Storage and Separation of CO2 and CH4 in Silicalite, C168

Nov 17, 2006 - Porous Polymer Networks: Synthesis, Porosity, and Applications in Gas Storage/Separation. Weigang Lu , Daqiang Yuan , Dan Zhao , Christ...
0 downloads 14 Views 701KB Size
Download PDF
Langmuir 2007, 23, 659-666

659

Storage and Separation of CO2 and CH4 in Silicalite, C168 Schwarzite, and IRMOF-1: A Comparative Study from Monte Carlo Simulation Ravichandar Babarao, Zhongqiao Hu, and Jianwen Jiang* Department of Chemical & Biomolecular Engineering, National UniVersity of Singapore, 4 Engineering DriVe 4, Singapore 117576

Shaji Chempath Department of Chemical Engineering, UniVersity of California, Berkeley, California 94720

Stanley I. Sandler Department of Chemical Engineering, UniVersity of Delaware, Newark, Delaware 19716 ReceiVed August 3, 2006. In Final Form: September 23, 2006 Storage of pure CO2 and CH4 and separation of their binary mixture in three different classes of nanostructured adsorbentsssilicalite, C168 schwarzite, and IRMOF-1shave been compared at room temperature using atomistic simulation. CH4 is represented as a spherical Lennard-Jones molecule, and CO2 is represented as a rigid linear molecule with a quadrupole moment. For pure component adsorption, CO2 is preferentially adsorbed than CH4 in all the three adsorbents over the pressure range under this study, except in C168 schwarzite at high pressures. The simulated adsorption isotherms and isosteric heats match closely with available experimental data. A dual-site LangmuirFreundlich equation is used to fit the isotherms satisfactorily. Compared to silicalite and C168 schwarzite, the gravimetric adsorption capacity of pure CH4 and CO2 separately in IRMOF-1 is substantially larger. This implies that IRMOF-1 might be a potential storage medium for CH4 and CO2. For adsorption from an equimolar binary mixture, CO2 is preferentially adsorbed in all three adsorbents. Predictions of mixture adsorption with the ideal-adsorbed solution theory on the basis of only pure component adsorption agree well with simulation results. Though IRMOF-1 has a significantly higher adsorption capacity than silicalite and C168 schwarzite, the adsorption selectivity of CO2 over CH4 is found to be similar in all three adsorbents.

I. Introduction Combustion of fossil fuels has generated a huge amount of greenhouse gas CO2. The relationship between anthropogenic emission of CO2 and increased temperature has been well recognized, and the effect of increasing atmospheric CO2 concentration on global warming is now regarded as one of the most pressing environmental issues. To reduce the atmospheric level of CO2 while minimizing the world economic impact, four strategies have been proposed: (1) carbon sequestration, (2) less carbon-intensive fuels, (3) more energy-efficient methods, and finally (4) increased conservation. It is expected that CO2 sequestration to be implemented in the coming 30 years will be both economically and environmentally attractive,1 and several approaches have been developed such as chemical conversion, solvent absorption, deep-sea deposition, and adsorption in porous media. Compared to the commonly used purification technique of CO2 absorption, adsorption is technically feasible, affordable, and energy-efficient.2 In the long run, use of less carbon-intensive fuels, for example, natural gas, will help in reducing overall CO2 emissions. The major component in natural gas is CH4, and thus it is essential to find a suitable adsorptive material for CH4 storage. On the other hand, CO2 is often found as a major impurity in * Author to whom correspondence should be addressed. Tel: (65) 6516 5083. Fax: (65) 6779 1936. E-mail: [email protected]. (1) White, C. M.; Smith, D. H.; Jones, K. L.; Goodman, A. L.; Jikich, S. A.; LaCount, R. B.; DuBose, S. B.; Ozdemir, E.; Morsi, B. I.; Schroeder, K. T. Energy Fuels 2005, 19, 659. (2) Ruthven, D. M.; Farooq, S.; Knaebel, K. Pressure Swing Adsorption; VCH Publishers: New York, 1994.

natural gas,3 and its presence can reduce the energy content of natural gas. Consequently, in addition to the storage of pure CO2 and CH4 separately, it is also important to separate them from their mixture. By a careful selection of the adsorbent, CO2 and CH4 can be effectively separated on the basis of the different adsorption affinities. Several experimental and simulation studies have been reported on the adsorption of gases in various adsorbents, and many of these have been summarized in two recent books.4,5 Using the Monte Carlo method, Yue and Yang6 studied the influence of temperature, pressure, and composition on the adsorption of pure and binary mixture of CO2 and benzene in silicalite. Goj et al.7 simulated the adsorption of CO2 and N2, both as single component and as binary mixture, in three zeolites with identical chemical composition but differing pore structures. Eckhard and Matthias8 analyzed the adsorption of binary mixture of CH4/CF4 in silicalite using a gravimetric method and compared with the prediction of the ideal-adsorbed solution theory (IAST) and a multisite Langmuir model on the basis of the adsorption of single components. Sarkar and Bose9 used activated carbon pellets to (3) Singh, D.; Croiset, E.; Douglas, P. L.; Douglas, M. A. Energy ConVers. Manage. 2003, 44, 3073. (4) Keller, J.; Staudt, R. Gas Adsorption Equilibria: Experimental Methods and AdsorptiVe Isotherms; Springer: New York, 2004. (5) Computer Modelling of Microporous Materials; Catlow, C. R. A., van Santen, R. A., Smit, B., Eds.; Elsevier: Amsterdam, 2004. (6) Yue, X. P.; Yang, X. N. Langmuir 2006, 22, 3138. (7) Goj, A.; Sholl, D. S.; Akten, E. D.; Kohen, D. J. Phys. Chem. B 2002, 106, 8367. (8) Buss, E.; Heuchel, M. J. Chem. Soc., Faraday Trans. 1997, 93, 1621. (9) Sarkar, S. C.; Bose, A. Energy ConVers. Manage. 1997, 38, S105.

10.1021/la062289p CCC: $37.00 © 2007 American Chemical Society Published on Web 11/17/2006

660 Langmuir, Vol. 23, No. 2, 2007

Babarao et al.

study the removal of CO2. Jiang and Sandler10-12 investigated the adsorption of O2 and N2 in carbon nanotube bundles and of CO2 and N2 in C168 schwarzite as a model for nanoporous carbon. In addition, there are a few studies of the adsorptive separation of CO2/CH4 mixtures in porous materials. Nicholson and Gubbins13 examined the effects of geometry and energetics on the selectivity from a CO2/CH4 mixture. Peng et al.14 measured the adsorption of pure and mixed CO2 and CH4 in activated mesocarbon microbeads and used an equation of state to correlate the experimental data. Vu et al.15 used carbon molecular hollow fiber membranes for CH4/CO2 separation at different temperatures with high pressure mixed-gas feed of 10% CO2 and 90% CH4. The selection of a suitable adsorbent is a key step in the design of adsorption-based storage or separation processes. As mentioned above, most studies have focused on zeolites and carbon-based adsorbents. Recently, a new class of porous materials has been developed, the metal organic frameworks (MOFs), which consist of metal-oxide clusters and organic linkers.16-18 Inorganic porous materials, such as zeolites in which the Si-O and Al-O bonds have tetrahedral oxide skeletons, generally can be produced in only a limited range of structures. Essentially as organic zeolites, MOFs allow the formation of flexible porous frameworks with a wide variety of architectures, topologies, and pore sizes. They provide almost unlimited opportunities to develop, control, and tune structures for specific applications.19 Because of their high porosity and well-defined pore size, MOFs are promising candidates for the storage of gases, the separation of mixtures, and ion-exchanges.20 In this work, using atomistic simulation, we have investigated the storage capacity for pure CO2 and CH4 and the separation of their binary mixture in three different adsorbents: silicalite, C168 schwarzite, and IRMOF-1. Each of them has a well-defined three-dimensional periodic structure with nanoscaled channels, and each represents a typical class of nanoporous material. In section II, we describe the models used for the three adsorbents and the two adsorbates. In section III, the Monte Carlo simulation method is briefly described. The adsorption isotherms of both pure and binary components, isosteric heats of adsorption, Henry constants, and simulation snapshots are presented in section IV, followed by concluding remarks in section V.

II. Models Silicalite. Usually denoted as MFI, silicalite is an Al-free zeolite existing in three distinct crystal forms: monoclinic and Pnma and P212121 orthorhombic structures. In this work, we consider the Pnma orthorhombic structure. The unit cell has 96 Si atoms and 192 O atoms, and the lattice constants are a ) 20.06 Å, b ) 19.80 Å, and c ) 13.36 Å. As shown in Figure 1a, MFI consists of two types of channels with 10-membered rings, one is straight and the other is zigzag (sinusoidal). These channels have diameters of approximately 5.4 Å. This implies that an adsorbate molecule with a van der Waals diameter of (10) Jiang, J. W.; Sandler, S. I. Langmuir 2003, 19, 5936. (11) Jiang, J. W.; Sandler, S. I. Langmuir 2004, 20, 10910. (12) Jiang, J. W.; Sandler, S. I. J. Am. Chem. Soc. 2005, 127, 11989. (13) Nicholson, D.; Gubbins, K. E. J. Chem. Phys. 1996, 104, 8126. (14) Peng, X.; Wang, W. C.; Xue, R. S.; Shen, Z. M. AIChE J. 2006, 52, 994. (15) Vu, D. Q.; Koros, W. J.; Miller, S. J. Ind. Eng. Chem. Res. 2002, 41, 367. (16) Yaghi, O. M.; O’Keeffe, M.; Ockwig, N. W.; Chae, H. K.; Eddaoudi, M.; Kim, J. Nature (London) 2003, 423, 705. (17) Eddaoudi, M.; Kim, J.; Rosi, N.; Vodak, D.; Wachter, J.; O’Keefe, M.; Yaghi, O. M. Science 2002, 295, 469. (18) Rosi, N. L.; Eckert, J.; Eddaoudi, M.; Vodak, D. T.; Kim, J.; O’Keeffe, M.; Yaghi, O. M. Science 2003, 300, 1127. (19) Rowsell, J. L. C.; Yaghi, O. M. Microporous Mesoporous Mater. 2004, 73, 3. (20) Snurr, R. Q.; Hupp, J. T.; Nguyen, S. T. AIChE J. 2004, 50, 1090.

Figure 1. Nanosized channels in MFI, C168, and IRMOF-1. (a) MFI has one straight channel and one zigzag channel, (b) C168 has two zigzag channels, and (c) IRMOF-1 has one straight channel.

about 5.4 Å or less can fit inside these channels. A unit cell has two straight channels, two zigzag channels, and two channel intersections.21 The potential parameters of the Si and O atoms were taken from the work of Hirotani et al.,22 as listed in Table 1, which had been optimized to reproduce the experimental heats of adsorption. In most of the previous simulation studies of adsorption in zeolites, the short-ranged dispersion interaction of Si atoms was neglected because of its weak contribution, and thus only electrostatic interaction was taken into account. To model the framework full atomistically, in this work both the (21) Flanigen, E. M. B.; Bennett, J. M.; Grose, R.W.; Cohen, J. P.; Patton, R. L.; Kirchner, R. M.; Smith, J. V. Nature (London) 1978, 271 (5645), 512. (22) Hirotani, A.; Mizukami, K.; Miura, R.; Takaba, H.; Miya, T.; Fahmi, A.; Stirling, A.; Kubo, M.; Miyamoto, A. Appl. Surf. Sci. 1997, 120, 81.

Storage and Separation of CO2 and CH4

Langmuir, Vol. 23, No. 2, 2007 661

Table 1. LJ and Coulombic Potential Parameters adsorbate/adsorbent CH4 CO2 MFI C168 IRMOF-1

site-site

σ (Å)

/kB (K)

q (e)

CH4 C O O Si C Zn C O H

3.73 2.789 3.011 2.708 0.677 3.40 2.462 3.431 3.118 2.571

148.0 29.66 82.96 128.21 18.60 28.00 62.343 52.791 30.166 22.122

0 +0.576 -0.288 -0.400 +0.800 0 in Figure 2

dispersion and electrostatic interactions are considered for the O and Si atoms. C168 Schwarzite. Nanoporous carbon membranes are amorphous and do not have well-defined structures, consequently, the hypothetical C168 schwarzite12 is used in this work to represent the nanoporous carbon. C168 schwarzite has a simple periodic structure with well-defined channels, and carbon-surface curvatures are similar to those in realistic samples. In addition to the primary six-membered rings, there are also five-, seven-, and eight-membered rings. The unit cell of the C168 schwarzite has a length of 21.8 Å and 672 carbon atoms. As shown in Figure 1b, there are two types of channels in C168 schwarzite with average diameters of approximately 7 and 9 Å, respectively. The channels in the same layer are isolated from each other, but they are connected with those in the neighboring layers by channel intersections. IRMOF-1. IRMOF-1 is an isoreticular MOF and is also known as MOF-5.16 It has a lattice constant of 25.832 Å, a crystal density of 0.593 g/cm3, a free volume of 79.2%, and a surface area of 2833 m2/g.23 For simulation, the atomic coordinates within the crystal were constructed using experimental X-ray crystallographic data.17 IRMOF-1 has a formula of Zn4O(BDC)3, where BDC is 1,4-benzenedicarboxylate.24 Each oxide-centered Zn4O tetrahedron is edge-bridged by six carboxylate linkers resulting in an octahedral Zn4O(O2C-)6 building unit, which reticulates into a three-dimensional cubic structure with benzene struts. As shown in Figure 1c, there is one type of straight channel in IRMOF-1 with sizes of 15 and 12 Å along the channel. The universal force field (UFF)25 was used to model the Zn, C, O, and H atoms in IRMOF-1 as listed in Table 1. The atom-centered partial charges were estimated with B3LYP density-functional theory (DFT) computation on a fragmental cluster and were subsequently fitted using the restrained electrostatic potential method.26 Figure 2 shows the cluster used, which was cleaved from the IRMOF-1 unit cell with dangling bonds terminated by H atoms. It has been recognized that quantum mechanically derived charges fluctuate largely with small basis sets, however, beyond a basis set of 6-31G(d), they tend to be convergent.27 As a consequence, 6-31G(d) basis set was used in our DFT computation with the Gaussian 03 suite of programs.28 Figure 2 shows the computed partial charges, in which there are two different types of O atoms and three different types of C atoms. Adsorbates. CH4 is modeled by the united-atom model, which has been demonstrated to give comparable adsorption isotherms for alkane adsorption in MFI but with less computational effort compared to the all-atom model.29 The intermolecular potential (23) Millward, A. R.; Yaghi, O. M. J. Am. Chem. Soc. 2005, 127, 17998. (24) Li, H.; Eddaoudi, M.; O’Keeffe, M.; Yaghi, O. M. Nature (London) 1999, 402, 276. (25) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024. (26) Bayly, C. I.; Cieplak, P.; Cornell, W. D.; Kollman, P. A. J. Phys. Chem. 1993, 97, 10269. (27) Hariharan, P. C.; Pople, J. A. Chem. Phys. Lett. 1972, 66, 217.

Figure 2. Atomic-centered partial charges in an IRMOF-1 cluster from B3LYP/6-31G(d) computation.

parameters of CH4 given in Table 1 are from the TraPPE force field developed to reproduce the critical parameters and saturated liquid densities of alkanes.30 The interactions between CH4 and adsorbent is modeled using the Lennard-Jones (LJ) potential, and the Lorentz-Berthelot mixing rules31 are used to calculate cross interaction parameters. CO2 is represented as a three-site rigid molecule. The intrinsic quadrupole moment is described by the partial charge model. The partial charge on the C atom is 0.576 e, and by electroneutrality, the partial charge on O atom is -0.288 e. The CO bond length is 1.18 Å, and the bond angle ∠OCO is 180°. The CO2-CO2 intermolecular interactions are modeled as a combination of LJ and Coulombic potentials with the potential parameters12 given in Table 1, which are very close to the elementary physical model fitted to the experimental vaporliquid equilibrium data of bulk CO2.32 III. Methodology Grand canonical Monte Carlo (GCMC) simulations at fixed temperature T, volume V, and adsorbate chemical potential µ were carried out for the adsorption of pure CO2 and CH4 and their mixture in MFI, C168 schwarzite, and IRMOF-1. GCMC simulation allows one to directly relate the chemical potential in adsorbed and bulk phases, and so it has been used widely for the simulation of adsorption. Unlike our previous simulation studies,10-12 the simulations here were performed using the MUSIC code.33 The adsorption was investigated at room temperature 300 K. The nonideal behavior of the bulk pure gas and gas mixture was described by the Peng(28) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; Montgomery, J. A.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Gonzalez, C.; Challacombe, M.; Gill, P. M. W.; Johnson, B. G.; Chen, W.; Wong, M. W.; Andres, J. L.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 03, revision D.01 ed.; Gaussian, Inc.: Wallingford, CT, 2004. (29) Macedonia, M. D.; Maginn, E. J. Fluid Phase Equilib. 1999, 19, 158. (30) Martin, M. G. S.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 2569. (31) Maitland, G. C.; Rigby, M.; Smith, E. B.; Wakeham, W. A. Intermolecular Forces; Claredon Press: Oxford, U.K., 1981. (32) Harris, J. G.; Yung, K. H. J. Phys. Chem. 1995, 99, 12021. (33) Gupta, A.; Chempath, S.; Sanborn, M. J.; Clark, L. A.; Snurr, R. Q. Mol. Simul. 2003, 29, 29.

662 Langmuir, Vol. 23, No. 2, 2007

Babarao et al.

Robinson equation of state (PR EOS).34 For CO2/CH4 mixture, the binary interaction parameter in the PR EOS was simply assumed to be zero. The simulation box representing MFI contained 12 (2 × 2 × 3) unit cells, while for C168 schwarzite and IRMOF-1 8 (2 × 2 × 2) unit cells were used. No finite-size effect was found in larger simulation box. All the three adsorbents were treated as rigid with atoms frozen during simulations, and the periodic boundary conditions were used in three dimensions to mimic the crystalline periodicity. A spherical cutoff length of 19.0 Å was used in all simulations to evaluate the intermolecular LJ interactions without long-range corrections. The Coulombic interaction between CO2 and adsorbent was accounted for using the Ewald sum technique.35 For CO2 molecules, the Coulombic interaction was calculated directly on the basis of the center-of-mass cutoff of 19.0 Å, because CO2 molecule is neutral with the quadrupole interaction, which converges rapidly with the cutoff distance. To accelerate the simulation, the LJ and Coulombic interactions between adsorbate and adsorbent were calculated on the basis of a pretabulated energy map with a grid of 0.2 × 0.2 × 0.2 Å cubic mesh constructed throughout the unit cell of adsorbent. The number of Monte Carlo trial moves used in a typical simulation was 6 million, though additional moves were used at high pressures. The first half of these moves was used only for equilibration and the second half was used for calculating the ensemble averages. For pure CH4, three types of moves were randomly attemptedstranslation, insertion, and deletion. For pure CO2, an additional move, rotation, was also included. For CO2/CH4 mixture, in addition to the abovementioned moves, species exchange was also included with equal probability to ensure microscopic reversibility. In this latter move, one random selected sorbate molecule is exchanged with the other type of sorbate molecule. While this move is not a requirement in GCMC for mixtures, its use allows fast equilibration and reduces statistical errors after equilibration.36 At specified T, V, and µ, GCMC simulation gives the absolute number of molecules adsorbed Nad. However, experiment data are usually reported as the excess amount of adsorption Nex. To make a comparison, the experimental Nex was converted into Nad by Nad ) Nex + FbVfree

(1)

where Fb is the density of bulk gas calculated with PR EOS, and Vfree is the free volume within adsorbent for adsorption estimated from Vfree )

∫ exp[-u V

He ad

(r)/kBT] dr

(2)

where uadHe is the interaction between a single helium atom and adsorbent. In this calculation, σHe ) 2.58 Å and He/kB ) 10.22 K were used.37 The free volume detected by helium is temperaturedependent, and usually the room temperature is chosen.38The porosity of an adsorbent can be estimated by Vfree/Vtotal, with Vtotal the total occupied volume. From the loading dependence of the total adsorption energy Uad, the isosteric heat of adsorption qst was calculated39 as the difference between the enthalpy of adsorbate in gas-phase Hb and the partial molar energy of the adsorbed phase40-42 qst ) Hb -

(

)

∂(Uad - Uintra) ∂Nad

(3)

T,V

(34) Elliott, J. R. L.; Lira, C. T. Introductory Chemical Engineering Thermodynamics; Prentice Hall PTR: London, 1999. (35) Heyes, D. M. Phys. ReV. B 1994, 49, 755. (36) Kofke, D. Mol. Simul. 1991, 7, 285. (37) Hirschfelder, J. O. C.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; John Wiley: New York, 1964. (38) Myers, A. L.; Monson, P. A. Langmuir 2002, 18, 10261. (39) Vuong, T.; Monson, P. A. Langmuir 1996, 12, 5425. (40) Karavias, F.; Myers, A. L. Mol. Simul. 1991, 8, 51. (41) June, R. L.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1990, 94, 8232. (42) June, R. L. J. Phys. Chem. 1991, 95, 1014.

Table 2. Density and Porosity of MFI, C168, and IRMOF-1. Limiting Adsorption Properties of Pure CH4 and CO2 adsorbent

density qst0 KH (g/cm3) porosity adsorbate (kJ/mol) (mmol/g/kPa)

MFI

1.793

0.37

C168

1.294

0.67

IRMOF-1

0.593

0.82

CH4 CO2 CH4 CO2 CH4 CO2

19.42 22.91 26.78 35.67 10.31 14.38

0.010 0.022 0.218 1.215 0.0046 0.0093

where Hb can be approximated as RT, Uad includes contributions from both adsorbate-adsorbent and adsorbate-adsorbate interactions, and Uintra is the intramolecular energy of the adsorbate molecules and is equal to zero for rigid molecules. The partial derivative in eq 3 can be calculated in GCMC simulations by fluctuation theory or direct differentiation of the simulation results. In this work, the latter was used.

IV. Results and Discussion Adsorption of Pure CO2 and CH4. Table 2 gives the density and porosity of MFI, C168 schwarzite, and IRMOF-1 as well as the limiting heats of adsorption qst0 and Henry constants KH of pure CO2 and CH4 in each adsorbent. The density decreases in the order of MFI > C168 > IRMOF-1, which is opposite to the porosity. For CO2 and CH4, both qst0 and KH are largest in C168 and are smallest in IRMOF-1. The fact that the limiting properties in C168 are larger than in the less porous MFI indicates that there is no direct relation between adsorption affinity and porosity. In a given adsorbent, both qst0 and KH of CO2 are larger than those of CH4, implying that CO2 is more strongly adsorbed. This is not unexpected because CO2 is a three-site molecule and has a greater interaction with adsorbent. Also for CH4 in MFI, our simulated qst0 is consistent with several reported values.8,43-45 For CO2 in MFI, qst0 is in close agreement with previous experimental (24.07 kJ/mol)43 and simulation results,6,12 however, it is slightly lower than one reported value (27.2 kJ/mol).44 For CH4 in IRMOF-1, again, our qst0 agrees well with the reported simulated values.46,47 Simulated and available experimentally measured adsorption isotherms of pure CO2 and CH4 separately in MFI, C168 schwarzite, and IRMOF-1 are shown in Figure 3 as a function of the bulk pressure. All isotherms are of type I (Langmuirian), which is the characteristic of a microporous adsorbent with pores of molecular dimensions (below 2 nm).48 In MFI, the extent of CO2 adsorption is consistently greater than that of CH4. The simulated isotherms match closely with the experimental results8,22 for both CH4 and CO2, though deviations are observed at high pressures for CH4 adsorption. In IRMOF-1, CO2 adsorption is again consistently larger than CH4 adsorption, as in MFI. At low pressures, the adsorption of both CO2 and CH4 is nearly negligible in IRMOF1, since their interactions with the IRMOF-1 framework are weak, as evidenced from qst0 and KH in Table 2. The simulated isotherms are in accord with previous simulation results,49 and experiment data,47,23 especially at low pressures. At high CO2 pressures, simulation slightly overestimates the measured values. The reason could be that in our work IRMOF-1 was considered to be a (43) Golden, T. C.; Sircar, S. J. Colloid Interface Sci. 1994, 162, 182. (44) Dunne, J. A.; Mariwals, R.; Rao, M.; Sircar, S.; Gorte, R. J.; Myers, A. L. Langmuir 1996, 12, 5888. (45) Sun, M. S.; Shah, D. B.; Xu, H. H.; Talu, O. J. Phys. Chem. B 1998, 102, 1466. (46) Jiang, J. W.; Sandler, S. I. Langmuir 2006, 22, 5702. (47) Duren, T.; Sarkisov, L.; Yaghi, O. M.; Snurr, R. Q. Langmuir 2004, 20, 2683. (48) Rouquerol, F.; Rouquerol, J.; Sing, K. Adsorption: By Powders and Porous Solids; Academic Press: London, 1999. (49) Skoulidas, A. I.; Sholl, D. S. J. Phys. Chem. B 2005, 109, 15760.

Storage and Separation of CO2 and CH4

Langmuir, Vol. 23, No. 2, 2007 663

A dual-site Langmuir-Freundlich (DSLF) equation50

No(f) )

Figure 3. Adsorption isotherms of CH4 and CO2 in MFI, C168, and IRMOF-1 as a function of bulk pressure. The filled symbols are simulation results, the lines are fits of the dual-site LangmuirFreundlich equation to simulation results, and the open symbols are experimental data.

perfect, pure crystalline material, whereas experimental samples usually contain impurities and defects leading to a decrease in the storage capacity. In addition, the empirical force fields used may not be accurate enough to describe such a small discrepancy. In C168 schwarzite, CO2 is preferentially adsorbed at low pressures because CO2 has three interactions sites and is more energetically favored. At high pressures near saturation, the smaller molecule CH4 can fit into the partially occupied pores more easily; as a consequence of this entropic effect, CH4 is adsorbed more. However, CO2 is more greatly adsorbed than CH4 in MFI and IRMOF-1 over the entire pressure range under the study, in which the saturation has not been approached. This is because the partially charged CO2 has much stronger interactions with charged frameworks MFI and IRMOF-1, compared with the neutral adsorbent C168 schwarzite. Nevertheless, it is expected that at even higher pressures close to saturation, CH4 may have greater adsorption because of the entropic effect.

N1k1f n1 1 + k1f n1

+

N2k2f n2 1 + k2f n2

(4)

was used to fit the adsorption isotherm of pure gas, where f is the fugacity of bulk gas at equilibrium with adsorbed phase, Ni is maximum loading in site i () 1 and 2), ki is the affinity constant, and ni is used to characterize the deviation from the simple Langmuir equation. As shown below, the fitted parameters will then be used to predict the adsorption of mixture. There is no restriction on the choice of the model to fit the adsorption isotherm, but data over the pressure range under study should be fitted very precisely. The fitted isotherms are shown as solid lines in Figure 3, and the adjustable parameters are given in Table 3. For CO2 or CH4 in each adsorbent, the fit is nearly perfect. A comparison of the CH4 adsorption isotherms in the three different adsorbents is presented in Figure 4 as a function of bulk pressure. It can be seen clearly that among the three adsorbents the greatest extent of adsorption is in IRMOF-1, which is not yet saturated even at the highest pressure considered here. This indicates that IRMOF-1 has a very high storage capacity for CH4. Also, the simulation results of CH4 in MFI and IRMOF-1 are in good agreement with experimental data. For CH4 in C168 schwarzite, no experimental data is available. Figure 5 shows the simulated and experimental adsorption isotherms for CO2 in MFI, C168 schwarzite, and IRMOF-1. As for CH4, there is greater adsorption of CO2 in IRMOF-1 than in MFI and C168 schwarzite. Recently, the U.S. Department of Energy (DoE) set the storage target for CH4 at 35 bar as 180 v/v,51 which is the excess volume of CH4 adsorbed at the standard temperature and pressure per volume of the storage vessel. Our simulated excess adsorption of CH4 at 35 bar is 140.3 v/v, slightly greater than the experimental result of 121.9 v/v.47 Though the predicted CH4 storage in IRMOF-1 is lower than the DoE target, the capacity is significantly higher than in MFI and C168 schwarzite. On the basis of this observation, IRMOF-1 could be an ideal starting material for the storage of CH447 as well as for CO2. With a proper choice of an organic linker, it may be possible to design an MOF with enhanced storage capacity and reach the DoE target. Figure 6a shows the isosteric heats qst of CO2 and CH4 adsorption in MFI. Consistent with the adsorption isotherm, CO2 has higher heat of adsorption than CH4. With increasing loading, qst initially increases, passes through a maximum at high loading, and finally decreases, though the extent of the change for CH4 is weaker. This type of behavior has been observed in experimental studies, for example, in the adsorption of Xe in zeolites X and Y,52 of Ar in AlPO4-5,53 and of CH4 in an fcc-structured silica gel.39 The initial increase in qst is attributed to the cooperative attractive interactions between adsorbate molecules, while the interaction between adsorbate and adsorbent remains nearly unchanged. The additional adsorbed adsorbate molecules must occupy the less favorable sites leading to a weaker adsorbateadsorbent interaction, and the adsorbate-adsorbate interaction becomes less attractive because of the shorter separation distance. As a consequence, qst tends to decrease at high loadings. Also included in Figure 6a are the experimentally determined qst at (50) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984. (51) Burchell, T.; Rogers, M. SAE Tech. Pap. Ser. 2000-01-2205 2000. (52) Woods, G. B.; Rowlinson, J. S. J. Chem. Soc., Faraday Trans. 1989, 85, 765. (53) Grillet, Y. L.; Llewellyn, P. L.; Tosi- Pelleng, N.; Rouquerol, J. Fundamentals of adsorption, Proceedings of the Fourth International Conference on Fundamentals of Adsorption, Kyoto, Japan, 1992.

664 Langmuir, Vol. 23, No. 2, 2007

Babarao et al.

Table 3. Parameters in the Dual-Site Langmuir-Freundlich Equation Fitted to Adsorption of Pure CH4 and CO2 adsorbent MFI C168 IRMOF-1

adsorbate CH4 CO2 CH4 CO2 CH4 CO2

N1

k1

n1

0.52 1.79 0.75 8.03 22.32 19.83

3.97 × 10 8.47 × 10-3 1.97 × 10-5 0.025 1.80 × 10-4 2.56 × 10-4 -3

1.23 0.62 2.79 0.27 1.03 1.16

N2

k2

n2

2.74 2.51 7.17 5.99 5.19 11.55

3.88 × 10 3.98 × 10-3 0.033 0.181 4.83 × 10-8 1.60 × 10-12 -3

1.03 1.03 0.90 0.94 2.15 4.02

Figure 4. Comparison of adsorption isotherms of CH4 in MFI, C168, and IRMOF-1 as a function of bulk pressure.

Figure 5. Comparison of adsorption isotherms of CO2 in MFI, C168, and IRMOF-1 as a function of bulk pressure.

Figure 6. Isosteric heats of adsorption of pure CH4 and CO2 in MFI, C168, and IRMOF-1. Legends are as in Figure 3.

low loadings.8,43-45 While our simulated limiting heats of adsorption qst0 as listed in Table 1 well reproduce the measured values, the heats of adsorption qst at low loadings seem to be underestimated. Figure 6b shows qst of CO2 and CH4 in C168 schwarzite. The heat of adsorption in C168 schwarzite shows different behavior in that with increasing coverage, qst first decreases to a minimum, then increases to a maximum, and finally decreases. Such behavior is not unusual and has been observed experimentally, such as in the adsorption of N2 and CO in AlPO4-5,53 of CH4 in a silica gel with a hard-sphere structure,39 of Ar in chabazite,54 and of CH4 in activated carbon.55 The initial

decrease of qst is a consequence of the heterogeneous character of the C168 schwarzite surface, in which the more energetically favorable sites for adsorption are occupied first, and then the less favorable sites are occupied as the loading increases. Figure 6c shows qst of CO2 and CH4 in IRMOF-1. The adsorption has not approached saturation, and as a result, qst increases monotonically with loading simply because of the increased cooperative interaction between adsorbate-adsorbate. However, a decrease in qst is expected at high loadings. Figure 7 shows the equilibrium snapshots of the adsorbed CO2 molecules at 500 and 2000 kPa in all the three adsorbents. In MFI, CO2 are adsorbed mostly in the straight channels at a low pressure, however, at a high pressure CO2 is also adsorbed in the zigzag channels. In C168 schwarzite, CO2 molecules occupy both the small and larger channels. As observed previously,12 on going from a low to a high pressure, the distribution of adsorbed

(54) Rudzinski, W. Fundamentals of Single-Gas and Mixed-Gas Adsorption on Heterogeneous Solid Surfaces. In Physical Adsorption: Experiment, Theory and Applications; Fraissard, J., Ed.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1997; p 181. (55) Choi, B. U.; Choi, D. K.; Lee, Y. W.; Lee, B. K.; Kim, S. H. J. Chem. Eng. Data 2003, 48, 603.

Storage and Separation of CO2 and CH4

Langmuir, Vol. 23, No. 2, 2007 665

Figure 7. Snapshots of pure CO2 adsorption in MFI, C168, and IRMOF-1 at 500 kPa (top) and 2000 kPa (bottom).

CO2 molecules changes from continuous in both channels to localized first in small channels and then in large channels. With increasing pressure, the adsorbate-adsorbate attraction first increases at low pressures, but then decreases. This is because as the number of admolecules increases, the channels become crowded and the separation distance between the admolecules decreases. In a competitive balance between energetic and entropic effects, a phenomenon similar to a first-order phase separation occurs, leading to the localized distribution in the channels, first in the small channels at modest pressures and then in the large pores at high pressures.12 In IRMOF-1, CO2 molecules are concentrated around the metal-oxide tetrahedra. At a high pressure, CO2 molecules also enter the straight channels within the framework. Adsorption of CO2/CH4 Mixture. For adsorption of a gas mixture, the equilibrium condition is the equality of fugacity in the gas and adsorbed phases.56

Pyiφi ) xiγifio

(5)

where P is bulk pressure, and y and x are the molar fraction in gas and adsorbed phases, respectively. The fugacity coefficient of component i in gas phase is φi calculated by PR EOS, fio is the fugacity of pure component i in a standard state, and γi is the activity coefficient of component i in the adsorbed phase. If a perfect mixing is assumed in the adsorbed phase and hence γi ) 1, we can use the ideal-adsorbed solution theory (IAST)56 to predict the adsorption of a mixture on the basis of the information for pure components. The standard state is specified by the surface potential Φi given by the Gibbs adsorption approach

∫0f

Φi ) -RT

o

i

Nio(fi)d ln fi

(6)

where Nio(f) is the adsorption isotherm of pure component i. The mixing process is carried out at a constant surface potential Φ1 ) Φ2 ) ‚‚‚ ) Φ. (56) Myers, A. L.; Prausnitz, J. M. AIChE J. 1965, 11, 121.

Figure 8 shows the adsorption isotherms for an equimolar mixture of CH4/CO2 in MFI, C168 schwarzite, and IRMOF-1 as a function of total bulk pressure. The closed symbols are from simulation and the lines are from IAST theory. In all adsorbents, CO2 is more preferentially adsorbed than CH4 as expected because of the stronger interaction between CO2 and surfaces. Again, in IRMOF-1 the loading at low pressures is negligible. The agreement between IAST predictions and simulation results is generally good, particularly, at low pressures because IAST becomes exact in the Henry law limit.57 However, at high pressures IAST either underestimates or overestimates the results compared to simulation. This may be attributed to the assumption intrinsically used in IAST, that is, that the adsorbed phase of mixture is an ideal phase with perfect mixing. Improved predictions can be obtained by removing this assumption. Adsorption selectivity in a binary mixture of component i and j is defined as

Si/j )

( )( ) xi yj xj yi

(7)

where xi, yi are the mole fractions of component i in the adsorbed and bulk phase, respectively. Although the general trend of selectivity can be properly estimated from simulation, it is remarked that the value of selectivity may not be as accurate as isotherm because a slight deviation in the number of adsorbed molecules may result in a larger deviation in selectivity. Figure 9 shows the simulated adsorption selectivity of an equimolar mixture of CO2 and CH4 in MFI, C168 schwarzite, and IRMOF-1 as a function of total bulk pressure. At a fixed total bulk pressure, selectivity is only a weak function of the bulk phase composition.10 In all the three adsorbents, when the bulk pressure is close to zero, the simulated selectivity is approximately equal to the ratio of the Henry constants, KH(CO2)/KH(CH4). In MFI, the selectivity increases slowly at low pressures, then decreases at modest pressures, and finally increases slightly at high pressures. In C168 schwarzite, the selectivity drops at high (57) Challa, S. R.; Sholl, D. S.; Johnson, J. K. J. Chem. Phys. 2002, 116, 814.

666 Langmuir, Vol. 23, No. 2, 2007

Babarao et al.

Figure 9. Adsorption selectivity of an equimolar mixture of CH4 and CO2 in MFI, C168, and IRMOF-1 as a function of bulk pressure from simulation. The dotted lines are to guide the eye.

V. Conclusions

Figure 8. Adsorption of an equimolar mixture of CH4 and CO2 in MFI, C168, and IRMOF-1 as a function of bulk pressure. The filled symbols are simulation results, and the lines are IAST predictions.

pressures since CO2 nearly reaches saturation while there is still a slight increase in CH4 adsorption. In IRMOF-1, the selectivity first remains nearly constant and then increases as pressure increases, which is consistent with the adsorption behavior seen above. The selectivity in C168 schwarzite is the highest among the three adsorbents, though the adsorption capacity in IRMOF-1 is the highest.

We have used Monte Carlo simulation to study the adsorption of pure and mixed CO2 and CH4 in three nanosized porous adsorbents, silicalite, C168 schwarzite, and IRMOF-1. The simulated adsorption isotherms and isosteric heats are consistent with available experimental data. Compared to silicalite and C168 schwarzite, the adsorption capacity of pure CH4 and CO2 separately in IRMOF-1 is substantially higher. CO2 is preferentially adsorbed over CH4 from their binary mixture in all three adsorbents. Predictions from the ideal-adsorbed solution theory on the basis of the adsorption of only pure gases agree well with the simulation results. Even though the storage capacity of IRMOF-1 is greater than silicalite and C168 schwarzite, the adsorption selectivity of CO2 over CH4 is found to be close in all the three adsorbents. It would be of interest to find a porous material showing both high storage capacity and high selectivity. While in this work we only focus on IRMOF-1 as a prototype MOF, the study of different MOFs will also be performed as the functionality of MOFs can be tuned at the atomic scale by changing the metal-oxide and the organic linker. Moreover, here we investigate the selectivity on the basis of adsorption equilibrium; in the future, we will explore the selectivity on the basis of diffusion to determine the kinetic selectivity in different adsorbents. Acknowledgment. The authors are grateful for the support from the National University of Singapore, the U.S. National Science Foundation, and the U.S. Department of Energy. LA062289P