Article pubs.acs.org/JPCC
Adsorption and Diffusion of CO2 and CH4 in Zeolitic Imidazolate Framework-8: Effect of Structural Flexibility Liling Zhang,*,†,‡ Gang Wu,† and Jianwen Jiang*,¶ †
Institute of High Performance Computing, 1 Fusionopolis Way, Connexis, 138632, Singapore Jiangsu Key Laboratory for Carbon-Based Functional Materials & Devices, Institute of Functional Nano & Soft Materials (FUNSOM), Soochow University, Suzhou, Jiangsu, 215123, China ¶ Department of Chemical and Biomolecular Engineering, National University of Singapore, 117576, Singapore ‡
ABSTRACT: A hybrid molecular simulation study is reported to examine adsorption and diffusion of CO2 and CH4 in zeolitic imidazolate framework-8 (ZIF-8). The structure flexibility of ZIF-8 is described using a recently developed force field (Zhang, L. et al. J. Am. Chem. Soc. 2013, 135, 3722). The simulated adsorption isotherms in rigid and flexible ZIF-8 are nearly identical and agree well with experimental data; thus, the effect of structure flexibility on adsorption is indiscernible. In remarkable contrast, the effect on diffusion is significant. No diffusive motion is observed for CO2 and CH4 in rigid ZIF-8; by incorporating structure flexibility, however, the predicted diffusivities are close to experimental and simulated data reported in the literature. From the analysis of free energy, CO2 has a lower barrier for diffusion than CH4 and hence a higher diffusivity. With increasing loading, CO2 and CH4 exhibit different trends. CO2 diffusivity slightly decreases due to enhanced steric hindrance; however, CH4 diffusivity substantially increases because CH4 is preferentially located near the aperture and thus the free energy barrier for diffusion is reduced. For a CO2/CH4 mixture, CO2 is more strongly adsorbed than CH4 and blocks the diffusion pathway of CH4; therefore, CH4 diffusivity in the mixture decreases upon comparison with pure CH4. This simulation study provides microscopic insight into adsorption and diffusion in ZIF-8 and highlights the indispensable effect of structure flexibility on diffusion behavior.
1. INTRODUCTION Consisting of tetrahedral metal clusters and imidazolate ligands, zeolitic imidazolate frameworks (ZIFs) are unique nanoporous crystalline materials.1 With zeolite-like topologies, they possess exceptionally high chemical and thermal stability. Nevertheless, the pore size and affinity of ZIFs can be readily tunable by altering imidazolate ligands. Consequently, there has been considerable interest to use ZIFs for many potential applications. While a large number of ZIFs have been synthesized, the prototypical ZIF-8 is the most extensively studied for gas separation,2 biofuel purification,3 water desalination,4 etc. For example, the separation of a CO2/CH4 mixture was examined in ZIF-8.5,6 The rationale is that the kinetic diameters of CO2 and CH4 are 3.3 and 3.8 Å, respectively, whereas the aperture size in ZIF-8 is approximately 3.4 Å.7 Therefore, a molecular sieving effect for CH4 and a high separation factor for the CO2/ CH4 mixture would be, in principle, expected. However, it turned out that CH4 is able to adsorb and diffuse in ZIF-8, leading to a moderate separation performance.5,6 This unexpected observation revealed that the crystalline structure of ZIF-8 is not completely rigid and the aperture is flexible to a certain extent, as confirmed by experimental studies. For example, several gas molecules (N2, CH4, C2H6, and C3H8) with kinetic diameters > 3.4 Å were found to easily pass through ZIF-8.5−8 On the basis of a series of probe molecules, © 2014 American Chemical Society
the effective aperture size in ZIF-8 was estimated to be between 4.0 and 4.2 Å.9 At cryogenic temperatures, stepped sorption behavior was reported for N2, O2, CO, and Ar.10−12 Meanwhile, several simulation studies have been conducted to examine adsorption and diffusion in ZIF-8.13−15 In these studies, however, the structure of ZIF-8 was assumed to be rigid. To describe the experimentally observed structural flexibility of ZIF-8, several force fields have been used or developed in a few simulation studies. Hertäg et al. and Zheng et al. investigated gas diffusion in ZIF-8 by adopting the Amber and Dreiding force fields and found that diffusivities are extremely sensitive to the parameters describing the aperture.16−18 Pantatosaki et al. also used the Dreiding force field to examine adsorption and diffusion in ZIF-8 and found a significant effect on diffusion exerted by the imidazolate ligand.19,20 Using a force field without partial charges, Battisti et al. simulated the adsorption and dynamics of CO2, CH4, N2, H2, and binary mixtures in ZIF-8.21 Combining quantum chemical calculation and the Amber force field, we developed a force field well reproducing the crystalline, mechanical, and thermophysical properties of ZIF-8.22 Recently, we developed a new force field that can describe the continuous structural Received: January 23, 2014 Revised: March 12, 2014 Published: April 11, 2014 8788
dx.doi.org/10.1021/jp500796e | J. Phys. Chem. C 2014, 118, 8788−8794
The Journal of Physical Chemistry C
Article
transition of ZIF-8 upon N2 sorption and revealed that the structural transition is largely related to the reorientation of imidazolate rings.23 In this study, we aim to further examine the capability of the newly developed force field to describe both adsorption and diffusion of CO2 and CH4 in ZIF-8. In particular, microscopic insight is provided into the mechanism of adsorption and diffusion, and the effect of structural flexibility is quantitatively evaluated. Following this section, the simulation models and methods are outlined in section 2. The simulation results for pure CO2 and CH4, as well as their equimolar mixture, are presented in Section 3. Finally, the concluding remarks are summarized in Section 4.
∑ kϕ[1 + cos(mϕijkl − ϕijkl0 )]
Unonbonded
∑ kξ[1 + cos(mξijkl − ξijkl0 )]
(3)
⎡⎛ ⎞12 ⎛ ⎞6 ⎤ σij σij = ∑ 4εij⎢⎢⎜⎜ ⎟⎟ − ⎜⎜ ⎟⎟ ⎥⎥ + r ⎝ rij ⎠ ⎦ ⎣⎝ ij ⎠
∑
qiqj 4πε0rij
(4)
where εij and σij are the well depth and collision diameter, rij is the distance between atoms i and j, qi is the atomic charge of atom i, and ε0 = 8.8542 × 10−12 C2 N−1 m−2 is the permittivity of vacuum. The universal force field (UFF)24 was used to assign the LJ potential with a scaling factor of ε = 0.54 εUFF for the well depth. The atomic charges in ZIF-8 were adopted from the calculations by plane-wave periodic density functional theory.25 This force field has been validated by reproducing the stepped adsorption isotherm of N2 in ZIF-8, as well as the crystalline and mechanical properties of ZIF-8.23 CO2 was represented as a three-site molecule to account for quadrupole moment.26 The C−O bond length was 1.18 Å, and the bond angle ∠OCO was 180°. The charges on the C and O atoms were +0.576e and −0.288e, respectively. CH4 was represented by a united-atom interacting with the LJ potential.27 The cross-interaction parameters between gases and ZIF-8 were modeled by the Lorentz−Berthelot combining rules. A simulation box with eight (2 × 2 × 2) unit cells of ZIF-8 was used to examine the adsorption and diffusion of CO2 and CH4 in ZIF-8. The initial structure of ZIF-8 was constructed from experimental crystallographic data.7 Unlike the conventional grand canonical Monte Carlo (GCMC) method, a hybrid Gibbs ensemble MC (GEMC) and molecular dynamics (MD) method developed in our previous study23 was applied to incorporate the structural flexibility of ZIF-8 upon adsorption. Specifically, the GEMC method was first performed to simulate adsorption in rigid ZIF-8 at 298 K and a given pressure; then, the MD method in the NPT (isothermal and isobaric)
tetrahedrally coordinated by four N atoms of 2-methylimidazolate. The sodalite cages possess a diameter of 11.6 Å, connected via small apertures with a diameter of 3.4 Å. Nevertheless, the ZIF-8 structure has certain flexibility, primarily due to the reorientation of the imidazolate ring, which allows the aperture size to vary. To investigate the adsorption and diffusion of CO2 and CH4 in ZIF-8 with structural flexibility, the force field developed for ZIF-8 in our previous study23 was used. It consists of bonded and nonbonded terms. The bonded term includes stretching, bending, and torsional potentials 1 kr(rij − rij0)2 2
Utorsional =
(2)
where kr, kθ, kϕ, and kξ are the force constants; rij, θijk, ϕijkl, and ξijkl are bond lengths and angles, and proper and improper dihedrals, respectively; m is the multiplicity; and r0ij, θ0ijk, ϕ0ijkl, and ξ0ijkl are the equilibrium values. The nonbonded term includes Lennard-Jones (LJ) and Coulombic potentials
Figure 1. (a) Unit cell and (b) atomic types of ZIF-8.
∑
∑
+
2. MODELS AND METHODS ZIF-8 has a sodalite zeolite-like topology with a cubic space group I4̅3m.7 Figure 1 illustrates that each Zn metal is
Ustretching =
1 kθ(θijk − θijk0 )2 2
Ubending =
(1)
Figure 2. Adsorption of (a) CO2 and (b) CH4 in ZIF-8 at 298 K. Experimental data for CO2 are from Pérez-Pellitero et al.13 and CH4 from Zhou et al.28 8789
dx.doi.org/10.1021/jp500796e | J. Phys. Chem. C 2014, 118, 8788−8794
The Journal of Physical Chemistry C
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Figure 3. Diffusivities of (a) CO2 and (b) CH4 in ZIF-8 at 298 K. Red: this study; green: from MD simulation in NPT ensemble by Pantatosaki et al.;20 black: from PFG-NMR experiment by Pantatosaki et al.20
Figure 4. Density contours of (a) CO2 and (b) CH4 at a loading of 6 mole./uc (c) CO2 and (d) CH4 at a loading of 25 mole./uc. Mole./uc refers to molecules per unit cell, and the unit of density is 1/Å3.
ensemble was conducted to relax the ZIF-8 structure with adsorbed gas molecules. The GEMC/MD simulation was repeated until the adsorption capacity converged. In each cycle, the number of trial moves in the GEMC simulation was 2 × 107. Four types of trial moves were attempted, namely, displacement, rotation, regrowth, as well as swap, though the regrowth has a negligible effect on the sampling. MD simulation was run for 600 ps with a time step of 1 fs. The temperature and pressure were controlled by the Berendsen
method with a relaxation time of 0.8 ps. With this hybrid GEMC/MD simulation, the ZIF-8 structure was allowed to relax upon adsorption. To evaluate the effect of structural flexibility, GCMC simulation was also performed to examine gas adsorption in rigid ZIF-8. In principle, gas diffusivity could be estimated from the above GEMC/MD simulation. Because of the fluctuation in the number of gas molecules during adsorption, however, the estimation might not be accurate. Moreover, the MD 8790
dx.doi.org/10.1021/jp500796e | J. Phys. Chem. C 2014, 118, 8788−8794
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Figure 5. Radial distribution functions for (a) CO2 and (b) CH4 around the framework atoms of ZIF-8 at a loading of five molecules in the simulation box.
molecules in the system, the error bar at a low loading is larger compared to that at a high loading. The Ds’s at a low loading [e.g., 3 molecules per unit cell (mole./uc)] are approximately 6.2 × 10−10 m2/s for CO2 and 6.4 × 10−11 m2/s for CH4. In our previous study,22 the Ds’s at the same loading were estimated to be 4.2 × 10−9 and 1.1 × 10−9 m2/s, respectively. The deviations between the two studies are due to different force constants used to mimic the bending potentials of Zn−N−C1 and Zn− N−C2, which largely govern the stiffness of the imidazolate linker near the aperture. The force constants in this study are 100 and 70 kcal/mol,23 while they were 40−43 kcal/mol.22 Thus, the imidazolate linker is stiffer here, leading to a less flexible aperture and hence lower Ds. This highlights the crucial effect of the organic linker in ZIF-8 on gas diffusion, especially for CH4 with a larger kinetic diameter than CO2. As shown in Figure 3, the Ds’s of CO2 and CH4 in ZIF-8 exhibit different trends. With increasing loading, the Ds of CO2 slightly decreases. This is because steric hindrance becomes strong at a high loading. In contrast, the Ds of CH4 increases by 8-fold from low to high loading. Similar trends were observed from MD simulation in the NPT ensemble by Pantatosaki et al.,20 despite the deviations in the magnitude. Using pulsed-field gradient nuclear magnetic resonance (PFG-NMR), the Ds’s of both CO2 and CH4 were measured to be ∼1.5 × 10−10 m2/s.20 The simulated Ds’s in the current study are close to this value. Figure 4 illustrates the density contours of CO2 and CH4 in ZIF-8 at two loadings of 6 and 25 mole./uc, respectively. At a low loading (6 mole./uc), both CO2 and CH4 primarily occupy site I proximal to the CC bond of 2-methylimidazolate. Therefore, the organic linker in ZIF-8 is the most preferential adsorption site, rather than the metal cluster. This phenomenon is also observed in a number of experimental and simulation studies for gas adsorption in ZIF-8,13,31−33 as well as methanol adsorption in ZIF-829 and ZIF-71.34 It should be noted, however, that metal clusters in many other MOFs appear to be the most preferential sites, e.g., CO2 adsorption in IRMOFs.35 At a high loading (25 mole./uc), CH4 is mostly populated at sites I and II near the aperture, with a small percentage in the cage center (site III). However, CO2 is located at all of these three sites. As will be discussed below, the locations of gas molecules affect the free energy barrier for diffusion. To quantify the locations, radial distribution functions around the framework atoms of ZIF-8 were calculated by
simulation duration was 600 ps, not sufficiently long to estimate diffusivity. As an alternative, the diffusivity was calculated from separate MD simulation in the NPT ensemble. The number of molecules was determined from the GEMC/MD simulation. The MD simulation was conducted for 20 ns, with 5 ns equilibrium and 15 ns production. A time step of 1 fs was used to integrate the equations of motion. In both MC and MD simulations, the LJ interactions were evaluated with a cutoff of 12.0 Å and the Coulombic interactions were evaluated using the Ewald summation with a precision of 10−5.
3. RESULTS AND DISCUSSION 3.1. Pure CO2 and CH4. Figure 2 shows the adsorption of pure CO2 and CH4 in ZIF-8 at 298 K. The simulated adsorption isotherms from rigid and flexible ZIF-8 are nearly identical, and both are in good agreement with experimentally measured data.13,28 Apparently, the structural flexibility of ZIF8 has an indiscernible effect on the adsorption of CO2 and CH4. A similar effect was also found in the simulation of methanol and ethanol in ZIF-8.29 This is remarkably different from N2 adsorption at 77 K,23 in which the stepped adsorption isotherm was not reproducible in rigid ZIF-8. Here, the negligible effect of structural flexibility is attributed to the low pressure range examined (
