J. Phys. Chem. B 2004, 108, 15703-15708
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Assessment of Isoreticular Metal-Organic Frameworks for Adsorption Separations: A Molecular Simulation Study of Methane/n-Butane Mixtures Tina Du1 ren† and Randall Q. Snurr* Department of Chemical and Biological Engineering, Northwestern UniVersity, 2145 Sheridan Road, EVanston, Illinois 60208 ReceiVed: May 22, 2004; In Final Form: July 13, 2004
A wide variety of new nanoporous metal-organic materials are being synthesized by many research groups using supramolecular chemistry and directed assembly in a building block approach based on corner units and linker molecules. These materials may lead to revolutionary advances in adsorption separations because the properties of these materials may be tailored in a synthetically predictable manner. In this paper, we use molecular simulations to assess the suitability of one group of metal organic materials, namely, isoreticular metal-organic frameworks (IRMOFs), as adsorbents for mixture separations. By using grand canonical Monte Carlo simulations, the influence of the linker molecule on the adsorption of methane, n-butane, and their mixtures is determined. Detailed analysis of the energetics as well as the siting of molecules in the cavities allows us to resolve the impact of the linker molecules on the selectivity and to propose new, not yet synthesized materials, which show even higher selectivities. The predicted selectivities are as good as or better than experimentally observed selectivities in other adsorbents, suggesting that IRMOFs are promising materials for the separation of hydrocarbons.
Introduction Recent advances in supramolecular chemistry and metal-based directed-assembly chemistry have yielded a large variety of metal-organic materials having stable pores in the microporous and mesoporous ranges. These materials are generated in a directed-assembly process at mild synthesis conditions and generally consist of metal vertices interconnected by organic linker molecules as shown schematically in Figure 1a. The structures of these materials are very diverse, ranging from discrete molecular objects such as squares, rectangles, or cubes to extended crystalline structures. More and more porous metalorganic materials that might find applications in gas storage or gas separation tasks are emerging.1-3 Because of the variety of possible linker molecules, which may be functionalized to introduce functionalities directly into the framework,4 these materials offer the possibility to tune the host/guest interactions and therefore to tailor the material rationally for a given adsorption separation or storage task. Adsorption isotherms for different sorbate molecules have been measured in several of these materials, as described in several recent reviews,1,2,5 although most of the studies published so far have concentrated on a single sorbate per material to prove that the pores in the materials are stable and accessible to guest molecules. Studies dealing with several different sorbate molecules and addressing the potential use for separations are still scarce.6-9 Molecular simulations are an ideal tool to screen existing structures for a given separation task, and because of the predictability of the syntheses of metal-organic materials, simulations also offer the possibility to test not yet synthesized materials. Additionally, they provide valuable insight at the * Corresponding author. E-mail:
[email protected]. † Present address: Institute for Materials and Processes, School of Engineering and Electronics, Edinburgh University, King’s Buildings, Edinburgh EH9 3JL, U.K.
molecular level, which might help explain phenomena observed macroscopically in metal-organic materials. For example, Vishnyakov et al. used grand canonical Monte Carlo (GCMC) simulations to identify the preferential adsorption sites in CuBTC and were able to determine the pore-filling mechanism of argon in this material.10 By using GCMC simulations and comparing properties of different adsorbents, Du¨ren et al. were able to explain the high methane uptake observed experimentally in some IRMOF materials and to propose new, not yet synthesized materials that are predicted to show an even higher uptake of methane.11 The aim of this paper is to use molecular simulations to assess the suitability of one group of metal-organic materials, namely, isorecticular metal organic frameworks or IRMOFs, as adsorbents for mixture separations and to determine how the linker molecules influence the selectivity. IRMOFs were first synthesized by Yaghi and co-workers.12,13 The corner units of these materials consist of oxide-centered Zn4O tetrahedra linked by six dicarboxylate molecules, resulting in extended 3D networks as illustrated in Figure 1c. By using different linker molecules, porous materials with different cavity sizes and different chemical functionalities have been synthesized.12 Because the linker molecules are oriented in a paddle wheel fashion, each material has two different cavities: one where all the linkers are pointing in and one where they are pointing out. The 3D networks are very open, and the crystal density is very low (see Table 1). Some of these materials showed in experiments a very high uptake of methane12 and hydrogen,14 and in a previous paper,11 we used molecular simulations to explain the role of the linker molecules for methane uptake. Here, we will concentrate on methane/n-butane mixtures. Heavy hydrocarbons such as n-butane are separated from natural gas not only for economical reasons (the price of heavier hydrocarbons is much higher than that of methane, which is used primarily as fuel) but also to prevent liquid slugs that can
10.1021/jp0477856 CCC: $27.50 © 2004 American Chemical Society Published on Web 09/08/2004
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Figure 1. (a) Schematic representation of the directed-assembly process of metal-organic materials from corner and linker units. (b) Building blocks for different IRMOF materials. The empty lines at the corner unit indicate where the linker molecules bind. (c) A full unit cell and the resulting extended 3D network of IRMOF-1. The blue sphere in the complete larger cavity shown here was added to illustrate its size.
TABLE 1: Properties of the IRMOF Materials Investigateda
IRMOF-1 IRMOF-8 IRMOF-10 IRMOF-14 IRMOF-16
dcavity Å
Sacc m2/cm3
Vfree %
Fcrys g/cm3
10.9/14.3 12.5/17.1 16.7/20.2 14.7/20.1 23.3
1891 1897 1611 1812 1294
81 86 89 85 92
0.59 0.49 0.33 0.37 0.21
a The cavity diameters (dcavity), accessible surface area (Sacc), free volume (Vfree), and crystal density (Fcrys) were calculated from the crystal structure as described in the text.
form from condensates during natural gas distribution. Currently, the separation is done with cryogenic processes or by adsorption in activated carbons.15 Furthermore, there are existing force fields that showed excellent quantitative agreement between experimentally measured and simulated isotherms for methane and n-butane in zeolites. For this study, we have chosen five different IRMOFs, namely, IRMOF-1, IRMOF-8, IRMOF-10, IRMOF-14, and IRMOF-16 (Figure 1b). The properties of these materials are summarized in Table 1. IRMOF-1, IRMOF-10, and IRMOF-16 form a series with increasing cavity diameter where the linker molecules are expanded by additional benzene molecules from benzenedicarboxylate to triphenyldicarboxylate. IRMOF-10 and IRMOF-14 have the same pore size, yet the pyrene molecule of IRMOF-14 contains more carbon atoms so that the interaction of sorbate molecules with the framework will be stronger in IRMOF-14. The size of the cavities in IRMOF-8 lies between the cavities for IRMOF-1 and IRMOF-
10, but IRMOF-8 with its 2,6-naphthalenedicarboxylate linker molecule has a higher concentration of carbon atoms per length of the linker molecule. Simulation Details Adsorption isotherms were simulated with grand canonical Monte Carlo (GCMC) simulations. Detailed descriptions of the simulation method are given in several references.16,17 In the grand canonical ensemble, the chemical potential of each component, the temperature, and the volume are kept constant as in adsorption experiments. For the sorbate molecules as well as for the IRMOF frameworks, atomistic models were employed. The van der Waals interactions between the sorbate molecules themselves as well as between the sorbate molecules and the IRMOF materials were described with the Lennard-Jones potential. Interactions beyond 12.8 Å were neglected, and the Lorentz-Berthelot mixing rules were used to calculate mixed Lennard-Jones parameters. The sorbate molecules were described with a united atom description, i.e., methane molecules were represented by a single interaction site, whereas n-butane was described by four interaction sites. The potential parameters for methane were taken from Goodbody et al.18 (σCH4 ) 3.73 Å, CH4/kB ) 148 K), and the TraPPE potential19 was used to describe the n-butane interactions (σCH3 ) 3.75 Å, CH3/kB ) 98 K, σCH2 ) 3.95 Å, CH2/kB ) 46 K). This potential has been successfully employed to describe the adsorption of alkanes in zeolites quantitatively.20 The Lennard-Jones parameters for the IRMOF framework were taken from the DREIDING force field.21 The atoms of the IRMOFs were held fixed at their
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crystallographic coordinates.12 We have shown before11 that the DREIDING potential together with the potential parameters given by Goodbody et al. gives quantitative agreement between experimentally measured and simulated methane isotherms in IRMOF-1 and IRMOF-6. This strongly suggests that similar results can be achieved for the other IRMOF materials for which experimental adsorption isotherms have not yet been measured. Standard GCMC simulations with one million steps were carried out for the pure methane adsorption isotherms. Careful checks revealed that the systems were fully equilibrated after 400 000 steps, leaving another 600 000 steps to sample the data. For the simulation of n-butane as well as for the simulation of the mixtures, the configurationally biased technique as described by Macedonia and Maginn22 was used with two million equilibration steps and three million production steps. The production period was divided into 20 blocks, and averages were calculated for each block separately. Afterward, the Student’s t distribution was used to calculate the statistical error. All simulations were carried out at 298 K. The output of a GCMC simulation is the absolute amount adsorbed, and experimentally the excess amount adsorbed is measured. The excess number of molecules, nex, is related to the absolute number of molecules, nabs, by
nex ) nabs - VgFg
(1)
where Vg is the pore volume of the adsorbent determined according to ref 23 and Fg is the molar density of the bulk gas phase calculated with the Peng-Robinson equation of state. All simulation results are reported as excess quantities unless otherwise specified. The isosteric heat of adsorption at low loading, Qst, was calculated from24
Qst ) HR + RT - 〈V 〉 - 〈N〉
( ) ∂〈V 〉 ∂〈N〉
(2)
T,V
where HR is the molar residual enthalpy of the pure component in the real gas state, R is the gas constant, 〈V 〉 is the average potential energy per molecule, and 〈N〉 is the average number of molecules adsorbed. At low loading and therefore at low pressure, the gas phase is ideal, and the average potential energy per molecule 〈V 〉 is constant so that eq 2 can be simplified to
Qst ) RT - 〈V 〉
(3)
Pore size distributions were calculated according to the method of Gelb and Gubbins.25 The accessible surface area defined by the center of a nitrogen molecule rolling on the surface was calculated by a simple Monte Carlo simulation.11 The nitrogen molecule had a diameter of 4.54 Å. This value corresponds to a cross-sectional area of 0.162 nm2, which is commonly used to get the surface area with the BET method.26 Results Figure 2a shows the calculated pure component isotherms of methane in the different IRMOF materials. They clearly show that the methane isotherms are still far from saturation even at 4000 kPa. This results directly from the rather large pores in the IRMOF materials, which are on the boundary between micropores and mesopores. See Table 1. The pure component isotherms of n-butane shown in Figure 2b demonstrate three trends. First, the maximum amount adsorbed clearly depends on the cavity size and increases with increasing cavity size. Consequently, IRMOF-16 shows the highest saturation loading of n-butane, and the maximum
Figure 2. Pure component adsorption isotherms in different IRMOF materials (*, IRMOF-1; 0, IRMOF-8; ×, IRMOF-10; O, IRMOF-14; 2, IRMOF-16) (a) methane and (b) n-butane. The error bars lie within the symbols.
amounts adsorbed for IRMOF-10 and IRMOF-14 are the same. A similar trend would presumably be observed for the methane isotherms at higher pressure. Yet, as the isotherms at 4000 kPa (40 bar) are still far away from saturation for methane, this phenomenon cannot be seen in Figure 2a. The second trend is that the point of capillary condensation is shifted toward lower pressure with decreasing cavity size. The bulk condensation pressure of n-butane at 298 K is 243 kPa, which is well predicted by the TraPPE potential.19 We note in passing that hysteresis was not observed for any of the materials. Finally, for a given pore size, capillary condensation, which is marked in the simulations by large fluctuations in the density, occurs at lower pressure for the material with more carbon atoms in the linker molecule, as revealed by the adsorption isotherms of IRMOF10 and IRMOF-14. Therefore, the point of capillary condensation strongly depends on the strength of the interaction of the n-butane molecules with the IRMOF frameworks. Two measures of the interaction strengthsHenry’s constant and the isosteric heat of adsorption at low coveragesare summarized in Table 2. A detailed analysis of the energetics is given in Figure 3, where the total interaction is split into the sorbate-sorbate interaction and the sorbate-framework interaction. At a given loading, the sorbate-sorbate interaction increases with decreasing cavity size as the molecules are forced to be closer together in smaller pores. This trend is the same for methane and n-butane. The sorbate-sorbate energy is mainly influenced by the size of the cavity and not by the linker molecule; therefore, the interaction between the molecules in IRMOF-10 and IRMOF-14 is the same. In small pores such as IRMOF-1, the sorbate-sorbate energy changes with loading faster than the sorbate-framework energy (i.e., the slope is larger in absolute value), resulting in a decrease in the total energy for IRMOF-1 with loading, whereas the total energy per molecule for IRMOF16 is nearly constant with loading (not shown). For the sorbate-framework interactions, Figure 3 shows two competing effects. In general, the interaction energy becomes stronger with decreasing cavity size and also with increasing number of carbon atoms in the linker molecule. Therefore, the methane-framework interaction for IRMOF-8 and IRMOF-14 is about the same, although IRMOF-8 has smaller cavities than IRMOF-14. In the case of n-butane, which consists of four united atom groups each interacting with the framework, the n-butane-framework energy is even stronger in IRMOF-14 than in IRMOF-8. In general, the sorbate-framework interaction weakens with increasing loading as more molecules are forced to the center of the cavities where the influence of the framework is smaller. The linker molecules also have a strong influence on the selectivity as demonstrated by Figure 4, which shows the
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TABLE 2: Henry’s Constants (KH) and Isosteric Heats of Adsorptions at Low Loading (Qst) for Methane and n-Butane in the Different IRMOF Materials KH(CH4)/10-9 mol cm-3 Pa-1 KH(C4H10)/10-9 mol cm-3 Pa-1 Qst(CH4)/kJ mol-1 Qst(C4H10)/kJ mol-1
IRMOF-1
IRMOF-8
IRMOF-10
IRMOF-14
IRMOF-16
2.83 197 10.5 25.3
4.02 246 10.1 25.4
1.39 53 9.0 23.8
2.03 139 10.1 26.2
0.79 26 7.8 23.6
Figure 3. Sorbate-sorbate potential energy (upper curves, dotted lines) and sorbate-IRMOF interactions (lower curves, solid lines) as function of the absolute number of molecules in the framework in different IRMOF materials (*, IRMOF-1; 0, IRMOF-8; ×, IRMOF-10; O, IRMOF-14; 2, IRMOF-16) (a) methane and (b) n-butane. Results are shown only in the range below the point of capillary condensation for n-butane.
Figure 4. Selectivity toward n-butane as a function of the bulk mole fraction of methane in different IRMOF materials (*, IRMOF-1; 0, IRMOF-8; ×, IRMOF-10; O, IRMOF-14; 2, IRMOF-16) (a) at 10 kPa and (b) at 100 kPa. The selectivity is defined as SC4H10/CH4 ) (xC4H10/ xCH4)/(yC4H10/yCH4), where x is the mole fraction in the adsorbed phase and y is the mole fraction in the bulk gas phase. Error bars that are not shown lie within the symbols.
selectivity toward n-butane at 10 and 100 kPa as a function of the methane mole fraction in the bulk. At 10 kPa, only the selectivity in IRMOF-1 varies with bulk mole fraction, showing a maximum around yCH4 ) 0.04. The selectivity in the other materials is nearly constant. This behavior is coupled to the point of capillary condensation of the pure n-butane adsorption isotherms. As shown in Figure 2b, the point of capillary condensation for n-butane is greater than 10 kPa for all materials except IRMOF-1. Consequently, for these materials the partial pressure of n-butane in Figure 4 corresponds to the linear region of the pure component isotherm. This is also the case for methane, so that the selectivity hardly changes. However, at high mole fractions of n-butane in IRMOF-1 (i.e., low mole fractions of methane), the partial pressure of butane corresponds to values beyond the steep increase in the pure component isotherm, resulting in large selectivities. At 100 kPa, the partial pressures of n-butane in all materials are large enough that this situation occurs in all materials except IRMOF-16. As shown in Figure 4b, the selectivity of all materials except IRMOF-16 is large and exhibits a sudden drop for smaller mole fractions of n-butane. In general, the selectivity increases with decreasing cavity size and with increasing number of carbon atoms in the
Figure 5. (a) Mixture adsorption isotherms in IRMOF-8 at 100 kPa as a function of the bulk mole fraction of methane from mixture GCMC simulations (methane, open symbols; n-butane, closed symbols) and from estimations from the pure component isotherms (methane, solid line; n-butane, dashed line). (b) Selectivity in IRMOF-8 at 100 kPa from mixture GCMC simulations (symbols) and estimates from pure adsorption isotherms (dashed dotted line). Error bars that are not shown lie within the symbols.
framework and therefore with increasing interaction between the sorbate molecules and the framework. Furthermore, the sudden drop in the selectivity is shifted toward higher mole fractions of methane with decreasing pore size or increasing interaction energy, which is desirable to remove trace amounts of n-butane from methane (e.g., in natural gas). An oscillation of the selectivity with pore size, which occurs in microporous cylindrical, slitlike, and spherical pores27 because of packing effects at high densities, is not observed in the IRMOF materials because they have a scaffold structure that hinders the formation of distinct layers and the pores are rather large. The packing effects are more pronounced in small pores where the interaction with the pore walls is strongly felt throughout the whole pore. This means that the large selectivity toward n-butane in Figure 4 is purely due to the energetic advantage that the n-butane molecules have over the methane molecules. That the drop in the selectivity is really connected to the pure component isotherm is demonstrated in Figure 5 for the example of IRMOF-8. A comparison between (1) the values predicted by the mixture GCMC simulations and (2) the values estimated from the pure component isotherm using the gas-phase partial pressures shows that the amount of adsorbed n-butane is independent of the presence of methane in the mixture whereas the methane molecules are affected by the presence of the n-butane molecules. Thus, mixture effects do not play a role. Similar behavior for the heavier hydrocarbon was also observed in some zeolites.28 Figure 5a also shows that at high mole fractions of n-butane the amount of adsorbed methane is much smaller than estimated from the pure component isotherms. Therefore, the selectivity presented in Figure 5b from GCMC is much larger than that estimated from the pure component isotherms. In IRMOF-8, the point of capillary condensation for pure n-butane is around 20 kPa, which corresponds to the desorption of n-butane at yCH4 ) 0.8 in Figure 5a and to the steep decrease in the selectivity of the mixture simulations in Figure 5b. The mechanism of the pore emptying is illustrated in Figure 6. At yCH4 ) 0.8, n-butane molecules greatly outnumber the methane molecules in the adsorbed phase (Figure 5a) and are closely packed throughout the cavities as revealed by Figure
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Figure 6. Snapshots of methane (black spheres) and n-butane (yellow molecules) mixtures in IRMOF-8 at 100 kPa and different mole fractions of methane in the bulk for (a) yCH4 ) 0.8 and (b) yCH4 ) 0.86.
Figure 7. Density distribution of methane/n-butane mixtures in IRMOF-8 at 100 kPa and yCH4 ) 0.8. Each dot represents the position of the center of mass of a molecule during the simulation (black, methane; yellow, n-butane). Note that the radius of the dots for methane is 1.5 times larger than that for n-butane in order to accent the less abundant methane molecules.
6a. With growing mole fraction of methane in the bulk, n-butane molecules start to desorb, and the cavities start to empty. Figure 6b shows that the emptying starts in the middle of the cavities where the interactions between the molecules and the framework are weaker. At both mole fractions, the methane molecules seem
to be pushed to the energetically less favorable center of the pores. This observation is backed up by Figure 7, which shows the density distribution in IRMOF-8 at yCH4 ) 0.8 over the whole course of the simulation. The n-butane molecules are primarily located in the favorable corner regions and force the methane molecules to adsorb more uniformly throughout the cavities. The observation that the selectivity toward n-butane increases with decreasing cavity size and increasing number of carbon atoms in the linker molecule makes IRMOF-993 an attractive candidate for the separation of n-butane/methane mixtures. IRMOF-993 is a structure that we proposed previously for the storage of methane.11 The 9,10-anthracenedicarboxylate linker molecule in IRMOF-993 introduces eight additional carbon atoms compared to the 1,4-benzenedicarboxylate linker molecule in IRMOF-1 and results in a reduced size of the smaller cavities (d ) 6.3 Å/14.5 Å in IRMOF-993, d ) 10.9/14.3 Å in IRMOF1), as illustrated in Figure 8a. Figure 8b shows the performance of IRMOF-993 in comparison to IRMOF-1 for the removal of trace amounts of n-butane from methane.29 The selectivity in IRMOF-993 is dramatically increased in comparison to that in IRMOF-1 and shows a maximum of 2720 at 25 kPa for yCH4 ) 0.99 and a maximum of 2460 kPa at 150 kPa for yCH4 ) 0.999, whereas the maximum selectivity for IRMOF-1 is 200 at 1000 kPa for yCH4 ) 0.99 and 90 at 2500 kPa for yCH4 ) 0.999. Because n-butane shows capillary condensation at the conditions studied here, a further increase in the pressure beyond the maximum does not enhance the amount of n-butane adsorbed, whereas
Figure 8. (a) Linker molecule of IRMOF-993 and the resulting material and (b) selectivity toward n-butane as a function of the bulk pressure (O yCH4 ) 0.99, ∆ yCH4 ) 0.999) in IRMOF-1 (open symbols) and IRMOF-993 (filled symbols). The error bars lie within the symbols.
15708 J. Phys. Chem. B, Vol. 108, No. 40, 2004 the amount of methane adsorbed is still increasing, thus causing the maximum in the selectivity curves. The absolute amount of butane adsorbed shows a maximum with increasing pressure in these mixtures (not shown). For example, for IRMOF-993 at yCH4 ) 0.99, this maximum is observed at around 1000 kPa. This indicates that because of their entropic advantage the smaller methane molecules are able to displace the energetically favored butane chains, thus contributing to the decrease in the selectivity with increasing pressure. To assess the performance of IRMOF materials for methane/ butane separations, we compared the simulated selectivities with experimentally measured selectivities in commonly used adsorbents. For example, the experimentally measured selectivity in silicalite for a methane/n-butane mixture containing 96.3% methane is 150,30 and the selectivity of a mixture containing 99.4% methane in BPL activated carbon shows a maximum selectivity of 1464 at 101 kPa.31 Our simulated selectivities fall into this range. Furthermore, molecular dynamics simulations of n-alkanes in IRMOF-132 and argon in Cu-BTC33 (a different metal-organic framework) showed that diffusion in metalorganic materials is similar to that in zeolites, implying that diffusion will not impose a serious restriction on the use of IRMOFs in separations. Conclusions In this paper, the suitability of IRMOF materials as adsorbents for the separation of hydrocarbons was assessed using molecular simulations. The influence of the linker molecule on the adsorption of pure methane, pure n-butane, and their mixtures was investigated. Because the pore sizes of the investigated IRMOF materials lie between 10.9 and 23.3 Å and are therefore on the boundary between microporous and mesoporous materials, the methane adsorption isotherms are far from saturation even at 4000 kPa. For the n-butane isotherms, three trends could be observed. First, the maximum amount adsorbed increases with increasing cavity size. Second, the smaller the cavity size, the further the point of capillary condensation is shifted toward lower pressure. Third, for a given pore size, capillary condensation occurs at lower pressure for materials with more carbon atoms in the linker molecule, which is directly related to the strength of the interaction of a sorbate molecule with the IRMOF material. The selectivity also varies strongly with the linker molecule. The selectivity toward n-butane increases with decreasing cavity size and increasing number of carbon atoms in the linker molecule. A detailed study of the siting of the molecules revealed that the energetically favored n-butane molecules prefer to sit in the corner regions of the IRMOF cavities whereas the smaller methane molecules are forced to occupy the energetically less favorable center of the cavities. On the basis of these analyses, we proposed a new, not yet synthesized IRMOF material that shows even higher selectivities. Using 9,10-anthracenedicarboxylate as the linker molecule, we predict selectivities for mixtures with trace amounts of n-butane that are comparable to the best values measured experimentally on activated carbons, suggesting that IRMOFs are promising materials for such separations. Because of the building block approach of metal-organic materials, there is a
Du¨ren and Snurr high probability of success in synthesizing IRMOFs with new linkers such as 9,10-anthracenedicarboxylate. This makes molecular simulations a very powerful tool for screening new and hypothetical materials for particular objectives and guiding the synthesis of new materials. Our future work will include experimental studies to confirm these results. Acknowledgment. We thank Omar M. Yaghi and his group for helpful discussions and the U.S. Department of Energy and the Alexander von Humboldt foundation for financial support. References and Notes (1) Janiak, C. Dalton Trans. 2003, 2781. (2) James, S. L. Chem. Soc. ReV. 2003, 32, 276. (3) Noro, S.; Kitaura, R.; Kondo, M.; Kitagawa, S.; Ishii, T.; Matsuzaka, H.; Yamashita, M. J. Am. Chem. Soc. 2002, 124, 2568. (4) Papaefstathiou, G. S.; MacGillivray, L. R. Coord. Chem. ReV. 2003, 246, 169. (5) Snurr, R. Q.; Hupp, J. T.; Nguyen, S. T. AIChE J. 2004, 50, 1090. (6) Wang, Q. M.; Shen, D. M.; Bulow, M.; Lau, M. L.; Deng, S. G.; Fitch, F. R.; Lemcoff, N. O.; Semanscin, J. Microporous Mesoporous Mater. 2002, 55, 217. (7) Dybtsev, D. N.; Chun, H.; Yoon, S. H.; Kim, D.; Kim, K. J. Am. Chem. Soc. 2004, 126, 32. (8) Pan, L.; Sander, M. B.; Huang, X. Y.; Li, J.; Smith, M.; Bittner, E.; Bockrath, B.; Johnson, J. K. J. Am. Chem. Soc. 2004, 126, 1308. (9) Kosal, M. E.; Chou, J. H.; Wilson, S. R.; Suslick, K. S. Nat. Mater. 2002, 1, 118. (10) Vishnyakov, A.; Ravikovitch, P. I.; Neimark, A. V.; Bulow, M.; Wang, Q. M. Nano Lett. 2003, 3, 713. (11) Du¨ren, T.; Sarkisov, L.; Yaghi, O. M.; Snurr, R. Q. Langmuir 2004, 20, 2683. (12) Eddaoudi, M.; Kim, J.; Rosi, N.; Vodak, D.; Wachter, J.; O’Keefe, M.; Yaghi, O. M. Science 2002, 295, 469. (13) Li, H.; Eddaoudi, M.; O’Keeffe, M.; Yaghi, O. M. Nature 1999, 402, 276. (14) Rosi, N. L.; Eckert, J.; Eddaoudi, M.; Vodak, D. T.; Kim, J.; O’Keeffe, M.; Yaghi, O. M. Science 2003, 300, 1127. (15) Arruebo, M.; Coronas, J.; Menendez, M.; Santamaria, J. Sep. Purif. Technol. 2001, 25, 275. (16) Frenkel, D.; Smit, B. Understanding Molecular Simulation: From Algorithms to Applications, 2nd ed.; Academic Press: San Diego, CA, 2002. (17) Allen, M. P.; Tildesley, D. J. Computer Simulations of Liquids; Clarendon Press: Oxford, U.K., 1987. (18) Goodbody, S. J.; Watanabe, K.; Macgowan, D.; Walton, J. P. R. B.; Quirke, N. J. Chem. Soc., Faraday Trans. 1991, 87, 1951. (19) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 2569. (20) Ndjaka, J. M. B.; Zwanenburg, G.; Smit, B.; Schenk, M. Microporous Mesoporous Mater. 2004, 68, 37. (21) Mayo, S. L.; Olafson, B. D.; Goddard, W. A. J. Phys. Chem. 1990, 94, 8897. (22) Macedonia, M. D.; Maginn, E. J. Mol. Phys. 1999, 96, 1375. (23) Myers, A. L.; Monson, P. A. Langmuir 2002, 18, 10261. (24) Heuchel, M.; Snurr, R. Q.; Buss, E. Langmuir 1997, 13, 6795. (25) Gelb, L. D.; Gubbins, K. E. Langmuir 1999, 15, 305. (26) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption by Powders and Porous Solids; Academic Press: San Diego, CA, 1999. (27) Keffer, D.; Davis, H. T.; McCormick, A. V. J. Phys. Chem. 1996, 100, 638. (28) Adhangale, P.; Keffer, D. Langmuir 2002, 18, 10455. (29) Du¨ren, T.; Sarkisov, L.; Snurr, R. Q. Molecular Modeling of Advanced Materials for Adsorption and Membrane Separations. 3rd International Conference on Computational Modeling and Simulation of Materials, in press. (30) Abdul-Rehman, H. B.; Hasanain, M. A.; Loughlin, K. F. Ind. Eng. Chem. Res. 1990, 29, 1525. (31) Grant, R. J.; Manes, M. Ind. Eng. Chem. Fundam. 1966, 5, 490. (32) Sarkisov, L.; Du¨ren, T.; Snurr, R. Q. Mol. Phys. 2004, 102, 211. (33) Skoulidas, A. I. J. Am. Chem. Soc. 2004, 126, 1356.
