Molecular Simulations and Theoretical Predictions for Adsorption and

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Molecular Simulations and Theoretical Predictions for Adsorption and Diffusion of CH4/H2 and CO2/CH4 Mixtures in ZIFs Jinchen Liu,†,‡ Seda Keskin,§ David S. Sholl,|| and J. Karl Johnson*,†,‡ †

Department of Chemical and Petroleum Engineering, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, United States National Energy Technology Laboratory, Pittsburgh, Pennsylvania 15236, United States § Department of Chemical and Biological Engineering, Koc- University, Istanbul, 34450, Turkey School of Chemical and Biomolecular Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332-0100, United States

)

‡

bS Supporting Information ABSTRACT: Adsorption and diffusion of CO2/CH4 and CH4/H2 mixtures were computed in zeolite imidazolate frameworks (ZIFs), ZIF-68 and ZIF-70, using atomically detailed simulations. Adsorption selectivity, diffusion selectivity, and membrane selectivity of ZIFs were calculated based on the results of atomistic simulations. Mixture adsorption isotherms predicted by the ideal adsorbed solution theory agree well with the results of molecular simulations for both ZIFs. Mixture diffusivity calculations indicate that diffusion of CH4 is increased with increasing concentration of H2 in the CH4/H2 mixture, while the diffusivity of H2 decreases with increasing CH4 concentration. In contrast, the diffusivity of CH4 is essentially independent of the concentration of CO2 in the CO2/CH4 mixture, while CO2 diffusivity decreases with increased CH4 loading, even though the diffusivity of CH4 is substantially larger than that of CO2. This unusual behavior can be explained in terms of differences in adsorption site preferences due to charge
quadrupole interactions.

1. INTRODUCTION Rational design of nanoporous materials is of tremendous importance for developing highly selective, low-cost, energyefficient sorbents and membranes for gas separations. Zeolite imidazolate frameworks (ZIFs) are a new subclass of porous metal coordination framework materials emerging as new alternatives for gas separation and CO2 capture applications.1 ZIFs have tetrahedral networks that resemble those of zeolites with transition metals linked by imidazolate ligands.2 One of the advantages of ZIFs over metal organic frameworks is that they generally have higher thermal and chemical stability.3 A large number of different ZIFs have been constructed by varying the imidazolate linker groups and metallic building blocks resulting in materials with varying properties.2,4 Since the number of different types of ZIFs that has been synthesized is large, molecular modeling of these materials can play an important role in providing information for the performance of ZIFs for specific applications.5,6 Quantitative prediction of adsorption and transport properties of gas mixtures in these materials would be a tremendous benefit to the design of new ZIFs as membranes and adsorbents. Some efforts have been made to characterize singlecomponent adsorption and diffusion in large numbers of nanoporous materials.7,8 Work of this kind needs to be combined with detailed studies of adsorbed mixtures to develop a full description of how these materials can be used in practical applications. r 2011 American Chemical Society

Molecular simulations have been used to understand adsorption of single-component gases and gas mixtures in ZIFs. Rankin et al. computed adsorption of CO2, N2, CH4, and H2 in ZIF-68 and ZIF-70 from atomistic simulations.9 Han et al. reported H2 uptake of several ZIFs using ab-initio-based grand canonical Monte Carlo (GCMC) simulations.10 Molecular simulations were used to study adsorption of Ar, H2, and CH4 in ZIF-8, CO2, CH4, and N2 in ZIF-8 and ZIF-76, water, methanol, and ethanol in ZIF-71, and CO2 and CO in ZIF-68 and ZIF69.3,11
13 Adsorption selectivity of ZIF-3, -8, -10, -65, and -67 for CH4/H2 mixtures and adsorption selectivity of ZIF-68 and ZIF-69 for CO2/N2, CO2/CH4, and CH4/N2 mixtures were predicted using GCMC.14,15 Guo et al.14 investigated adsorption sites of ZIF-3 and ZIF-10 for CH4 from GCMC simulations, and Han et al.10 presented the adsorption sites for H2 in ZIF-3 and ZIF-10 from ab-initio-based GCMC simulations. In contrast to the large number of adsorption simulations published for ZIFs, studies of gas diffusivity are very limited. Liu et al. computed the self-diffusion coefficient for CO2 in ZIF-68 and ZIF-69.16 Rankin and co-workers studied self- and transport diffusivities of CO2, CH4, N2 and H2 in ZIF-68 and ZIF-70.9 Krishna and van Baten computed diffusion selectivities for Received: April 1, 2011 Revised: May 18, 2011 Published: May 23, 2011 12560

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The Journal of Physical Chemistry C CO2/H2 and CH4/H2 in ZIF-8 and CO2/CH4 in ZIF-68.17 Keskin calculated diffusion selectivities for CH4/H2, CO2/CH4, and CO2/H2 mixtures in ZIF-3 and ZIF-10.18 No information is available for mixture diffusion in other ZIF structures to the best of our knowledge. Two recent experiments have shown that fabrication of thinfilm ZIF membranes is feasible and ZIF membranes can be successfully used for separation of gas mixtures. Bux et al. prepared a continuous intergrown layer of ZIF-8 on a porous titania support and reported that permeance of H2 is almost five times faster than that of CO2.19 Li et al. studied H2/CO2 mixture permeation through ZIF-7 films using membranes fabricated with the seeded secondary growth method on an alumina support and reported an H2/CO2 ideal selectivity of 6.7 and mixture selectivity of 6.5.20 ZIFs have also been used as components in polymer composite membranes.21 Mixed matrix membranes of this kind are an attractive path toward enhancing the performance of polymeric membranes.22 In this study, we focus on two ZIFs, ZIF-68 and ZIF-70, that exhibit high adsorption and selectivity capacity for CO2 at ambient temperature. Experiments of Banerjee and co-workers reported that these ZIFs have high thermal stability (up to 390 °C) and chemical stability.23 The CO2 selectivities from CO were reported based on the ratio of Henry’s constants as 19.2 and 37.8 for ZIF-68 and ZIF-70, respectively, significantly higher than the CO2 selectivity of BPL carbon (7.5). We here report atomically detailed simulations to assess the separation performance of ZIF-68 and ZIF-70 membranes for CO2/CH4 and CH4/H2 mixtures. These gas mixtures are relevant in a number of large-scale industrial applications. For example, separation of CO2 from CH4 is important in natural gas purification, while separation of CH4/H2 mixtures is relevant for hydrogen recovery from plants and refineries.

2. COMPUTATIONAL DETAILS We computed adsorption and diffusion of gases in ZIFs using GCMC and equilibrium molecular dynamics (EMD), respectively. Both types of simulations were performed at room temperature using rigid ZIF-68 and ZIF-70 structures. The positions of the atoms and the atomic charges for the ZIFs were obtained from density functional theory-optimized structures from previous work by some of us, wherein we reported adsorption and diffusion of light gases in these same ZIFs.9 We note that methods for accounting for atomic charges in periodic solids using density functional theory have become available24
27 after the publication of our previous work.9 Nevertheless, we used the charges from the large cluster calculations of Rankin et al.9 in this work to be consistent with the previously published pure fluid calculations. The universal force field (UFF)28 was used for the framework atoms. We used the Lennard
Jones (LJ) 12
6 potential to model CH4 and H2, whereas CO2 was modeled as a rigid three-site molecule with LJ interactions and partial point charges located at the center of each site. The interaction potential parameters used in our simulations are given in Table 1. The Lorentz
Berthelot mixing rules were employed to calculate the fluid
solid LJ cross interaction parameters. The fluid
fluid and fluid
solid intermolecular LJ potentials were truncated at 17 Å for adsorption simulations, and no long-range corrections were applied. Fluid
fluid and fluid
solid intermolecular LJ potentials were truncated at 13 Å for diffusion simulations, with long-range corrections applied. Diffusivities

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Table 1. Interaction Potential Parameters for Adsorbate Molecules Used in This Work adsorbate

ref

ε/k (K)

σ(Å)

q (e)

H2
H2

41

34.2

2.960

CH4
CH4 C
C (in CO2)

42 43

148.2 27.0

3.812 2.800

þ0.7

O
O (in CO2)

43

79.0

3.050


0.35

calculated using a cutoff radius of 13 Å with long-range corrections gave results that are indistinguishable from calculations using a truncation of 17 Å without long-range corrections. Electrostatic interactions between CO2 molecules were truncated at 25 Å. Electrostatic interactions between CO2 molecules and the framework were calculated by summation of the charge
charge interactions between each framework atom and each charge site of the CO2 molecule. These charge
charge interactions were pretabulated by direct calculation of the atomic charge
charge interactions.29 Our molecular simulations of CH4/H2 and CO2/CH4 mixtures in ZIFs used similar methods to earlier simulations of singlecomponent gas adsorption and diffusion in these materials.9 A conventional GCMC technique was used to compute adsorption isotherms.30
32 We specified the temperature and fugacity of the adsorbing gases and calculated the number of adsorbed molecules at equilibrium. Simulations at the lowest fugacity for each system were started from an empty ZIF matrix. Each subsequent simulation at higher fugacity was started from the final configuration of the previous run. Simulations consisted of a total of 1  107 trial configurations, with the last half of the configurations used for data collection. The Monte Carlo moves used in these simulations included particle translation, creation, deletion, and, in the case of mixtures, identity swaps. The pure component adsorption isotherm at 298 K we obtained in this work is identical to the results of Rankin et al.9 since we used the same potential parameters and ZIF structures. We used EMD simulations to compute the self-diffusivities for pure adsorbates and mixture self-diffusion coefficients for adsorbed mixtures of CH4/H2 and CO2/CH4 with compositions of 75:25, 50:50, and 25:75. The details of these calculations are discussed elsewhere.31,33
35 We used a Nos
e
Hoover thermostat in the NVT-MD simulations30 and performed 40 independent MD simulations, each having a simulation length of 4
8 ns, for each loading and composition considered. After creating initial states with the appropriate loading using GCMC, each system was first equilibrated with EMD for about 150 ps prior to taking data. After mixture adsorption isotherms and mixture diffusivities were calculated, membrane selectivities of ZIF-68 and ZIF-70 for each mixture were predicted by the approximate expression proposed by Keskin and Sholl:36 perm

sorp

R1, 2 ¼ Rdiff 1, 2 R1, 2 ¼

D1, S ðq1 , q2 Þ q1 =q2 D2, S ðq1 , q2 Þ y1 =y2

ð1Þ

sorp diff In this expression, Rperm 1,2 , R1,2 , and R1,2 are the membrane (permeance) selectivity, adsorption selectivity, and diffusion selectivity for component 1 over 2, respectively. The adsorption selectivity is defined as the ratio of the adsorbed amounts (qi) normalized by the bulk gas compositions (yi), whereas the diffusion selectivity is calculated as the ratio of self-diffusivities

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Figure 1. Adsorption isotherms for pure CH4, H2, and their mixtures in (a) ZIF-68 and (b) ZIF-70 at 298 K. The symbols are simulation results, and the lines are the predictions from IAST. Filled (open) symbols represent CH4 (H2) with circles representing the pure fluids, while triangles and squares correspond to 50% and 10% CH4 in the bulk, respectively. Fugacity refers to the total fugacity (sum of component fugacities in the mixture).

Figure 2. Adsorption selectivities for CH4/H2 mixtures in ZIF-68 and ZIF-70 at 298 K. Filled (open) circles and squares represent 10% and 50% CH4 in the bulk for ZIF-68 (ZIF-70). Lines are predictions from the IAST approach. Fugacity refers to the total fugacity (sum of component fugacities in the mixture).

in a binary mixture, Di,S, evaluated directly at their corresponding adsorbed compositions(q1,q2).

3. RESULTS AND DISCUSSION We computed the adsorption isotherms for pure CH4, H2, and their mixtures in ZIF-68 and ZIF-70 at 298 K. We also used the ideal adsorbed solution theory (IAST)37 to predict the mixture isotherms based on the pure component isotherms. The isotherms for pure components and two CH4/H2 mixtures (10% and 50% CH4 in the bulk) and the predictions of IAST are plotted in Figure 1. The calculations were performed by specifying the component fugacities of each species in the mixture, and

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Figure 3. Self-diffusivities for CH4/H2 mixtures in (a) ZIF-68 and (b) ZIF-70 at 298 K: (circles) pure components; (squares/solid lines, diamonds/dotted lines, and triangles/dashed lines) 25%, 50%, and 75% CH4 in the CH4/H2 mixture, respectively. The lines are KP predictions.

the resulting total fugacity, which is the sum of the component fugacities, is given as the independent variable on the abscissa. This convention was also used in Figures 2, 5
7, and 10. The predictions of IAST agree well with the simulation results for CH4/H2 mixture adsorption in ZIFs. As expected, CH4 is preferentially adsorbed over H2. The adsorption selectivities for a CH4/H2 mixture with bulk gas compositions of 10% and 50% CH4 are plotted in Figure 2. In both ZIFs, adsorption selectivity for CH4 decreases with the increase of pressures. At low pressures, energetic effects dominate and favor adsorption of CH4. At higher loadings, entropic effects come into play; small H2 molecules fit into the available pores of ZIFs easily. Therefore, the adsorption selectivity for CH4 decreases as the pressure increases. We found that ZIF-68 exhibits higher CH4/H2 adsorption selectivities than ZIF-70. This is due to the fact that ZIF-68 has smaller pores compared with ZIF-70, which leads to stronger adsorption of CH4 over H2 than in ZIF-70. The selectivities predicted from IAST are also plotted in Figure 2. We note that small errors in the predictions of the mixture adsorption isotherms at low loading give rise to large errors in the adsorption selectivities predicted from IAST. We plot the pure component and mixture self-diffusivities for CH4 and H2 in ZIF-68 and ZIF-70 calculated from EMD simulations in Figure 3. The self-diffusivities of CH4 in the mixtures are larger than the pure component self-diffusivities of CH4 at higher loadings. On the other hand, H2 exhibits the opposite trend. This is due to momentum transfer correlation effects in the mixture that tend to slow faster diffusing species and speed up the slower species.31,32 When the fraction of H2 (CH4) in the mixture increases, the increase (decrease) of CH4 (H2) diffusivities is more profound. We also computed the mixture self-diffusivities using the Krishna and Paschek (KP)38 approach, which uses only pure component adsorption isotherms and diffusivities, and compared 12562

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Figure 5. Predicted membrane selectivities for CH4 over H2 in ZIF-68 and ZIF-70 at 298 K: (circles) ZIF-68 and (squares) ZIF-70. Fugacity refers to the total fugacity (sum of component fugacities in the mixture).

Figure 4. Diffusion selectivities for CH4/H2 mixtures in (a) ZIF-68 and (b) ZIF-70 at 298 K: (squares/solid lines, diamonds/dotted lines, and triangles/dashed lines) 25%, 50%, and 75% CH4 in the CH4/H2 adsorbent, respectively. Lines are predictions from the KP approach.

the predictions of the KP approach with our direct EMD simulations of adsorbed mixtures in Figure 3. The predictions for mixture self-diffusivities of CH4 and H2 are in reasonable agreement with the results of EMD simulations. KP predictions deviate from EMD results at high loadings if the adsorbed mixtures have highly asymmetric compositions.39 For example, KP predictions agree with EMD results for H2 (CH4) diffusivity but overestimate (underestimate) CH4 (H2) diffusivity in CH4/ H2:25/75 (75/25) mixture. The diffusion selectivities of ZIF-68 and ZIF-70 are plotted in Figure 4. These were calculated as the ratio of mixture selfdiffusivities of each species at the adsorbed loading concentrations of 25%, 50%, and 75% CH4 in the mixtures. The diffusion selectivities for CH4 over H2 are less than unity, meaning that a membrane favors H2 in terms of diffusion, as expected. They are in the range of 0.07
0.22 and 0.08
0.25 in ZIF-68 and ZIF-70, respectively. ZIF-70 exhibits slightly higher CH4/H2 diffusion selectivities than ZIF-68. This is opposite to the adsorption selectivities, where ZIF-68 is larger than ZIF-70 (compare Figures 2 and 4). Diffusion selectivities computed from the KP approach are also plotted in Figure 4. We note that the KPpredicted diffusion selectivities are especially poor for ZIF-68, although the trends are correct. The agreement between simulations and KP predictions is better for ZIF-70, but the agreement is only qualitative. We also predicted the membrane selectivities for CH4/H2 mixtures in ZIF-68 and ZIF-70 at 298 K for an adsorbed phase composition of 75% CH4 using eq 1 and plotted the predictions in Figure 5. Although ZIF-68 and ZIF-70 exhibit high adsorption selectivities for CH4 over H2, the competing diffusion selectivity, which favors H2 over CH4, leads to only moderate membrane selectivities for CH4/H2 mixtures, in the range of 2.4
3.8 and 1.2
2.5 for ZIF-68 and ZIF-70, respectively. ZIF-68 exhibits

Figure 6. Adsorption isotherms for pure CH4, CO2, and their mixtures in (a) ZIF-68 and (b) ZIF-70 at 298 K. The symbols are simulation results, and the lines are the predictions from IAST. Filled squares, filled circles, open squares, and open circles represent the isotherms for pure CO2, pure CH4, CO2, and CH4 in the CO2/CH4 mixture of 90% CH4 in the bulk, respectively. Fugacity refers to the total fugacity (sum of component fugacities in the mixture).

higher CH4/H2 membrane selectivities than ZIF-70 due to its higher adsorption selectivity. We could have computed predicted membrane selectivities based on the IAST/KP calculations, but given the poor agreement between simulations and predictions in Figures 2 and 4 there is no justification for making such predictions. We computed the CO2/CH4 mixture adsorption isotherms in ZIF-68 and ZIF-70 and predicted the mixture isotherms with IAST. The simulated isotherms for pure CH4, CO2, and a CO2/ CH4 mixture of 90% CH4 in the bulk are plotted in Figure 6, along with the IAST predictions for the same mixture. ZIFs exhibit very high adsorption preference for CO2 from the CO2/ CH4 mixture. For example, even for a gas mixture of 90% CH4 in the bulk, the adsorbed phase in both ZIFs has a larger mole 12563

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Figure 7. Adsorption selectivity for CO2 over CH4 in ZIF-68 (circles/ solid line) and ZIF-70 (squares/dashed line) at 298 K for a bulk gas composition of 90% CH4 (10% CO2). Lines are predictions from the IAST approach. Fugacity refers to the total fugacity (sum of component fugacities in the mixture).

Figure 9. Diffusion selectivities for CO2/CH4 mixtures in (a) ZIF-68 and (b) ZIF-70 at 298 K: (squares/solid lines, diamonds/dotted lines, and triangles/dashed lines) 25%, 50%, and 75% CH4 in the mixture. Lines are predictions from the KP approach.

Figure 8. Self-diffusivities for CO2/CH4 mixtures in (a) ZIF-68 and (b) ZIF-70 at 298 K: (circles) pure components and (squares/solid lines, diamonds/dotted lines, and triangles/dashed lines) 25%, 50%, and 75% CH4 in the CO2/CH4 mixture. The lines are KP predictions.

fraction of CO2 than CH4, especially at higher pressures, as can be seen in Figure 6. IAST predictions agree with simulations in the low-pressure region but deviate slightly from simulations at high pressures. The adsorption selectivities for the CO2/CH4 mixture are plotted in Figure 7. The selectivity is a maximum in both materials at zero coverage, then decreases very abruptly with increasing pressure, then either increasing slightly with pressure (ZIF-70) or remaining roughly constant (ZIF-68) for fugacities greater than about 20 bar. Adsorption selectivities from IAST predictions are also plotted in Figure 7. The predictions are qualitatively correct but substantially overpredict the selectivities, especially at low pressures. We present the pure and mixture CH4 and CO2 self-diffusivities in Figure 8. The mixture diffusivities of CH4 in ZIF-70 are almost unchanged from their pure component values. For ZIF68, CH4 diffusivities are slightly smaller than the pure component

diffusivities at low to intermediate loadings but are essentially the same as for pure CH4 at high loadings. This is very unusual given that CH4 diffusivities are considerably larger than those for CO2. The CO2 diffusivities decrease with increasing concentration of CH4 in the mixtures. This is just the opposite of what happens in the CH4/H2 mixture, where the diffusivity of the slower diffusing species is increased in the mixture by momentum transfer from the faster diffusing species, as seen in Figure 3. We plot the predictions of the KP approach for CO2/CH4 mixtures in Figure 8. The predictions for mixture self-diffusivities of CH4 are in reasonable agreement with the results of EMD simulations for ZIF-68. However, KP predictions fail to predict the mixture self-diffusivities of CH4 in ZIF-70. Moreover, the KP approach fails to even capture the qualitative trends for the self-diffusivity of CO2 in both ZIFs. For example, the KP approach predicts that the mixture self-diffusivities of CO2 should be larger than the selfdiffusivities of pure CO2, but in fact, simulations give smaller selfdiffusivities in the mixture than for pure CO2. This is the opposite of what one would expect from momentum transfer correlation effects, as seen in CH4/H2 mixtures. We carefully analyzed the preferential adsorption sites and trajectories of CH4 and CO2 in the pure component and mixture diffusion simulations to understand the origin of this unexpected behavior. We computed density histograms for CO2 and CH4 in both the pure fluid and mixture systems and used these to characterize the differences in adsorption site preference. CO2 preferentially adsorbs close to the pore walls due to strong charge
quadrupole interactions for both pure CO2 and CO2 in the adsorbed mixtures. CO2 is located closer to the pore walls in the mixtures than in the pure fluid state at the same loading (see Figure S1 in the Supporting Information). In contrast, CH4 is much more likely to traverse the entire pore volume (Figure S2 in the Supporting Information) and hence spends a significant amount of time near the center of the pore, where the solid
fluid 12564

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shown in Figure 10 for ZIF-68 and ZIF-70 are qualitatively correct. The calculations in Figure 10 are for an equimolar mixture in the adsorbed phase. As with the CH4/H2 mixture, the diffusion and adsorption selectivities compete and the membrane selectivity is dominated by the adsorption selectivity. The membrane selectivities for CO2 over CH4 are modest due to the competition between adsorption and diffusion selectivities and fall in the range of 2.0
4.7 and 1.6
2.8 for ZIF-68 and ZIF-70, respectively. ZIF-68 exhibits higher membrane selectivity than ZIF-70 for CO2/CH4, as was the case for the CH4/H2 mixture. Figure 10. Predicted membrane selectivities for an adsorbed phase equimolar mixture of CO2/CH4 in ZIF-68 (circles) and ZIF-70 (squares) at 298 K. Fugacity refers to the total fugacity (sum of component fugacities in the mixture).

interactions are at their weakest and diffusivity is at its fastest. This is because the CH4 binding energy is relatively small, so entropic effects favor traversing the entire pore volume. There is a slight shift in the most probable CH4 positions away from the pore walls when going from pure CH4 to the mixture. Hence, the trajectory of CH4 in the mixture is not dramatically perturbed that of the pure fluid. For this reason, the diffusivity of CH4 in the mixture is largely independent of the fraction of CO2 in the pore. Conversely, the diffusivity of CO2 is adversely affected by an increase in the fraction of CH4 in the pore (see Figure 8). The reason for this is that CO2 preferentially occupies positions near the pore walls, as discussed above, and the distance from the walls decreases with increasing CH4 loading. The CH4 molecules near the center of the pore exert a net force upon the CO2 molecules, pushing them even closer to the pore walls than in the pure CO2 case and further slowing the diffusivity of CO2 due to fluid
wall collisions. We calculated the diffusion selectivities for CO2 over CH4 in ZIFs and plotted these selectivities in Figure 9. The diffusion again favors the lighter species, as seen in Figure 4, and hence, the CO2/CH4 diffusion selectivities are less than unity. The diffusion selectivities for CO2 over CH4 are in the range of 0.06
0.5 and 0.07
0.42 for ZIF-68 and ZIF-70, respectively. The diffusion selectivity decreases with an increase of the CH4 composition in the adsorbed phase, due to the decrease in CO2 diffusivity with mole fraction of CH4, as discussed above. The predictions of the diffusion selectivities from the KP approach are also plotted in Figure 9. We see that the KP predictions are not even qualitatively correct in this case. The predicted membrane selectivities for CO2/CH4 mixtures in ZIF-68 and ZIF-70 are plotted in Figure 10. Keskin and Sholl hypothesized a connection between the approximate model (eq 1) and two computationally efficient correlations, IAST and the KP approach for mixture self-diffusion.36 They suggested that if both IAST and the KP diffusion correlation accurately predict the mixture isotherm and self-diffusion coefficients for the adsorbed mixture of interest, then eq 1 is expected to give accurate estimates for membrane selectivities. Conversely, if these theories do not give accurate predictions, then we are not able to judge the reliability of the approximate model. However, Keskin showed that predictions of membrane selectivities from the approximate model were still qualitatively accurate, even when IAST and the KP approach are not quantitatively accurate.40 On the basis of this observation, it is reasonable to assume that the predicted selectivities

4. CONCLUSIONS We performed grand canonical Monte Carlo and equilibrium molecular dynamics simulations to calculate the adsorption and diffusion properties of CH4/H2 and CO2/CH4 mixtures in ZIF68 and ZIF-70 at 298 K. The ZIF frameworks were assumed to be rigid in all cases. This is likely to be a reasonably good approximation for both equilibrium and transport properties in these materials because the pores are relatively large and diffusivities are fast. We found that IAST gives fairly accurate predictions of mixtures adsorption isotherms in these ZIFs. We calculated the adsorption, diffusion, and membrane selectivities for CH4/H2 and CO2/CH4 mixtures in ZIF-68 and ZIF-70. These membranes are selective for CH4 over H2 and CO2 over CH4 in CH4/H2 and CO2/CH4 mixtures, respectively. The mixture diffusivities for CH4/H2 and CO2/CH4 are qualitatively different from one another. The CH4/H2 mixture diffusivities are governed by momentum transfer, wherein the faster diffusing species (H2) diffuses slower in the mixture relative to the pure component and the slower diffusing species (CH4) diffuses faster in the mixture than in the pure state. In contrast, for the CO2/ CH4 mixture, CH4 (faster diffusing) is essentially unaffected by the concentration of CO2 in the mixture whereas the diffusion of CO2 is significantly slower in the mixture. This counterintuitive behavior is due to differences in the preferred adsorption sites of the two fluids. The CO2 molecules preferentially adsorb near the walls of the pore due to strong charge
quadrupole interactions between CO2 and the framework atoms. CH4 molecules primarily occupy the center of the pore, and therefore, its diffusivity is not substantially impacted by addition of CO2. In contrast, CH4 in the center of the pore provides an effective force pushing CO2 closer to the pore walls and hence decreasing its diffusivity relative to pure CO2 at the same loading. In both mixtures the diffusion and adsorption selecdiff tivities compete, with Rsorp 1,2 > 1 and R1,2 < 1, and the adsorption selectivities dominate, giving membrane selectivities that are modest. ’ ASSOCIATED CONTENT

bS

Supporting Information. Probability density distributions for CO2 and CH4 in ZIF-68 at different loadings. This material is available free of charge via the Internet at http://pubs. acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]. 12565

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’ ACKNOWLEDGMENT This technical effort was performed in support of the National Energy Technology Laboratory’s ongoing research in CO2 capture under the RES contract DE-FE0004000. ’ REFERENCES (1) Keskin, S.; van Heest, T.; Sholl, D. S. ChemSusChem 2010, 3, 879. (2) Banerjee, R.; Furukawa, H.; Britt, D.; Knobler, C.; O’Keeffe, M.; Yaghi, O. M. J. Am. Chem. Soc. 2009, 131, 3875. (3) P
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dx.doi.org/10.1021/jp203053h |J. Phys. Chem. C 2011, 115, 12560–12566