Understanding the Potential of Zeolite Imidazolate Framework

Article pubs.acs.org/JPCC

Understanding the Potential of Zeolite Imidazolate Framework Membranes in Gas Separations Using Atomically Detailed Calculations Erhan Atci and Seda Keskin* Department of Chemical and Biological Engineering, Koç University, Rumelifeneri Yolu Sariyer, 34450, Istanbul, Turkey S Supporting Information *

ABSTRACT: Zeolite imidazolate frameworks (ZIFs) offer considerable potential for gas separation applications due to their tunable pore sizes, large surface areas, high pore volumes, and good thermal and mechanical stabilities. Although a significant number of ZIFs has been synthesized in the powder form to date, very little is currently known about the potential performance of ZIFs for membranebased gas separation applications. In this work, we used atomically detailed calculations to predict the performance of 15 different ZIF materials both in adsorption-based and membrane-based separations of CH4/H2, CO2/CH4, and CO2/H2 mixtures. We predicted adsorption-based selectivity, working capacity, membrane-based selectivity, and gas permeability of ZIFs. Our results identified several ZIFs that can outperform traditional zeolite membranes and widely studied metal organic framework membranes in CH4/H2, CO2/CH4, and CO2/ H2 separation processes. Finally, the accuracy of the mixing theories estimating mixture adsorption and diffusion based on single component data was tested.

1. INTRODUCTION There has been a continuous growth in the development of novel nanoporous materials for gas storage and gas separation applications. Metal organic frameworks (MOFs) are one of the recent groups of nanoporous crystals that combine metal organic complexes with organic linkers to create highly porous frameworks with numerous attractive properties such as high surface area, high porosity, low density, and good thermal and mechanical stability. Zeolite imidazolate frameworks (ZIFs) are considered as a subclass of MOFs. ZIFs are composed of tetrahedral networks that resemble those of zeolites with transition metals connected by imidazolate ligands.1,2 Zeolites are known with the Al(Si)O2 unit formula, whereas ZIFs are recognized by M(Im)2, where M is the transition metal (zinc, cobalt, copper, etc.) and Im is the imidazolate type linker. The greatest advantage of ZIFs compared to other traditional nanoporous materials such as zeolites and carbon nanotubes (CNTs) is the ability to control linker functionality and pore size during synthesis.3 Several ZIFs with various physical and chemical properties have been synthesized to date and considered as potential candidates specifically for gas separation applications due to variety in their pore sizes and higher thermal and moisture stability compared to zeolites and other MOFs.1,4,5 A large number of ZIFs have been synthesized in the powder form to date, but we know very little about the potential of ZIF membranes in specific gas separations of interest. Huang et al.6,7 fabricated ZIF-22 and ZIF-90 membranes and measured gas permeances of H2/CO2, H2/CH4, and H2/N2 mixtures. Liu et al.8,9 measured permeances of CO2/N2, CO2/CH4, and © 2012 American Chemical Society

CO2/CO mixtures through ZIF-69 membranes. Li and coworkers10,11 studied permeances of H2/CO2, H2/N2, and H2/ CH4 mixtures through ZIF-7 membrane. Several research groups fabricated ZIF-8 membranes and studied H2/CH4,12 CO2/CH4,13,14 and C2H6/C2H415 permeances. Considering the large number of available ZIFs, experimental fabrication and testing of new ZIF membranes is very time-consuming and the number of studies on ZIF membranes is currently limited to these five ZIFs. An alternative approach is to use computational methods to screen a large number of materials and narrow down the number of candidates to a handful of promising materials that can be subjected to more detailed experimental investigations.16−18 Molecular simulations have been recently used to assess the performance of ZIFs in adsorption-based separation applications. Guo et al.19 reported the adsorption selectivity of ZIF-3, ZIF-8, ZIF-10, ZIF-60, and ZIF-67 for CH4/H2 mixtures. Liu and Smit20 studied the adsorption selectivity of ZIF-68 and ZIF-69 for CO2/N2, CO2/CH4, and CH4/N2 mixtures. Li and co-workers21 calculated the adsorption selectivity of ZIF-78 and ZIF-79 for CO2/CH4 and CO2/N2 mixtures. Wu et al.22 recently screened several ZIFs for adsorption-based separation of CH4/H2 mixtures. Molecular simulation studies for predicting the membrane performance of ZIFs is very limited compared to the studies for predicting adsorption-based separation performance. Keskin23 reported the permeation Received: June 11, 2012 Revised: June 26, 2012 Published: June 26, 2012 15525

dx.doi.org/10.1021/jp305684d | J. Phys. Chem. C 2012, 116, 15525−15537

The Journal of Physical Chemistry C

Article

Table 1. Structural Properties of ZIFs Studied in This Work material

composition

porosity22,26,71 (%)

density (g/cm3)

pore size4,72 (Å)

volume (Å)

ZIF-1

Zn(Im)2

55.75

1.194

3.00/6.94

2221

ZIF-2

Zn2(Im)4

49.20

0.929

6.4/6.9

5707

ZIF-3

Zn2(Im)4

57.80

0.880

4.6/6

6024

ZIF-6

Zn(Im)2

62.70

0.764

8.2/8.8

6940

ZIF-8

Zn(mIm)2

43.30

0.924

3.4/11.6

4905

ZIF-10

Zn(Im)2

65.00

0.746

8.2/12.12

14210

ZIF-60

Zn2(Im)3(mIm)

70.82

0.769

7.2/9.4

14270

ZIF-65

Co(nIm)2

67.90

1.095

3.4/10.4

5152

ZIF-67

Co(nIm)2

62.27

0.904

3.4/11.6

4877

ZIF-68

Zn(cbIm)(nIm)

60.69

1.033

7.5/10.3

11364

ZIF-69

Zn(cbIm)(nIm)

57.41

1.145

4.4/7.8

11436

ZIF-70

Zn(Im)1.13(nIm)0.87

72.09

0.854

13.1/15.9

11387

ZIF-79

Zn(mbIm)(nIm)

56.87

1.075

4.0/7.5

11441

ZIF-81

Zn(brbIm)(nIm)

56.65

1.292

3.9/7.4

11527

ZIF-90

Zn(Ica)2

60.40

0.974

3.5/11.2

5233

selectivity of ZIF-3 and ZIF-10 membranes for CH4/H2, CO2/ CH4, and CO2/H2 mixtures. Liu et al.24 studied permeationbased separation of CH4/H2 and CO2/CH4 mixtures in ZIF-68 and ZIF-70 membranes. Krishna and Van Baten25 studied ZIF8 membrane for separation of CO2/H2 and CH4/H2 mixtures. Battisti et al.26 predicted the permeation selectivities of ZIF-2, ZIF-4, and ZIF-8 for CO2/H2, CH4/H2, CO2/CH4, CO2/N2, and CH4/N2 mixtures at zero-pressure limit. We recently described molecular simulation methods to model pure ZIF-90 and ZIF-65 membranes in addition to the mixed matrix membranes composed of various polymers, ZIF-90 and ZIF65.27 As can be seen from this literature review, most of the molecular simulations have focused on a few specific ZIFs and information about the potential of several ZIFs as adsorbents and membranes is lacking. The aim of this work is to provide the first information on permeation-based selectivities of ZIFs for CH4/H2, CO2/CH4, and CO2/H2 separations. Separation of these gas mixtures is important for practical industrial applications such as natural gas purification, hydrogen recovery from plants, and refineries. In this work, we used atomically detailed simulations to study adsorption and diffusion of gas mixtures in a large group of ZIFs. On the basis of adsorption and diffusion data, we predicted adsorption-based (permeation-based) selectivities and working capacities (gas permeabilities) of ZIF adsorbents (membranes). In order to assess the potential of ZIFs in gas separation applications, we compared their performances with well-known zeolites and widely studied MOFs. The accuracy of two mixing theories which are widely used to estimate adsorption and diffusion of binary gas mixtures based on single component adsorption and diffusion data was also tested. Finally, we compared our theoretical predictions with the

cell dimensions (a, b, c) (Å) cell angles (α, β, γ) (deg) 9.7405 × 15.266 × 14.936 90, 98.62, 90 9.679 × 24.114 × 24.450 90, 90, 90 18.9701 × 18.9701 × 16.740 90, 90, 90 18.515 × 18.515 × 20.245 90, 90, 90 16.9910 × 16.9910 × 16.9910 90, 90, 90 27.0608, 27.0608,19.406 90, 90, 90 27.2448 × 27.2448 × 19.2254 90, 90, 90 17.2715 × 17.2715 × 17.2715 90, 90, 90 16.9589 × 16.9589 × 16.9589 90, 90, 90 26.6407 × 26.6407 × 18.4882 90, 90, 120 26.0840 × 26.0840 × 19.4082 90, 90, 120 27.0111 × 27.0111 × 18.0208 90, 90, 120 25.9263 × 25.9263 × 19.6532 90, 90, 120 25.9929 × 25.9929 × 19.6997 90, 90, 120 17.3612 × 17.3612 × 17.3612 90, 90, 90

topology BCT BCT DFT GIS SOD MER MER SOD SOD GME GME GME GME GME SOD

available experimental data of ZIF membranes to validate the accuracy of our calculations.

2. COMPUTATIONAL DETAILS 2.1. ZIFs and Adsorbates. We studied 15 different materials in this work: ZIF-1, ZIF-2, ZIF-3, ZIF-6, ZIF-8, ZIF-10, ZIF-60, ZIF-65, ZIF-67, ZIF-68, ZIF-69, ZIF-70, ZIF79, ZIF-81, and ZIF-90. The data for ZIF-68 and ZIF-70 were taken from our previous study.24 The atomic positions of ZIFs were taken from experimental X-ray diffraction (XRD) studies, and solvent-free, rigid structures were used in all molecular simulations.1,28−30 The structural properties of the ZIFs studied in this work are given in Table 1, and unit cell representations (a unit cell is the smallest unit of volume that contains all of the structural and symmetry information of the crystal) are given in Figures S1−S13 of the Supporting Information. We first performed all simulations using the universal force field (UFF)31 because UFF fully defines the interatomic potentials needed for all ZIF atoms and several previous molecular simulation studies have used UFF for ZIFs.3,19,23,32−35 We recently showed that results of molecular simulations employing UFF agreed well with the experimental measurements of gas permeances through ZIF membranes.27 In order to examine the effect of force fields on the results, we repeated molecular simulations using the DREIDING36 force field. The aim of our calculations is to study a large group of materials to identify the most promising ones using generic force fields and the least amount of experimental input. The only experimental input of our calculations is the ZIF crystal structures, and we did not use any force field adjustment in our simulations. Refining force field parameters to match the results of molecular simulations with the experimentally measured gas adsorption isotherms is 15526



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20 ps prior to taking data. In order to apply mixing theory for diffusion, we computed both single component self- and corrected diffusivities. For the single component corrected (self) diffusivities, 20 (10) independent EMD simulations were performed, since using a large number of independent trajectories is vital in order to accurately compute the corrected diffusivities. Mixture self-diffusivities of each species were computed directly at the adsorbed concentrations calculated from binary mixture GCMC simulations. The details of using EMD simulations to obtain various diffusion coefficients have been described in previous studies of zeolites, CNTs, MOFs, and ZIFs.23,45−47 2.3. Application of Mixing Theories. The prediction of adsorption and transport properties of mixtures from data taken from single component studies has been a long-standing goal in describing equilibrium and mass transport in nanoporous materials. The validation of methods for this task can have great practical significance, but this type of validation can only be considered when high quality mixture adsorption and diffusion data is available. We used our GCMC and EMD data from binary mixtures in some ZIFs to test the validity of the mixing theories that have been proposed to predict mixture properties from single component data. For adsorption, we tested ideal adsorbed solution theory (IAST)48 which is well-known to give accurate predictions for mixture adsorption isotherms based on adsorption data of pure gases in many nanoporous materials except in materials characterized by strong energetic or geometric heterogeneity.49 In order to apply IAST, single component adsorption isotherms of CH4 and H2 (CO2) were fitted to dual site Langmuir (Freundlich) models. For diffusion, we used the Krishna and Paschek (KP)50 approach which predicts the self-diffusion coefficients of species in a binary mixture using the following correlations:

not a well developed strategy because the accuracy of the experiments can be significantly affected by the defects of assynthesized ZIFs or trapped residual solvent molecules present in the samples. For example, two different research groups5,13 reported different gas adsorption isotherms for the same ZIF. Spherical Lennard-Jones (LJ) 12−6 potentials were used to model H2 and CH4 molecules.37,38 The CO2 molecule was modeled as a rigid linear molecule which is an all-atom LJ potential with atomic charges to approximate CO2’s quadrupole moment.39 The N2 molecule was represented as a three-site model with two sites located at two N atoms and the third one located at its center of mass (COM) with partial point charges.40 Pairwise interactions between adsorbates and each atom in ZIFs were used to model interaction between adsorbate molecules and the atoms of ZIFs. Mixed atom interactions were calculated using Lorenz−Berthelot mixing rules. Partial point charges were defined for each atom in ZIFs for the simulations including CO2 and N2. The atomic partial charges for all ZIFs except ZIF-90 were assigned using the connectivity-based atom contribution method (CBAC)41 which assumes that the partial charge of an atom in a framework is determined by its bonding connectivity and the atoms with the same connectivity have identical charges. Xu and Zhong41 tested this approach on 43 MOFs and showed that CBAC charges give nearly identical results to those from the quantum mechanical (QM) calculations as well as good reproduction of the experimental isotherm data. Recent studies23 also showed that adsorption isotherms computed using the CBAC method are very similar to the ones computed using QM methods based on the ChelpG42 density functional theory (DFT) calculations. In our recent study,27 the atomic partial charges of ZIF-90 were defined using REPEAT charges of Watanabe et al.,43 and to be consistent, we used the same charges for further calculations of ZIF-90. 2.2. Details of Atomic Simulations. Conventional grand canonical Monte Carlo (GCMC) simulations were employed to compute single component and binary mixture adsorption isotherms of gases in ZIFs. By specifying the temperature and fugacity of the adsorbing gases, the number of adsorbed molecules was calculated at equilibrium. For pure components, four types of trial moves, attempts to translate a molecule, attempts to rotate a molecule, attempts to create a new molecule, and attempts to delete an existing molecule, were included. For gas mixtures, in order to speed up the equilibrium, an additional type of trial, attempts to exchange molecular identity, was also included. More details of GCMC can be found elsewhere.44 A cutoff distance of 13 Å was used for LJ interactions, and 25 Å was used for electrostatic interactions. Periodic boundary conditions were applied in all simulations. The size of the simulation box was increased up to 7 × 7 × 7 unit cells in cases to accommodate enough adsorbates to guarantee the simulation accuracy at the lowest loadings. Simulations at the lowest fugacity for each system were started from an empty ZIF matrix, and each subsequent simulation at higher fugacity was started from the final configuration of the previous run. Simulations included a minimum 1.5 × 107 cycle equilibration period followed by a 1.5 × 107 cycle production run. Single component and mixture diffusivities were computed using equilibrium molecular dynamics (EMD) simulations in the canonical ensemble with a Nosé−Hoover thermostat.44 After creating initial states with the appropriate loadings using GCMC, each system was first equilibrated with EMD for about

Di ,self =

1 1 Đi

+

θi

+

Đii corr

θj Đij corr

,

Dj ,self =

1 1 Đj

+

θi Đji corr

+

θj Đjj corr

(1)

In these correlations, Di,self is the self-diffusivity of species i in a binary mixture with species j, Đi is the single component corrected diffusivity, Điicorr and Đijcorr are the self-exchange and binary-exchange diffusivities which reflect the correlation effects in a mixture, and θi is the fractional loading of species i. In order to use eq 1, we first fitted single component self-diffusivities, Di,self(θ) and corrected diffusivities, Di(θ) of pure gases to continuous functions and then evaluated these coefficients at the total fractional loading for mixtures. The self-exchange diffusivities and binary-exchange diffusivities were calculated using Di ,self (θ ) =

1 1 Đi(θ )

+

θi Đii corr(θ )

(2)

Θj ,satĐij corr(θ ) = [Θj ,satĐii corr(θ )]θi / θi + θj [Θi ,satĐjj corr(θ )]θj / θi + θj (3)

where Θi,sat defines the saturation loading of species i. The KP approach has been tested in the past for CNTs,51 MFI,52 and CuBTC,53 and the predictions were found to be in good agreement with EMD simulations. 2.4. Predicting Adsorption-Based and PermeationBased Selectivities. In order to assess the potential of ZIFs as membranes, the permeation selectivity of component i from 15527



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Figure 1. Equimolar mixture adsorption isotherms of (a) CH4/H2, (b) CO2/CH4, and (c) CO2/H2 in ZIF-1 and ZIF-2 at 298 K. Symbols are the results of mixture GCMC simulations, and dotted lines represent the predictions of IAST.

component j was calculated as the multiplication of adsorptionbased selectivity and diffusion-based selectivity:

Gas permeability is as important as gas selectivity because membranes having high gas permeability and selectivity are desired to reduce the capital cost of separation processes. Permeability of gases in a binary mixture through a ZIF membrane was defined as55

Spermeation(i / j) = Sadsorption(i / j)·Sdiffusion(i / j) =

xi /xj Di ,self (xi , xj) · yi /yj Dj ,self (xi , xj)

Pi =

(4)

In this expression, x is the molar fraction of the adsorbed phase calculated from mixture GCMC simulations, y is the molar fraction of the bulk gas phase, and Di,self is the mixture self-diffusivity of component i evaluated directly at the corresponding adsorbed compositions of the mixture from GCMC simulations. This expression approximates a membrane’s selectivity at a given feed pressure, temperature, and feed gas composition assuming that the permeate side of the membrane is at a vacuum. More details of this approximation and its validation can be found in an earlier study.54 It is important in this context to note that we intend that the calculations we described in this study will be used in the context of materials screening, meaning that when materials with promising properties are found they can be characterized more accurately using detailed calculations at the full range of membrane operating conditions of interest.

ϕ·Di ,self ·ci fi

(5)

where Pi is the permeability of the species i (mol/m/s/Pa), ϕ is the fractional pore volume of the membrane material, ci is the concentration of species i at the upstream face of the membrane (mol/m3), and f i is the bulk phase fugacity of the species i (Pa).

3. RESULTS AND DISCUSSION 3.1. Adsorption-Based Separations of Gas Mixtures in ZIFs. In order to compute adsorption-based separation performance of ZIFs for CH4/H2, CO2/CH4, and CO2/H2 mixtures, we computed binary mixture adsorption equilibria of gases in all ZIFs. As an example, adsorption isotherms for CH4/ H2, CO2/CH4, and CO2/H2 mixtures in ZIF-1 and ZIF-2 at 298 K are shown in Figure 1. Adsorption of CO2 is strongly favored over CH4 (H2) in CO2/CH4 (CO2/H2) mixtures due to the electrostatic interactions of CO2 molecules with the ZIF 15528



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Figure 2. Predicted adsorption selectivity of ZIFs for (a) CH4/H2, (b) CO2/CH4, and (c) CO2/H2 mixtures at 298 K. Compositions of the bulk gas mixtures are CH4/H2:10/90, CO2/CH4:10/90, and CO2/H2:1/99. The first species in the label represents the selected component. Data for CO2/ CH4 selectivity of ZIF-68 and ZIF-70 was taken from calculations of Liu et al.24

recent molecular simulation study22 which computed the CH4 adsorption selectivity of ZIF-1 as 76 at 1 bar. Materials having large cages connected with narrow windows such as ZIF-65, ZIF-67, and ZIF-90 exhibit mediocre CH4 selectivity (15−20), since adsorbate molecules are not very strongly confined in the large cages. The two ZIFs with large cavities, ZIF-10 and ZIF60, exhibit the lowest CH4 selectivity (∼10). Our predictions for CH4/H2 adsorption selectivity of ZIFs are in good agreement with the predictions of Wu et al.22 and Guo et al.19 who employed DREIDING and UFF in their molecular simulations, respectively. For example, we predicted CH4 selectivities of 14, 21, 11, 21, and 40 for ZIF-6, ZIF-8, ZIF60, ZIF-67, and ZIF-81, respectively, whereas Wu et al. computed selectivities as 12, 18, 10, 15, and 35 at 10 bar, 298 K for the same materials. Adsorption selectivities of ZIFs for CO2/CH4 mixtures are shown in Figure 2b. The CO2 selectivities are not very high (2−12) due to the competitive adsorption between CO2 and CH4 molecules in the ZIF pores. There is a slight increase in CO2 selectivity at high pressures which can be attributed to the collective interaction of CO2 molecules at high loadings. We computed CO2 selectivity as 6.6 (5) in ZIF-69 (ZIF-79) for a CO2/CH4:10/90 mixture which agrees with the value of 5.6

atoms. Adsorption of CH4 is preferred over H2 in CH4/H2 mixtures, since H2 has weaker interactions with ZIFs. We also used IAST to predict the mixture adsorption isotherms based on pure gas adsorption data. There is a good agreement between IAST predictions and GCMC simulations for all mixtures, suggesting that IAST can be used to get accurate predictions for binary adsorption equilibria of CO2, CH4, and H2 gases in ZIFs. Adsorption-based separation performances of ZIFs were examined by computing the adsorption selectivity (Sadsorption) using eq 4. Figure 2a shows adsorption selectivity of ZIFs as a function of fugacity for CH4/H2 mixtures. All ZIFs are CH4 selective, and selectivity generally shows a slight decrease at high pressures. This can be explained by the interplay of energetic and size effects. At low pressures, energetic effects favor CH4 adsorption, whereas, at high loadings, small H2 molecules can find adsorption sites in the pores due to entropic effects. Materials having narrow pore apertures and small cavities such as ZIF-1, ZIF-79, and ZIF-81 exhibit high adsorption selectivities (>40) because the degree of confinement of CH4 molecules in these narrow pores is much stronger compared to the small H2 molecules. Our result for high CH4 selectivity of ZIF-1 (71) is in agreement with the result of a 15529



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Figure 3. Adsorption-based separation performance of ZIFs for (a)CH4/H2, (b)CO2/CH4, and (c)CO2/H2 mixtures. The compositions of the bulk gas mixtures are (a) 10/90, (b) 10/90, and (c) 1/99 for ZIFs at 298 K and (a) 50/50, (b) 50/50, and (c)15/85 for zeolites at 300 K.

(7.3) calculated by Liu and Smit20 (Li et al.21) for equimolar mixtures at 10 bar, 298 K. As can be seen from Figure 2c, CO2/ H 2 selectivities are significantly higher than CO 2 /CH 4 selectivities, since CO2 is strongly selected over H2 due to weak interactions of H2 with ZIFs. Similar to the previous discussion, ZIFs with narrow pores (ZIF-1, ZIF-69, ZIF-79, ZIF-81) provide stronger confinement and hence show higher selectivity (200−400) for CO2, whereas ZIFs with large cavities like ZIF-6, ZIF-10, and ZIF-60 are less promising materials for CO2/H2 separations. One striking feature of Figure 2c is that ZIFs having the same topology (ZIF-8, ZIF-65, ZIF-67, ZIF90) exhibit different CO2/H2 selectivities of ∼35, 102, 43, and 137, respectively. Although the adsorbed H2 amounts in these materials are similar, the CO2 adsorption amounts are different in each material. This can be attributed to the complex interplay of several material properties such as available free volume, pore shape, type of metal sites, and organic linkers forming the pores. For example, the type of imidazolate linkers in ZIF-90 (Zn(Ica)2) is different from the ones in ZIF-8, ZIF65, and ZIF-67 (Zn(mIm)2, Co(nIm)2, and Co(mIm)2, respectively), which causes differences in electrostatic and

dispersion interactions of CO2 with the pore walls of the materials. Adsorption selectivity and working capacity are the two important factors determining the efficiency of an adsorptionbased separation process. Working capacity also known as delta loading was calculated as the difference of the adsorbed loadings at adsorption pressure (10 bar) and desorption pressure (1 bar).25 Figure 3 compares adsorption selectivities and delta loadings of ZIFs considered in this study for separation of CH4/H2, CO2/CH4, and CO2/H2 mixtures at 10 bar and room temperature. In order to assess the performance of ZIFs, data for zeolites and MOFs taken from the literature25 are shown in Figure 3. The best adsorbent candidates are expected to be in the upper right corner of Figure 3, exhibiting high selectivity and high working capacities. Figure 3a shows that ZIF-1, ZIF-2, ZIF-3, ZIF-68, ZIF-69, ZIF-79, and ZIF-81 are promising materials for CH4/H2 separation because they have higher selectivities than traditional zeolites CHA, ITQ-29, and LTA-Si and their working capacities are similar to zeolites. The remaining ZIFs have mediocre selectivities, but their working capacities are low due to smaller pore volumes. As 15530



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Figure 4. Self-diffusivities of (a) CH4/H2:75/25, (b) CH4/H2:50/50, and (c) CH4/H2:75/25 mixtures in ZIF-2 at 298 K. Symbols (dotted lines) represent the results of EMD simulations (predictions of KP theory). (d) Comparison of theory predictions with the EMD simulations at various loadings.

in these applications.57 Kinetic-based separations are widely done industrially with established nanoporous adsorbents,58 and these kinds of processes cannot be evaluated for ZIFs without information on diffusion rates. In order to assess the performance of ZIFs as membranes for gas separation applications, we computed the mixture self-diffusivities of each species using EMD simulations in addition to the single component self-diffusivities. Both single component selfdiffusivities and mixture self-diffusivities of gases in all ZIFs are given in Figures S14−S47 of the Supporting Information. Theoretical methods that can predict multicomponent diffusion coefficients from single component data can be extremely useful in modeling of new membrane materials if these methods are known to be accurate. We tested the accuracy of the KP approach for a ZIF material in this work. Since ZIF-2 has the best membrane-based separation performance and the highest diffusion-based selectivity for CH4/H2 and CO2/H2 separations, as will be discussed in the next section, KP theory was tested for this material. Figure 4 shows the selfdiffusivities of CH4/H2 mixtures in ZIF-2 computed by EMD simulations and predicted by KP theory at three different adsorbed compositions. There is a good agreement between theory predictions and MD simulations. The self-diffusivities of both CH4 and H2 decrease as the total adsorbed loading

discussed previously, more open MOF structures with high pore volumes and high surface areas such as IRMOF-1, CuBTC, MOF-177, ZnMOF-74, and MgMOF-74 tend to yield higher working capacities than zeolites and ZIFs.25,55 The performance of ZIF adsorbents for CO2/CH4 separation is similar to that of zeolites DDR, MFI, and ITQ-29. The CO2 selectivities are around 10, and the CO2 working capacities are in the range 1−2.4 mmol/g. It is obvious from Figure 3b that NaX and NaY have high CO2 selectivities due to the strong electrostatic interaction between CO2 and nonframework cations (Na+).56 However, molecular simulations clearly demonstrated the drawbacks of these commonly used adsorbents, very low working capacities.25 These zeolites are also among the best candidates for CO2/H2 separations. A significant portion of the ZIFs examined in this work have greater CO2/H2 adsorption selectivities than the widely studied MFI, CHA, DDR, and CuBTC, but none of the ZIFs considered in this work can outperform MgMOF-74, which offers the best combination of adsorption selectivity and working capacity for CO2/H2 separations. 3.2. Diffusion of Gas Mixtures in ZIFs. Membrane-based separations intrinsically rely on both adsorption and diffusion; therefore, knowledge of how species in adsorbed mixtures diffuse is a prerequisite for considering new materials like ZIFs 15531



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Figure 5. Predicted permeation selectivity of ZIFs for (a) CH4/H2, (b) CO2/CH4, and (c) CO2/H2 mixtures at 298 K. The compositions of bulk gas mixtures are CH4/H2:10/90, CO2/CH4:10/90, and CO2/H2:1/99.

of this method for CO2/CH4 mixture diffusion in ZIF-6824 gave good results, and we speculate similar outcomes will be found for other ZIFs. 3.3. Permeation-Based Separation of Gas Mixtures in ZIFs. Once adsorption and diffusion-based selectivities of ZIFs are computed, permeation-based selectivities can be predicted using eq 4. Data for adsorption selectivity, diffusion selectivity, and permeation selectivity of all ZIFs for CH4/H2, CO2/CH4, and CO2/H2 mixtures are given in Tables S1−S3 in the Supporting Information. Figure 5 shows the permeation selectivity of ZIFs as a function of pressure for CH4/H2, CO2/CH4, and CO2/H2 mixtures. Here, the abscissa of the figures can be considered as the feed pressure of the membrane, since the permeate side is assumed to be a vacuum. Figure 5a shows that ZIF-2 and ZIF-79 exhibit the highest permeation selectivities for CH4 (∼10). The adsorption selectivity of ZIF79 for CH4 (∼50) was higher than ZIF-2 (∼30); however, the diffusion selectivity is higher in ZIF-2 (∼0.30) due to the faster diffusion of CH4 in the broader pores of ZIF-2 (6.4 Å) compared to ZIF-79 (4 Å). It is important to note that, in contrast to other ZIF membranes, ZIF-65 and ZIF-90 act as H2 selective membranes due to slow diffusion of CH4 (3−6) × 10−7 cm2/s) compared to H2 (∼3 × 10−4 cm2/s). The difference in the transport rates of CH4 and H2 causes high

increases due to steric hindrance. Theory predictions get better for diagonal composition (50/50), whereas the diffusivity of H2 (CH4) was underestimated for a nondiagonal adsorbed composition of CH4/H2:75/25 (25/75), as previously discussed by Keskin et al.53 Single component self-diffusivities of CH4 and H2 were also shown in Figure 4. As expected, when the fraction of H2 (CH4) in the mixture increases, the increase (decrease) of CH4 (H2) diffusivities is more profound. The application of KP theory for diffusion of CH4/H2 mixtures in ZIF-2 suggested that it is possible to make accurate predictions for the diffusivity of adsorbed gas mixtures in ZIFs by using the single component diffusion data. We can think that similar levels of agreement can be expected for CH4/H2 mixtures in other ZIFs because ZIF-2 does not have any structural characteristics that suggest it defines a potential energy surface for these adsorbed species that differs greatly in character from other ZIFs. In fact, this idea is already supported by the observation that qualitative aspects of molecular diffusion in ZIFs have been found to be similar to diffusion in zeolites and MOFs and the same correlations that we have tested here have been shown to work well in a variety of noncationic zeolites, CuBTC, IRMOF-1, and COFs.52,53,59 The other aspect to think is how well these correlations can perform for a more chemically complex adsorbed mixture in ZIFs. Previous tests 15532



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Figure 6. Permeation-based separation performance of ZIFs for (a) CH4/H2, (b) CO2/CH4, and (c) CO2/H2 mixtures. The bulk gas mixtures are CH4/H2:10/90, CO2/CH4:10/90, and CO2/H2:1/99 for ZIFs at 298 K and (a) 50/50, (b) 50/50, and (c) 15/85 for zeolites at 300 K.

diffusion selectivity toward H2 and makes ZIF-65 and ZIF-90 weakly H2 selective membranes. This is also true for CO2/H2 separations, as shown in Figure 5c. ZIF-90 has the highest CO2 selectivity in CO2/CH4 separations due to slow diffusion of CH4. Both adsorption selectivity (9.54) and diffusion selectivity (2.34) favor CO2, and eq 4 predicts a high CO2 permeation selectivity (22.31) for ZIF-90 compared to other ZIFs. This is actually a rare situation because in most of the MOFs high adsorption selectivities for CO2 are compensated by low diffusion selectivities.23,54 For example, Figure 5c shows that permeation selectivities of ZIF-69 (4.1) and ZIF-79 (3.4) are low. The adsorption selectivities of these ZIFs (240 and 195, respectively) were high, but lower diffusion selectivity toward CO2 made them unpromising materials. For an efficient membrane-based separation, both high selectivity and permeability are desired. Membranes having high selectivity and low permeability are not economic, since they require large surface areas and high capital costs. In order to assess the performance of ZIF membranes for CH4/H2, CO2/CH4, and CO2/H2 separations, we compared them with well-known zeolite and MOF membranes. Figure 6a shows that ZIF-90 and ZIF-65 are H2 selective membranes for CH4/H2

separation similar to LTA and CHA because of their molecular sieving properties. Both the selectivity and permeability performance of other ZIF membranes are similar to MOF membranes CuBTT and MOF-177. None of the ZIFs considered in this work can outperform CNTs which show the highest permeation selectivity and permeability for CH4/H2 mixtures due to their specific potential energy surface, as reported by experiments and predicted by molecular simulations.60,61 Among the ZIFs studied, ZIF-2 and ZIF-79 can be identified as the best candidates with high gas selectivity (10.63 and 9.19) and permeability (∼3 × 105 and ∼1.6 × 105 Barrer, respectively) compared to zeolite and MOF membranes. The CO2/CH4 permeation selectivity and CO2 permeability of ZIFs, zeolites, and MOFs are shown in Figure 6b together with Robeson’s upper bound62 established for CO2/CH4 separations using polymer membranes. Materials that can exceed this upper bound are highly promising candidates. All ZIFs except ZIF-90 are located below the Robeson’s upper bound, and the reason for high CO2 permeation selectivity of ZIF-90 is that both adsorption and diffusion selectivity favor CO2 (see Figures S23 and S46, Supporting Information). This was also observed for DDR and CHA due to their narrow 15533



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Figure 7. Predicted permeation selectivities of ZIFs based on molecular simulations employing UFF and DREIDING force fields for (a) CH4/H2, (b) CO2/CH4, and (c) CO2/H2 mixture separations at 298 K. The bulk gas mixtures are CH4/H2:10/90, CO2/CH4:10/90, and CO2/H2:1/99.

that the quantitative accuracy of the theoretical predictions must allow making confident judgments for separating promising and unpromising materials. It is obvious from Figure 7 that changing the force field of molecular simulations does not change the conclusion about the performance of a material. The largest change was observed for ZIF-90, and even for this material, both force fields suggest that ZIF-90 is a H2 selective membrane for CH4/H2 (CO2/H2) separation with low CH4 (CO2) permeability. 3.4. Comparison of Simulations with Experiments. Among the ZIFs we considered in this work, thin film membranes were made for two of them: ZIF-69 and ZIF-90. Figure 8 compares the permeance of mixed gases (CO2/H2, N2/H2, CH4/H2, CO2/CH4, CO2/H2) from our molecular simulations employing UFF with the experimental measurements of Huang et al.7 and Liu et al.8 through ZIF-90 and ZIF69 membranes. There is a reasonable agreement between our theoretical predictions and experimental measurements for mixed gas permeance through ZIF membranes considering the fact that the only experimental input of our simulations is the XRD structures of the ZIFs. The predictions for mixed gas permeance of H2 and CO2 in ZIF-90 membranes were remarkably good. Our simulations predicted lower CO2

windows that control molecular transport inside the pores, as evidenced by experiments and molecular simulations.63,64 Figure 6c shows that ZIF-65 and ZIF-90 are H2 selective membranes, since high diffusion selectivities of these materials toward H2 dominated the high adsorption selectivities toward CO2. Gas permeability and permeation selectivity of ZIF-2 are significantly high compared to CHA, DDR, MFI, CuBTC, MOF-177, and other ZIFs. On the other hand, MgMOF-74 offers high permeation selectivity and permeability due to increased correlation effects within the one-dimensional channels when there is a preponderance of CO2 molecules.25 In order to examine how the predictions of simulations would change if a different force field was used, we carried out GCMC and EMD simulations for selected ZIFs using the DREIDING force field. We specifically repeated our calculations for ZIF-2, ZIF-69, ZIF-79, ZIF-81, and ZIF-90, since these materials were identified as the membrane candidates with the highest permeation selectivities for CH4/H2, CO2/ CH4, and CO2/H2 mixtures. The results are shown in Figure 7, and we also included the uncertainties of the calculations to show that the predictions of simulations employing different force fields are remarkably close to each other in terms of selectivity and permeability. The idea of our methodology is 15534



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bar. The reason for this discrepancy can be discussed as follows: First, Battisti et al. rescaled UFF parameters to match their simulation results to one of the experimentally reported CO2 adsorption isotherm5 for ZIF-8 and then used the same set of parameters for simulation of ZIF-2. Transferability of adjusted force field parameters has not been tested among different ZIFs. Second, they did not consider partial charges for ZIFs which is most likely the reason of their low CO2/H2 selectivities compared to ours. Recent work showed that partial framework charges are important in computing CO2 adsorption and diffusion in ZIFs.33

4. CONCLUSIONS We used atomically detailed simulations to assess the performance of a series of ZIF materials in adsorption-based and membrane-based separations of CH4/H2, CO2/CH4, and CO2/H2 mixtures. Our calculations identified several ZIF membranes (adsorbents) that can outperform widely studied MOFs and zeolites due to higher selectivity and/or permeability (working capacity). For example, ZIF-2 was found to be very promising as a membrane for CH4/H2 and CO2/H2 separations. In any effort to use theoretical modeling in studying performances of materials, the assumptions associated with modeling methods should be clearly stated to allow judgments to be made about the potential impact of these factors in real world performance of materials.68 The strongest assumption in our calculations is that ZIFs are rigid in their reported crystallographic structure. Almost all of the molecular simulations for MOFs and ZIFs used this assumption because it saves a significant amount of computational time and molecular simulations should be performed for multiple materials on time scales shorter than the same materials can be assessed experimentally. However, it is not possible to argue that rigid framework assumption is totally correct because experiments reported that structural changes can occur in some MOFs upon adsorption or heating.70 Molecular simulations that do not consider framework flexibility can overestimate the selectivity of the membranes, since they assume that the gas species larger than the material’s pore size cannot permeate through the membrane. Since ZIFs are a subclass of MOFs, there can be ZIFs showing framework flexibility among the ones we considered in this work. Using DFT calculations for this type of materials will be appropriate to evaluate the performance of the material, especially for diffusion characteristics.67 A recent study on ZIFs showed that there is a very good agreement between isotherms computed from DFT optimized structures and isotherms from the XRD structures.35 The idea of our calculations is that, once the potential value of a material has been demonstrated using molecular simulations, a more detailed calculation approach including framework flexibility can be used to increase the precision of the assessment. Our calculations do not provide any information about the stability of the materials. For example, a material cannot find place in practical membrane applications if it is not stable in the presence of water vapor, although it has a high selectivity. This issue is more likely to be handled by experiments, and the aim of our calculations is to motivate extensive experimental studies for the materials identified as highly promising.

Figure 8. Comparison of the experimental data with the predictions of molecular simulations for permeation of mixed gases through ZIF-90 (circles) and ZIF-69 (diamond) membranes at 473 and 298 K, respectively. The mixed gases are at 1 bar and equimolar in composition.

permeances for CO2/CH4 and CO2/N2 mixtures in ZIF-69 membrane. In fact, Liu et al.8 reported that measured CO2 diffusion in their experiments was exceptionally higher than Knudsen diffusion rate and CO2 permeance in mixtures was higher than single component permeance. As discussed previously,27 predictions for mixed gas permeances of CH4 and N2 through narrow pore membranes were less than the experimental measurements due to the rigid framework assumption of our molecular simulations. Since the narrow pore sizes of ZIF-90 (3.5 Å) and ZIF-69 (4.4 Å) are close to the kinetic diameter of CH4 (3.8 Å) and N2 (3.6 Å), the diffusion rate of these molecules can be affected by the lattice flexibility, which will be discussed in detail in the following section. One important point to mention is that, although the ZIF-8 membrane was fabricated and tested for separation of CH4/H2 and CO2/CH4 mixtures,12−15,65,66 we did not make any prediction for separation of these mixtures in ZIF-8. This is because our molecular simulations showed that CH4 experiences a large energy barrier (∼45 kJ/mol) in the narrow pore windows of ZIF-8 (3.4 Å) and the diffusion coefficient of CH4 is far too slow to be directly observed with EMD.67 This situation was previously observed and discussed by Haldoupis et al.68 who used computational methods and predicted extremely high H2/CH4 selectivities for ZIF-8 due to very slow diffusion of CH4. They concluded that the high discrepancy between their predicted CH4 selectivity (∼107) and the experimentally reported one12 (11.2) is mostly associated with defects in the microstructure of the intergrown thin films of ZIF-8 membrane, where defects associated with grain boundaries can allow significant fluxes of CH4 through the membrane. More detailed modeling studies are required to assess the contribution of fluxes through microstructural defects to solve this discrepancy.69 On the other hand, our predictions for CO2 selectivity (1.39) of ZIF-8 membrane from CO2/H2:1/ 99 mixture agreed with the CO2 selectivity (0.5) predicted by Krishna and van Baten25 for CO2/H2:15/85 mixture and selectivity (0.96) predicted by Battisti et al.26 In addition to ZIF-8, Battisti et al. also studied ZIF-2 and computed very low CO2 and CH4 permeation selectivities (∼1.5) for CO2/H2 and CH4/H2 separations, respectively, at zero pressure limit. We predicted selectivities of 15.3 and 8.2 for the same mixtures at 1 15535



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ASSOCIATED CONTENT

S Supporting Information *

Adsorption selectivity, diffusion selectivity, and permeation selectivity of ZIFs for CH4/H2, CO2/CH4, and CO2/H2 separations at 10 bar, 298 K; unit cell representation of ZIFs considered in this work; single component self-diffusivities and mixture self-diffusivities of gases in ZIFs. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support provided by The Scientific and Technological Research Council of Turkey (TUBITAK) National Young Researchers Career Development Programme (3501) Grant MAG-111M314 is gratefully acknowledged.

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