pubs.acs.org/Langmuir © 2008 American Chemical Society
Molecular Simulations for Adsorptive Separation of CO2/CH4 Mixture in Metal-Exposed, Catenated, and Charged Metal-Organic Frameworks Ravichandar Babarao, Jianwen Jiang,* and Stanley I. Sandler Department of Chemical & Biomolecular Engineering, National University of Singapore, Singapore 117576, and Department of Chemical Engineering, University of Delaware, Newark, Delaware 19716, Received September 19, 2008. Revised Manuscript Received October 22, 2008 The adsorption and separation of CO2/CH4 mixture are studied using molecular simulations in a series of metal-organic frameworks (MOFs) with unique characteristics such as exposed metals (Cu-BTC, PCN-60 and PCN-6), catenation (IRMOF-13 and PCN-6), and extraframework ions (soc-MOF). Because of the strong affinity with the framework, CO2 is preferentially adsorbed over CH4 in all MOFs. Framework catenation leads to constricted pores and additional adsorption sites and enhances the interaction with the adsorbate. Therefore, catenated IRMOF-13 and PCN-6 exhibit a greater extent of adsorption, particularly for CO2, at low pressures than IRMOF-14 and PCN-60 ; however, the opposite is true at high pressures. CO2/CH4 selectivity in IRMOF-1 and IRMOF-14 is almost constant at low pressures and increases with increasing pressure. As a result of a counterbalance between energetic and entropic effects, the selectivity in IRMOF-13 initially decreases at low pressures and then increases with pressure and finally approaches a constant value. Catenated MOFs have a higher selectivity than their non-catenated counterparts. The presence of electrostatic interaction between CO2 and the framework leads to an increase in CO2 adsorption and a corresponding decrease in CH4 adsorption and consequently enhanced selectivity. In charged soc-MOF, the extraframework NO3 ions are identified to be equally distributed from the nearest metal atoms and vibrate around the favorable sites. The selectivity in soc-MOF is substantially higher than in the other IRMOFs and PCNs and is the highest among various MOFs reported to date. The simulation results reveal that the selectivity of CO2 over CH4 in MOFs is enhanced slightly by exposed metals, catenation, and significantly by extraframework ions and that charged MOFs are promising candidates for the separation of CO2/CH4 mixture.
I. Introduction Natural gas is an ideal substitute for environmentally unfriendly fossil fuels. However, an impurity such as CO2 reduces the calorie content of natural gas and needs to be removed. Several approaches have been proposed to separate CO2 from gas mixtures, such as adsorption by porous materials, amine absorption, chemical conversion, and membrane separation. Of these, adsorptive separation is technically feasible and perhaps the most economical. To achieve efficient separation, the use of a highperformance adsorbent is crucial. Over the past few years, metalorganic frameworks (MOFs), a new class of organic-inorganic hybrid materials, have received considerable attention for gas storage and separation. Unlike zeolitic and carbonaceous structures, the controllable length of organic linkers and the variation of metal oxides in MOFs allow for the rational tailoring of their pore size, volume, and functionality.1 A large number of MOFs have been synthesized to date for emerging applications.2,3 Nevertheless, experimentally synthesizing and screening MOFs for a particular application can be a difficult and timeconsuming task. With ever growing computational power, molecular simulations are playing an increasingly important role in the development of new materials. Simulations on the molecular scale can provide microscopic pictures that otherwise are experimentally inaccessible or difficult to obtain. In conjunction with experiment, * To whom correspondence should be addressed. E-mail: chejj@ nus.edu.sg. (1) Yaghi, O. M.; O’Keeffe, M.; Ockwig, N. W.; Chae, H. K.; Eddaoudi, M.; Kim, J. Nature 2003, 423, 705. (2) Ferey, G. Chem. Soc. Rev. 2008, 37, 191. (3) Mueller, U.; Schubert, M.; Teich, F.; Puetter, H.; Schierle-Arndt, K.; Pastre, J. J. Mater. Chem. 2006, 16, 626.
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fundamental insight gained from molecular simulations can assist in the rational design of novel materials and products. Numerous simulation studies have been reported on the adsorption of pure and mixed gases in MOFs. For example, CH4 adsorption was simulated in MOFs for the storage of environmentally friendly energy sources.4 Adsorption of light gases in MOFs was predicted by taking into account quantum effects and framework charges and was compared with available experimental data.5 From simulations, good correlations of H2 uptake in IRMOFs were found with the heat of adsorption at low pressure, with surface area at moderate pressure, and with free volume at high pressure.6 A simulation study of linear and branched alkanes suggested that IRMOF-1 might be a good candidate for the storage and separation of hydrocarbons.7 Among three different types of nanoporous structures;IRMOF-1, MFI silicalite, and a nanoporous carbon;IRMOF-1 was found to have the largest capacity for adsorption, but it was unsatisfactory for separation.8,9 MOFs with various linkers, pore sizes, and topologies were investigated for CO2 storage, and the capacity was found to be a complex interplay of framework density, surface area, free volume, and porosity.10 CO2 storage was also studied in 1D, 2D, and 3D covalent organic frameworks (COFs), and exceptionally high capacity was predicted.11 The electrostatic interactions of CO2 molecules were found to be responsible for the inflections (4) Duren, T.; Sarkisov, L.; Yaghi, O. M.; Snurr, R. Q. Langmuir 2004, 20, 2683. (5) Garberoglio, G.; Skoulidas, A. I.; Johnson, J. K. J. Phys. Chem. B 2005, 109, 13094. (6) Frost, H.; Duren, T.; Snurr, R. Q. J. Phys. Chem. B 2006, 110, 9565. (7) Jiang, J. W.; Sandler, S. I. Langmuir 2006, 22, 5702. (8) Babarao, R.; Hu, Z. Q.; Jiang, J. W.; Chempath, S.; Sandler, S. I. Langmuir 2007, 23, 659. (9) Babarao, R.; Jiang, J. W. Langmuir 2008, 24, 5474. (10) Babarao, R.; Jiang, J. W. Langmuir 2008, 24, 6270. (11) Babarao, R.; Jiang, J. W. Energy Environ. Sci. 2008, 1, 139.
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and steps observed in the adsorption isotherms of CO2 in IRMOF-1 at five different temperatures and also in IRMOF-3 and MOF-177 at 298 K.12 CO2 adsorption in MIL-53 (MIL: Material Institute Lavoisier) confirmed that there is a structural interchange between large- and narrow-pore forms in MIL-53 but not in MIL-47.13 A number of experimental and simulation studies have also been reported for gas adsorption and separation in metal-exposed MOFs.14-17 Simulations of syngas in MOF-5 and Cu-BTC showed that geometry, pore size, and electrostatic interaction can enhance the separation efficiency for gas mixtures with components of different chemistries.18 Cu-BTC was found to be potentially useful for the purification of CO, capture of CO2, and separation of C2H4/C2H6. The presence of side pockets in Cu-BTC results in a higher selective adsorption at low loadings.19 The role of exposed metal sites in Cu-BTC was examined by simulations on the separation of CO from binary mixtures containing CH4, N2, or H2 at different compositions.20 Using both experimental techniques and simulations, the separation of CO2 from CH4 was studied in mixed-ligand MOFs, where mixture adsorption was predicted from single-component adsorption isotherms using ideal adsorption solution theory (IAST)21 and was subsequently verified by simulations.22 Separation of the CO2/CH4 mixture was studied in carborane-based MOFs both with and without exposed metal sites, and a higher selectivity was observed in the former case.23 In addition, catenation in MOFs has been found to enhance the adsorption of gases at low pressures and the separation factor of gas mixtures. Using simulations, the effect of catenation on the interaction between H2 and IRMOFs was examined, and catenated frameworks were found to store H2 more densely and to exhibit a higher adsorption capacity than non-catenated counterparts.24 The separation of light-gas mixtures in several catenated MOFs has been measured, and enhanced selectivity was observed.25-27 The adsorptive separation of CH4/H2 mixtures was simulated at room temperature, and the results showed that CH4 selectivity is enhanced in catenated IRMOFs.28 In this study, we present a systematic simulation study on the separation of CO2/CH4 mixture in a series of MOFs. The presence of exposed metal sites and catenation can enhance both (12) Walton, K. S.; Millward, A. R.; Dubbeldam, D.; Frost, H.; Low, J. J.; Yaghi, O. M.; Snurr, R. Q. J. Am. Chem. Soc. 2008, 130, 406. (13) Ramsahye, N. A.; Maurin, G.; Bourrelly, S.; Llewellyn, P. L.; Devic, T.; Serre, C.; Loiseau, T.; Ferey, G. Adsorption 2007, 13, 461. (14) Chen, B. L.; Ockwig, N. W.; Millward, A. R.; Contreras, D. S.; Yaghi, O. M. Angew. Chem., Int. Ed. 2005, 44, 4745. (15) Farha, O. K.; Spokoyny, A. M.; Mulfort, K. L.; Hawthorne, M. F.; Mirkin, C. A.; Hupp, J. T. J. Am. Chem. Soc. 2007, 129, 12680. (16) Dinca, M.; Dailly, A.; Liu, Y.; Brown, C. M.; Neumann, D. A.; Long, J. R. J. Am. Chem. Soc. 2006, 128, 16876. (17) Xiao, B.; Wheatley, P. S.; Zhao, X. B.; Fletcher, A. J.; Fox, S.; Rossi, A. G.; Megson, I. L.; Bordiga, S.; Regli, L.; Thomas, K. M.; Morris, R. E. J. Am. Chem. Soc. 2007, 129, 1203. (18) Yang, Q. Y.; Zhong, C. L. J. Phys. Chem. B 2006, 110, 17776. (19) Wang, S. L.; Yang, Q. Y.; Zhong, C. L. Sep. Purif. Technol. 2008, 60, 30. (20) Karra, R. J.; Walton, K. S. Langmuir 2008, 24, 8620. (21) Myers, A. L.; Prausnitz, J. M. AIChE J. 1965, 11, 121. (22) Bae, Y. S.; Mulfort, L. K.; Frost, H.; Ryan, P.; Punnathanam, S.; Broadbelt, L. J.; Hupp, J. T.; Snurr, R. Q. Langmuir 2008, 24, 8592. (23) Bae, Y. S.; Farha, O. K.; Spokoyny, A. M.; Mirkin, C. A.; Hupp, J. T.; Snurr, R. Q. Chem. Commun 2008, 4135. (24) Jung, D. H.; Kim, D.; Lee, T. B.; Choi, S. B.; Yoon, J. H.; Kim, J.; Choi, K.; Choi, S. H. J. Phys. Chem. B 2006, 110, 22987. (25) Chen, B. L.; Ma, S. Q.; Hurtado, E. J.; Lobkovsky, E. B.; Zhou, H. C. Inorg. Chem. 2007, 46, 8490. (26) Chen, B. L.; Liang, C. D.; Yang, J.; Contreras, D. S.; Clancy, Y. L.; Lobkovsky, E. B.; Yaghi, O. M.; Dai, S. Angew. Chem., Int. Ed. 2006, 45, 1390. (27) Bastin, L.; Barcia, P. S.; Hurtado, E. J.; Silva, J. A. C.; Rodrigues, A. E.; Chen, B. J. Phys. Chem. C 2008, 112, 1575. (28) Liu, B.; Yang, Q. Y.; Xu, C. H.; Zhong, C. L.; Chen, B.; Smit, B. J. Phys. Chem. C 2008, 112, 9854.
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adsorption and selectivity; therefore, we have chosen MOFs with exposed metal sites (Cu-BTC, PCN-60 , and PCN-6) and with catenated frameworks (IRMOF-13 and PCN-6); PCN-6 contains both exposed metal sites and catenated framework. In addition, a charged MOF with extraframework ions is considered and its possible utility for CO2/CH4 separation is compared with that of other MOFs. The extraframework ions located in the pores of molecular dimensions increase the interaction strength between the framework and guest molecules and consequently enhance the storage, separation, or ion-exchange capability. For example, lithium- and calcium-exchanged faujasites are currently used in the separation of air by a pressure swing adsorption process,29 and the barium-exchanged form is used for the selective separation of aromatic molecules.30 Cation-exchanged zeolites are also promising materials for the selective adsorption and separation of CO2.31 To the best of our knowledge, however, no simulation study has yet been reported for gas adsorption and separation in a charged MOF. In section II, the models for CO2, CH4, and the MOFs are described; the simulation methods are briefly introduced in section III. Specifically, canonical (NVT) Monte Carlo (MC) simulations were used to identify the locations of extraframework ions in soc-MOF, and grand canonical Monte Carlo (GCMC) simulations were used to calculate the adsorption of an equimolar CO2/CH4 mixture at room temperature. The adsorption isotherms, simulation snapshots, adsorption selectivity, and effect of electrostatic interactions on selectivity are presented and discussed in section IV, with concluding remarks in section V.
II. Models CO2 was represented as a three-site rigid molecule, and its intrinsic quadrupole moment was described by a partial charge model. The partial charges on C and O atoms were qC = 0.576e and qO = -0.288e (e = 1.6022 10-19 C), respectively. The CO bond length was 1.18 A˚, and bond angle—OCO was 180. CO2CO2 interactions were modeled as a combination of LennardJones (LJ) and Coulombic potentials " 6 # σij 12 σij qi qj þ uij ðrÞ ¼ 4εij r r 4πε0 r
ð1Þ
where r is the interatomic distance and ε0 = 8.8542 10-12 C2 N-1 m- 2 is the permittivity of vacuum; the LJ parameters were the same as used in our previous work.8 CH4 was represented by a united-atom model with the LJ potential parameters from the TraPPE force field that was developed to reproduce the critical parameters and saturated liquid densities of alkanes.32 Figure 1 shows the atomic structures of seven MOFs considered in this study, constructed from the experimental crystallographic data.33-37 As a prototype of isoreticular MOFs, IRMOF-1 consists of Zn4O as the metal oxide cluster and 1,4benzenedicarboxylate (BDC) as the organic linker.33 It has (29) Coe, C. G. U.S. Patent 5,813,815, 1992 . (30) Neuzil, R. W. U.S. Patent 3,558,561, 1971. (31) Harlick, P. J. E.; Tezel, F. H. Microporous Mesoporous Mater. 2004, 76, 71. (32) Martin, M. G.; Siepmann, J. I. J. Phys. Chem. B 1998, 102, 2569. (33) Eddaoudi, M.; Kim, J.; Rosi, N.; Vodak, D.; Wachter, J.; O’Keefe, M.; Yaghi, O. M. Science 2002, 295, 469. (34) Chui, S. S. Y.; Lo, S. M. F.; Charmant, J. P. H.; Orpen, A. G.; Williams, I. D. Science 1999, 283, 1148. (35) Sun, D. F.; Ma, S. Q.; Ke, Y. X.; Collins, D. J.; Zhou, H. C. J. Am. Chem. Soc. 2006, 128, 3896. (36) Ma, S. Q.; Sun, D. F.; Ambrogio, M.; Fillinger, J. A.; Parkin, S.; Zhou, H. C. J. Am. Chem. Soc. 2007, 129, 1858. (37) Liu, Y. L.; Eubank, J. F.; Cairns, A. J.; Eckert, J.; Kravtsov, V. C.; Luebke, R.; Eddaoudi, M. Angew. Chem., Int. Ed. 2007, 46, 3278.
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Figure 1. Atomic structures of (a) IRMOF-1, (b) IRMOF-14, (c) IRMOF-13, (d) Cu-BTC, (e) PCN-60 , (f) PCN-6, and (g) soc-MOF. N, blue; C, grey; O, red; Zn, cyan; H, white; and Cu and In, orange. The structures are not drawn to scale.
straight pores with alternating diameters of 15 and 12 A˚ along the pores. IRMOF-14 is formed by substituting BDC in IRMOF-1 with pyrene dicarboxylate (PDC), which is longer and leads to a larger pore size. The pore diameters in IRMOF-14 are approximately 20.1 and 14.7 A˚.33 Despite the identical metal oxide and organic linker in IRMOF-13 and IRMOF-14, IRMOF-13 has a catenated framework and differs in topology from IRMOF-14. The pore diameters in IRMOF-13 are only 12.4 and 8.7 A˚ as a result of catenation.33 Cu-BTC (BTC: benzene-1,3,5-tricarboxylate) is a face-centered cubic crystal composed of paddle-wheel building blocks of dimeric cupric tetracarboxylate. There are square pores of 9.0 9.0 A˚ and tetrahedral side pockets of diameter 5 A˚ connected by 3.5 A˚ windows.34 PCN-6 consists of dimeric coppers linked with TATB (4,40 ,400 s-triazine-2,4,6-triyl-tribenzoate) to form a paddle-wheel secondary building unit resulting in a catenated framework.35 It has triangular channels of 9.2 A˚ along an edge connected by 5 A˚ windows. With boracite net topology, PCN-60 is considered to be a non-catenated counterpart of PCN-6 and isostrucutral with Cu-BTC.36 Similar to Cu-BTC, PCN-60 has open square pores along the diagonals, but with a larger size of 21.44 21.44 A˚2. The experimentally determined surface area is 3800 m2/g in PCN-6, whereas it is only 2700 m2/g in PCN-60 . Unlike neutral MOFs, soc-MOF has a cationic framework with charge balancing extra37 framework NO3 ions. As an assembly of trimer building block with square-octahedral connectivity nets, soc-MOF contains nanometer-scale pores and carcerand capsules. In this work, the extraframework ions were assumed being distributed freely in the crystalline structure and their locations were characterized by simulation. The atomic charges of framework atoms were calculated from density functional theory (DFT) on the basis of the fragmental clusters as illustrated in Figure 2. Because of identical primary building blocks, the same cluster was used for IRMOF-13 and IRMOF-14 and for PCN-60 and PCN-6. To maintain the correct hybridization, the dangling bonds on the fragmented clusters were terminated by -CH3 in all fragmented clusters. It is widely recognized that quantum mechanically derived charges can vary Langmuir 2009, 25(9), 5239–5247
greatly with the basis set when a small basis set is used but tend to converge for 6-31G(d) basis sets and larger.38 Consequently, the 6-31G(d) basis set was used in our DFT calculations for all atoms except the transition metals, for which the LANL2DZ basis set was used. LANL2DZ is a double-zeta basis set and contains effective pseudopotentials to represent the potentials of the nucleus and core electrons experienced by the valence electrons. This allows only the softer valence electron wavefunctions, which usually control the chemistry, to be explicitly treated and can significantly reduce the computational cost. The DFT computations used the Lee-Yang-Parr correlation functional (B3LYP) and were carried out with the Gaussian 03 electronic structure package.39 The concept of atomic charges is solely an approximation, and no unique straightforward method is currently available to determine atomic charges rigorously. Commonly adopted methods include the Mulliken population analysis,40 the electrostatic potential (ESP),41 the restrained electrostatic potential (RESP),42 and the charges from electrostatic potentials using a grid (CHELPG).43 Mulliken’s method is based on the wave functions and usually overestimates the charges. In the ESP method, the electrostatic potentials are fitted at grids located with equal density on different layers around the molecule. The RESP method further sets the charges on the (38) Hariharan, P. C.; Pople, J. A. Chem. Phys. Lett. 1972, 66, 217. (39) 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.; HeadGordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 03, revision D.01;Gaussian, Inc.: Wallingford, CT, 2004. (40) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833. (41) Besler, B. H.; Merz, K. M.; Kollman, P. A. J. Comput. Chem. 1990, 11, 431. (42) Bayly, C. I.; Cieplak, P.; Cornell, W. D.; Kollman, P. A. J. Phys. Chem. 1993, 97, 10269. (43) Breneman, C. M.; Wiberg, K. B. J. Comput. Chem. 1990, 11, 361.
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Figure 2. Fragmented clusters used in the B3LYP/6-31g(d) calculations for IRMOF-1, IRMOF-14, IRMOF-13, Cu-BTC, PCN-60 , PCN-6, and soc-MOF. To maintain the correct hybridization, the dangling bonds on all fragmented clusters were terminated by -CH3.
buried atoms to zero by using a penalty function in the fit. Similar to the ESP method, the electrostatic potentials are calculated in the CHELPG method at grids distributed on a cubic lattice. In this study, the atomic charges were estimated using the ESP method, as listed in Table 1. The atomic charges of extraframework NO3 in soc-MOF were adopted from ab initio calculations with 0.197e for the N atom and -0.399e for the O atom.44 NO3 was mimicked as rigid with a bond length of 1.302 A˚ and a bond angle — ONO of 120. The dispersion interactions of the framework atoms in MOFs were modeled using the universal force field (UFF).45 A number of simulation studies have shown that UFF leads to accurate predictions of gas adsorption in MOFs.5,8 The interactions between CO2 and framework atoms were modeled using LJ and Coulombic potentials, whereas only the LJ potential was used between CH4 and the framework atoms. The LorentzBerthelot combining rules were used to calculate the cross LJ interaction parameters.
III. Methods Canonical (NVT) MC simulations were used to characterize the locations of NO3 ions in soc-MOF at 300 K. The simulation box contained a unit cell of soc-MOF with eight NO3 ions, and the periodic boundary conditions were applied in all three directions. The framework atoms were fixed during simulation, but the NO3 ions were allowed to move. The unit cell was divided into 3D grids with the potential energy maps tabulated in advance and then used during simulation by interpolation. This accelerated the simulation by two orders of magnitude. A spherical cutoff of 11.2 A˚ was used to evaluate the LJ interactions. Beyond the cutoff, the usual long-range corrections for a homogeneous (44) Lu, G. W.; Li, C. X.; Wang, W. C.; Wang, Z. H. Fluid Phase Equilib. 2004, 225, 1. (45) Rappe, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A.; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024. (46) Frenkel, D.; Smit, B. Understanding Molecular Simulations: From Algorithms to Applications, 2nd ed.; Academic Press: San Diego, 2002.
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system were used.46 The use of the usual long-range corrections is an appropriate approximation because the error introduced by assuming homogeneity is small compared with the magnitude of the long-range corrections.47 For the Coulombic interactions, a simple spherical truncation could result in significant error; consequently, the Ewald sum method with a tin-foil boundary condition (a surrounding dielectric constant of infinity) was used. The real/reciprocal space partition parameter and the cutoff for the reciprocal lattice vectors were chosen to be 0.2 A˚-1 and 8 (a dimensionless parameter), respectively, to ensure the convergence of the Ewald sum. Eight NO3 ions were initially randomly introduced into the system, followed by 107 trial moves. Three types of trial moves were used with equal probability, including displacement, rotation, and regrowth. The acceptance criteria for the trial moves were based on the Metropolis algorithm.46 Grand canonical Monte Carlo (GCMC) simulations at fixed adsorbate chemical potential μ, volume V, and temperature T were carried out for the adsorption of an equimolar CO2/ CH4 mixture at 300 K. Because the chemical potentials of adsorbates in the adsorbed and bulk phases are identical at thermodynamic equilibrium, GCMC simulation allows one to directly relate the chemical potentials of the adsorbates in both phases and has been widely used for the simulation of adsorption. In this study, the simulation boxes representing MOF adsorbents varied from (1 1 1) to (2 2 2) unit cells, and the periodic boundary conditions were used in three directions. The MOF frameworks were assumed to be rigid, and the potential energy between adsorbate atoms and frameworks was pretabulated. This is because low-energy equilibrium configurations are involved in adsorption and framework flexibility has only a marginal effect.48 As in the canonical MC simulation described above, the LJ interactions were evaluated with a spherical cutoff with long-range corrections added; the Coulombic interactions were calculated (47) Siperstein, F.; Myers, A. L.; Talu, O. Mol. Phys. 2002, 100, 2025. (48) Smit, B.; Loyens, L.; Verbist, G. Faraday Discuss. 1997, 93.
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Article Table 1. Atomic Charges on the Fragmental Clusters in Figure 2
atom no.
1
2
3
4
5
6
7
8
IRMOF-1 IRMOF-13 and -14 Cu-BTC PCN-6 and PCN-60 soc-MOF
1.514 (Zn) 1.463 (Zn) 1.026 (Cu) 0.937 (Cu) 2.173 (In)
-1.798 (O) -1.753 (O) -0.671 (O) -0.636 (O) -1.549 (O)
-0.715 (O) -0.770 (O) 0.875 (C) 0.840 (C) -0.725 (O)
0.698 (C) 0.848 (C) -0.197 (C) -0.084 (C) 0.996 (C)
0.203 (C) -0.047 (C) 0.028 (C) -0.107 (C) -0.184 (C)
-0.252 (C) 0.144 (C) 0.123 (H) 0.762 (C) -0.260 (C)
0.162 (H) -0.204 (C)
0.110 (H)
-0.724 (N) 0.314 (C)
0.130 (H) -0.147 (N)
9
0.189 (H)
Figure 3. Adsorption isotherms of the CO2/CH4 mixture in (a) IRMOF-1, (b) IRMOF-14 and IRMOF-13, (c) Cu-BTC, and (d) PCN-60 and PCN-6: (4, 2) CO2 and (3, 1) CH4. In the legend, C denotes that framework charges were used in the simulations.
using the Ewald sum method. To investigate the effect of framework charges, additional simulations were also performed in the absence of framework charges (i.e., the electrostatic interactions between the adsorbate and framework were switched off). The number of trial moves in a typical GCMC simulation was 2 107, though additional trial moves were used at high loadings. The first 107 moves were used for equilibration, and the following 107 moves were used to obtain ensemble averages. Six types of trial moves were randomly attempted in the GCMC simulation, displacement, rotation, and partial regrowth at a neighboring position; complete regrowth at a new position; and exchange with the reservoir including creation and deletion with equal probability and the exchange of molecular identity (i.e., CO2 to CH4 and vice versa) with equal probability. Whereas the last trial move is usually not required in GCMC simulation, its use allows faster equilibration and reduces fluctuation after equilibration. In socMOF, NO3 ions were allowed to move during the adsorption of adsorbate molecules. Unless otherwise mentioned, the simulation uncertainties were smaller than the symbol sizes presented in the Figures.
IV. Results and Discussion We first present the adsorption isotherms for the CO2/CH4 mixture in the six neutral MOFs: IRMOF-1, IRMOF-13, IRMOF-14, Cu-BTC, PCN-60 , and PCN-6. Typical simulation snapshots are illustrated in Cu-BTC and PCN-60 , and the separation of CO2 and CH4 is characterized in terms of adsorption selectivity. Then we investigate the effect of electrostatic interactions between CO2 and the framework on adsorption and selectivity. Finally, the locations of extraframework ions in charged soc-MOF are predicted from simulation, followed by adsorption and separation of the CO2/CH4 mixture in soc-MOF. Figure 3 shows the adsorption isotherms of the CO2/CH4 mixture in IRMOF-1, IRMOF-13, IRMOF-14, Cu-BTC, PCN60 , and PCN-6. CO2 is preferentially adsorbed over CH4 in all MOFs as a result of its stronger interaction with the framework atoms because CO2 is a three-site quadrupolar molecule. Substituting organic linker BDC in IRMOF-1 with PDC leads to larger pores in IRMOF-14 and consequently a greater uptake of both CO2 and CH4. Catenated IRMOF-13 consists of small pores and additional adsorption sites. This enhances the interaction of adsorbate molecules with the framework and promotes a higher Langmuir 2009, 25(9), 5239–5247
uptake at low pressure, particularly for CO2. Nevertheless, IRMOF-14 has a larger free volume than does IRMOF-13 and can accommodate more molecules; consequently, the adsorption of both CO2 and CH4 is greater in IRMOF-14 at high pressure. PCN-6 exhibits similar behavior to that observed in IRMOF-13 compared to that of noncatenated PCN-60 . In IRMOF-1, IRMOF-13, IRMOF-14, Cu-BTC, and PCN-6, CH4 reaches saturation at approximately 2000-3000 kPa, and CO2 tends to be saturated at the highest pressure considered. In contrast, the adsorption behavior appears to be different in PCN-60 , which is isostructural with Cu-BTC. Both CO2 and CH4 exhibit linear isotherms in PCN-60 with increasing pressure as a result of the substantially larger pore size compared to that in Cu-BTC. The linear adsorption increase in PCN-60 indicates that a large space is available to accommodate adsorbate molecules even at high pressures. This observation is further elucidated from the simulation snapshots in Cu-BTC and PCN-60 . Figure 4 shows the simulation snapshots of the CO2/CH4 mixture in Cu-BTC and PCN-60 at various pressures. At a low pressure (100 kPa in Figure 4a), CO2 molecules in Cu-BTC are preferentially adsorbed within the tetrahedral side pockets, and CH4 molecules are a bit away from the pockets. With an increase in pressure (300 kPa in Figure 4b), the side pockets are first saturated with CO2 molecules, followed by adsorption around the exposed metal sites and organic linkers. At high pressure (1000 kPa in Figure 4c), the open square pores become filled with adsorbed molecules. The order of occupation with increasing pressure is a result of the strength of the interactions at the different adsorption sites. Isostructural to Cu-BTC, PCN-60 also consists of tetrahedral pockets and square pores, but of larger dimensions. Similar to that observed in Cu-BTC, CO2 molecules in PCN-60 are adsorbed within the side pockets at low pressure (300 kPa in Figure 4d) whereas CH4 molecules are dispersed throughout the framework. As pressure increases (1000 kPa in Figure 4e), the pockets are fully saturated, and adsorption occurs near the exposed metal sites and organic linkers. With a further increase in pressure (3000 kPa in Figure 4f), CO2 molecules are bound to the square pore surfaces, but the pores are not completely occupied. This observation is consistent with the adsorption behavior in Figure 3d, which shows a linear increase as a function of pressure, indicating that sufficient space is available to accommodate adsorbate molecules at high pressure. DOI: 10.1021/la803074g
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Figure 4. Simulation snapshots of the CO2/CH4 mixture at pressures of (a) 100, (b) 300, and (c) 1000 kPa in Cu-BTC (top) and (d) 300, (e) 1000, and (f) 3000 kPa in PCN-60 (bottom): Cu, green; O, red; C, cyan; N, pink; H, white; CH4, orange; and CO2, purple for C and yellow for O.
Figure 5. Adsorption selectivity of the CO2/CH4 mixture in (a) IRMOF-1, IRMOF-13, and IRMOF-14 and (b) Cu-BTC, PCN-6, and PCN60 . In the legend, C denotes that framework charges were used in the simulations.
Adsorptive separation in a binary mixture of components i and j is characterized by selectivity Si/j =(xi/xj)(yj/yi), where xi and yi are the mole fractions of component i in the adsorbed and bulk phases, respectively. Figure 5 shows the simulated selectivity of the CO2/CH4 mixture in IRMOF-1, IRMOF-13, IRMOF-14, Cu-BTC, PCN-6, and PCN-60 . The selectivity in IRMOF-1 remains nearly constant at low pressure and increases with pressure as a result of the preferential interaction of CO2 with the framework. The selectivity in IRMOF-14 follows a similar trend but is slightly reduced because the pore size in IRMOF-14 is approximately one-fourth greater than in IRMOF-1. As a result of catenation, the pore size in IRMOF-13 is constricted and the selectivity is increased compared to its non-catenated counterpart. With increasing pressure, the selectivity in IRMOF-13 initially decreases slightly, then increases as pressure increases, and finally approaches a plateau. This behavior is due to the counterbalance between energetic and entropic (packing) effects. At low pressure, CO2 molecules in IRMOF-13 are preferentially adsorbed in the constricted pores. The volume of these constricted pores is small and gets saturated rapidly. In addition, the adsorption sites are heterogeneous. Consequently, CO2 molecules tend to occupy less adsorptive sites with increasing pressure, and the selectivity decreases slightly. With a further increase in pressure, CO2 molecules intercalate the large pores, and the cooperative 5244
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attraction between adsorbed CO2 molecules further promotes CO2 adsorption so that the selectivity increases. Finally, the selectivity becomes almost independent of pressure as both CO2 and CH4 reach saturation at high pressure. In Cu-BTC and PCN-6, the selectivity increases with increasing pressure and approaches a constant at high pressure, as in IRMOF-1 and IRMOF-14. In PCN-60 , the selectivity increases linearly with pressure, consistent with the isotherm in Figure 3d. As mentioned above, because of the large pores, adsorption in PCN-60 is not saturated at the pressures considered here. Nevertheless, it is expected that the adsorption isotherm and selectivity in PCN-60 will approach saturation at still higher pressures. The catenated framework in PCN-6 shows a higher selectivity than in PCN-60 , which is due to the presence of additional adsorption sites and constricted pores that enhance the interaction with CO2. To investigate the effect of electrostatic interactions between CO2 and the framework, simulations were also carried out for the adsorption of the CO2/CH4 mixture in the absence of framework charges. Figure 6 shows the adsorption isotherms in IRMOF-1, IRMOF-13, IRMOF-14, Cu-BTC, PCN-6, and PCN-60 in the presence and absence of framework charges. In all MOFs, the presence of framework charges and thus an electrostatic interactions with CO2 lead to a slight increase in CO2 adsorption. CH4 is neutral, and in principle its adsorption is not influenced by Langmuir 2009, 25(9), 5239–5247
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Figure 6. Effect of framework charges on the adsorption isotherms of the CO2/CH4 mixture in (a) IRMOF-1, (b) IRMOF-13, (c) IRMOF-
14, (d) Cu-BTC, (e) PCN-6, and (f) PCN-60 . The open (closed) symbols indicate the isotherms in the presence (absence) of framework charges: (4, 2) CO2 and (3, 1) CH4.
framework charges. However, there is competitive adsorption between CO2 and CH4. While CO2 adsorption is enhanced by electrostatic interactions with the framework so that more adsorption sites are occupied by CO2 molecules, CH4 adsorption is thus slightly reduced. Compared to other MOFs, Cu-BTC exhibits a larger effect of framework charges on both CO2 and CH4 adsorption because of the exposed metal sites. PCN-60 and PCN-6 also have exposed metal sites; however, the effect of their framework charges on adsorption is smaller than with Cu-BTC. The reason is that PCN-60 contains larger tetrahedral side pockets and wider square pores, and in the case of PCN-6, most of the exposed metal sites are blocked as a result of catenation. Figure 7 shows the effect of electrostatic interactions on the selectivity in IRMOF-1, IRMOF-13, IRMOF-14, Cu-BTC, PCN-60 , and PCN-6. As mentioned above, the electrostatic interactions between CO2 and the framework cause a slight increase in CO2 adsorption and a marginal decrease in CH4 adsorption. This leads to a higher selectivity for the CO2/ CH4 mixture in all MOFs with framework charges. In IRMOF-1 and IRMOF-14, the selectivity is almost constant at low pressure and then increases as the pressure increases. The selectivity in IRMOF-13 first decreases slightly and then increases with increasing pressure but then remains almost constant with further increases in pressure. The effect of electrostatic interactions on the selectivity is weaker in non-catenated IRMOF-14 because of its larger pore size compared to that of IRMOF-13. In Cu-BTC, the presence of framework charges as well as the exposed metal sites enhances the interaction with CO2, which leads to a selectivity that increases over the whole pressure range. In the absence of framework charges, however, the selectivity decreases at low pressures, then increases with pressure, Langmuir 2009, 25(9), 5239–5247
and finally becomes constant. This behavior is similar to that observed in Figure 5a for IRMOF-13. Increasing selectivity in PCN-6 and PCN-60 is seen over the whole pressure range, as was found with the IRMOFs, and the effect of electrostatic interactions is more pronounced in the catenated framework. PCN-60 is considered to be isostructural with Cu-BTC; however, charges in the PCN-60 framework do not significantly affect the selectivity compared to that in Cu-BTC. This is because PCN-60 consists of larger tetrahedral side pockets and wider square pores. The exposed metal sites are largely blocked in catenated PCN-6; therefore, the effect of electrostatic interactions on selectivity is also weaker in PCN-6 than in Cu-BTC. In our recent study, we showed that the effect of electrostatic interactions between CO2 and the framework was insignificant for the adsorption of pure CO2 and the main contribution to adsorption was from the LJ interaction.10 This was also observed for CO2 adsorption in IRMOF-1, IRMOF-3, and MOF-177.12 These simulation findings show that, except for Cu-BTC, the electrostatic interactions have only a small effect on the adsorption of CO2 and on the separation of the CO2/CH4 mixture. Figure 8 illustrates the typical locations and center-of-mass distributions of NO3 ions in soc-MOF. All eight NO3 ions in the ˚ unit cell are located approximately 3.6-4.5 A from the nearest indium atoms (created by removing the apical water molecules upon dehydration) of the trimer building units. We also examined the mobility of the NO3 ions in soc-MOF using molecular dynamics simulation (data not shown). The NO3 ions essentially vibrate around their favorable location sites. Their small mobility is attributed to the strong binding energy of the extraframework ions with the framework, which restrains ion hopping from one site to the other. In addition, the steric hindrance of the metal DOI: 10.1021/la803074g
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Figure 7. Effect of framework charges on the adsorption selectivity of the CO2/CH4 mixture in (a) IRMOF-1, (b) IRMOF-13 and IRMOF-
14, (c) Cu-BTC, and (d) PCN-60 and PCN-6. The open (closed) symbols indicate the selectivity in the presence (absence) of framework charges.
˚ Figure 8. (a) Typical locations of NO3 ions approximately 3.6-4.5 A from the nearest In atoms. (b) Center-of-mass distributions of NO3
ions in soc-MOF.
Figure 9. (a) Adsorption isotherms and (b) selectivity of the CO2/CH4 mixture in soc-MOF.
oxides connecting organic linkers also reduces ion mobility in the framework. The presence of extraframework ions has a significant impact on adsorption and selectivity. Figure 9a shows the adsorption isotherms of the CO2/CH4 mixture in soc-MOF where CO2 is strongly adsorbed, whereas CH4 adsorption is vanishingly small. The extraframework NO3 ions in soc-MOF act as additional sites, particularly for quadrupolar CO2 molecules, and thus substantially enhance the selectivity of CO2 over CH4. Figure 9b shows that the selectivity in soc-MOF increases from 22 to 36 as pressure rises. The predicted selectivity in soc-MOF is the highest yet reported in MOFs and higher than the selectivity in IRMOF-1 (2-3),8,18 Cu-BTC (6-9),18 mixed-ligand MOFs (∼30),22 carborane-based MOFs (∼17),23 and MOF-508b (3-6).27 The high selectivity in soc-MOF is achievable at a pressure of about 300 kPa, which is the typical operating condition for pressure-swing adsorption. Currently, there is no experimental study on the influence of extraframework ions on the 5246
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adsorption of gas mixture in a charged MOF. Consequently, we cannot make a comparison for our simulation predictions.
V. Conclusions In this work the adsorptive separation of an equimolar CO2/ CH4 mixture was studied systematically in seven MOFs, including the prototype IRMOF-1, metal-exposed Cu-BTC, PCN-60 and PCN-6, catenated IRMOF-13 and non-catenated IRMOF-14, and charged soc-MOF. There is a greater uptake of both CO2 and CH4 in IRMOF-14 than in IRMOF-1 because substituting organic linker BDC with PDC leads to a larger pore size. Because of catenation, constricted small pores and additional adsorption sites are formed in IRMOF-13 and PCN-6. Consequently, adsorption increases at low pressure in IRMOF-13 and PCN-6 but decreases at high pressure as compared to that in noncatenated IRMOF-14 and PCN-60 . This behavior is more pronounced for CO2, which has a stronger affinity for the framework Langmuir 2009, 25(9), 5239–5247
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than does CH4. Over the pressure range in this study, CH4 adsorption reaches saturation at approximately 2000-3000 kPa in all MOFs, and CO2 tends towards saturation except in PCN-60 with a large pore volume. The selectivity in IRMOF-1 and IRMOF-14 remains nearly constant at low pressure and increases as pressure rises. The selectivity in IRMOF-13 initially decreases slightly, then increases with pressure, and finally approaches a constant value. This is a consequence of the counterbalance between energetic and entropic effects in the constricted pores at low pressure and in the large pores at high pressure. Framework catenation enhances the interaction with CO2; therefore, catenated IRMOF-13 and PCN-6 exhibit a higher selectivity than IRMOF-14 and PCN-60 . The electrostatic interactions between CO2 and framework atoms lead to a slight increase in CO2 adsorption and a marginal decrease in CH4 adsorption and a higher selectivity in the CO2/ CH4 mixture in all MOFs. Compared to the other MOFs, there is a larger effect of framework charges on both CO2 and CH4
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adsorption in Cu-BTC as a result of the exposed metal sites, small side pockets, and narrow pores. The effect of electrostatic interactions on selectivity is stronger in IRMOF-13 and PCN-6 compared to that in their non-catenated counterparts. In charged soc-MOF, the extraframework NO3 ions were identified as being approximately 3.6-4.5 A˚ from the nearest indium atoms. The NO3 ions have small mobility, attributed to their strong binding with the framework. The presence of extraframework ions can augment the interactions with guest molecules and act as additional adsorption sites. The adsorption selectivity of CO2 over CH4 in charged soc-MOFs is predicted to be one order of magnitude greater than in IRMOF and PCN structures and the highest among the various MOFs reported to date. Acknowledgment. We are grateful for the support from the National University of Singapore (R-279-000-198-112/133) and the Singapore National Research Foundation (R-279-000261-281).
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