Nitrogen and Oxygen Mixture Adsorption on Carbon Nanotube

On a small isolated hexagonal bundle with an external surface, adsorption at a subcritical temperature is of type II. With increasing pressure, nitrog...
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Nitrogen and Oxygen Mixture Adsorption on Carbon Nanotube Bundles from Molecular Simulation Jianwen Jiang* and Stanley I. Sandler Center for Molecular and Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received March 24, 2004. In Final Form: September 7, 2004 The adsorption of a nitrogen and oxygen mixture (air) on two types of single-walled carbon nanotube bundles at both sub- and supercritical temperatures is studied using grand canonical Monte Carlo molecular simulation. On an infinite periodic hexagonal bundle without an external surface, adsorption at a subcritical temperature is of type I. With increasing pressure, nitrogen adsorption first increases and then decreases until saturation; oxygen adsorption continues increasing, displacing nitrogen, until saturation. Both nitrogen and oxygen first form annuli inside the nanotubes, then with increased coverage they occupy the nanotube centers, and at the highest coverage some oxygen also adsorbs in the interstitial channels between the nanotubes. The selectivity of nitrogen over oxygen decreases with increasing pressure and reaches a constant near saturation. Adsorption at a supercritical temperature is also of type I, with both nitrogen and oxygen adsorption increasing with increasing pressure, though the selectivity of nitrogen to oxygen first increases slightly and then decreases with increasing pressure. On a small isolated hexagonal bundle with an external surface, adsorption at a subcritical temperature is of type II. With increasing pressure, nitrogen adsorption first increases, then decreases, and finally increases again due to wetting by liquid air, while oxygen adsorption increases continually. Both nitrogen and oxygen adsorb first at the internal annuli and at the grooves, and with increasing pressure, they then adsorb at the ridges and at the nanotube centers; at higher pressures, only oxygen adsorbs in the interstitial channels, and multilayer adsorption and wetting occur on the external surface as the bulk phase approaches saturation. The selectivity, like that of subcritical temperature adsorption on the infinite periodic bundle, decreases with increasing pressure and reaches a constant upon wetting. Adsorption at a supercritical temperature is of type I, with both nitrogen and oxygen adsorption increasing with increasing pressure. The selectivity of nitrogen to oxygen, like that of supercritical temperature adsorption on the infinite periodic bundle, first increases slightly and then decreases with increasing pressure. These results indicate that the adsorption selectivity strongly depends on temperature but only weakly depends on the type of the bundle and that a nitrogen-oxygen mixture (air) might be separated by competitive adsorption on the carbon nanotube bundles.

I. Introduction Carbon nanotubes have many fascinating properties.1,2 Their well-defined structures with hollow nanosize interiors suggest their potential use as sorbents for gas adsorption and separation. The internal and external adsorption sites of the curved nanotubes enhance surface proximity for adsorbates and hence influence the extent of adsorption.3 A large number of experimental studies have been carried out thus far on the adsorption of nitrogen,4-11 oxygen,9 carbon dioxide,12 argon,13 krypton,14 xenon,15,16 methane,14,17 and butane18 on various carbon nanotubes, single- or multiwalled, closed- or open-ended. In addition, there are many studies on the adsorption of * Corresponding author. E-mail: [email protected]. Phone: 302-831-6953. Fax: 302-831-1048. (1) Ajayan, P. M.; Zhou, O. Z. Applications of carbon nanotubes. Carbon Nanotubes; Springer-Verlag (Berlin): Berlin, 2001; Vol. 80, p 391. (2) Baughman, R. H.; Zakhidov, A. A.; de Heer, W. A. Science 2002, 297, 787. (3) Calbi, M. M.; Cole, M. W.; Gatica, S. M.; Bojan, M. J.; Stan, G. Rev. Mod. Phys. 2001, 73, 857. (4) Ciuparu, D.; Chen, Y.; Lim, S.; Haller, G. L.; Pfefferle, L. J. Phys. Chem. B 2004, 108, 503. (5) Paredes, J. I.; Suarez-Garcia, F.; Villar-Rodil, S.; Martinez-Alonso, A.; Tascon, J. M. D.; Bottani, E. J. J. Phys. Chem. B 2003, 107, 8905. (6) Yoo, D. H.; Rue, G. H.; Chan, M. H. W.; Hwang, Y. H.; Kim, H. K. J. Phys. Chem. B 2003, 107, 1540. (7) Yoo, D. H.; Rue, G. H.; Hwang, Y. H.; Kim, H. K. J. Phys. Chem. B 2002, 106, 3371. (8) Murata, K.; Kaneko, K.; Steele, W. A.; Kokai, F.; Takahashi, K.; Kasuya, D.; Hirahara, K.; Yudasaka, M.; Iijima, S. J. Phys. Chem. B 2001, 105, 10210. (9) Fujiwara, A.; Ishii, K.; Suematsu, H.; Kataura, H.; Maniwa, Y.; Suzuki, S.; Achiba, Y. Chem. Phys. Lett. 2001, 336, 205.

hydrogen on carbon nanotubes as part of the development of the next-generation fuel cell technology.19-23 In these experimental investigations, all adsorption isotherms were observed to be of type II at bulk adsorbate subcritical temperatures and of type I or IV at supercritical temperatures. Molecular simulations have also been performed to study gas adsorption on carbon nanotubes, including the (10) Alain, E.; Yin, Y. F.; Mays, T. J.; McEnaney, B. Molecular simulation and measurement of adsorption in porous carbon nanotubes. Characterization of Porous Solids V; Elsevier Science B.V.: Amsterdam, The Netherlands, 2000; Vol. 128, p 313. (11) Inoue, S.; Ichikuni, N.; Suzuki, T.; Uematsu, T.; Kaneko, K. J. Phys. Chem. B 1998, 102, 4689. (12) Cinke, M.; Li, J.; Bauschlicher, C. W.; Ricca, A.; Meyyappan, M. Chem. Phys. Lett. 2003, 376, 761. (13) Yoo, D. H.; Rue, G. H.; Seo, J. Y.; Hwang, Y. H.; Chan, M. H. W.; Kim, H. K. J. Phys. Chem. B 2002, 106, 9000. (14) Muris, M.; Dufau, N.; Bienfait, M.; Pavlovsky, N. D.; Grillet, Y.; Palmari, J. P. Langmuir 2000, 16, 7019. (15) Kuznetsova, A.; Yates, J. T.; Simonyan, V. V.; Johnson, J. K.; Huffman, C. B.; Smalley, R. E. J. Chem. Phys. 2001, 115, 6691. (16) Kuznetsova, A.; Yates, J. T.; Liu, J.; Smalley, R. E. J. Chem. Phys. 2000, 112, 9590. (17) Mackie, E. B.; Wolfson, R. A.; Arnold, L. M.; Lafdi, K.; Migone, A. D. Langmuir 1997, 13, 7197. (18) Hilding, J.; Grulke, E. A.; Sinnott, S. B.; Qian, D.; Andrews, R.; Jagtoyen, M. Langmuir 2001, 17. (19) Zuttel, A.; Sudan, P.; Mauron, P.; Kiyobayashi, T.; Emmenegger, C.; Schlapbach, L. Int. J. Hydrogen Energy 2002, 27, 203. (20) Darkrim, F. L.; Malbrunot, P.; Tartaglia, G. P. Int. J. Hydrogen Energy 2002, 27, 193. (21) Cheng, H. M.; Yang, Q. H.; Liu, C. Carbon 2001, 39, 1447. (22) Ding, R. G.; Lu, G. Q.; Yan, Z. F.; Wilson, M. A. J. Nanosci. Nanotechnol. 2001, 1, 7. (23) Dillon, A. C.; Heben, M. J. Appl. Phys. A 2001, 72, 133.

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N2 and O2 Mixture Adsorption on SWNT Bundles

adsorption of nitrogen,24 xenon,25 methane,26 ethane,27 hydrogen,28-30 and so forth. The adsorption isotherms were all predicted to be of type I regardless of temperature, which is not in agreement with the experimental observation of type II isotherms at subcritical temperatures. The reason for this difference is that these simulations used infinite periodic nanotube bundles to represent nanotube samples; this representation, however, is unrealistic. Experiments have shown that carbon nanotubes form bundles of nearly uniform and finite diameter.9,31,32 As a result, the external surface of a finite nanotube bundle is also available for gas adsorption, as evidenced experimentally by gas adsorption on closed-ended nanotubes.33-36 Recently, there have been a few simulations examining the effect of the external surface of a nanotube bundle on the adsorption of hydrogen at supercritical temperatures37,38 and the adsorption of neon, argon, krypton, xenon, and methane at subcritical temperatures.39-41 In the latter, the adsorption isotherms were predicted to be of type II, consistent with experiment. This suggests that, to correctly predict adsorption on a finite-sized nanotube bundle, the external surface must be taken into account. To more thoroughly explore the role of the external surface in gas physisorption, nitrogen adsorption has been investigated by us at both sub- and supercritical temperatures on two types of single-walled carbon nanotube (SWNT) bundles: an infinite periodic hexagonal bundle without an external surface and a small finite isolated hexagonal bundle with an external surface.42 That work demonstrated the important role of the external surface of a nanotube bundle in gas adsorption. On the infinite periodic bundle, the adsorption is of type I at both suband supercritical temperatures and adsorption occurs inside the nanotubes, first at the annuli and then at the nanotube centers. However, on the finite isolated bundle, the adsorption is of type II at subcritical temperatures, as has been observed in experiments. Adsorption occurs first at the annuli inside the nanotubes and at the grooves between the nanotubes. At higher pressures, adsorption also occurs at the ridges surrounding the nanotubes and at the nanotube centers, and at still higher pressures, on the external surface. The formation of the external (24) Yin, Y. F.; Mays, T.; McEnaney, B. Langmuir 1999, 15, 8714. (25) Simonyan, V. V.; Johnson, J. K.; Kuznetsova, A.; Yates, J. T. J. Chem. Phys. 2001, 114, 4180. (26) Zhang, X. R.; Wang, W. C. Fluid Phase Equilib. 2002, 194, 289. (27) Zhang, X.; Wang, W. Phys. Chem. Chem. Phys. 2003, 4, 3048. (28) Levesque, D.; Gicquel, A.; Darkrim, F. L.; Kayiran, S. B. J. Phys.: Condens. Matter 2002, 14, 9285. (29) Gu, C.; Gao, G. H.; Yu, Y. X.; Mao, Z. Q. Int. J. Hydrogen Energy 2001, 26, 691. (30) Simonyan, V. V.; Diep, P.; Johnson, J. K. J. Chem. Phys. 1999, 111, 9778. (31) Thess, A.; Lee, R.; Nikolaev, P.; Dai, H. J.; Petit, P.; Robert, J.; Xu, C. H.; Lee, Y. H.; Kim, S. G.; Rinzler, A. G.; Colbert, D. T.; Scuseria, G. E.; Tomanek, D.; Fischer, J. E.; Smalley, R. E. Science 1996, 273, 483. (32) Journet, C.; Maser, W. K.; Bernier, P.; Loiseau, A.; delaChapelle, M. L.; Lefrant, S.; Deniard, P.; Lee, R.; Fischer, J. E. Nature (London) 1997, 388, 756. (33) Lasjaunias, J. C.; Biljakovic, K.; Sauvajol, J. L.; Monceau, P. Phys. Rev. Lett. 2003, 91, 025901. (34) Talapatra, S.; Krungleviciute, V.; Migone, A. D. Phys. Rev. Lett. 2002, 89, 246106. (35) Talapatra, S.; Migone, A. D. Phys. Rev. Lett. 2001, 8720, 206106. (36) Talapatra, S.; Zambano, A. Z.; Weber, S. E.; Migone, A. D. Phys. Rev. Lett. 2000, 85, 138. (37) Smith, M. R.; Bittner, E. W.; Shi, W.; Johnson, J. K.; Bockrath, B. C. J. Phys. Chem. B 2003, 107, 3752. (38) Williams, K. A.; Eklund, P. C. Chem. Phys. Lett. 2000, 320, 352. (39) Calbi, M. M.; Cole, M. W. Phys. Rev. B 2002, 66, 115413. (40) Calbi, M. M.; Gatica, S. M.; Bojan, M. J.; Cole, M. W. J. Chem. Phys. 2001, 115, 9975. (41) Gatica, S. M.; Bojan, M. J.; Stan, G.; Cole, M. W. J. Chem. Phys. 2001, 114, 3765. (42) Jiang, J. W.; Sandler, S. I. Phys. Rev. B 2003, 68, 245412.

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multilayer leads to wetting as the bulk phase approaches saturation. As the temperature increases from sub- to supercritical, the adsorption on the finite isolated bundle changes from type II to type I. These results provide a physical explanation for the difference between experimental observation and previous theoretical prediction. Less studied is the competitive adsorption of a gas mixture on carbon nanotubes, which could have potential industrial applications. Only recently have there been a few studies on the adsorption of gas mixtures on carbon nanotubes. From vibrational spectroscopy and simulation of the adsorption of a carbon tetrafluoride-xenon mixture on the internal and external surfaces of opened SWNTs, it was found that xenon preferentially displaces internally adsorbed carbon tetrafluoride at high coverages.43 The adsorption of a nitrogen oxides-sulfur dioxide-carbon dioxide mixture in the presence of oxygen on carbon nanotubes showed that the uptake of nitrogen oxides is much higher than that of sulfur dioxide and carbon dioxide and indicated that carbon nanotubes are a very good and reversible sorbent for the removal of nitrogen oxides at room temperature.44 Path integral Monte Carlo simulations were used to explore the adsorption of hydrogen isotope mixtures on carbon nanotubes, and the results suggest that carbon nanotubes can act as highly effective quantum sieves to separate hydrogen isotopes.45,46 The objective of the present work is to explore the adsorption of a nitrogen-oxygen mixture (representing air) on the two types of open-ended SWNT bundles investigated previously for nitrogen adsorption.42 In section II, the atomistic models of the two types of SWNT bundles are described briefly, along with the simulation method. In section III, the density distributions of the adsorbed nitrogen and oxygen molecules, the locations of their centers of mass, the adsorption isotherms, and the selectivities between the two gases obtained from simulations are shown on both types of bundles at a subcritical temperature, 77 K, and a supercritical temperature, 300 K. Finally, concluding remarks are given in section IV. Note that the critical temperature of air is ∼132.5 K.47 Traditionally, one uses the terms “gas adsorption” and “vapor adsorption” to refer to the adsorption at a supercritical temperature and at a subcritical temperature, respectively. Throughout this manuscript, we simply use the term “gas adsorption” to refer to both cases. II. Models and Method The adsorbates, nitrogen and oxygen, are represented as two-site rigid molecules with pairwise site-site Lennard-Jones (LJ) potentials. For nitrogen, the bond length is lN-N ) 1.10 Å and the LJ potential parameters are N-N/ kB ) 36.4 K (kB is the Boltzmann constant) and σN-N ) 3.32 Å. For oxygen, the bond length is lO-O ) 1.208 Å and the LJ potential parameters are O-O/kB ) 52.0 K and σO-O ) 2.99 Å. These parameters had been fitted by others to the experimental bulk properties of nitrogen48 and oxygen,49 respectively. The cross parameters of the unlike pair nitrogen-oxygen are obtained by the LorentzBerthelot combining rules, in which σN-O ) (σN-N + σO-O)/ (43) Byl, O.; Kondratyuk, P.; Forth, S. T.; FitzGerald, S. A.; Chen, L.; Johnson, J. K.; Yates, J. T. J. Am. Chem. Soc. 2003, 125, 5889. (44) Long, R. Q.; Yang, R. T. Ind. Eng. Chem. Res. 2001, 40, 4288. (45) Challa, S. R.; Sholl, D. S.; Johnson, J. K. J. Chem. Phys. 2002, 116, 814. (46) Wang, Q. Y.; Challa, S. R.; Sholl, D. S.; Johnson, J. K. Phys. Rev. Lett. 1999, 82, 956. (47) Lemmon, E. W.; Jacobsen, R.; Penoncello, S. G.; Friend, D. G. J. Phys. Chem. Ref. Data 2000, 29, 331. (48) Murthy, C. S.; Sing, K.; Klein, M. L.; McDonald, I. R. Mol. Phys. 1980, 41, 1387.

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Table 1. Parameters ck in the Endohedral and Exohedral Averaged Potentials of a Nitrogen Atom and an Oxygen Atom, Respectively, along the Radial Distance from the Center of a (10, 10) SWNT N O

k

0

1

2

3

4

5

6

7

8

endohedral exohedral endohedral exohedral

9276.09 5.797 10645.0 4.472

-49227.1 66.41 -53364.2 51.92

105086 314.03 109803 245.80

-121229 799.83 -123382 619.76

83007.9 1185.09 83046.1 899.23

-34674.7 1150.62 -34430.0 854.13

8608.90 651.71 8590.34 469.20

-1173.05 210.08 -1191.93 146.13

72.31 30.73 74.07 20.58

Figure 1. Potential energy u(r)/kB of a nitrogen atom (solid line) and an oxygen atom (dashed line), respectively, along the radial distance, r, from the center of a (10, 10) SWNT. The dotted line indicates the (10, 10) SWNT radius.

2 and N-O ) (N-NO-O)1/2. As in our previous work,42 the SWNT is of the metallic armchair type with a Hamada index of (10, 10) defining the chiral vector and a diameter of 13.56 Å.31 By comparing the measured and simulated adsorption of xenon on nanotubes,25 it was proposed that the nanotube-xenon interaction could be approximated by the graphite-xenon interaction, as a nanotube can be considered to be a rolled up graphene sheet. Similarly, to model the nanotube-nitrogen and nanotube-oxygen interactions, the LJ potentials with the parameters C-N/ kB ) 33.4 K and σC-N ) 3.36 Å and C-O/kB ) 37.6 K and σC-O ) 3.19 Å are respectively used in this work. These parameters were fitted by Bojan and Steele to reproduce measured nitrogen and oxygen adsorption, respectively, on graphite in the limit of zero coverage.50,51 The interaction potential between a gas atom and a nanotube at a radial distance of r from the nanotube center is calculated and fitted to a polynomial function of r, 8 ∑k)0 ck[R/(R - r)]k, where R ) 6.78 Å is the radius of the (10, 10) nanotube. Using this averaged potential that only depends on the radial distance, r, from the tube center, simulations are greatly accelerated without a significant loss of accuracy. Table 1 gives the fitted parameters in the endohedral (inside) and exohedral (outside) potentials for a nitrogen atom and an oxygen atom, respectively. Figure 1 shows the potential energy u(r)/kB of a nitrogen atom (solid line) and an oxygen atom (dashed line), respectively, along the radial distance, r, from the center of a (10, 10) SWNT. For both nitrogen and oxygen, the endohedral potential is greater (more negative) than the exohedral potential. Both inside and outside the nanotube, the nitrogen-nanotube attraction is slightly greater than the oxygen-nanotube attraction. Experimentally produced nanotubes form hexagonal bundles of finite diameters due to inter-tube van der Waals interactions. The average number of nanotubes within a (49) Klein, M. L.; Levesque, D.; Weis, J. J. Phys. Rev. B 1980, 21, 5785. (50) Bojan, M. J.; Steele, W. A. Langmuir 1987, 3, 116. (51) Bojan, M. J.; Steele, W. A. Langmuir 1987, 3, 1123.

bundle varies with the synthesis method. For example, bundles between 100 and 500,31 and of the order of 20 nanotubes,32 have been reported. As in our previous work,42 two types of (10, 10) SWNT bundles are considered here: (i) an infinite periodic hexagonal bundle without an external surface and (ii) a finite isolated hexagonal bundle with an external surface. The van der Waals gap between nanotubes is set as a constant 3.2 Å.31,32 That is, the SWNTs within the bundle are assumed to be rigid regardless of the extent of adsorption. Compared to a bundle with small lattice dilation upon adsorption, as considered in theoretical studies,52,53 we expect that the assumption of a rigid bundle leads to slightly less adsorption, though the general features of the adsorption isotherm will be unchanged. A periodic rectangular parallelepiped of 33.5 Å × 29.0 Å × 36.9 Å with hexagonally aligned (10, 10) SWNTs is used to represent the infinite periodic bundle. The finite isolated bundle is assumed to be composed of seven hexagonal (10, 10) SWNTs with a diameter of ∼47 Å in a periodic rectangular parallelepiped of 100.0 Å × 100.0 Å × 36.9 Å. The lengths in the x and y directions are sufficiently large to eliminate the nearest neighbor interactions with periodic images, ensuring that the finite bundle is truly isolated. Although this homogeneous finite isolated bundle does not exactly represent a real experimental sample, which consists of heterogeneous nanotubes of various diameters,54 the external surfaces of the model and of the real bundles were found to play a similar role.55 Also, in our previous work,42 we found that the homogeneous finite bundle can reproduce the same type of adsorption isotherm in experimental observation. To identify the energetically favorable adsorption sites on the two types of (10, 10) SWNT bundles, the potential energy u(x, y)/kB in the x-y plane was calculated for a gas molecule parallel to the tube axis in the z direction at a given position with all the nanotubes in the bundle. The energy contours for oxygen are qualitatively similar to those of nitrogen plotted in previous work, though quantitatively they are somewhat different, particularly, at the interstitial sites. Shown in Table 2 are the energy values at the favorable adsorption sites located at the positions indicated in parentheses. On the infinite periodic bundle, all the nanotubes are identical; consequently, there are no external groove and ridge sites. The internal annulus at 3.4 Å from the nanotube center is the most energetically favorable adsorption site for nitrogen with u/kB ) -1771.0. For oxygen, the annulus is at 3.6 Å with u/kB ) -1724.8, though this is not the most favorable site. A less favorable site is the nanotube center with u/kB ) -600.6 for nitrogen and u/kB ) -500.5 for oxygen. The adsorption site at the interstice bounded by three nanotubes at 9.7 Å from the (52) Calbi, M. M.; Toigo, F.; Cole, M. W. Phys. Rev. Lett. 2001, 86, 5062. (53) Calbi, M. M.; Mizel, A.; Cole, M. W. Phys. Rev. B 2004, 69, 195408. (54) Rinzler, A. G.; Liu, J.; Dai, H.; Nikolaev, P.; Huffman, C. B.; Rodriguez-Macias, F. J.; Boul, P. J.; Lu, A. H.; Heymann, D.; Colbert, D. T.; Lee, R. S.; Fischer, J. E.; Rao, A. M.; Eklund, P. C.; Smalley, R. E. Appl. Phys. A 1998, 67, 29. (55) Matranga, C.; Chen, L.; Smith, M.; Bittner, E.; Johnson, J. K.; Bockrath, B. J. Phys. Chem. B 2003, 107, 12930.

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Table 2. Potential Energy u(x, y)/kB at the Favorable Adsorption Sites for a Nitrogen Molecule and an Oxygen Molecule, Respectively, Aligned Parallel to the Nanotube Axisa (i) periodic bundle

(ii) isolated bundle

adsorption site

N2

O2

N2

O2

annulus center interstice groove ridge

-1771.0 (3.4) -600.6 (0.0) -338.8 (9.7) f f

-1724.8 (3.6) -500.5 (0.0) -2040.5 (9.7) f f

-1755.6 (3.4)b -585.2 (0.0)d -338.8 (9.7) -1771.0 (20.2) -877.8 (26.9)

-1717.1 (3.6)c -485.1 (0.0)e -2040.5 (9.7) -1824.9 (19.9) -893.2 (26.8)

a The values in parentheses indicate the positions of the adsorption sites. b -1755.6 inside the middle nanotube and inhomogeneous inside the neighboring nanotubes. c -1717.1 inside the middle nanotube and inhomogeneous inside the neighboring nanotubes. d -585.2 inside the middle nanotube and -554.4 inside the neighboring nanotubes. e -485.1 inside the middle nanotube and -454.3 inside the neighboring nanotubes. f Due to the periodic geometry, there are no groove and ridge sites on the periodic bundle.

nanotube center has a very narrow region with attractive energy, u/kB ) -338.8 for nitrogen, much less attractive than u/kB ) -2040.5 for oxygen, which is the most favorable adsorption site. On the finite isolated bundle, the most favorable adsorption site for nitrogen is the groove between two adjacent nanotubes at 20.2 Å from the bundle center with u/kB ) -1771.0. The groove site for oxygen is at 19.9 Å from the bundle center with u/kB ) -1824.9, but this is not the most favorable site. Another favorable site is the internal annulus, for nitrogen at 3.4 Å from the center of the middle nanotube with u/kB ) -1755.6 and for oxygen at 3.6 Å with u/kB ) -1717.1. The interaction energy at the annulus inside the nanotube surrounding the middle nanotube is not uniform, as the attraction is somewhat greater closer to the center of the nanotube bundle. The next favorable site is the ridge surrounding the nanotube on the external surface, for nitrogen with u/kB ) -877.8 and for oxygen with u/kB ) -893.2; the center of the middle nanotube, for nitrogen with u/kB ) -585.2 and for oxygen with u/kB ) -485.1; then, the center of the neighboring nanotube is u/kB ) -554.4 for nitrogen and u/kB ) -454.3 for oxygen. For nitrogen, similar to the periodic bundle, the interstice here also has the energy u/kB ) -338.8 at 9.7 Å from the bundle center. However, for oxygen, the energy of attraction u/kB ) -2040.5 is much stronger than that for nitrogen, and this is the most favorable adsorption site. On the external surface starting from the ridge, the attractive energy decreases with increasing distance from the bundle. Sufficiently far from the bundle, bulk gas behavior is found, as the gas molecules do not interact with the nanotubes. Consequently, the number of admolecules is the total number of gas molecules in the simulation cell with the adsorbent as corrected by subtracting the number of gas molecules behaving as bulk gas. To do so, a cutoff distance from the center of the isolated bundle is selected, within which the gas molecules are considered adsorbed. Grand canonical Monte Carlo (GCMC) simulations are used in this work in which the temperature, T, volume, V, and chemical potential, µk, of each adsorbate, k, are fixed a priori. At thermodynamic equilibrium, the chemical potentials in the adsorbed phase and in the bulk reservoir are equal, which allows one to directly relate the adsorption information to the bulk phase properties. For simplicity, in this work, the nitrogen-oxygen mixture (air) in the bulk is assumed to be an ideal gas. Five types of trial moves are randomly attempted in the GCMC simulation, namely, displacement and rotation of a randomly chosen existing molecule, creation of a new molecule at a random position, deletion of an existing molecule, and exchange of molecular identity. While the exchange trial move is not required in the GCMC simulation, its use allows equilibrium to be reached faster and reduces fluctuations

after equilibration.56 The cutoff length used for the calculation of the Lennard-Jones site-site interaction is 14.5 Å on the periodic bundle and 18.4 Å on the isolated bundle. Periodic boundary conditions are used in all three dimensions. The GCMC simulations consist of 2 × 104 cycles and 50 000 trial moves per cycle, with the initial 1.5 × 104 cycles used for equilibration and 0.5 × 104 cycles used to determine ensemble averages. The trial moves for mixture adsorption here are 10 times as many as in our previous work for nitrogen adsorption, to ensure that adsorption has reached mechanical and compositional equilibrium, especially at a high density and at a low temperature, and to obtain precise ensemble averages. III. Results and Discussion A. The Infinite Periodic Bundle. Figure 2 shows the density profiles, F(r), of the centers of mass of nitrogen (solid line) and oxygen (dashed line) molecules, respectively, adsorbed from air (nitrogen/oxygen ) 0.79:0.21) on the infinite periodic bundle at a bulk subcritical temperature of 77 K. Here, F(r) ) δN/(2πrδrz) is the density at a radial distance of r from the center of the bundle with length z. The insets are the snapshots of the locations of centers of mass generated by accumulating 50 equilibrium configurations. Since each nanotube in the infinite periodic bundle behaves identically, the adsorption behavior therein is the same. At 10-5 kPa, more nitrogen than oxygen is adsorbed, as there is more nitrogen in the bulk gas mixture (air) and its chemical potential is higher. Both nitrogen and oxygen adsorb at the internal annuli indicated by the peaks at 3.4 and 3.6 Å, respectively. Although the interstitial channel is the most energetically favorable site for oxygen, no oxygen molecules are observed there at this pressure. This is because the interstitial channel has a very narrow attractive region, and oxygen molecules can only enter there parallel to the channel. In order for oxygen molecules to enter, the external force (bulk pressure) must be high, as we shall see below. That is, the interstitial channel, while energetically favorable, leads to a decrease in entropy and produces a free energy change, which is not favorable for adsorption. With increasing pressure, the densities of adsorbed molecules increase. At 10-3 kPa, both nitrogen and oxygen also adsorb at the nanotube centers indicated by the peaks at r ) 0, and at this pressure, oxygen starts to intercalate into the interstitial channels. At 1 kPa, the adsorption is close to saturation and more oxygen than nitrogen is adsorbed. Compared with the results at 10-5 and 10-3 kPa, the density of nitrogen increases at the nanotube centers but decreases at the annuli; however, the density of oxygen continues increasing everywhere. In addition, oxygen molecules align in the interstitial channels endto-end parallel to the nanotube axis. (56) Kofke, D. Mol. Simul. 1991, 7, 285.

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Figure 2. Density profiles of the centers of mass of nitrogen (solid line) and oxygen (dashed line) molecules, respectively, versus the distance from the center of the periodic bundle at 77 K. The insets are snapshots generated by accumulating 50 equilibrium configurations.

Figure 3. (a) Adsorption isotherms and (b) selectivity for air adsorption on the periodic bundle at 77 K on a semilogarithmic scale of bulk pressure. The inset is on a linear scale of bulk pressure. The points are simulation data, and the lines are drawn for visual clarity.

Figure 3a shows the adsorption isotherms of nitrogen and oxygen, respectively, for the adsorption of air on the periodic bundle at 77 K on a semilogarithmic scale of bulk pressure, in which the extent of adsorption is expressed as the ratio of the number of admolecules to the number of carbon atoms on the bundle. The points are simulation results, and the lines are drawn for visual clarity. Clearly, competitive adsorption occurs between the two gases. At low pressures, nitrogen adsorbs more, while, at high pressures, oxygen does. With increasing pressure, oxygen adsorption continues increasing until saturation, while nitrogen adsorption first increases, then decreases, and finally approaches a constant saturation value. The dew point (saturation) pressure of air at 77 K is roughly 50 kPa obtained from a separate NVT Gibbs ensemble Monte Carlo simulation, close to the experimentally determined 55.86 kPa.47 The highest pressure shown is 30 kPa, at which the adsorption has almost saturated. It is expected that the adsorption will not change discernibly even when the bulk pressure is above the saturation pressure. On the linear scale of bulk pressure shown in the inset, the adsorption isotherms of both nitrogen and oxygen appear to be of type I (Langmuirian), which is characteristic of a highly microporous adsorbent with pores of molecular dimensions (i.e., below 2 nm).57 The replacement of nitrogen by oxygen at moderate and high coverages is mainly due to an entropic effect; that is, (57) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption: By Powders and Porous Solids; Academic Press: London, 1999.

oxygen has a smaller molecular size than nitrogen and can fill the confined space more easily. Such behavior has been observed previously, for example, in simulation studies on the adsorption of a carbon tetrafluoride-xenon mixture on a nanotube bundle,43 of air in C168 schwarzite,58 and of alkane mixtures in silicalite;59 in theoretical predictions on the adsorption of hard rods on a linear substrate60 and of square-well mixtures in one dimension;61 and also in experimental measurements on the adsorption of nitrogen-oxygen mixtures on anatase.62 Figure 3b shows the selectivity of nitrogen over oxygen, SN2/O2, for air adsorption on the periodic bundle at 77 K on a semilogarithmic scale of bulk pressure; the inset has the same results on a linear scale. With increasing pressure, the selectivity drops until reaching nearly a constant near saturation. At low pressures, the selectivity is >1 and hence nitrogen is preferentially adsorbed. This is an enthalpic effect, as nitrogen has a larger collision diameter with a carbon atom than oxygen and interacts more strongly with the surface, as has been discussed in detail for the adsorption of nitrogen and oxygen in C168 schwarzite.58,63 At 2 × 10-5 kPa, the selectivity is equal (58) Jiang, J. W.; Sandler, S. I. Langmuir 2003, 19, 5936. (59) Schenk, M.; Vidal, S. L.; Vlugt, T. J. H.; Smit, B.; Krishna, R. Langmuir 2001, 17, 1558. (60) Talbot, J. AIChE J. 1997, 43, 2471. (61) Heuchel, M. Langmuir 1997, 13, 1150. (62) Arnold, J. R. J. Am. Chem. Soc. 1949, 71, 104. (63) Jiang, J. W.; Klauda, J. B.; Sandler, S. I. Langmuir 2003, 19, 3512.

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Figure 4. Density profiles of the centers of mass of nitrogen (solid line) and oxygen (dashed line) molecules, respectively, versus the distance from the center of the periodic bundle at 300 K. The insets are snapshots generated by accumulating 50 equilibrium configurations.

Figure 5. (a) Adsorption isotherms and (b) selectivity for air adsorption on the periodic bundle at 300 K on a semilogarithmic scale of bulk pressure. The inset is on a linear scale of bulk pressure. The points are simulation data, and the lines are drawn for visual clarity.

to 1, the isoselective point. At pressures higher than 2 × 10-5 kPa, the selectivity is 1; that is, nitrogen is preferentially adsorbed. The isoselective point is 103 kPa, above which the selectivity reversal occurs; that is, the selectivity is 1, and the reverse is true at high pressures above the selectivity reversal. When the pressure is higher than 10-2 kPa, the selectivity is very different from 1, suggesting that an isolated nanotube bundle might be useful for separating air under these conditions. This selectivity is like that on the periodic bundle at 77 K in Figure 3b. This may imply that, although the types of nanotube bundles and the adsorption isotherms are different, their efficiencies to the separation of a gas mixture are almost identical at the same temperature. Figure 8 shows the density profiles, F(r), of the centers of mass of nitrogen and oxygen molecules, respectively, for air adsorption on the isolated bundle at 300 K, with the insets showing snapshots. At 103 kPa, nitrogen and oxygen molecules are inside the nanotubes and in the bulk region. The densities in both regions increase as the pressure increases to 104 kPa and further to 105 kPa, but with a larger density change in the bulk region. Due to the increased thermal motion, nitrogen and oxygen molecules are not in ordered structures within the nanotubes. Contrary to the situation on the periodic nanotube bundle at 300 K shown in Figure 4, oxygen molecules are not observed to intercalate into the interstitial channels at 105 kPa, the highest pressure studied here, however, that can be expected to occur at even higher (64) Lide, D. R. CRC Handbook of Chemistry and Physics; CRC Press: Boca Raton, FL, 2003; Vol. 84.

pressures. As mentioned earlier, not all the molecules in the simulation cell of the isolated bundle are admolecules, and we need to correct for this in determining the extent of coverage. From the density profiles, the densities of both nitrogen and oxygen approach their bulk values at a distance of ∼40 Å, so that we consider only molecules within this cutoff distance to be adsorbed. This correction is negligible at low pressures at 77 K in Figure 6, where there are few gas molecules beyond the cutoff distance; however, it is a significant correction at high pressures. Figure 9a shows the adsorption isotherms of nitrogen and oxygen, respectively, calculated in this way for air adsorption on the isolated bundle at 300 K on a semilogarithmic scale of bulk pressure. The adsorption of both nitrogen and oxygen is negligible at low pressures but increases with increasing pressure; saturation can be expected at still higher pressures. Over the entire range of bulk pressures studied, more nitrogen is adsorbed. On the linear scale of bulk pressure shown in the inset, the isotherms of both nitrogen and oxygen appear to be of type I, as on the periodic bundle at 300 K in Figure 5a. Figure 9b shows the selectivity of nitrogen over oxygen for air adsorption on the isolated bundle at 300 K on a semilogarithmic scale of bulk pressure, and on a linear scale in the inset. Over the range of bulk pressures, the selectivity toward nitrogen first increases and then decreases with increasing pressure. At low pressures, the selectivity is >1, as nitrogen is more strongly adsorbed; however, at high pressures, the selectivity is