Monte Carlo Simulation of O2 and N2 Mixture Adsorption in

The adsorption of O2 and N2 mixture in nanoporous carbon (NPC) has been investigated by both grand canonical and Gibbs ensemble Monte Carlo simulation...
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Monte Carlo Simulation of O2 and N2 Mixture Adsorption in Nanoporous Carbon (C168 Schwarzite) Jianwen Jiang* and Stanley I. Sandler† Center for Molecular & Engineering Thermodynamics, Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716 Received December 18, 2002. In Final Form: April 22, 2003 The adsorption of O2 and N2 mixture in nanoporous carbon (NPC) has been investigated by both grand canonical and Gibbs ensemble Monte Carlo simulations. The gases are represented as diatomic molecules, and the NPC is represented as a rigid C168 Schwarzite structure. Interactions between gas-gas and gascarbon atoms in the NPC are modeled with additive pairwise site-site Lennard-Jones potentials. Competitive adsorption occurs between the two gases. At fixed bulk composition, the selectivity of O2 to N2 first decreases slightly with increasing external pressure, reaches a minimum, and then increases. The isoselective point (ISP) of selectivity reversal is independent of bulk composition. At fixed pressure lower than the ISP, the selectivity monotonically decreases with increasing O2 bulk composition; however, at fixed pressure higher than the ISP, the reverse is found. With increasing temperature, the selectivity decays approximately exponentially. As with pure gas adsorption, a slight orientational preference of the adsorbed gas molecules toward the intersectional channels is observed, and the center-of-mass density distribution of gas molecules changes from continuous to discontinuous within the NPC as external pressure increases. The predictions of the mixture adsorption using the ideal-adsorbed-solution theory based solely on the adsorption of the pure gases agree well with the simulation results.

I. Introduction The adsorption of pure O2 and N2 separately in nanoporous carbon (NPC) has been investigated recently by grand canonical Monte Carlo (GCMC) simulation.1 We found that the energetically favored N2 is slightly more adsorbed than O2 at low pressures; however, at high pressures, the size of the gas molecule controls, and O2 is preferentially adsorbed. The adsorption isotherm shows two steps with an inflection point. The center-of-mass density distribution of the adsorbed gas molecules within the NPC changes from continuous to discontinuous with increasing pressure, first in the small pores and then at higher pressures in the large pores. This two-stage adsorption results from the differences in available spaces and loading capacities of the two types of pores in the NPC. While that study provided a deep understanding of how a pure gas adsorbs in the NPC, the adsorption from gas mixture is more important for the design of practical gas separation processes. Indeed, a potential major application of the NPC is to separate O2 and N2 from the air. For this reason, a better understanding of the adsorption in the NPC of O2 and N2 from their mixture is desired. There have been a number of methods to predict the adsorption of binary or multicomponent mixtures on the basis of the known adsorption of the pure species. Examples include the potential theory originally introduced by Polanyi2 and improved by Dubinin;3 the statistical approach due largely to Hill;4 the ideal-adsorption solution theory (IAST) of Myers and Prausnitz;5 the vacancy solution theory of Suwanayuen and Danner;6 and * E-mail: [email protected]. † E-mail: [email protected]. (1) Jiang, J. W.; Klauda, J. B.; Sandler, S. I. Langmuir 2003, 19, 3512. (2) Polanyi, M. Trans. Faraday Soc. 1932, 28, 316. (3) Dubinin, M. M. Chem. Rev. 1960, 60, 235. (4) Hill, T. L. Introduction to Statistical Thermodynamics; AddisonWesley: Reading, MA, 1960. (5) Myers, A. L.; Prausnitz, J. M. AIChE J. 1965, 11, 121.

various empirical and semiempirical theories. Among these, IAST is the most widely used and has served as a benchmark for the prediction of gas mixture adsorption. In recent years, molecular simulation has become a powerful tool to investigate adsorption behavior.1 It provides a microscopic picture of fluid in the interaction field of confined structure. Many molecular simulation studies have been reported on the adsorption of binary mixtures, such as the adsorption of an O2 and N2 mixture and of an inert gas mixture in zeolite,7-9 of a methane and ethane mixture on activated carbon and carbon fiber,10 of a water and methanol mixture in carbon and aluminosilicate pores,11 of an alkane mixture in zeolite,12,13 and of a xylene isomeric mixture in silicalite.14 All of the above have used GCMC simulation, which is a common method to simulate adsorption behavior. In this work we use both GCMC and the isobaric isothermal Gibbs ensemble Monte Carlo (NPT-GEMC) simulations to study the adsorption of O2 and N2 binary mixture in the NPC. We will see below that NPT-GEMC has advantages over GCMC. As in ref 1, the gases are represented as diatomic molecules, and the NPC as a rigid hypothetical C168 Schwarzite structure,15 in which there are two types of pores with average sizes of about 7 and 9 Å, respectively. Interactions between gas-gas and gascarbon atoms in the NPC are modeled with the additive pairwise site-site Lennard-Jones potential with param(6) Suwanayuen, S.; Danner, R. P. AIChE J. 1980, 26, 68 and 76. (7) Razmus, D. M.; Hall, C. K. AIChE J. 1991, 37, 769. (8) Van Tassel, P. R.; Davis, H. T.; McCormick, A. V. Mol. Simul. 1996, 17, 239. (9) Jameson, C. J.; Jameson, A. K.; Lim, H. M. J. Chem. Phys. 1997, 107, 4364. (10) Cracknell, R. F.; Nicholson, D. Adsorption 1995, 1, 7. (11) Shevade, A. V.; Jiang, S. Y.; Gubbins, K. E. J. Chem. Phys. 2000, 113, 6833. (12) Du, Z. M.; Manos, G.; Vlugt, T. J. H.; Smit, B. AIChE J. 1998, 44, 1756. (13) Calero, S.; Smit, B.; Krishna, R. J. Catal. 2001, 202, 395. (14) Mohanty, S.; Davis, H. T.; McCormick, A. V. Chem. Eng. Sci. 2000, 55, 2779. (15) Vanderbilt, D.; Tersoff, J. Phys. Rev. Lett. 1992, 68, 511.

10.1021/la027030v CCC: $25.00 © 2003 American Chemical Society Published on Web 06/10/2003

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eters determined from O2 and N2 adsorption on graphite.16 The Lorentz-Berthelot combining rules (arithmetic mean for collision diameter and geometric mean for well depth) are used for the interaction between gas molecules of different species. In section II, the simulation methodology of both GCMC and NPT-GEMC is presented. In section III, we describe IAST briefly and give the underlying equations used to predict mixture adsorption from the adsorption of pure gases. In section IV, the simulation results are presented and compared with the predictions of IAST. The selectivity between the two gases is calculated as functions of bulk pressure, bulk composition, and temperature. Finally, section V summarizes our conclusions. II. Simulation Methodology A. Grand Canonical Monte Carlo (GCMC). GCMC simulation is employed at fixed temperature T, volume V, and chemical potential µk of each adsorbate k. The grand canonical ensemble is an open system in equilibrium with an infinite bulk fluid reservoir; therefore, during GCMC simulation the number of molecules is allowed to fluctuate. The chemical potentials in the adsorbed and bulk phases are equal at thermodynamic equilibrium. Five types of trial moves for gas molecules are chosen randomly in the GCMC simulation: displacement, rotation, creation, deletion, and identity exchange. For the first two moves, the number of molecules in the system is fixed and a randomly chosen molecule is moved. The acceptance probability for both these moves is determined by the Metropolis criterion

min[1, exp(-β∆U)]

(1)

where ∆U is the change of total energy due to a trial move. In a creation trial move a new adsorbate molecule is created at a random location with the acceptance probability

min[1, zk exp(-β∆U)V/(Nk + 1)]

(2)

where zk is the configurational activity of species k defined by zk ) exp(βµk)/Λk3 and Λk is the de Broglie thermal wavelength; in a deletion trial move an adsorbed molecule is randomly chosen and deleted from the system with the acceptance probability

min[1, Nk exp(-β∆U)/(zkV)]

(4)

While this trial move is not required in GCMC simulation, we have found it to reduce fluctuations after adsorption reaches equilibrium. Usually, adsorption is analyzed as a function of bulk pressure, so an accurate equation of state (EOS) or simulations of the bulk phase are needed to convert chemical potential to bulk pressure. However, an accurate EOS may not be available, and additional simulations are not straightforward and may be time-consuming, especially for the wide range of temperatures, pressures, and compositions needed for mixtures. For this reason, the ideal gas assumption of the bulk phase is usually used; (16) Bojan, M. J.; Steele, W. A. Langmuir 1987, 3, 1123.

min{1, exp[-β(∆UA + ∆UB)]NAk VB/(NBk + 1)VA} (5) Similarly, the probability of acceptance for the deletion of a molecule of species k in the A phase and its creation in the B phase is

min{1, exp[-β(∆UA + ∆UB)]NBk VA/(NAk + 1)VB} (6) The acceptance probability for the trial move of a volume change in the bulk phase is

(3)

Another type of trial move is the exchange of the identity of a molecule, that is, O2 to N2 or vice versa. For an exchange from i to j, the acceptance probability is

min[1, exp(-β∆U)zjNi/zi(Nj + 1)]

however, this assumption may not be accurate. Here, to describe the bulk phase, we use the Peng-Robinson EOS,17 which has been widely used in the petrochemical industry, especially for refinery and reservoir operation. B. NPT Gibbs Ensemble Monte Carlo (NPTGEMC). NPT-GEMC simulation was initially proposed by Panagiotopoulos et al.18 to simulate phase equilibria in mixtures. Two simulation boxes are used, one for the low-density phase and the other for the high-density phase. In such a simulation, the total number of molecules is fixed, but molecules can be transferred from one box to the other. The volume of each simulation box is allowed to fluctuate to maintain pressure equality between the two phases. McGrother and Gubbins19 extended this scheme for adsorption in a narrow pore. The volume of the adsorbed phase within the pore is fixed, but that of the bulk phase is permitted to change at fixed bulk pressure. In this simulation it is not necessary for the pressure to be equal in the adsorbed and bulk phases. Although the computation time required for a NPTGEMC simulation is a little bit longer than that for a GCMC simulation due to the additional moves in the bulk phase, from a NPT-GEMC simulation one can obtain directly the amount of adsorbed gas at fixed bulk pressure, as well as the bulk density; this information is particularly useful if one wants to calculate the excess adsorption isotherm. Five types of trial moves are implemented randomly in the NPT-GEMC simulation: displacement, rotation, creation, deletion in each phase, and volume change of the bulk phase. The first two moves are identical to those in the GCMC, and the acceptance probability is given by eq 1. The creation of a molecule of species k in the adsorbed (A) phase, corresponding to its deletion in the bulk (B) phase, is accepted with the probability of

min{1, exp[-β∆UB - βP∆VB + NB ln(1 + ∆VB/VB)]} (7) where P is the bulk pressure. We have verified that NPT-GEMC and GCMC simulations give nearly identical results for the adsorption of pure O2 and N2 separately in the C168 Schwarzite, and as we will see below, this is also the case for binary mixture adsorption. III. Ideal-Adsorbed-Solution Theory (IAST) IAST developed by Myers and Prausnitz5 is based on a hypothetical mixing process; it is thermodynamically consistent and exact in the limit of zero pressure. This theory has been used widely to calculate the adsorption of mixtures solely from adsorption information on the pure (17) Peng, D. Y.; Robinson, D. B. Ind. Eng. Chem. Res. 1976, 15, 59. (18) Panagiotopoulos, A. Z.; Quirke, N.; Stapleton, M.; Tildesley, D. J. Mol. Phys. 1988, 63, 527. (19) McGrother, S. C.; Gubbins, K. E. Mol. Phys. 1999, 97, 955.

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Table 1. Parameters in the Four-Site Langmuir Model To Fit the Adsorption Isotherms of Pure O2 and N2, Respectively, at 300 K

O2 N2

Nm 1

k1

Nm 2

k2

Nm 3

k3

Nm 4

k4

62.58 38.44

3.68 × 10-3 6.54 × 10-3

16.70 26.20

4.73 × 10-5 7.54 × 10-4

21.24 13.32

1.43 × 10-6 1.20 × 10-6

8.93 19.98

1.42 × 10-9 1.47 × 10-8

components, and the structure of the adsorbent does not appear explicitly. The equilibrium criterion in IAST is

Pi ) P°i (πi)xi

(8)

where Pi is the bulk pressure of gas i, xi is the mole fraction of gas i in the adsorbed phase, and P°i is the hypothetical pressure of pure gas i at the spreading pressure πi when the bulk and adsorbed gases are in equilibrium. The Gibbs adsorption approach gives the spreading pressure πi per unit area as

∫0P°N°i (p) d ln p

πi ) RT

i

(9)

where N°i (p) is the adsorption isotherm of pure gas i. The mixing process is carried out at a constant spreading pressure;20 that is, for every component, we have

π1 ) π2 ) ... ) π

(10)

The amount of gas i adsorbed in the mixture is calculated from

Ni ) xi/

xk

∑k N°(P°) k

(11)

k

In ref 1, we have used a two-site Langmuir model to fit the isotherms of pure O2 and N2. The fit was fairly good but not perfect. To predict the adsorption of the mixture with IAST, there is no restriction on the choice of the model to fit N°i (p), but data over the entire range should be fit very precisely. For this very reason, in this work we use a four-site Langmuir model

kj exp(βµ) Nm j 1 + kj exp(βµ) j)1

Figure 1. Adsorption of an equimolar O2 and N2 mixture at 300 K as a function of the bulk pressure. (a) Average number of the adsorbed gas molecules. The circles are from GCMC, and the lines are from IAST. The inset shows the gas-NPC adsorption energy with the lines to guide the eye. (b) Selectivity of O2 to N2. The triangles are from GCMC, and the solid line is from IAST. The inset shows the portion of low pressure.

4

N° )

∑

(12)

to refit the isotherms of pure O2 and N2, respectively, at 300 K, and the parameters in this model are given in Table 1. We then predict the adsorption of O2 and N2 binary mixture with IAST, which is compared with the simulation results. IV. Results and Discussion Figure 1a shows the adsorption isotherm of an equimolar O2 and N2 mixture as a function of the bulk pressure at 300 K. The solid and open circles are the GCMC simulation results for O2 and N2, respectively. The solid and dashed lines are the predictions of IAST for O2 and N2, respectively. Good agreement between simulation and IAST is found for both gases. At low pressures, N2 is slightly more adsorbed than O2, as was the case for pure gas adsorption. This is a consequence of two factors. First, the bond length lN-N ) 1.10 Å is shorter than lO-O ) 1.208 Å; and second, the collision diameter σC-N ) 3.36 Å is larger than σC-O ) 3.19 Å. Previous NVT ensemble simulations1 at fixed (20) IAST was originally developed for a two-dimensional surface. For a three-dimensional system, rather than the spreading pressure, the grand potential density should be held constant.

number of gas molecules in the C168 Schwarzite have confirmed that either a decrease of the bond length l or an increase of the collision diameter σ leads to an increase in the adsorption energy between adsorbate and adsorbent. Though the well depth C-O/kB ) 37.6K is larger than C-N/ kB ) 33.4K, overall, N2 is energetically favored for adsorption in the C168 Schwarzite. However, above 500 kPa, O2 is preferentially adsorbed, as the size of O2 (σO-O ) 2.99 Å) is smaller than that of N2 (σN-N ) 3.32 Å), and therefore, O2 can fit more easily into a partially filled pore. At higher pressures, the size effect becomes dominant and the amount of adsorbed N2 begins to decrease after having achieved a maximum. The inset, in which the lines have been drawn to guide the eye, shows the adsorption energy of gas-NPC calculated from the interactions between all gas molecules and all carbon atoms. From this we see that at low pressures the adsorption energy of N2-NPC is slightly more attractive (negative) than that of O2-NPC; however, with increasing bulk pressure, the adsorption energy of O2-NPC exceeds that of N2-NPC. Similar to the case of pure gas adsorption, the change from continuous to discontinuous in the center-of-mass density distribution of the adsorbed gas molecules within the pores is also observed here with increasing bulk pressure.

O2 and N2 Mixture Adsorption in C168

Figure 2. Adsorption of an O2 and N2 mixture at 300 K and 102 kPa as a function of the O2 bulk composition. (a) Average number of the adsorbed gas molecules. The circles are from GCMC, the crosses are from NPT-GEMC, and the lines are from IAST. (b) O2 composition in the adsorbed phase. The diamonds are from GCMC, the crosses are from NPT-GEMC, and the solid line is from IAST.

In mixture adsorption, the selectivity (or separation factor) of component i with respect to j is defined by Si/j ) (xi/yi)/(xj/yj), where xi and yi are the compositions of component i in the adsorbed and bulk phases, respectively. The selectivity is a key parameter to quantify the competitive adsorption between two components. When Si/j > 1, component i is preferentially adsorbed; in contrast, if Si/j < 1, component j is preferentially adsorbed. Of course, Si/j ) 1 implies that there is no competition; it is the isoselective point (ISP) at which there is a selectivity reversal from Si/j < 1 to Si/j > 1 or vice versa. Figure 1b shows the selectivity of O2 to N2, SO2/N2, as a function of the bulk pressure. The triangles are from GCMC, and the solid line is from IAST using simulation results of pure gas adsorption. Reasonably good agreement between the simulation results and IAST predictions is obtained. A slight variation in xi or yi can cause a large change in the calculated selectivity, so usually, it is difficult to predict selectivity accurately. The extrapolated limiting value of SO2/N2 at zero pressure is about 0.81, consistent with the value predicted from the Henry’s constants1 by N2 2 KO H /KH ) 0.244/0.301 ) 0.811. With increasing pressure, SO2/N2 first decreases slightly, as shown in the inset for the portion of low pressure, and then increases. The ISP of selectivity reversal is at 500 kPa. Lower than 500 kPa, SO2/N2 is less than 1, implying that N2 is preferentially adsorbed; higher than 500 kPa, SO2/N2 is greater than 1 and O2 is preferentially adsorbed. For an O2 and N2 mixture of yO2:yN2 ) 0.21:0.79 corresponding to air, the selectivity similar to Figure 1b is obtained as a function of the bulk pressure. Intriguingly, the ISP is also at 500 kPa. This implies that the ISP does

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Figure 3. Adsorption of an O2 and N2 mixture at 300 K and 105 kPa as a function of the O2 bulk composition. (a) Average number of the adsorbed gas molecules. The circles are from GCMC, and the lines are from IAST. (b) O2 composition in the adsorbed phase. The diamonds are from GCMC, and the solid line is from IAST.

not change with the bulk composition, and the variation of composition cannot lead to selectivity reversal at fixed pressure. This phenomenon was predicted by a theoretical analysis in a one-dimensional model system.21 Figure 2a shows the adsorption isotherm of an O2 and N2 mixture at 300 K and 102 kPa as a function of yO2, the O2 bulk composition. The circles and crosses are from GCMC and NPT-GEMC simulations, respectively, and are in good agreement with the predictions of IAST denoted by the lines. The amount of adsorbed O2 increases monotonically with increasing yO2, and that of N2 decreases monotonically. Figure 2b shows xO2, the O2 composition in the adsorbed phase as a function of yO2. The diamonds and crosses are from GCMC and NPT-GEMC simulations, respectively, the solid line is from IAST, and agreement between all these results is good. Also, all results are below the dotted diagonal line, which implies that the selectivity of O2 to N2 is less than 1. Similar to Figure 2, Figure 3 shows the adsorption isotherm of an O2 and N2 mixture as a function of yO2 at 300 K and a higher pressure of 105 kPa. Again, the agreement between the results of GCMC simulation and the predictions of IAST is good. With increasing yO2, there is a monotonic increase in the amount of adsorbed O2 but a monotonic decrease in that of N2. Unlike the case of Figure 2 at low pressure, the simulated and predicted xO2 curves are above the dotted diagonal line, which implies that the selectivity of O2 to N2 is larger than 1. Figure 4 shows the center-of-mass density distribution of adsorbed O2 and N2 molecules at 300 K and 105 kPa generated by accumulating 100 configurations within 107 (21) Talbot, J. AIChE J. 1997, 43, 2471.

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Figure 4. Center-of-mass density distribution of O2 and N2 molecules at 300 K and 105 kPa generated by accumulating 100 configurations within 107 trial moves. The black network is the C168 Schwarzite unit cell structure, the red points are the centerof-mass of O2 molecules, and the blue points are the center-of-mass of N2 molecules. (a) yN2 ) 0.90 and xN2 ) 0.86; (b) yO2 ) 0.90 and xO2 ) 0.94.

Figure 5. Angular distribution between the bonds of O2 or N2 molecules and the z axis in the C168 Schwarzite at 300 K and 105 kPa. (a) yN2 ) 0.90 and xN2 ) 0.86; (b) yO2 ) 0.90 and xO2 ) 0.94.

trial moves. The black network is the C168 Schwarzite unit cell structure, red points are the center-of-mass of O2 molecules, and the blue points are the center-of-mass of N2 molecules. The bulk phase is yN2 ) 0.90 in Figure 4a and is yO2 ) 0.90 in Figure 4b. However, due to its smaller size, O2 is preferentially adsorbed over N2. Consequently, the equilibrated adsorbed phase is xN2 ) 0.86 in Figure 4a, while it is xO2 ) 0.94 in Figure 4b. Furthermore, we observe that the center-of-mass distribution in Figure 4a is more discontinuous (and localized) in the small pores than that in Figure 4b. As in ref 1, a phenomenon similar to phase separation occurs, leading to the discontinuous density distribution in the small pores. This is due to the adsorbate-adsorbate repulsion in the small pores because of the short intermolecular distance in the limited pore space. We can expect that, at higher pressures, the density distribution in the large pores will be discontinuous. Figure 5 shows the angular distribution as a function of cos(R) at 300 K and 105 kPa, where R is the angle between the bond of a diatomic molecule and the z axis in the C168 Schwarzite. The angular distribution of O2 and N2, respectively, departs slightly from the value of 0.5 (a uniform angular distribution in the bulk) and shows a maximum at R at 45° (and by symmetry at 135°), implying that there is a slight orientational preference of the adsorbed gas molecules in the direction of the intersectional channels. In Figure 5a, with the N2 bulk composition yN2 ) 0.90, more N2 molecules are adsorbed, and the

Figure 6. Selectivity of O2 to N2 as a function of the O2 bulk composition at 102 and 105 kPa. The triangles are from GCMC, and the lines are from IAST.

variation in the angular distribution of N2 is less than that of O2; the reverse is found in Figure 5b with the O2 bulk composition yO2 ) 0.90. Figure 6 shows the selectivity SO2/N2 as a function of yO2 at two bulk pressures, 102 and 105 kPa. The triangles are from GCMC simulation, the lines are from IAST, and again they are in good qualitative agreement. At 102 kPa lower than the ISP, SO2/N2 is less than 1 and monotonically

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that of N2 first increases and then decreases. This is a consequence of the competitive adsorption between the two gases. Figure 7b shows that the selectivity SO2/N2 decays approximately exponentially with increasing temperature. So these results suggest that temperature, in addition to pressure, can be an important factor in optimizing adsorptive separation for a gas mixture.

Figure 7. Adsorption of an equimolar O2 and N2 mixture at 104 kPa as a function of temperature: (a) average number of the adsorbed gas molecules; (b) selectivity of O2 to N2. The lines are drawn to guide the eye.

decreases with increasing yO2, while, at 105 kPa higher than the ISP, the reverse is found. Additionally, at high pressure, the selectivity is more sensitive to the bulk composition. This type of trend was correctly predicted in a one-dimensional model system.21 Figure 7a shows the adsorption isotherm of an equimolar O2 and N2 mixture as a function of temperature at 104 kPa. The circles are from GCMC simulation, and the lines are drawn to guide the eye. Because adsorption is an exothermic process, a monotonic decrease of adsorption capacity with increasing temperature might be expected, as in ref 1 for pure gases. But this is not the case for the mixture studied here. With increasing temperature, the amount of adsorbed O2 decreases monotonically; however,

V. Conclusions In this work, the adsorption of O2 and N2 mixture in NPC has been investigated by molecular simulations. We show that NPT-GEMC simulation can be used to simulate adsorption at fixed bulk pressure, and consistent results are obtained with those from GCMC simulation. Also, good agreement between the simulation results and the predictions from IAST is found. Competitive adsorption between O2 and N2 occurs at various conditions. At fixed bulk composition, the selectivity of O2 to N2 first decreases slightly and then increases with increasing bulk pressure. The reason for this is that at low pressures the interaction between the gas molecule and the NPC is more attractive for N2 than O2. However, at high pressures the size of the gas molecule becomes more important. Since O2 is a smaller molecule, it can fit into the pores more easily. The ISP of selectivity reversal is independent of the bulk composition. If the bulk pressure is lower than the ISP, the selectivity decreases slightly and monotonically with increasing O2 composition. However, if the bulk pressure is greater than the ISP, the selectivity increases monotonically. With increasing temperature, the selectivity decreases approximately exponentially. These results demonstrate that many factors can affect adsorptive separation for a gas mixture; therefore, optimization of the conditions is needed in practical gas separation processes. Finally, the gas-carbon interaction used in this work is modeled with the site-site Lennard-Jones potential with parameters obtained from a previous study by others of gas adsorption on graphite. The use of these potential parameters is an approximation and, for example, assumes that the interaction of gas with carbon atom is not affected by surface curvature; that is, that it is the same for both graphite and C168 Schwarzite. Ongoing work is to test this assumption using interaction potential in the C168 Schwarzite obtained from quantum chemistry calculations. Acknowledgment. This work is supported by the National Science Foundation under Grant EEC-0085461. LA027030V