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Langmuir 2007, 23, 12154-12158
Computer Simulation of the Adsorption of Light Gases in Covalent Organic Frameworks G. Garberoglio† Dipartimento di Fisica dell’UniVersita` di Trento, Via SommariVe, 14, 38100 PoVo (TN), Italy ReceiVed June 12, 2007. In Final Form: August 23, 2007 Grand canonical Monte Carlo simulations of argon, hydrogen, and methane adsorption in four covalent organic frameworks are presented. Argon adsorption isotherms from computer simulations overestimate the amount adsorbed by 25% upon saturation, with respect to the available experiments at T ) 87 K. Hydrogen adsorption isotherms show that these materials might attain a 30% increase for the uptake when compared with analogous simulations performed for metal organic frameworks at T ) 77 K and T ) 298 K. Methane adsorption isotherms give a strong indication that at least one material in this class, COF-102, could meet or exceed the Department of Energy’s target of 180 cm3 (STP)/cm3 for P ) 35 bar and room temperature. The origin of this large affinity for methane is investigated by analyzing the structure of the potential energy surface of interaction between the adsorbate and the adsorbent.
1. Introduction The attainment of an effective adsorption of gases within microporous materials requires a careful design to tailor the structural characteristics of the sorbents, particularly the size of the surface area and the value of the solid-fluid interaction at the adsorption sites. In recent years, many advances in chemical synthesis have been focused on the creation of materials having a reticular structure of given properties. In this respect, metal organic frameworks (MOFs)1-4 have attracted a lot of interest for their potential application in the field of gas storage and separation.5-9 MOFs are a new class of materials whose microscopic structure is composed by organic molecules covalently linked to metal-oxide clusters. The presence of carbonbased linkers gives these structures a remarkably low density and potentially a large surface area, with many sites available for gas adsorption. As an example, the material named IRMOF-1 has a density of 0.59 g/cm3 and a surface area that has been estimated at 2900 m2/g.1 These numbers can be compared with the density of diamond (3.5 g/cm3) and the surface area of Zeolite Y (904 m2/g). Early experiments seemed to indicate the potential of very large uptakes for gas adsorption, especially hydrogen,6 even at room temperature. Computer simulation studies were successively carried out to investigate in detail the origin of this behavior10,11 without confirming the first experimental data. A new round of experiments8,12 indicated a better agreement between the results of the computer model and the real adsorption isotherms. †
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(1) Li, H.; Eddaoudi, M.; O’Keeffe, M.; Yaghi, O. M. Nature 1999, 402, 276. (2) Eddaoudi, M.; Li, H. L.; Yaghi, O. M. J. Am. Chem. Soc. 2000, 122, 1391. (3) Eddaoudi, M.; Kim, J.; Rosi, N.; Vodak, D.; Wachter, J.; O’Keefe, M.; Yaghi, O. M. Science 2002, 295, 469. (4) Yaghi, O. M.; O’Keeffe, M.; Ockwig, N. W.; Chae, H. K.; Eddaoudi, M.; Kim, J. Nature 2003, 423, 705. (5) Li, H.; Eddaoudi, M.; Groy, T. L.; Yaghi, O. M. J. Am. Chem. Soc. 1998, 120, 8571. (6) Rosi, N. L.; Eckert, J.; Eddaoudi, M.; Vodak, D. T.; Kim, J.; O’Keeffe, M.; Yaghi, O. M. Science 2003, 300, 1127. (7) Vishnyakov, A.; Ravikovitch, P. I.; Neimark, A. V.; Bulow, M.; Wang, Q. M. Nano Lett. 2003, 3, 713. (8) Rowsell, J. L.; Millward, A. R.; Park, K. S.; Yaghi, O. M. J. Am. Chem. Soc. 2004, 126, 5666. (9) Snurr, R.; Hupp, J.; Nguyen, S. T. AIChE J. 2004, 50, 1090. (10) Sagara, T.; Klassen, J.; Ganz, E. J. Chem. Phys. 2004, 121, 12543. (11) Garberoglio, G.; Skoulidas, A.; Johnson, J. J. Phys. Chem. B 2005, 109, 13094. (12) Dailly, A.; Vajo, J.; Ahn, C. J. Phys. Chem. B. 2006, 110, 1099.
The general outcome of computer simulation studies13 is that even potential models based on general force fields, such as UFF14 or DREIDING,15 are able to predict adsorption isotherms in good quantitative agreement with the experimental findings.11 This fact has been used to predict the structure of novel sorbents that would optimize the adsorption of a particular gas.16,17 Very recently, a new class of materials, named covalent organic frameworks (COFs), has been characterized and synthesized.18,19 The microscopic structure of these substances is made of organic linkers held together by boron-oxide clusters by means of covalent bonds. As a result, the good stability and tailorability characteristic of MOFs are retained, but the resulting materials have an even lower density than MOFs, mostly because of the absence of the heavy metallic atoms. An element of this class, named COF108, has the lowest density ever reported for a crystalline material, 0.17 g/cm3.19 Because of the recent synthesis of these materials, neither experimental nor computer simulation data exist regarding the adsorption properties of gases within COFs, to the best of my knowledge, with the exception of two argon isotherms.19 In this work I will present computer simulation results for the adsorption of Ar, methane, and hydrogen on all of the four COFs described in ref 19. Comparison of computer data with experimental Ar isotherms shows that the prediction of the classical force fields overestimates the actual amount of gas adsorbed within these materials. This discrepancy is not worse than the one observed in the case of Ar adsorption in MOFs, where it is known that the force fields adopted here reproduce methane and hydrogen adsorption fairly well in a wide range of temperatures and pressures. The possible origins of this difference will be discussed. The same model will be used to predict the adsorption isotherms of hydrogen and methane in the same materials, at temperatures (13) Sarkisov, L.; Du¨ren, T.; Snurr, R. Q. Mol. Phys. 2004, 102, 211. (14) Rappe´, A. K.; Casewit, C. J.; Colwell, K. S.; Goddard, W. A., III; Skiff, W. M. J. Am. Chem. Soc. 1992, 114, 10024. (15) Mayo, S. L.; Olafson, B. D.; Goddard, W. A., III. J. Phys. Chem. 1990, 94, 8897. (16) Du¨ren, T.; Sarkisov, L.; Yaghi, O. M.; Snurr, R. Q. Langmuir 2004, 20, 2683. (17) Sagara, T.; Ortony, J.; Ganz, E. J. Chem. Phys. 2005, 123, 214707. (18) Cote´, A.; Benin, A.; Ockwig, N.; O’Keeffe, M.; Matzger, A.; Yaghi, O. Science 2005, 310, 1166. (19) El-Kaderi, H.; Hunt, J.; Mendoza-Corte´s, J.; Cote´, A.; Taylor, R.; O’Keeffe, M.; Yaghi, O. Science 2007, 316, 268.
10.1021/la701736m CCC: $37.00 © 2007 American Chemical Society Published on Web 10/23/2007
Computer Simulation of Light Gas Adsorption in COFs
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Table 1. Lennard-Jones Parameters for the Adsorbate Molecules
a
adsorbate
/kB (K)
σ (Å)
Hea Arb CH4c H2d
10.22 119.8 148.0 34.2
2.556 3.4 3.73 2.96
Reference 27. b Reference 28. c Reference 29. d Reference 30.
of 77 K and 298 K. The computer simulation results will show an increase in the amount of gas adsorbed, when compared with analogous simulations performed in the case of MOFs, and one of the materials analyzed in this study, COF-102, will be shown to have the potential to meet or even exceed the Department of Energy (DoE) target of 180 cm3 (STP)/cm3 at 35 bar for methane adsorption.20,21 The origin of the better performance of COFs with respect to MOFs will be discussed by analyzing the potential energy surface (PES) for solid-fluid interactions.
Figure 1. Isotherms of adsorption for argon at T ) 87 K. Circles and squares correspond to adsorption on COF-102 and COF-103, respectively. Filled and open symbols correspond to the UFF and DREIDING potential models for the adsorbent, respectively. The solid and dashed lines are the experimental values reported in ref 19.
2. Simulation Details The adsorbate particles were modeled using the LennardJones parameters reported in Table 1. The structure files of COF-102, COF-103, COF-105, and COF108 were downloaded from the Cambridge Crystallographic Data Centre22 following the instructions given in ref 19. The frameworks were assumed to be rigid, and both the UFF14 and DREIDING15 force fields were used to calculate the solid-fluid interaction, using Lorentz-Berthelot rules with a cutoff set to 17 Å. The solid-fluid potential energy was precalculated on a cubic grid with 0.2 Å spacing and interpolated using cubic splines during the simulation. In the case of hydrogen, the solid-fluid and fluid-fluid interaction potential V(x) was corrected at all the temperatures using the quadratic Feynman-Hibbs (FH) formula23
VFH(x) ) V(x) +
(
)
p2 ∇2V(x) 24µkBT
(1)
to take into account quantum diffraction effects. In eq 1, the parameter µ is the reduced mass of the two interacting particles and has been set to half of the hydrogen molecule’s mass for the fluid-fluid interaction and set to the hydrogen molecule’s mass for the solid-fluid interaction. When computing the solid-fluid interaction grid with the FH potential, the grid spacing was reduced to 0.1 Å. Adsorption was simulated using the grand canonical Monte Carlo technique. The probability for an insertion or a deletion attempt was set to 0.35, and, as a consequence, the probability of a displacement move was set to 0.3. Displacement moves were attempted with unit probability on a cubic box whose edge length was adjusted during the equilibration phase so as to have an acceptance ratio between 0.45 and 0.55. The number of steps for equilibration was usually of the order of 4 million, and the number of steps for production was usually of the order of 8 million. Some runs were performed with 10 million steps for both the equilibration and production runs to verify the (20) Burchell, T.; Rogers, M. SAE Tech. Pap. Ser. 2000, 2000-01-2205. (21) STP: standard temperature and pressure; 298 K and 1 atm. This is the definition used in ref 20. (22) Cambridge Crystallographic Data Centre Homepage. http://www.ccdc.cam.ac.uk/. (23) Feynman, R.; Hibbs, A. Quantum Mechanics and Path Integrals; McGraw-Hill: New York, 1965.
Table 2. Unit Cell Masses, Volumes, and Free Volumes for the Materials Studied in This Work
material
mass (g/mol unit cell)
unit cell volume (Å3)
free volume (Å3)
density (g/cm3)
COF-102 COF-103 COF-105 COF-108
5083.7 5276.6 9612.5 2339.7
20072.9 22539.8 90434.2 22908.7
13575.5 15711.9 77624.0 19656.1
0.41 0.38 0.18 0.17
independence of the measured quantities on the length of the equilibration phase. The chemical potential used to perform the simulations was converted to pressure for each of the adsorbates using the van der Waals equation of state, whose parameters were chosen so that its critical point corresponds to the actual critical point of the fluid under consideration. The total amount of molecules adsorbed per unit cell Ntot was converted to excess adsorption using the formula24
Nexc ) Ntot - F(T,P)Vfree
(2)
where F(T,P) represents the density at the given temperature obtained from the van der Waals equation, and Vfree is the free volume for adsorption. This latter quantity was calculated as the volume within one unit cell where the potential energy of interaction of a helium atom with the solid framework is less than 104 K. Values of the free volume and other relevant parameters for the adsorbents studied in this work are reported in Table 2.
3. Results 3.1. Argon. The simulated isotherms for argon in COF-102 and COF-103 are shown in Figure 1 together with the experimental data reported in ref 19. The isotherms from computer simulation show a region around 1 mbar where the adsorption has a significant step upward. This is known to correspond to the condensation of Ar, and the same behavior has been observed experimentally in the case of Ar adsorption in the Cu-BTC MOF.7 The simulation results obtained using the two force fields are in quite good agreement with each other. The UFF model results in a more attractive solid-fluid interaction than the DREIDING (24) Myers, A. AIChE J. 2002, 48, 145.
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force field for both COF-102 and COF-103, as might be observed by the discrepancy between the UFF and DREIDING isotherms of the same material in the low-pressure region, where the solidfluid interaction largely determines the adsorption. At higher pressures, the fluid-fluid part of the interaction dominates with respect to the solid-fluid part, and hence the isotherms obtained with the two force fields for the same material tend to converge. Comparison between the simulated isotherms and the actual experimental data shows that simulations overestimate the measured data by 25% at high pressures, and perform worse at lower pressures. This discrepancy is of the same order as the discrepancy observed for argon adsorption in the MOF CuBTC at pressures larger than 1 mbar, even when an ad hoc force field, tailored to reproduce the low-pressure Henry’s constant of the adsorption isotherm, is used in the simulations.7 The discrepancy observed at near-saturation pressures can be due to a variety of factors, apart from the wrong strength of the solid-fluid interaction. It is a priori possible that, under high loadings, the material undergoes a structural change, a phenomenon that is not taken into account with the present model, where a rigid framework is assumed. It might also be possible that these materials presented kinetically inaccessible regions: since the grand canonical Monte Carlo method assumes that any point within the simulation cell can, in principle, be accessed, the presence of insurmountable bottlenecks would result in an experimental saturation adsorption lower than the one expected on the basis of computer simulations. If this was the case, molecular dynamics simulations would be the preferred tool to identify and characterize these regions. Even without resorting to this simulation technique, visual inspection of the potential energy isosurfaces (see Supporting Information) does not show the appearance of low energy “pockets” that would be the signature of kinetically inaccessible regions. The solid-fluid potential energy minima, localized around the metal-oxide region, are continuously connected to the isosurfaces of zero energy, which develop along the center of the channels and represent the main routes for adsorbate access and diffusion within the material. It is also well-known that, from an experimental point of view, the activation procedure following the synthesis has an influence on the amount of gas that can be adsorbed.25 A comparison between hydrogen adsorption isotherms on Cu-BTC as reported in the literature shows that fluctuations as high as 25% can be observed for the amount adsorbed at saturation when different activation procedures are employed. Despite the discrepancy observed between simulation and experiments in the case of Ar adsorption in COF-102 and COF103, it is known that numerical experiments of gas adsorption using transferable force fields and rigid frameworks for the adsorbent can provide fairly good quantitative estimates for the adsorption isotherms in MOFs, especially when the adsorbed gas is above criticality.11,16 Hence we will assume in the following that, by comparing computer generated isotherms for adsorption in COFs with adsorption isotherms in MOFs, the model we have used will be able to capture the general trend. 3.2. Hydrogen. The calculated gravimetric adsorption isotherms of hydrogen at T ) 77 K on all four of the COF subjects of this study are reported in the upper panel of Figure 2. All of the four materials display the same qualitative behavior, with only slight quantitative differences. We notice that COF102 and COF-103 have the largest adsorption at low pressure, but they tend, upon saturation, to a value that is less than the one reached by COF-105 and COF-108. Anticipating the results of (25) Liu, J.; Culp, J.; Natesakhawat, S.; Bockrath, B.; Zande, B.; Sankar, S.; Garberoglio, G.; Johnson, J. J. Phys. Chem. C 2007, 111, 9305.
Garberoglio
Figure 2. Isotherms of hydrogen adsorption on COF-102 (circles), COF-103 (squares), COF-105 (diamonds), and COF-108 (triangles) at T ) 77 K (upper panel) and T ) 298 K (lower panel), using the UFF force field. The open symbols correspond to the isotherm of adsorption obtained without the quantum corrections of eq 1.
an analysis that will be carried out in detail in the case of methane, this difference is due to the larger pore volume of COF-105 and COF-108 with respect to COF-102 and COF-103. The more compact microscopic structure of the two latter materials19 results in a stronger solid-fluid interaction energy and, hence, a larger adsorption at low pressures, where this term dominates. As the loading increases, the smaller free volume of COF-102 and COF103 results in saturation at a lower pressure than in COF-105 and COF-108. In these two other materials, though, the larger free volume does not lead to a correspondingly larger saturation adsorption. This effect is more apparent when the volumetric adsorption is taken into consideration: COF-102 and COF-103 can adsorb hydrogen up to 470 cm3 (STP)/cm3 at T ) 77 K, whereas COF-105 and COF-108 do not exceed 250 cm3 (STP)/ cm3 at the same temperature. It is the considerable lower density of these two latter materials (see Table 2) that favors their gravimetric adsorption. The main reason for the poor volumetric performance of the low-density COF-105 and COF-108 is that, in the largest part of the free volume, the solid-fluid potential energy gain is not enough to result in a sizable excess adsorption, a disadvantage that has also been noticed in the case of hydrogen adsorption on large-pore MOFs.11,26 (26) Latroche, M.; Surbl, S.; Serre, C.; Mellot-Draznieks, C.; Llewellyn, P.; Lee, J.-H.; Chang, J.-S.; Jhung, S.; Frey, G. Angew. Chem., Int. Ed. 2006, 45, 8227. (27) de Boer, J.; Michels, A. Physica 1938, 5, 945.
Computer Simulation of Light Gas Adsorption in COFs
Figure 3. Adsorption isotherms for methane on COF-102 (circles), COF-103 (squares), COF-105 (diamonds), and COF-108 (triangles) at T ) 298 K. Filled symbols correspond to the UFF force field, and open symbols correspond to the DREIDING force field. The star symbol indicates the DoE target of 180 cm3 (STP)/cm3 at P ) 35 bar. The gravimetric adsorption in cm3 (STP)/g is readily obtained by dividing each isotherm by the density of the corresponding material, reported in Table 2.
The excess amount of hydrogen adsorbed is slightly larger than 10% in weight at P = 100 bar for COF-105 and COF-108. This is almost 50% larger than the gravimetric adsorption observed in the case of the most adsorbing MOF (IRMOF-14) at the same temperature,11 where the excess amount adsorbed does not exceed 7.5% in weight. The hydrogen adsorption isotherms on COFs at T ) 298 K, reported in the lower panel of Figure 2, display a structure qualitatively similar to the corresponding isotherms of adsorption in MOFs. It is apparent from Figure 2 that the adsorption at room temperature does not exceed 0.8% in weight at a pressure of =100 bar. Despite the fact that this value is quite far from the DoE target of 6%, it is nonetheless a considerable improvement with respect to the value observed in MOFs. The best hydrogen sorbent (IRMOF-14) does not adsorb more than 0.6% in weight of hydrogen at the same thermodynamic conditions. It is important to notice that the effect of quantum diffraction is not significant only at cryogenic temperatures, where the difference between a quantum and a classical adsorption simulation can be as high as 35%, but also at room temperature. In this last case, neglecting quantum effect would overestimate the adsorption by around 15% at the highest loading. This is of course due to the light mass of the hydrogen molecule: even at room temperature, the thermal de Broglie wavelength (Λ ) h/x2πmkBT ) 0.71Å) is a significant fraction of the LennardJones diameter for this molecule (σ ) 2.96 Å). 3.3. Methane. The isotherms for methane adsorption at T ) 298 K are reported in Figure 3. It is interesting to note that, in this case, COF-102 and COF103 materials display a quantitatively different adsorption behavior than COF-105 and COF-108. In the case of COF-102 and COF-103, the amount of adsorbed methane rises steeply at low pressures and, at P ) 35 bar, is comparable to or greater than the DoE target of 180 cm3 (STP)/cm3.20,21 The exact amount adsorbed at this pressure depends quite significantly on the force field used in the simulation, which can give a discrepancy of (28) Maitland, G. C.; Rigby, M.; Smith, E. B.; Wakeham, W. A. Intermolecular Forces: Their Origin and Determination; Clarendon Press: Oxford, 1981. (29) Goodboy, S.; Watanabe, K.; MacGowan, D.; Walton, J.; Quirke, N. J. Chem. Soc., Faraday Trans. 1991, 87, 1952. (30) Buch, V. J. Chem. Phys. 1994, 100, 7610-7629.
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Figure 4. The volume density of states F(U) for the four materials studied in this work.
around 20%. Nevertheless, the COF-102 material meets or exceeds the DoE requirement for both the UFF and DREIDING models. The reason for this quantitatively different behavior between COF-102-COF-103 and COF-105-COF-108 can be understood by the analysis of the PES of interaction between the frameworks and the methane molecule. We report in Figure 4 the volume density of states F(U). This quantity is defined as the derivative with respect to the potential energy U of the volume V(U) within the unit cell of the material where the solid-fluid interaction energy is less than U. F(U) measures the volume available for adsorption as a function of the solid-fluid potential energy.11 The driving force for an adsorption process is the result of a balance from the potential energy difference between the bulk and the adsorbed phase due to the solid-fluid interaction and the entropy loss, which, as a first approximation, depends on the fact that the adsorbed phase has a reduced dimensionality: a gas passes from a three-dimensional (3D) bulk state to a twodimensional (2D) adsorbed state on the external surface of the porous material. This entropic contribution to the free energy of adsorption can be estimated from the Sackur-Tetrode equation: considering an ideal gas with the mass of methane at P ) 100 bar adsorbing onto a 2D surface with close packing density at T ) 298 K, the entropic contribution to the free energy difference is -T∆S = 1600 K. As a consequence, one expects to obtain significant methane adsorption on materials whose PES of interaction with methane has a large volume at this value of the potential energy. One can see from Figure 4 that indeed COF-102 and COF-103 have more volume available at low energy than COF-105 and COF-108. Analysis of the spatial structure of the potential energy isosurfaces (qualitatively similar to the one obtained in the case of argon; see Supporting Information) reveals that this is indeed due to the more compact nature of the atoms within the unit cell in COF-102 and COF-103. On the other hand, the structure of COF-105 and COF-10819 shows the presence of large volumes within the unit cell, as is also apparent from Table 2 and the fact that F(U) is much larger for COF-105 than for all the other materials in the region U > -900 K. Unfortunately, not all of the space in these large voids is available for adsorption, because, in the greatest part of this volume, the solid-fluid interaction potential is not strong enough to overcome the entropic loss. As a consequence, the volumetric adsorption of methane is greater in the more compact materials COF-102 and COF-103, where more space is available with low values of the interaction energy.
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On the other hand, the lighter COF-105 and COF-108 materials have an advantage from a gravimetric point of view, especially at high pressures. Analysis of the isotherms shows that the amount of methane adsorbed per gram of adsorbent is larger in COF-102 and COF-103 for pressures less than =55 bar. At that point, the four isotherms cross each other at a value of =570 cm3 (STP)/g, which also corresponds to the maximum gravimetric adsorption for COF-102 and COF-103. For larger pressures, the amount adsorbed per gram in COF-105 and COF-108 grows further, reaching a maximum of 720 and 670 cm3 (STP)/g, respectively, around P = 100 bar.
4. Conclusions In this paper we have shown results of computer simulation for the adsorption of Ar, H2, and CH4 in COFs, a new class of microporous materials. The performance of the model was evaluated by comparing its results for the adsorption in the case of argon, the only gas for which experimental isotherms are available. The results show a 25% discrepancy in the adsorbed amount of Ar near saturation at T ) 87 K, which is of the same order as the discrepancy observed for Ar adsorption under the same conditions in MOFs. Despite this shortcoming, a generally good agreement is obtained between experiments and simulations using the same force fields to compute adsorption isotherms in MOFs. Therefore we have extended our calculations to compute the isotherm of adsorption of hydrogen and methane in COFs as well. In the first case, we observed a marked increase in the gravimetric adsorption, when compared with MOFs, even if the adsorbed amount at room-temperature still falls short of the DoE target of 6% in weight. An analogous increase has been observed
Garberoglio
in the adsorption at T ) 77 K. In all of these materials and at the two temperatures that we have tested, the isotherms of gravimetric adsorption are quantitatively the same. Simulation of methane adsorption give a strong indication that at least one of the materials that we have considered, COF102, could meet or exceed the DoE target of 180 cm3 (STP)/cm3 for P ) 35 bar and T ) 298 K. An analysis of the microscopic reason of this significant adsorption showed that the solid-fluid interaction potential between COF-102 and methane is low enough in energy to overcome the entropic loss upon adsorption. The presence of such an attractive region of the PES has been traced back to COF-102 having the highest density with respect to the other COFs analyzed in this work. In this material, one obtains a good trade-off between the dimensions of the geometrical pores and the density of the adsorption sites. The disposition of atoms within the unit cell of COF-102 is such that there is a significant overlap of the regions of attractive interaction with the adsorbed species. As a consequence a large part of the unit cell volume is found with the right potential energy to overcome the entropic loss upon adsorption. Acknowledgment. The computations were performed on the HPC facility “Wiglaf” of the Department of Physics, University of Trento. This work has been done with partial contribution from the Provincia Autonoma di Trento. Supporting Information Available: A movie showing the evolution of the potential energy isosurfaces for the interaction of Ar with COF-102, using the UFF force field. The framework atoms are shown in blue, and the isosurfaces are shown in red. This material is available free of charge via the Internet at http://pubs.acs.org. LA701736M
