ARTICLE pubs.acs.org/JPCC
Effect of Pore Topology and Accessibility on Gas Adsorption Capacity in ZeoliticImidazolate Frameworks: Bringing Molecular Simulation Close to Experiment Ravichandar Babarao,† Sheng Dai,†,‡ and De-en Jiang*,† † ‡
Chemical Science Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37966, United States
bS Supporting Information ABSTRACT: When all cages are assumed to be accessible, popular force fields such as universal force field (UFF) and DREIDING dramatically overpredicted gas adsorption capacity in two widely studied zeoliticimidazolate frameworks (ZIFs), ZIF-68 and -69. Instead of adjusting the force-field parameters to match the experiments, herein we show that when the pore topology and accessibility are correctly taken into account, simulations with the standard force fields agree very well with the experiments. Careful inspection shows that ZIF-68 and -69 have two one-dimensional channels, which are not interaccessible to gases. The small channel consists of alternating small (HPR) and medium (GME) cages, while the large channel comprises the large (KNO) cages. Our analysis indicates that the small channel is not accessible to gases such as CO2. So when the cages in the small channel are intentionally blocked in our simulation, the predicted adsorption capacities of CO2, CH4 and N2 at room temperature from standard force-field parameters for the framework show excellent agreement with the experimental results. In the case of H2, all cages are accessible, so simulation results without cage-blocking show excellent agreement with experiment. Due to the promising potential of ZIFs in gas storage and separation, our work here shows that pore topology and accessibility should be carefully examined to understand how gases adsorb in ZIFs.
1. INTRODUCTION Development of functionalized nanoporous materials for gas adsorption and separation is of tremendous importance, particularly for highly energy-efficient CO2 capture from other gas mixtures.1,2 In this regard, metalorganic frameworks (MOFs) are considered as a promising material for gas storage and separation, with a wide-variety of topology, pore-size, and functionality. In recent years, a new class of materials, zeolitic imidazolate frameworks (ZIFs),3,4 have been developed, which exhibit both MOF and zeolite characteristics. Due to their exceptional chemical and thermal stability, ZIFs have attracted increasing attention.5 ZIF structures are based on the threedimensional (3D) networks of aluminosilicate zeolites by substituting tetrahedral Si(Al) and bridging O with metal and imidazolate (IM or derivatives), respectively. ZIFs are chemically and thermally stable (up to 550 C) and also remarkably resistant to water and organic solvents. This is largely due to the hydrophobic pore in ZIFs, which repels solvent molecules, and the stable tetrahedral MN4 (M = Co, Cu, Zn, etc.) clusters formed between metal cations and IM. Unlike the inorganic oxide surface in zeolites, ZIFs’ cages and pores are lined with organic groups. Because of the exceptional stability and porous nature, ZIFs are proposed as ideal candidates for gas storage and separation. r 2011 American Chemical Society
Many studies have been reported to understand the fundamental mechanism of adsorption and diffusion of gases such as CO2, CH4, H2 and N2 in ZIFs, particularly in ZIF-68 and ZIF-69. Banerjee et al. determined the capacity of CO2 and the separation selectivity of CO2/CO in ZIF-68, ZIF-69 and ZIF-70.3 Later, the effects of functionality on the selective capture of CO2 were studied in different ZIFs with the Gmelinite (GME) topology.6 Recently, the effects of functional group on the adsorption of gases in ZIF with RHO topology were assessed using both experimental and computational techniques.7 Liu et al. simulated the adsorption and diffusion of CO2 in ZIF-68 and ZIF-69 and found that CO2 is preferentially adsorbed in the small pores of the two ZIFs.8 Sirjoosingh et al. studied the nature of binding sites and diffusion of CO2 and CO in ZIF-68 and -69 with the universal force field (UFF).9 Rankin et al. computed the adsorption and diffusion of CO2, CH4, H2, and N2 in ZIF-68 and -70 from atomistic simulation.10 They observed that the estimated capacity for CO2 in ZIF-68 at 273 K and 1 bar was substantially greater than the measured values by almost 90% and 65% using UFF and DREIDING force fields, respectively. Similarly, in ZIF70, the simulated CO2 isotherm overestimated the experiments Received: December 9, 2010 Revised: March 18, 2011 Published: April 05, 2011 8126
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Figure 1. Schematic representation of ZIF-68 (top) and different types of cages present in ZIF-68: (a) HPR, (b) GME, and (c) KNO cages (bottom). Top views are showed.
by ∼150% at 273 K and 1 bar. Later Liu and Smit11 examined the gas-separation ability of ZIF-68 and -69. Using UFF, they found that the predicted adsorption capacities at 273 K and 1 bar were much greater than the experimental measurements by ∼80% in ZIF-68 and 40% in ZIF-69 for CO2, by 133% in ZIF-68 and 100% in ZIF-69 for CH4, and by 105% in ZIF-68 and 90% in ZIF-69 for N2. They then adjusted the atomic charges and the potential parameters of UFF to match the experimental adsorption isotherm of pure gases.11 In another recent study, simulations also significantly overpredicted the adsorption capacity of CO2, CH4, and N2 in ZIF-8 and ZIF-76, and again the force field parameters had to be adjusted to match the experimental isotherms.12 The fact that standard force fields dramatically overpredicted adsorption of CO2, CH4, and N2 in some ZIFs (particularly in ZIF-68 and -69 of GME topology) prompted us to ask if the assumptions used in the previous studies are valid. One such assumption is that all the pores are accessible in ZIF-68 and 69. Herein, we show that this assumption is in fact not valid after carefully analyzing the pore topology and accessibility for gas adsorption in ZIF-68 and -69. To reflect the pore accessibility to CO2, CH4, and N2, the cages in the small channels were intentionally blocked to predict its effect on gas adsorption capacity using grand-canonical Monte Carlo (GCMC) simulations. (Several studies have been recently reported highlighting the effect of blocking on adsorption capacity and diffusion in zeolites and MOFs.1315) We show that after the pore accessibility is correctly taken into account, the simulated adsorption capacities for CO2, CH4, N2, and H2 all agree well with the experiments, and the simulations are based on the two commonly used force fields (UFF and DREIDING) without adjusting the potential parameters. The rest of the paper is organized as follows: the models for adsorbent and adsorbate and atomic partial charge calculations are described in Section 2, followed by the simulation methodology in Section 3; in Section 4 the results are discussed, followed by concluding remarks in Section 5.
2. MODELS 2.1. Adsorbent. ZIF-68 and -69 are of the same topology and the only difference between them is benzene-imidazolate in ZIF68 versus 5-chlorobenzene-imidazolate in ZIF-69. Both ZIF-68 and ZIF-69 have GME zeolite-like topology and consist of two one-dimensional channels. The small channel is composed of alternating small (HPR) and medium (GME) cages, while the large channel comprises the large cages (KNO). Schematic representation of ZIF-68 and different types of cages present in ZIF-68 are shown in Figure 1. The small cages (Figure 1a) consist of double six-membered rings. The ring is formed from ZnN4 tetrahedra linked by two chemically different linkers, 2-nitroimidazole (nIM) projecting inside the cage and the substituted imidazolate (benzene-imidazolate in ZIF-68 and 5-chlorobenzene-imidazolate in ZIF-69). The medium cages (Figure 1b) are also located in the small channel connecting the small cages along the pore surface of the smaller channel, and each medium cage is connected to five small cages by four- and six-membered rings. Each medium cage is connected to three large cages through an eight-membered ring-opening. It should be noted that the medium cages are accessible only through the small cage. The large channels hold the large cages (Figure 1c) with the substituted-imidazole projecting inside the channel. Each large cage is surrounded by three medium and small cages. The two channels are interconnected through the eight-membered ring-opening located in the medium cage, but the openings are obstructed by the substituted-imidazole linkers. 2.2. Adsorbate. The adsorbates CO2 and N2, were mimicked as a three-site model to account for the quadrupole moment, whereas a united-atom model for CH4 were employed, respectively. The CO bond length in CO2 was 1.18 Å, and the bond angle — OCO was 180. The charges on the C and O atoms were þ0.576e and 0.288e (e = 1.6022 1019 C, the elementary charge), resulting in a quadrupole moment of 1.29 1039 C 3 m2. The model reproduced the isosteric heat and isotherm of CO2 adsorption in slilicate.16 N2 had a NN bond length of 8127
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Table 1. Force Field Parameters for Adsorbates species CO2 CH4
site
σ (Å)
ε/kB (K)
q (e)
C
2.789
29.66
þ0.576
O
3.011
82.96
0.288
CH4
3.72
158.5
0
N
3.320
36.4
0.482
0
0
þ0.964
2.59
12.5
0
N2
COM
H2
H
1.10 Å, a charge of 0.482e on N atom, and a charge of þ0.964 at the center-of-mass, which were fitted to the experimental bulk properties of N2.17 On the basis of this model, the quadrupole moment of N2 was 4.67 1040 C 3 m2. CH4 was represented by a united-atom model interacting with the Lennard-Jones (LJ) potential. The potential parameters were adopted from the work of Dubbeldam et al.18,19 H2 was mimicked by a two-site model with the LJ potential parameters fitted to the isosteric heat of H2 adsorption on a graphite surface.20 The interactions of gasadsorbent and gas-gas were modeled as a combination of pairwise sitesite LJ and Coulombic potentials. The LJ potential parameters of the framework atoms are adopted from both UFF21 and DREIDING force fields.22 A number of simulation studies have revealed that both UFF and DREIDING force fields can accurately predict gas adsorption in porous materials such as MOFs and covalent organic frameworks (COFs). For example, the simulated adsorption isotherm of CO2, H2 and CH4 adsorption in isoreticular MOFs (IRMOFs) matches well with experiment.2325 The influence of framework charges on the adsorption of CO2 in various MOFs were predicted from simulation and found good agreement with experimental data.26 Table 1 lists the LJ parameters and atomic charges of the adsorbates. The cross LJ parameters were evaluated by the LorentzBerthelot combining rules. 2.3. Atomic Partial Charge Calculation. The atomic charges are estimated from the B3LYP density functional theory (DFT) using a cleaved cluster for each adsorbent as shown in Figures S1 and S2 in the Supporting Information (SI). It is worth noting that the concept of atomic charges is solely an approximation, and no unique straightforward method is currently available to determine them on a rigorous level. Commonly used methods in the literature are based on Mulliken population analysis,27 the electrostatic potential (ESP),28 the restrained electrostatic potential (RESP),29 and the charges from ESPs using a grid (CHELPG).30 Mulliken’s method is from the wave functions and usually overestimates the charges. In the ESP method, the ESPs are fitted at grids located with equal density on different layers around the molecule. The RESP method further sets the charges on the buried atoms to zero by using a penalty function in the fit. Similar to the ESP method, the ESPs are calculated in the CHELPG method at grids distributed on a cubic lattice. In this work, the CHELPG method is used to estimate the atomic charges. Fitting of the electrostatic charges on the atoms was performed at the B3LYP level of theory, and the 6-311þþG(d,p) basis set is used for all atoms except the transition metals, for which the LANL2DZ basis set is used. All DFT computations are carried out with the Gaussian 03 suite of programs.31 The CHELPG method is generally accepted to be the most reliable charge fitting scheme for MOFs.3234 CHELPG charges for ZIF-68 are taken from the work of Rankin et al.35 and for ZIF-69 calculated in this work. For comparison, Mulliken charges for ZIF-68 and -69 are taken from the work of Liu et al.36 Tables S1 and S2
in the SI show both CHELPG and Mulliken charges for ZIF-68 and -69.
3. SIMULATION METHODOLOGY The adsorption of pure CO2, N2, H2, and CH4 was simulated by the GCMC method. Because the chemical potentials of adsorbate in adsorbed and bulk phases are identical at thermodynamic equilibrium, GCMC simulation allows one to relate the chemical potentials of adsorbate in both phases and has been widely used for the simulation of adsorption. The framework atoms are kept frozen during simulation. This is because adsorption involves low-energy equilibrium configurations, and the flexibility of framework has a marginal effect, particularly on the adsorption of small gases. The LJ interactions were evaluated with a spherical cutoff equal to half of the simulation box with long-range corrections added; the Coulombic interactions were calculated using the Ewald sum method. The number of trial moves in a typical GCMC simulation was 2 107, although additional trial moves were used at high loadings. The first 107 moves were used for equilibration, and the subsequent 107 moves were used for ensemble averages. Five types of trial moves were attempted in the GCMC simulation, namely, displacement, rotation, and partial regrowth at a neighboring position, entire regrowth at a new position, and swap with reservoir. Unless otherwise mentioned, the uncertainties are smaller than the symbol sizes in the figures presented. GCMC simulations involve nonphysical insertions and destructions of molecules over the entire framework, and the energetically favorable configurations are accepted under the prescribed chemical potential. In some cases, these may result in accepted configurations where the sorbate molecules reside within the framework which is physically not accessible, resulting in overestimation of simulation results with respect to the experimental findings. So, in this study, we considered three cases based on pore topology to understand the mechanism of adsorption in ZIF-68 and -69. Case 1: The molecules are allowed to adsorb within the entire framework under the prescribed chemical potential. Case 2: The medium (GME) cages were blocked. Case 3: Both the small (HPR) and the medium (GME) cages present in the small channel were blocked. The experimental adsorption isotherm is usually reported in the excess amount Nex, while simulation gives the absolute amount Nab. To convert Nab to Nex, we use Nex ¼ Nab Fb Vfree
ð1Þ
where Fb is the density of bulk adsorbate, and Vfree is the free volume in adsorbent available for adsorption and is estimated from Z Vfree ¼ V
exp uHe ðrÞ=k T dr B ad
ð2Þ
where uHe ad is the interaction between Helium and adsorbent, in which σHe = 2.58 Å and εHe/kB = 10.22 K.37 Note that the free volume detected by helium is temperature dependent, and usually room temperature is chosen. The ratio of the free volume Vfree to the occupied volume Vtotal gives the porosity φ of the adsorbent. 8128
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Figure 2. Channel morphologies and diameter along the Z-direction [(a) small channel and (b) larger channel] and along the Y-direction (c) in ZIF-68. The inset refers to the pore surface perpendicular to the Z-direction. Different cages located in both small and large channels are shown.
4. RESULTS AND DISCUSSION 4.1. Porosity of ZIF-68 and ZIF-69 Structures. Assynthesized ZIFs always have solvent molecules inside their crystal structures and therefore need to be activated to remove solvent molecules before experimental adsorption measurements. The ZIF-68 and ZIF-69 samples were activated by heating at 85 C under vacuum for 72 h, and it was concluded that solvent molecules (H2O and dimethylformamide in the case of ZIF-68 and H2O only in the case of ZIF-69) are completely removed after activation.3 To confirm that the experimental adsorption data collected on ZIF-68 and ZIF-69 were from fully activated samples, we estimated their surface areas and simulated N2 adsorption at 77 K (Figure S3 in the SI); then compared them with the experimental BrunauerEmmettTeller (BET) surface areas and adsorption isotherm. It has been shown for several MOFs that the accessible surface areas agree well with the BET surface areas determined from the adsorption isotherm of N2 as well as with the experimental values.38 We estimated the accessible surface area of ZIF-68 and ZIF-69 using a probe molecule with a diameter equal to 3.681 Å (assuming all cages are accessible) and the LJ parameters for the framework atom are taken from the DREIDING force field. The calculated values are 1060 m2/g for ZIF-68 and 854 m2/g for ZIF-69, in reasonable agreement with the experimental BET surface areas of 1090 m2/g (ZIF-68) and 950 m2/g (ZIF-69).3 In addition, the simulated adsorption isotherm for N2 at 77 K in ZIF-68 using UFF and CHELPG charges agrees well with the experimental data.10 Recently, in their study of H2 uptake in several ZIFs, Han et al. predicted the Connolly surface area for ZIF-68 and ZIF-69 at 1557 m2/g and 1515 m2/g, respectively, which are much higher than the experimental BET surface areas and our estimates.39,40 D€uren et al. showed that the Connolly surface area either underpredicts or overpredicts the experimental BET surface area.38 Our estimate of the surface areas and simulation of N2 adsorption at 77 K confirmed that the experimental samples were fully activated and that the activated samples show permanent porosity. We now analyze the pore structure and accessibility of ZIF-68 and ZIF-69. Figure 2 shows the morphologies
Table 2. Pore Apertures da and Pore Diameters dp of Different Cages Located in ZIF-68 and -69 Calculated Using the HOLE Programa ZIF-68 cages
a
da (Å)
dp (Å)
ZIF-69 da (Å)
dp (Å)
HPR cage
3.8 (3.4)
4.4
3.8 (3.4)
4.4
GME cage
3.8 (3.4)
7.0
3.8 (3.4)
5.26.0
KNO cage
8.6 (7.5)
4.8 (4.4)
7.08.6 (7.8)
11.0(10.3)
The values in the parentheses are from the refs 4 and 6.
and diameters of the channels in ZIF-68 calculated using the HOLE program.41 The small channels (Figure 2a) have a pore aperture diameter of 3.8 Å, slightly greater than those reported in the literature (3.4 Å) for ZIF-8, which consist of a similar sixmembered ring with different linkers.4,12 Figure 2b shows the large channel along the Z-direction with a pore aperture diameter of 8.6 Å. The two channels are connected by the small windows of diameter ∼2.8 Å located in the GME cages along the Y axis (Figure 2c). Therefore, for relatively large molecules such as CO2, CH4, and N2, the two channels are not interaccessible, and the molecules have to pass through the small HPR cages to access the medium GME cages in the small channel. From a chemical viewpoint, the only difference between ZIF-68 and -69 is that ZIF-69’s imidazolate has a chloro group on the benzene ring instead of a hydrogen atom as in ZIF-68, so it is not surprising that the pore topology and accessibility of ZIF-69 (Figure S4 in the SI) is similar to that of ZIF-68. Table 2 summarizes the pore apertures and pore diameters of the three cages present in ZIF-68 and -69. Even though the predicted pore aperture and pore diameters of the channel are slightly greater than those mentioned in the literature, it gives us information about the channel topology and accessibility for gas adsorption. 4.2. Adsorption Isotherms of CO2. On the basis of our analysis of the pore topology, we now investigate the adsorption mechanism of CO2, CH4, N2, and H2 in ZIF-68 and -69 using GCMC simulations. First, let us consider the case where all cages are accessible (Case 1). The purpose here is to reproduce previous simulations by others. Figure 3 shows the adsorption 8129
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Figure 3. Adsorption of CO2 in ZIF-68 and ZIF-69 from UFF (top) and DREIDING potential (bottom) at 298 K using atomic partial charges calculated from the CHELPG method (see the SI for details). Filled symbols are experiment data, 6 and the open symbols are simulation results. Case 1: without blocking (upward triangle); Case 2: blocking GME cages (downward triangle); Case 3: blocking HPR and GME cages (rectangle).
Figure 4. Simulation snapshot of CO2 location in HPR cage of ZIF-68 at 1 kPa (a) perpendicular and (b) parallel to the Z-axis. The distance between CCO2 and ONO2 is in angstroms.
isotherm of CO2 in ZIF-68 and -69 at 298 K using UFF and DREIDING potentials, in comparison with the experiments. One can see that both the UFF and DREIDING force fields dramatically overpredict the experiments at 298 K and 1 bar, respectively, consistent with the earlier findings from others.1012 So we have confirmed that this overprediction occurs when all cages in ZIF-68 and -69 are assumed to be accessible. However, our analysis of pore topology and accessibility indicates that the cages in the small channel are probably not experimentally accessible to CO2. To simulate the experiments more accurately, we should take into account the pore accessibility by comparing the pore
aperture with kinetic diameters. We consider two more scenarios of adsorption: Case 2, where the molecule can enter the small channel but adsorb very strongly inside the small HPR cage, so in the low-pressure regime examined (
