanotube Membranes for Separation of H2/CH4 and CO2/CH4 Mixtures Benjamin J. Bucior,† De-Li Chen,†,‡ Jinchen Liu,†,‡ and J. Karl Johnson*,†,‡ †

Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States National Energy Technology Laboratory, Pittsburgh, Pennsylvania 15236, United States

‡

ABSTRACT: Porous carbon nanotubes, which are single-walled carbon nanotubes having tailored pores in their sidewalls, are proposed as potential membrane materials for separating gas mixtures with high selectivity and high permeance. We present both quantum mechanical calculations and classical statistical mechanical calculations with empirical potentials showing that porous carbon nanotubes having the correct pore size can very effectively separate mixtures of H2/CH4 and also of CO2/CH4. In each of these mixtures, CH4 is effectively prevented from entering the pore due to size exclusion. These porous carbon nanotubes could be used in mixed matrix polymer membranes to increase both the permeance and the selectivity for targeted gas mixtures.

I. INTRODUCTION Membranes offer the potential to separate gas mixtures with high efficiency. However, the performance of polymeric membranes is limited by a fundamental trade-off between membrane selectivity and permeability. This trade-off is sometimes referred to as the Robeson upper bound.1−3 Designing new membrane materials that are able to transcend this upper bound, offering both high selectivity and high permeability, is a major focus of research in membrane science today. Moreover, developing high-flux/high-selectivity membranes for separating mixtures of gases containing CO2 has important implications for carbon capture and sequestration. Membranes containing carbon nanotubes (CNTs) have the potential to significantly exceed Robeson’s upper bound because the interior of the CNTs is atomically smooth, which results in nearly specular reflections as gas molecules collide with the nanotube walls.4 Indeed, experiments have shown that transport of fluids through CNT membranes is extremely rapid.5−7 However, CNTs with opened ends (i.e., having their end-caps etched off) typically have diameters that are not small enough to be used for size selectivity for gas phase molecules. Additionally, there is currently no way to synthesize CNTs of a given diameter, so that a sample of CNTs includes nanotubes having a range of different diameters. Recent theoretical work by Jiang et al. has proposed porous graphene8 as a promising material for highly selective membranes. Porous graphene can be thought of as the ultimate membrane since it has a thickness of only one layer of atoms. Jiang et al. have demonstrated that a graphene membrane having a tailored pore has extremely high selectivity for H2 over CH4.8 They constructed pores in graphene sheets by removing two adjacent rings from the sheet, creating a pore with eight carbons having dangling bonds. Four nitrogen molecules were © 2012 American Chemical Society

then substituted for unsaturated carbons at the most narrow part of the pore, and the remaining four dangling bonds were terminated with hydrogen atoms. Similarly, Hauser et al. have used simulations to design nanopores in graphene9−11 for separating the isotopes helium-3 and helium-4 and for separating CH4 from other small gases. Du et al. designed porous graphene membranes having different pore sizes for separating H2 from N2.12 They found that the smallest nanopore exhibited size-selectivity, but larger nanopores favored N2 transport over H2 due to stronger adsorption of N2 to the graphene surface. These porous graphene structures are idealized membranes that would prove difficult to incorporate into current membrane technologies; they would be too thin and fragile for practical use. Moreover, they are not readily adaptable for use in mixed matrix membranes. However, CNTs have been used to increase flux in mixed matrix polymer membranes.7 We propose to apply the ideas for tailored pores in graphene to construct a porous carbon nanotube (PCNT) combining high permeability and high selectivity for gas separations by generating pores on the wall of a CNT. The structure of our proposed PCNT is shown in Figure 1. The membrane is generated by introducing specifically designed holes in the sidewall of a (19,0) single-walled CNT. For each pore, two adjacent six-membered carbon rings are removed from the nanotube wall. Four of the resulting dangling bonds were saturated with H atoms; nitrogen atoms were substituted for the four remaining unsaturated carbons.8 The size of this pore facilitates separations based on size-exclusion in graphene, as shown by Received: October 3, 2012 Revised: November 20, 2012 Published: November 21, 2012 25904

dx.doi.org/10.1021/jp3098022 | J. Phys. Chem. C 2012, 116, 25904−25910

The Journal of Physical Chemistry C

Article

illustrated in Figure 1. We used the Perdew−Burke−Ernzerhof (PBE)14 generalized gradient approximation functional in our DFT calculations. All DFT calculations were performed with the Vienna ab initio simulation package (VASP).15−18 The PBE functional was used to optimize the PCNT structure. van der Waals (vdW) interactions between the gas molecules used in this study and the PCNT are expected to be very important. We have therefore employed dispersion-corrected DFT methods and have compared the results with and without vdW corrections. There are several different methods to include vdW interactions within DFT. Among these, the DFT-D2 method developed by Grimme19 provides a simple and very efficient way to approximately account for the long-range vdW interactions. In our study, we used the DFT-D2 approach with the PBE functional (denoted PBE-D2 herein) to calculate the potential energies of gas molecules entering the pores of the PCNT. The potential energy barriers for gases traversing the PCNT pore were computed from DFT by specifying a total of 16 points along a vector starting from the PCNT axis and passing through the center of the pore (equidistant from the 4 N atoms making up a pore, as shown in Figure 1). The center of mass of the gas molecules (CH4 and CO2) was fixed at each of these points, and all other atomic positions were allowed to relax to a local minimum at each point. The distance from the center of mass of the gas molecule to the center of the pore is plotted as the x axis in Figures 3 and 4; positive and negative values indicate exterior and interior positions, respectively. The spacing between points was 1 Å, except when the gas molecule was within ±2 Å of the pore, where a spacing of 0.5 Å was used. The potential energy barriers computed from classical potentials were computed in a similar fashion, but with a point spacing of 0.2 Å. Another difference between the DFT and classical calculations is that the gas molecules were treated as rigid in the classical potential. This means that the orientation of CO2 was held fixed (perpendicular to the plane of the pore) during the optimization of the atom positions in the PCNT. We also computed the potential barrier with classical potentials using a rigid PCNT model, where no relaxation was allowed. Molecular dynamics simulations were carried out in a simulation cell containing a single periodic PCNT of length 3.834 nm. The size of the supercell used in the MD simulations was 3.4 × 3.4 × 3.834 nm. The effective free volume of the box, excluding the volume occupied by the PCNT, was about 30 nm3; this volume was used to mimic the bulk gas region in contact with a model PCNT membrane. All MD calculations were carried out with the Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) software package.20 Resultant trajectories were visualized with the Visual Molecular Dynamics (VMD) software.21,22 The Lennard-Jones (LJ) 12−6 potential was used to describe fluid−PCNT and fluid−fluid interactions. CH 4 and H2 were modeled as single-site molecules. Our simulations with CO2 included the chargequadrupole interactions between framework and fluid atoms. CO2 was modeled as a rigid three-site molecule with LJ interactions and partial point charges located at the center of each site. The atomic charges for each atom in the PCNT, required for the classical potential calculations, were fitted to the electrostatic potential (ESP) computed from DFT by employing the fitting algorithm developed by Chen et al.23 During the ESP fitting, Ewald summation was used to compute the long-range

Figure 1. PCNT model based on a (19,0) zigzag nanotube. Dark blue represents nitrogen; cyan, carbon; and white, hydrogen.

Jiang et al.8 Our hypothesis is that molecules with a larger radius, such as CH4, will be blocked from entering the pore due to size-exclusion. Smaller, more linear molecules, such as H2 and CO2, should be able to pass through the pore more easily. We will analyze the ability of the PCNT membrane to separate H2/CH4 and CO2/CH4 mixtures. We note that Jiang et al. have independently and simultaneously studied a very similar system of windowed carbon nanotubes for CO2/CH4 separation.13 There is currently no way to synthesize PCNTs having precisely tailored pores. Moreover, if the nanotubes are open at the ends, the size-selectivity that comes from having tailored pores would be eliminated. Notwithstanding the synthetic challenges, our purpose is to investigate the potential for separating gas mixtures using a hypothetical membrane consisting of single-walled CNTs having intact caps to prevent gas molecules entering the ends of the tubes, yet having tailored pores in the nanotube side-walls. These PCNTs might be embedded into a polymer to form a mixed matrix membrane. Additionally, if the PCNTs protruded through the polymer, then gas molecules could enter the pores of the PCNTs and be readily transported across the polymer barrier. While such an idealized membrane does not currently exist, our purpose is to study the performance of this system as a way to assess whether effort in synthesizing PCNT membranes would be, in principle, worthwhile.

II. COMPUTATIONAL DETAILS The performance of an idealized PCNT membrane was evaluated for separating gas mixtures of either H2/CH4 or CO2/CH4 using both quantum mechanical and classical statistical mechanical simulation techniques. Periodic plane wave density functional theory (DFT) calculations were employed to optimize the structure of the PCNT and compute the energy barriers for gases entering the PCNT. Classical simulations with model potentials were also used to compute gas entry barriers and were compared with the DFT calculations to assess the accuracy of the classical potentials. Classical molecular dynamics (MD) simulations were carried out to simulate separation of gas mixtures. The porous carbon nanotube model was constructed from a (19,0) zigzag nanotube containing four unit cells. The PCNT supercell used in DFT calculations was tetragonal with dimensions 3.00 × 3.00 × 1.704 nm. Only the Γ-point was used to sample the Brillouin zone; a plane wave cutoff energy of 500 eV was used. Three nitrogen-functionalized pores were constructed on the surface of the (19,0) nanotube supercell, as 25905



Article

Nitrogen was represented as a carbon because the REBO potential only contains parameters for carbon and hydrogen. However, this substitution should not drastically change the physical properties of the model PCNT. One computational study showed that nitrogen doping in a graphene sheet did not have a substantial impact on the elastic modulus, as long as there were no nitrogen−nitrogen bonds.32 In our PCNT structure, nitrogen atoms at the pore are bonded to carbon, not directly to another nitrogen, so this is indeed the case. Comparison of potential energy surfaces from classical and DFT calculations also indicate that this substitution is justified. The selectivity of the PCNT was determined by running dynamic simulations of the PCNT in fluid mixtures. All fluid molecules were loaded in the volume outside of the PCNT. Then, a nonequilibrium molecular dynamics simulation was run and fluid molecules inside the PCNT were counted as a function of time. This determined the conductance through the pore wall. The MD simulations were run isochorically and isothermally with periodic boundary conditions. The system temperature was maintained at 300 K using the Nosé−Hoover chains thermostat33,34 with 10 chains. A time step of 1 fs was used for the MD simulations.

electrostatic energy, and the cutoff radius was set to 10 Å. The charges computed from the ESP fitting procedure are graphically represented in Figure 2.

Figure 2. Charges on the atoms of the PCNT as computed from the electrostatic potential fitting approach of Chen et al.23

III. RESULTS AND DISCUSSION Our potential energy surface calculations characterize the energetics of each fluid molecule passing through the pore into the PCNT using PBE, PBE-D2, and classical potentials with rigid and flexible PCNTs. There is essentially no barrier for H2 entering the pore, as shown previously for graphene.8 For CH4, all four calculation methods indicate an energy barrier at the pore wall for entry into the PCNT. This barrier suggests that CH4 could be separated from smaller molecules via sizeexclusion using a PCNT with this pore size. PBE-D2 indicates an energy barrier of 0.26 eV (from minimum energy outside the pore to the highest energy at the pore center) for CH4 entering the pore. The classical flexible model qualitatively agrees with the PBE-D2 model with an energy barrier of 0.16 eV. In contrast, the classical rigid and PBE models yield much larger energy barriers of 0.43 and 0.49 eV, respectively. The kinetic diameter of CO2 is smaller than that of CH4.35 Therefore, we would expect the energy barrier for CO2 to be less than CH4. In fact, the potential energy surfaces computed from PBE-D2 and rigid and flexible classical potentials showed no energy barrier for CO2 moving from the outside of the PCNT to the center of the mouth of the pore, as can be seen from Figure 4. There is a barrier for CO2 moving from the center of the pore mouth to the interior of the PCNT; however, the increase in energy in moving from the pore mouth to the center (axis) of the PCNT is smaller than the decrease in energy for CO2 moving from the exterior to the center of the pore mouth. Moreover, entropy will favor CO2 molecules moving to the interior of the PCNT since it is highly constricted while residing at the pore mouth. DFT calculations showed that the favorable orientation for CO2 moving through the pore is perpendicular to the surface. We observed this preferred orientation in our nonequilibrium MD calculations as well. This can be seen in Figure 5, where the trajectory of a single CO2 molecule is shown as it moves from the outside of the PCNT and rotates to an orientation that is perpendicular to the PCNT axis as it enters the pore. The mechanism of CO2 entry through the pore, as shown in Figure 5, highlights the importance of adsorption in this system. Analysis of the MD trajectories shows that CO2 typically

The LJ potential interaction parameters employed in our simulations are reported in Table 1. Cross-interaction potential Table 1. Lennard-Jones Potential Parameters for Adsorbate Molecules and PCNT Atoms adsorbate/PCNT

ref

ε/k (K)

σ (Å)

q (e)

H2 CH4 C (in CO2) O (in CO2) C (in PCNT) H (in PCNT) N (in PCNT)

25 26 27 27 24 24 24

34.20 148.20 27.00 79.00 28.00 7.65 38.95

2.960 3.812 2.800 3.050 3.400 2.846 3.263

+0.7 −0.35 DFTa DFT DFT

PCNT charges varied by atom, as computed from fitting the electrostatic potential. a

parameters were computed from the Lorentz−Berthelot combining rules. The fluid−fluid and fluid−PCNT intermolecular LJ potentials were truncated at 16.9 Å. Fluid−fluid and solid−fluid electrostatic interactions were calculated using the Ewald summation. The LJ parameters for the PCNT atoms were determined from the DREIDING force field.24 We have used both rigid and flexible structures for the PCNT in order to assess the impact of membrane flexibility on the selectivity and kinetics of the separations process. In the rigid model, the PCNT atoms remained spatially fixed at their initial coordinates throughout the MD simulation. As such, relationships between PCNT atoms, such as bond lengths and bond angles, remained constant, and no interactions were calculated between atoms within the PCNT. In the flexible model, interactions between PCNT atoms were computed using the reactive empirical bond order (REBO) potential.28 This potential was selected for its applicability in previous studies of carbon nanotubes.29−31 A few PCNT atoms were anchored to their initial coordinates with Hookean springs to prevent rotation or translation of the PCNT for the flexible model. Using the REBO potential, carbon and hydrogen atoms in the PCNT were represented as their respective atom types. 25906



Article

to the PCNT external surface, with the CO2 roughly perpendicular to the PCNT surface normal, in the neighborhood of the pore. As CO2 approaches the pore, it changes to an orientation that is approximately parallel to the surface normal, possibly aided by electrostatic interactions between the charges around the PCNT pore (Figure 2) and the quadrupole of the CO2 molecule. We observe from our MD simulations that, when CO2 traverses the pore, it often spends several femtoseconds located at the center of the pore before finally moving through the pore to the inside of the PCNT. This dynamic picture is consistent with the potential energy surface shown in Figure 4, where there is a clear minimum when CO2 is located at the center of the pore entrance. The electrostatic interactions are favorable here since the partial positive charge on the carbon of CO2 can interact with the partial negative charges on the nitrogens of the PCNT pores, shown in Figure 2. In addition to indicating that PCNTs can function as molecular sieves for separating gas mixtures, the barrier calculations gave a few additional insights. For both the CH4 and CO2 systems, there is a significant difference between potential energy surfaces from the PBE and PBE-D2 calculations. For example, for CH4, PBE-D2 gives an energy barrier of about 0.26 eV, whereas the energy barrier from PBE calculations is much larger at 0.49 eV. Likewise, the PBE calculations indicate a significant barrier for CO2 entering the PCNT, followed by an attractive potential well at the center of the pore mouth that is due to favorable electrostatic interactions, and then an increase in energy as CO2 moves to the nanotube axis, where it is unbound relative to the external state. Thus, the van der Waals correction has a large contribution to the potential energy surfaces for both CH4 and CO2, dramatically reducing the energy barrier for entry through the pore in both cases. There is good agreement between the PBE-D2 and classical flexible models for the potential barriers of both CH4 and CO2. This indicates that the classical flexible model can serve as a good approximation for DFT to capture many of the same features in this system. This is important in allowing the simulation of the PCNT in a dynamic system, which require nanosecond simulation time scales impractical for DFT but readily accessible through classical MD simulations. The most important gas−PCNT interaction in this simulation involves fluid molecules entering the pore. The good agreement between the PBE-D2 and classical flexible energy barriers indicates that the dynamics of fluids entering the PCNT would be similar whether computed from PBE-D2 or classical MD with a flexible PCNT. The barrier computed from the classical rigid PCNT model for CH4 entry is significantly larger than that predicted by PBE-D2 or the classical flexible model. This indicates that the dynamics of a system modeled with rigid potentials will be inaccurate for simulations involving CH4. However, we see from Figure 4 that the classical flexible and rigid models give almost identical results for CO2. This demonstrates that the size of the pore relative to the size of the molecule traversing the pore is critical in determining whether rigid models may reasonably be used. We note that the binding energy of CO2 to the center of the pore entrance computed from the rigid potential model is in better agreement with PBED2 calculations than that computed from the flexible potential model (see Figure 4). This is a fortuitous result that is due to the flexible potential giving a relaxed configuration of the PCNT (without CO2) having the N and H atoms of the pore

Figure 3. Potential energy barriers for CH4 entering the PCNT computed from DFT and classical model potentials. Black squares are from PBE, red circles are from PBE-D2 (van der Waals corrected), green diamonds are from classical potentials with a rigid PCNT, and blue triangles are from classical potentials with a flexible PCNT. The pore center (zero on the x-axis) is identified as the point that is equidistant from the four N atoms making up a pore and located in the plane containing these N atoms (see Figure 1).

Figure 4. Potential energy barriers for CO2 entering the PCNT computed from DFT and classical potential models. Black squares are from PBE, red circles are from PBE-D2 (van der Waals corrected), green diamonds are from classical potentials with a rigid PCNT, and blue triangles are from classical potentials with a flexible PCNT.

Figure 5. Trajectory of a single CO2 molecule as it approaches and enters the pore of a PCNT from a molecular dynamics simulation. Note that the CO2 rotates to an orientation that is perpendicular to the PCNT axis as it enters the pore.

adsorbs to the exterior surface before entering the PCNT pore. A CO2 molecule normally begins pore entry by being adsorbed 25907



Article

separating H2 from CH4. We note that there is a small difference in the kinetics of H2 entry for the rigid and flexible PCNTs. As seen from Figure 7, the steady-state loading for the flexible PCNT was reached in about 100 ps, whereas the rigid nanotube required about 300 ps. As expected, the equilibrium loadings for the flexible and rigid PCNTs are essentially the same. We note that the gas phase (outside the PCNT) contained about 100 molecules of H2 at the end of the simulation. We next simulated a 1:1 CO2:CH4 mixture with 128 molecules of each initially in the gas phase. This corresponds to an initial pressure of about 200 bar, as computed from the equations of state for CO238 and CH4.37 As with the H2/CH4 mixture, both the rigid and flexible PCNTs exhibited an effectively infinite selectivity for CO2 over CH4. The starting and ending configurations for this system are shown in Figure 8. The dynamics of CO2 entry into the PCNTs is plotted in

pointing slightly outward compared with the coordinates of the rigid model. We used nonequilibrium MD simulations to evaluate separations of gas mixtures at room temperature using the PCNT membrane. Using both the rigid and flexible PCNT models, we measured the number of each type of gas molecule inside the PCNT as a function of time starting from a configuration of a mixture of either H2/CH4 or CO2/CH4 in the bulk gas phase outside the PCNT. We first studied a 1:1 H2:CH4 mixture, 128 molecules of each, initially placed in the space outside the PCNT. The effective initial pressure of the gas in the bulk region was about 340 bar, as computed from the equations of state for H236 and CH4,37 and assuming an ideal solution. The initial configuration for the H2/CH4 mixture is shown in the left-hand panel of Figure 6. During the course of the MD simulation, H2

Figure 6. Initial (left) and final (right) snapshots for the H2/CH4 mixture simulation. The final configuration was obtained after 500 ps. The cyan, dark blue, and white balls on the PCNT represent carbon, nitrogen, and hydrogen atoms, respectively, while the white and pink balls represent H2 and CH4, respectively.

Figure 8. Initial (left) and final (right) snapshots for the CO2/CH4 mixture simulation. The cyan, dark blue, red, and white balls represent carbon, nitrogen, oxygen, and hydrogen atoms, respectively, while the pink balls represent CH4.

molecules were observed to rapidly enter the PCNT, while none of the CH4 molecules entered. The ending configuration, after the simulation reached an apparent steady-state, is shown in the right-hand panel of Figure 6. The time-dependent conductance of gas molecules into the PCNT is plotted in Figure 7. The dynamics for the rigid PCNT is shown in the left

Figure 9. Conductance of CO2 into the PCNT for rigid and flexible PCNT models from an equimolar mixture of CO2 and CH4. The conductance of CH4 was zero for both the flexible and rigid simulations. Note that the CO2 reached steady-state in the flexible PCNT within about 1 ns, whereas the rigid PCNT required about 8 ns to reach a steady-state loading.

Figure 7. Conductance of H2 and CH4 into the PCNT for rigid (left) and flexible (right) PCNT models from an equimolar mixture of H2 and CH4.

panel, while the flexible PCNT simulation is shown on the right. Our short-time simulations predict that the selectivity of H2 over CH4 is infinite, both for the rigid and flexible PCNT. This is somewhat unexpected, given that the barrier for CH4 entry into the flexible PCNT is significantly smaller than for the rigid tube. Over a very long time we do expect to see some CH4 entering the PCNT, but this is a rare event for the time scales accessible through MD simulations. Hence, our simulations predict that a PCNT membrane should be effective for

Figure 9. The CH4 conductance is not shown in this figure because it is identically zero. We note that the simulations took a much longer time to reach equilibration than for the H2/CH4 mixture. The steady-state loading for CO2 in the flexible nanotube was reached after about 1 ns, about 10 times longer than for H2. More strikingly, the time to reach steady-state for CO2 entering the rigid PCNT is about 8 ns or roughly a factor 25908



Article

interactions are very important for obtaining accurate estimates of the potential barrier for these gases crossing the pore. Furthermore, classical potential models that allow for nanotube flexibility are in better agreement with the DFT calculations than calculations that assume a rigid nanotube framework. This is especially true for CH4, where the size of the molecule is essentially the same as the pore. However, differences in the dynamics can be observed even for H2, which has essentially no barrier for crossing the pore entrance.

of 27 longer than for H2 in the rigid PCNT. As expected, the equilibrium loading of CO2 in each PCNT is essentially identical. The difference in the kinetics of CO2 entry between the rigid and flexible PCNTs is especially surprising because their potential energy curves appear to be almost identical in Figure 4. The potential well at the center of the pore is about 0.02 eV lower in energy for the rigid PCNT compared with the flexible PCNT. This small difference in well depth may indicate that CO2 molecules spend more time at the pore mouth in the rigid model, hence resulting in a slower flux of molecules through the pore. Another possibility is that the dynamic motion of the flexible nanotube provides a concerted kinetic effect not captured in the simple potential barrier calculations. Investigation of this effect is beyond the scope of this work. In practice, the differences in kinetics would not be measurable on macroscopic time scales. It is well-known that gases readily adsorb on the external and internal surfaces of carbon nanotubes. We observe that both CO2 and CH4 adsorb on the external surface of the PCNT, forming a ring-like layer on the external surface. Similarly, many of the CO2 molecules inside the PCNT preferentially adsorb to the inside surface of the PCNT. However, because of the high loading at steady-state, an axial phase is also present. After we completed our calculations, we became aware of the work of Hauser and Schwerdtfeger,11 who computed barrier heights for CH4, N2, CO2, O2, and H2 through two different pores in cluster models of graphene. Their work is similar to ours in that they used van der Waals corrected DFT methods to compute the barriers for gas entry, including the effects of relaxation of the graphene framework atoms. The two pores they used in their work were both smaller than the pore we examined in our PCNT. Their pore B is closest in size to our pore, the difference being that two of the N atoms on one side of the pore shown in Figure 1 were replaced by C atoms and terminated with H atoms. The results of their calculations appear to be consistent with ours. For example, they find that CO2 is bound to the center of pore B by 0.22 eV,11 which compares very well to the value of 0.33 eV we computed for the larger pore used in our work (see Figure 4). They also ascribe the binding of CO2 to the pore as being mainly due to electrostatic interactions, as we have. They computed barriers for the case where the graphene framework was held rigid, as we did with our classical models, and they found a dramatic reduction in the barrier for CH4 entry, consistent with our classical calculations. For example, they reported that the barrier for CH4 entry into pore B was reduced from 0.21 to 0.02 eV when the graphene structure was allowed to relax. This is similar to the values we obtained from classical potential calculations of 0.32 and 0.05 eV for rigid and flexible PCNTs, respectively. However, we note that our barrier for CH4 entry computed from DFT (Figure 4) is significantly larger than the 0.02 eV barrier they reported.11 The larger reduction in barrier might be due to the increased flexibility of the cluster model of graphene they used.

■

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS We thank De-en Jiang for many helpful discussions. This work was partially supported by a grant from NSF-CBET 0755937. B.J.B. was supported through an NSF REU site grant, EEC1005048. Calculations were performed at the University of Pittsburgh Center for Simulation and Modeling. This technical effort was performed in support of the National Energy Technology Laboratory’s ongoing research in CO2 capture under the RES contract DE-FE0004000. This project was funded by the Department of Energy, National Energy Technology Laboratory, an agency of the United States Government, through a support contract with URS Energy & Construction, Inc. Neither the United States Government nor any agency thereof, nor any of their employees, nor URS Energy & Construction, Inc., nor any of their employees, makes any warranty, expressed or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States Government or any agency thereof. The views and opinions of the authors expressed herein do not necessarily state or reflect those of the United States Government or any agency thereof.

■

REFERENCES

(1) Robeson, L. M. J. Membr. Sci. 1991, 62, 165−185. (2) Robeson, L. M. J. Membr. Sci. 2008, 320, 390−400. (3) Freeman, B. D. Macromolecules 1999, 32, 375−380. (4) Skoulidas, A. I.; Ackerman, D. M.; Johnson, J. K.; Sholl, D. S. Phys. Rev. Lett. 2002, 89, 185901. (5) Majumder, M.; Chopra, N.; Andrews, R.; Hinds, B. J. Nature 2005, 438, 44−44. (6) Holt, J. K.; Park, H. G.; Wang, Y.; Stadermann, M.; Artyukhin, A. B.; Grigoropoulos, C. P.; Noy, A.; Bakajin, O. Science 2006, 312, 1034−1037. (7) Kim, S.; Jinschek, J. R.; Chen, H.; Sholl, D. S.; Marand, E. Nano Lett. 2007, 7, 2806−2811. (8) Jiang, D. E.; Cooper, V. R.; Dai, S. Nano Lett. 2009, 9, 4019− 4024. (9) Hauser, A. W.; Schwerdtfeger, P. J. Phys. Chem. Lett. 2012, 3, 209−213. (10) Hauser, A. W.; Schrier, J.; Schwerdtfeger, P. J. Phys. Chem. C 2012, 116, 10819−10827.

IV. CONCLUSIONS Both quantum mechanical and classical potential model simulations provide proof-in-principle that porous carbon nanotubes can be used to efficiently separate mixtures of H2/ CH4 or CO2/CH4. In each case, CH4 is effectively blocked from entering the pore due to size exclusion. Our simulations, while carried out for equimolar mixtures, should be essentially independent of the gas phase composition. van der Waals 25909



Article

(11) Hauser, A. W.; Schwerdtfeger, P. Phys. Chem. Chem. Phys. 2012, 14, 13292−13298. (12) Du, H.; Li, J.; Zhang, J.; Su, G.; Li, X.; Zhao, Y. J. Phys. Chem. C 2011, 115, 23261−23266. (13) Liu, H.; Cooper, V. R.; Dai, S.; Jiang, D. E. J. Phys. Chem. Lett. 2012, 3, 3343−3347. (14) Perdew, J. P.; Burke, K.; Ernzerhof, M. Phys. Rev. Lett. 1996, 77, 3865−3868. (15) Kresse, G.; Hafner, J. Phys. Rev. B 1993, 47, 558−561. (16) Kresse, G.; Hafner, J. Phys. Rev. B 1994, 49, 14251−14269. (17) Kresse, G.; Furthmüller, J. Phys. Rev. B 1996, 54, 11169−11186. (18) Kresse, G.; Furthmüller, J. Comput. Mater. Sci. 1996, 6, 15−50. (19) Grimme, S. J. Comput. Chem. 2006, 27, 1787−1799. (20) Plimpton, S. J. Comput. Phys. 1995, 117, 1−19. (21) Humphrey, W.; Dalke, A.; Schulten, K. J. Mol. Graphics 1996, 14, 33−38. (22) Stone, J. An Efficient Library for Parallel Ray Tracing and Animation. M.Sc. Thesis, University of Missouri-Rolla, 1998. (23) Chen, D.-L.; Stern, A. C.; Space, B.; Johnson, J. K. J. Phys. Chem. A 2010, 114, 10225−10233. (24) Mayo, S. L.; Olafson, B. D.; Goddard, W. A., III. J. Phys. Chem. 1990, 94, 8897−8909. (25) Buch, V. J. Chem. Phys. 1994, 100, 7610−7629. (26) Jiang, S. Y.; Gubbins, K. E.; Zollweg, J. A. Mol. Phys. 1993, 80, 103−116. (27) Potoff, J. J.; Siepmann, J. I. AIChE J. 2001, 47, 1676−1682. (28) Brenner, D. W.; Shenderova, O. A.; Harrison, J. A.; Stuart, S.; Ni, B.; Sinnott, S. B. J. Phys.: Condens. Matter 2002, 14, 783−802. (29) Wang, J.; Kemper, T.; Liang, T.; Sinnott, S. B. Carbon 2012, 50, 968−976. (30) Heo, S.; Sinnott, S. B. J. Appl. Phys. 2007, 102, 064307. (31) Lee, K. H.; Sinnott, S. B. J. Phys. Chem. B 2004, 108, 9861− 9870. (32) Okamoto, S.; Ito, A. Eng. Lett. 2012, 20, 169−175. (33) Martyna, G. J.; Klein, M. L.; Tuckerman, M. J. Chem. Phys. 1992, 97, 2635−2643. (34) Kamberaj, H.; Low, R. J.; Neal, M. P. J. Chem. Phys. 2005, 122, 224114. (35) Shelekhin, A. B.; Dixon, A. G.; Ma, Y. H. J. Membr. Sci. 1992, 75, 233−244. (36) Leachman, J. W.; Jacobsen, R. T.; Penoncello, S. G.; Lemmon, E. W. J. Phys. Chem. Ref. Data 2009, 38, 721−748. (37) Setzmann, U.; Wagner, W. J. Phys. Chem. Ref. Data 1991, 20, 1061−1151. (38) Span, R.; Wagner, W. J. Phys. Chem. Ref. Data 1996, 25, 1509− 1596.

25910


CH4 and

Recommend Documents