Atomically Detailed Models for Transport of Gas Mixtures in ZIF

Article pubs.acs.org/IECR

Atomically Detailed Models for Transport of Gas Mixtures in ZIF Membranes and ZIF/Polymer Composite Membranes Erhan Atci and Seda Keskin* Department of Chemical and Biological Engineering, Koç University Rumelifeneri Yolu, Sariyer, 34450 Istanbul, Turkey S Supporting Information *

ABSTRACT: In this work, we introduced atomic models for transport of single component gases (CH4, CO2, H2, and N2) and binary gas mixtures (H2/CO2, H2/N2, H2/CH4) in zeolite imidazolate framework (ZIF) membranes and ZIF/polymer composite membranes. The predictions of atomic models were validated by comparing with the available experimental data for a ZIF-90 membrane. Motivated from the good agreement between experimental measurements and predictions of our molecular simulations for single gas and mixture permeances, we extended atomic modeling methods to an unfabricated ZIF membrane, ZIF-65, for predicting its separation performance. Various selectivities of ZIF membranes such as ideal selectivity, mixture selectivity, adsorption selectivity, and diffusion selectivity were computed for a wide range of operating conditions to assess the potential of ZIF membranes in H2/CO2 separations. We then combined atomic simulations with continuum modeling to estimate the performance of ZIF-90/Matrimid and ZIF-90/Ultem composite membranes for gas separations. Our theoretical predictions agreed very well with the experimental measurements for these two composite membranes, and therefore, we assessed the performances of several ZIF/polymer membranes composed of various polymers, ZIF-90 and ZIF-65, for separation of H2 from CO2.

1. INTRODUCTION Metal organic frameworks (MOFs) have attracted significant attention due to their potential in gas storage and gas separation applications. Several hundreds of MOF materials have been synthesized in the past decade, and the number continues to grow.1,2 Many characteristics of MOFs, such as large surface areas, low densities, uniform pore sizes, and tunable structure properties, make them promising candidates in various applications, including gas separations, gas storage, catalysis, and chemical sensing.3−6 The greatest advantage of MOFs over traditional nanoporous materials is the possibility of tailoring these materials in terms of linker functionality and pore size. The potential of MOFs as membrane materials has been well recognized both experimentally and computationally.7−10 Thin continuous MOF membranes for gas separations have been reported by several research groups using MOF-5, CuBTC, and Cu(hfipbb)(H2hfipbb)0.5.9−11 Zeolite imidazolate frameworks (ZIFs) are a subfamily of MOFs with tetrahedral networks that resemble those of zeolites with transition metals linked by imidazolate ligands.12,13 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. A large variety of ZIF structures has been reported with high chemical stability and permanent porosity.14,15 Atomically detailed simulations are powerful tools for screening many ZIFs in gas adsorption and gas diffusion studies. Using molecular simulations, Guo et al.16 reported adsorption of CH4/H2 mixtures in ZIF-3, ZIF-8, ZIF-10, ZIF-60, and ZIF-67; Liu and Smit17 studied adsorption of CO2/N2, CO2/CH4, and CH4/N2 mixtures in ZIF-68 and ZIF-69; Liu et al.18 reported the self-diffusion coefficient of CO2 in ZIF-68 and ZIF-69; Rankin and co-workers19 studied self- and transport diffusivities © 2012 American Chemical Society

of CO2, CH4, N2, and H2 in ZIF-68 and ZIF-70; Krishna and van Baten20 computed diffusivities for CO2/H2 and CH4/H2 mixtures in ZIF-8 and for CO2/CH4 mixtures in ZIF-68; Keskin21 studied adsorption and diffusion of CH4/H2, CO2/ CH4, and CO2/H2 mixtures in ZIF-3 and ZIF-10, Liu et al.22 investigated CO2/CH4 and CH4/H2 mixtures in ZIF-68 and ZIF-70. Very recently a few ZIF membranes, such as ZIF-7,23 ZIF24,25 ZIF-22,26 and ZIF-90,27 have been fabricated and tested 8, for gas separations. Among these membranes, ZIF-90 was found to exhibit high stability and selectivity for separation of H2 from larger molecules, such as CO2, N2, and CH4.27 The high number of ZIF materials indicates that purely experimental techniques will be inefficient at best to identify the most promising ZIF membranes among many candidates for targeted gas separations. Atomically detailed simulations are helpful to complement experimental efforts for screening many ZIF membranes and selecting the most promising ones for the desired gas separations.4,28,29 These simulations also provide molecular level information on the structural properties of the materials, which is crucial to design new ZIF membranes. In this work, using atomically detailed simulations, we first modeled transport of single component gases (CH4, CO2, H2, and N2) and binary gas mixtures (H2/CO2, H2/N2, H2/CH4) through a ZIF-90 membrane and validated our atomic models by comparing the results with the available experimental data. Motivated from the good agreement between experimental measurements and the predictions of our molecular simuReceived: Revised: Accepted: Published: 3091

November 4, 2011 December 24, 2011 January 9, 2012 January 9, 2012 dx.doi.org/10.1021/ie202530f | Ind. Eng.Chem. Res. 2012, 51, 3091−3100

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lations, we extended the atomic modeling methods to an unfabricated ZIF membrane, ZIF-65, which is similar to ZIF-90 in topology. Various selectivities of ZIF membranes, such as ideal selectivity, mixture selectivity, adsorption selectivity, and diffusion selectivity, were computed for a wide range of operating conditions to assess the potential of ZIF membranes in H2/CO2 separations. Since fabrication and testing of pure ZIF membranes have recently started, considering ZIFs as filler particles in polymers to make composite membranes shows much greater promise for short-term commercial implementation. For example, Liu and co-workers30 incorporated ZIF-8 nanoparticles into a polymer matrix to provide preferential pathways for the permeation of organic compounds; Yang et al.31 synthesized ZIF-7/polybenzimidazole (PBI) composite membranes which showed enhanced H2 permeability and ideal H2/CO2 permselectivity, surpassing those of PBI membranes; and Zhang et al.32 fabricated ZIF-8/6FDA-DAM polyimide membranes and showed that both propylene selectivity and permeability increase as the amount of ZIF-8 increases. Motivated from these, we combined atomic simulations with continuum modeling and predicted the performance of various ZIF-based composite membranes for separation of CO2/CH4 and H2/CO2 mixtures.

2. COMPUTATIONAL DETAILS 2.1. Models for ZIFs and Adsorbates. The atomic positions of ZIFs were taken from experimental XRD structures.15,33 The density functional theory (DFT) optimized structures were found to be consistent with the XRD structure within a few percent in volume.34 ZIF-90 (ZIF-65) has a threedimensional porous structure with large pores having a diameter of 11.2 Å (10.4 Å) and narrow pore openings having a diameter of 3.5 Å (3.4 Å). Unit cell representations of both ZIFs are shown in Figure 1. All molecular simulations were performed with rigid ZIF structures. The universal force field (UFF)35 was used for the framework atoms. Several previous studies showed that adsorption simulation results based on this force field agree well with the experimental measurements for many different ZIF structures. For example, good agreement between experiments and simulations employing the UFF has been observed for CH4, CO2, and N2 adsorption in ZIF-68, ZIF-69, ZIF-70; for CO2, CH4, and H2 adsorption in ZIF-8; and for CO2 adsorption in ZIF-25, ZIF-71, ZIF-93, ZIF-96, and ZIF-97 for a large range of pressures.16,18,19,36−38 A recent study showed that molecular simulations with rescaled UFF parameters give better agreement with the experimental measurements for adsorptions of CH4 and CO2 in ZIF-8.39 As we will show in the Results and Discussions section, the predictions of our molecular simulations with the original UFF parameters agreed well with the available experimental data both for single component and mixture gas permeances through ZIF-90 membranes; therefore, we kept the original UFF parameters. It is important to note that no parameter refining was used in molecular simulations of this study and the only experimental input of molecular simulations is the crystal structure of ZIFs. Spherical Lennard-Jones (LJ) 12−6 potentials were used to model H2 and CH4 molecules.40,41 The CO2 molecule was modeled as a rigid linear molecule, and the EPM242 model was used which is an all-atom LJ potential with atomic charges to approximate CO2’s quadrupole moment. 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.43 The

Figure 1. Unit cell representations of ZIF-90 (top) and ZIF-65 (bottom) structures: gray, carbon; white, hydrogen; pink, zinc; purple, nitrogen; blue, cobalt; red, oxygen.

potential parameters for adsorbent and adsorbate atoms used in this study are given in Table 1. Interactions between adsorbate molecules and the atoms of ZIFs were modeled using pairwise interactions between adsorbates and each atom in ZIFs. Mixedatom interactions were defined using the Lorenz−Berthelot mixing rules. Charges were added for each atom in ZIFs for the simulations involving CO2 and N2. The atomic partial charges for ZIF-90 were taken from a recent work of Watanabe et al.,34 who showed that REPEAT charges gave the best results for producing the CO2 adsorption isotherm in ZIF-90 among the several quantum mechanical calculation-based point charges they tested. The atomic partial charges for ZIF-65 were assigned using the connectivity-based atom contribution method (CBAC).44 In our earlier studies we showed that the CBAC charges give nearly identical results to the results of quantum mechanical calculation-based point charges for adsorption isotherms of CO2 in many ZIFs.21,34 The partial 3092

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self-diffusivities, single component corrected diffusivities and mixture self-diffusivities of each species were calculated using EMD simulations. The self-diffusivity, Dself,i describes the motion of individual tagged particles and in an isotropic three-dimensional material, it is related to the mean-squared displacement of tagged particles by the Einstein relation,

Table 1. Interaction Potential Parameters for Adsorbent and Adsorbate Atoms/Molecules Used in This Study adsorbate CH4 H2 C (CO2) O (CO2) N (N2) COM (N2) ZIF atoms C Co H N O Zn

ε/k (K)

σ (Å)

148.0 34.2 27.0 79.0 36.4 0

3.73 2.96 2.80 3.05 3.32 3.32

52.873 7.050 22.160 34.745 30.210 62.440

1 t →∞ 6t

Dself, i = lim

1 Nt

Ni

∑ [ril(t ) − ril(0)]2 l=1

(1)

where N is the number of molecules, ril(t) is the threedimensional position vector of molecule l of species i at time t, and the angular brackets denote the ensemble average.50 The corrected diffusivity includes information on the collective motion of multiple adsorbed molecules that is relevant to the net mass transport and can be calculated using the following expression:50,51

3.431 2.559 2.570 3.261 3.118 2.462

atomic charges of ZIFs are shown in Figure S1 and given in Table S1 of the Supporting Information. 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.45 A cutoff distance of 13 Å was used for LJ interactions. Periodic boundary conditions were applied in all simulations. The size of the simulation box was varied from 2 × 2 × 2 crystallographic unit cells to 6 × 6 × 6 unit cells so that enough molecules were accommodated to guarantee the simulation accuracy at the lowest loadings to contain more particles. 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 Nose−Hoover thermostat.45 We computed both self-diffusivities and corrected diffusivities of gases to model transport through ZIF membranes. 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. After creating initial states with the appropriate loadings using GCMC, each system was first equilibrated with EMD for about 20 ps prior to taking data. 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, carbon nanotubes, MOFs, and ZIFs.21,46−49 2.3. Predicting Gas Permeabilities through ZIF Membranes Using Atomic Simulations. Single component

1 Do, i = lim t →∞ 6Nt

⎛ Ni ⎞2 ⎜ ∑ [ril(t ) − ril(0)]⎟ ⎜ ⎟ ⎝ l=1 ⎠

(2)

EMD simulations provided the loading dependent corrected diffusivities (Do), which are required to compute the permeance of single gases in ZIF membranes. The transport diffusivity (Dt) is then defined without any approximation in terms of corrected diffusivity and a thermodynamic correction factor, a partial derivative relating the adsorbate concentration, c, and the bulk gas phase fugacity, f:51

∂ ln f (3) ∂ ln c The thermodynamic correction factor is fully defined once the single component adsorption isotherm is known. Steady state fluxes of each gas across a single ZIF crystal were then calculated using Fick’s law,52 which relates the flux of each species with the concentration gradient (∇c) through transport diffusivities: Dt(c) = Do(c)

J = − Dt(c)∇c (4) The concentration gradient of the adsorbed species was calculated on the basis of the difference between the feed and permeate side pressures of the membrane. The shell description of the membrane, which calculates the transport diffusivity at the mean concentration, was used to calculate the steady state fluxes.53 More details of the methods used to calculate single component fluxes on the basis of atomistic simulations and the shell model were described in our earlier studies.7,8 The gas flux in a ZIF membrane was then converted to single component gas permeability, P, using the pressure drop (∇p) and the membrane thickness (L) by the following:54

P=

J Δp /L

(5)

Once the single component steady state fluxes through a ZIF membrane are known, the ideal selectivity of the ZIF membrane is simply defined by the ratio of the single component fluxes of each species:

J Sideal(i / j) = i Jj 3093

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3. RESULTS AND DISCUSSIONS Figure 2 compares Huang et al.’s experimental data27 with the predictions of this study for permeance of single component

Past studies showed that ideal and mixture selectivities of a membrane can be significantly different for some MOF membranes if the multicomponent effects dominate in the mixture.59 Therefore, characterizing the selectivity of a ZIF membrane based on mixed-gas feeds is crucial. The mixture selectivity of a nanoporous membrane can be approximated as the multiplication of adsorption selectivity and diffusion selectivity:55

Smixture(i / j) = Sads(i / j)Sdif(i / j) =

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

(7)

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 phase, and Di,self is the mixture selfdiffusivity of component i evaluated directly at the corresponding adsorbed composition of the mixture from GCMC simulations. The selectivity of ZIF membranes for binary gas mixtures was computed using eq 7. The permeance of gases in a binary mixture through a ZIF membrane was then defined following Krishna and van Baten,20

Pi =

Figure 2. Comparison of the experimental data27 with the predictions of our molecular simulations for permeation of single gases and mixed gases through the ZIF-90 membrane at 200 °C and 1 bar. The mixed gases are equimolar in composition.

ϕDi ,self ci fi

(8)

gases (CH4, CO2, H2, N2) and mixed gases (H2/CH4, H2/CO2, H2/N2) through the ZIF-90 membrane at 200 °C and 1 bar. There is good agreement between our theoretical predictions and experimental measurements both for single component and mixture gas permeances. The single component gas permeance of H2 was well predicted by molecular simulations, whereas permeances of larger molecules such as CH4 and N2 were slightly underestimated by theory. This can be attributed to the rigid framework assumption of our molecular simulations. As discussed in the experimental work of Huang et al.,27 the kinetic diameter of CH4 (3.8 Å) is larger than the narrow pore size of the ZIF-90 membrane (3.5 Å), yet it can pass through the membrane, which indicates that there is a small lattice flexibility in the ZIF-90 membrane. The structure of ZIF-90 is very similar to that of ZIF-8 in terms of topology, and in a recent study, Luebbers et al.58 showed that ZIF-8 also exhibits flexibility to adsorb n-alkane molecules. Since our molecular simulations did not include lattice flexibility effects, the permeance of gas molecules having kinetic diameters larger than the narrow pore opening of the ZIF-90 membrane (CH4 and N2) was slightly underestimated. The kinetic diameters of H2 and CO2 are smaller than the narrow pore diameter of the ZIF-90 membrane; therefore, both single gas (H2, CO2) and mixture (H2/CO2) permeances of these two species were well predicted by the molecular simulations. Motivated from this result, we extended our atomic modeling methods to a currently unfabricated ZIF membrane, ZIF-65, which is similar to ZIF-90 in topology. Since the experimental study for the ZIF-90 membrane was carried out at a single pressure (1 atm) and at a single temperature (200 °C), we investigated the H2/ CO2 separation performances of the ZIF-90 and ZIF-65 membranes at a wide range of operating conditions and computed their various types of selectivities, such as ideal selectivity, mixture selectivity, adsorption selectivity, and diffusion selectivity. In order to calculate the mixture selectivity of a ZIF membrane using eq 7, both adsorption and diffusion selectivities are required. To calculate the adsorption selectivity,

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). We performed both single component and mixture permeance calculations at the conditions of the experiments (1 bar and 200 °C, equimolar gas mixtures) to be able to make comparisons. 2.4. Predicting Gas Permeabilities through ZIF/ Polymer Composite Membranes. Designing a composite membrane-based gas separation process requires knowledge of the permeability of gases through the continuous phase (the polymer matrix) and the dispersed phase (the filler particles, ZIFs). In this study, we used the Maxwell model56 to predict gas permeabilities through polymer/ZIF composite membranes:

Pr =

⎡ 2(1 − ϕ) + (1 + 2ϕ)λ ⎤ P dm =⎢ ⎥ Pm ⎣ (2 + ϕ) + (1 − ϕ)λdm ⎦

(9)

In this model, λdm is the permeability ratio (Pd/Pm), Pd is the permeability of the dispersed phase (ZIF-90 or ZIF-65), Pm is the permeability of the continuous phase (polymers), Pr is the relative permeability, P is the permeability in the ZIF/polymer composite membrane, and ϕ is the volume fraction of ZIF particles. The Maxwell model is valid for low to moderate values of volume fractions (0 < ϕ < 0.2), since it assumes that nearby particles do not affect the streamlines around particles. This model does not consider the packing limit of particles or the effect of particle size distribution, particle shape, and aggregation of particles. The experimental data for gas permeability through polymers, Matrimid and Ultem, was taken from the work of Bae et al.57 Similar experimental data is not available for ZIFs, and a key ingredient of our results is that the gas permeabilities through ZIFs were predicted from detailed molecular simulations as explained in the previous section. We calculated gas permeance through ZIFs at 308 K and at 4.5 bar feed pressure to be consistent with the experimental data of Matrimid and Ultem polymers. 3094



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dual-site Langmuir isotherm to apply IAST, and the predictions of IAST for mixtures with different compositions are also shown for ZIF-90 and ZIF-65 in Figure 3. Similar to the earlier results, there is a very good agreement between GCMC simulation results and IAST predictions for both ZIFs. Figure 4 shows the adsorption selectivity, diffusion selectivity, mixture selectivity, and ideal selectivity of ZIF-90

adsorption isotherms of H2/CO2 mixtures were computed using GCMC simulations. Figure 3 shows both single

Figure 3. Single component and mixture adsorption isotherms for CO2 and H2 in (a) ZIF-90 and (b) ZIF-65 at 25 °C as computed from GCMC simulations. The composition of the bulk mixture is 50% and 85% H2. Dotted lines represent the predictions of IAST for CO2/H2 mixture adsorption, and continuous lines represent the single component adsorption isotherm fits.

Figure 4. Different types of selectivities of (a) ZIF-90 and (b) ZIF-65 membranes at 25 °C as a function of fugacity.

component adsorption isotherms and mixture isotherms of H2/CO2 for 50% and 85% H2 in the bulk phase. ZIF-65 has exactly the same topology as that of ZIF-90; the only difference between these two materials is the type of the metal. ZIF-90 has zinc as the metal whereas ZIF-65 has cobalt. Therefore, it is expected to see similarities in the adsorption isotherm trends of the gases. As should be expected from the single component isotherms, adsorption strongly favors CO2 over H2 in the mixtures because the more strongly adsorbing CO2 molecules exclude H2 molecules in the pores. The amount of adsorbed CO2 (H2) in the mixture increases (decreases) as the amount of CO2 increases in the bulk phase. Keskin21 and Liu et al.22 previously showed that ideal adsorbed solution theory (IAST) gives accurate predictions for the adsorbed mixtures of several gas mixtures in ZIFs. IAST59 is well-known to give accurate predictions for mixture adsorption isotherms based on single component adsorption isotherms of pure gases in many nanoporous materials except in materials characterized by strong energetic or geometric heterogeneity.60−62 Single component isotherms of CO2 and H2 were fitted using a

and ZIF-65 membranes for separation of H2/CO2 mixtures at room temperature as a function of pressure. The selectivities greater (less) than 1 indicate that the ZIF membrane is selective for H2 (CO2). As shown in Figure 3, adsorption favors CO2 in H2/CO2 mixtures due to energetic effects, and the adsorption selectivities for H2 (CO2) are less than 0.01. Since ZIF-90 and ZIF-65 have the same topology (SOD), the adsorption selectivities of ZIFs for H2 are very similar: 0.007 for ZIF-90 and 0.009 for ZIF-65. The adsorption selectivities of both ZIFs were found to be higher than those of isoreticular MOFs (IRMOFs)8 and similar to those of CuBTC63 and Zn(bdc)(ted)0.564 under the same conditions. As Figure 3 suggests, the adsorption selectivities are not significantly affected by the compositions of the gas mixtures. In contrast to adsorption selectivity, diffusion selectivity favors H2, since the weakly adsorbed species (H2) diffuse faster than the strongly adsorbed species (CO2). ZIF-65 has higher diffusion selectivity for H2 over CO2 compared to ZIF-90. This can be explained by examining the self-diffusivities of each component in a binary mixture. The degree of confinement of H2 molecules 3095



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35 (55) for a feed pressure of 50 bar. This increase in ideal selectivity can be explained by the trends of single component gas fluxes as shown in Figure 5. As the fugacity increases, CO2

in the pores of ZIF-90 and ZIF-65 is similar because the H2 molecule is very small relative to the pore sizes of ZIFs. The self-diffusivities of H2 molecules are ∼2−3 × 10−4 cm2/s in both ZIFs. On the other hand, the degree of confinement of larger CO2 molecules depends on the pore sizes of the materials. Since ZIF-90 has larger pores than ZIF-65, the selfdiffusivities of CO2 molecules in the less confined pores of ZIF90 (6−7 × 10−7 cm2/s) are slightly higher than the ones in ZIF65 (4−5 × 10−7 cm2/s). This difference resulted in higher H2 diffusion selectivities for ZIF-65. In examining the mixture selectivity results, the x axis of Figure 4 can be thought of as the feed pressure of the ZIF membrane because the permeate side is assumed to be at vacuum by eq 7. The mixture selectivity of ZIFs for H2 is smaller than the diffusion selectivity, as the latter is compensated by the low adsorption selectivity. Mixture selectivities of ZIF-65 for H2 (∼5−6) are higher than those of ZIF-90 (∼2), since diffusion selectivities are higher in the former, as discussed above. In our early studies, we showed that several IRMOF membranes, ZIF-3 and ZIF-10 membranes, are CO2 selective.8,21,55,61 For example, the mixture selectivities of ZIF-3 and ZIF-10 for CO2 were predicted to be 4.3 and 1.7, respectively, for CO2/H2:1/99 mixtures at 10 bar, 298 K.21 Under the same conditions, the mixture selectivities of ZIF-90 and ZIF-65 for H2 were predicted to be 3.1 and 8.4, respectively, in this study. These results underline the importance of the choice of membrane material for a specific gas separation. Large pore materials such as IRMOFs, ZIF-3, and ZIF-10 are known to give CO2 selective membranes because separation in these membranes is generally driven by the adsorption selectivity.55 Materials having large cages connected with narrow pore openings, like ZIF-90 and ZIF65, on the other hand, are H2 selective due to hindrance in transport of molecules which are larger than the narrow pore diameter of the material (CO2 for H2/CO2 separation). Previous studies showed that the ideal selectivity can be enormously different than the mixture selectivity for MOF membranes.7,61 To see whether this is the case for ZIF membranes, ideal selectivity of ZIF membranes was predicted using the shell model approach as described in section 2.3 and compared with the mixture selectivity. Figure 4 shows that, at low pressures, ideal and mixture selectivities are very similar but as the pressure increases the ideal selectivity becomes larger than the mixture selectivity. For instance, at 50 bar, the ideal selectivity of the ZIF-65 (ZIF-90) membrane for H2 is approximately 55 (35), meaning that the ZIF membrane is highly selective for H2. Under the same conditions, the mixture selectivity of ZIF-65 (ZIF-90) is around 9 (3), indicating that ZIF-65 and ZIF-90 membranes are slightly H2 selective for separation of H2/CO2 mixtures. The difference between ideal and mixture selectivity at high loadings can be attributed to the multicomponent mixture effects.7,65 At high loadings, strongly adsorbing gas component CO2 reduces the concentration gradient of the weakly adsorbed gas component H2 (see Figure 3). Furthermore, the diffusion rate of the more mobile species, H2, is decreased by the strongly adsorbing component, CO2 (see Figure S2 and S3). As a result of these two effects, the mixture selectivities are lower than the ideal selectivities of the ZIF membranes. Figure 4 shows that the ideal selectivity of both ZIF membranes for H2 increases as the fugacity increases. For example, the ideal selectivity of ZIF-90 (ZIF-65) is around 3.5 (9) at a feed pressure of 1 bar whereas this value increases up to

Figure 5. Single component gas fluxes in ZIF-90 and ZIF-65 membranes at 25 °C as a function of feed pressure.

approaches saturation (see Figure 3) and its concentration gradient remains almost constant. Therefore, the flux of CO2 is almost constant after the saturation loading (see Figure 5). In contrast to CO2, H2 is further away from saturation, and as the fugacity increases, its concentration gradient keeps increasing. Increasing H2 flux and constant CO2 flux resulted in an increasing H2 ideal selectivity for both ZIF membranes. The two important factors determining the performance of membranes are selectivity and permeability. A highly selective membrane is useless if the permeability is very low, since a membrane with low permeability requires high surface area and, therefore, large capital costs. Figure 6 compares the selectivity

Figure 6. Comparison of the gas selectivities and gas permeabilities of ZIF membranes with zeolite membranes and MOF membranes. Data for ZIF-8 and zeolite membranes were taken from a recent study of Krishna and Van Baten.20

and permeability of ZIF-65 and ZIF-90 membranes with the widely studied zeolite and MOF membranes. Data for ZIF-3, ZIF-10, ZIF-65, and ZIF-90 membranes were calculated at 298 K and at a feed pressure of 10 bar for CO2/H2:1/99 composition. Data for other membranes were taken from the 3096



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study of Krishna and Van Baten,20 in which molecular simulations were carried out at 300 K and 10 bar for CO2/ H2:15/85 composition. Membranes located on the right-hand side of Figure 6 are desired to achieve high CO2 selectivity and high CO2 permeability. Materials such as DDR, MFI, CHA, ITQ-29, ZIF-3, ZIF-10, CuBTC, MOF-177, and IRMOF-1 exhibit high CO2 permeability (∼105 Barrer) due to their large pore volumes. Except MOF-177 and IRMOF-1, these materials are moderately/highly CO 2 selective membranes with selectivities between 1.7 and 12.5. On the other hand, ZIF-8, ZIF-65, ZIF-90, IRMOF-1, and MOF-177 act as H2 selective membranes. As discussed earlier, the CO2 permeability of the ZIF membranes is very low due to their narrow pore openings compared to those of MOF membranes. In the following lines, we will show that both ZIF-90 and ZIF-65 membranes have high H2 permeabilities as pure membranes and as composite membranes. Figure 6 shows that ZIF-8, ZIF-65, and ZIF-90 membranes have different CO2 permeabilities and CO2/H2 permeation selectivities although they have the same zeolite topology. Here it is important to note that a ZIF membrane’s characteristics, such as permeability and selectivity, are determined by adsorption and diffusion of gas molecules in the pores. Gas adsorption and diffusion are driven by a complex interplay of several properties, such as materials’ pore size, pore shape, available pore volume, type of metal sites, and linkers forming the pores. For example, the type of imidazolate linkers is different in ZIF-8 (Zn(mIm)2) compared to ZIF-65 and ZIF-90 (Co(nIm)2 and Zn(Ica)2, respectively);14 therefore, the affinity of gas molecules to ZIF-8 is not the same with ZIF-65 and ZIF90. Another example is that the size of the large pore, which affects the diffusion rate of gas molecules, is different in these materials. As can be seen from these examples, although they share the same topology, these three ZIFs have various structural properties, which result in different membrane performances. Therefore, predicting the performance of a membrane by only examining the topology of the material still remains challenging. Very recently, the first ZIF-90/polymer composite membrane was synthesized and tested for separation of CO2 from CH4.57 ZIF-based composite membranes present great promise for short-term commercial implementation because experiments reported a good adhesion and well dispersion of ZIF-90 particles in polymers. In order to evaluate the potential of ZIFs in composite membrane applications, we predicted the gas permeability and gas selectivity through several ZIF-90/ polymer and ZIF-65/polymer membranes composed of various polymers. To validate the accuracy of our atomic and continuum models (as described in section 2.4), we compared our theoretical predictions with the available experimental data of Bae et al.57 for separation of CO2/CH4 mixtures using ZIF90/polymer composite membranes. Figure 7a shows the selectivity and gas permeability of pure polymer membranes (Matrimid and Ultem), pure ZIF-90 membrane, and ZIF-90/ polymer composite membranes. The line on this figure represents the upper bound established for CO 2 /CH 4 separations for pure polymer membranes. There is very good agreement between our theoretical predictions and experimental measurements for selectivity and permeability of ZIF90/polymer composite membranes. For example, experimental work measured that the ZIF-90/Ultem (ZIF-90/Matrimid) composite membrane has a CO2 selectivity of 38.7 (34.7) and a CO2 permeability of 2.9 (12.1) barrer, whereas our calculations

Figure 7. (a) Comparison of experimental data57 and our theoretical predictions for ZIF-90/Matrimid and ZIF-90/Ultem composite membranes for CO2/CH4 separations. (b and c) Predictions for the H2 selectivity and permeability of composite membranes composed of different types of polymers, ZIF-90 and ZIF-65. In b (c), stars represent the predictions of the Maxwell model for composite membranes having ZIF-90 (ZIF-65) with volume fractions varying from 0.1 to 0.5. The line represents the present upper bound established for H2/CO2 separations.

predicted CO2 selectivity and permeability as 38 (35.1) and 2.4 (13.1) barrer, respectively. Both our predictions from molecular simulations and experiments suggested that adding ZIF-90 as filler particles into polymer matrices increases the permeability of CO2 in polymers. In the case of Ultem, CO2 permeability was increased from 1.4 to 2.4 barrer, and in Matrimid, it was increased from 7.9 to 13.1 barrer. Since the CO2/CH4 selectivity of pure ZIF-90 (8.7) is not as high as those of 3097



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by the good agreement between our theoretical predictions and experimental measurements for the ZIF-90 membrane, we applied the same modeling methods to a currently unfabricated ZIF membrane, ZIF-65, to make predictions for its membrane performance. An important challenge for future work in this area will be to perform extensive calculations that allow multiple ZIFs to be compared as possible membrane materials and to use these calculations to identify the key structural or chemical characteristics that lead to desirable properties. The methods we have introduced here will be useful for examining the large variety of ZIFs and related materials that are known for specific examples that will provide exceptional performance as membranes or as fillers in polymer membranes.

pure Matrimid (35.1) or Ultem (38) membranes, there is no significant change in the ZIF-90/polymer composite membrane’s selectivity relative to the pure polymer membrane’s selectivity. Once we validated our atomic and continuum models for two ZIF-90/polymer composite membranes, we applied these models to assess the performances of composite membranes having ZIF-90 and ZIF-65 as filler particles for H2/CO2 separations. Parts b and c of Figure 7 show the H2/CO2 selectivity and H2 permeability of liquid crystalline polyester, polyaniline, polyimide, and poly(trimethylsilypropyne) (PTMSP). These polymers are the ones forming the upper bound (the line in Figure 7b,c) for separation of H2 from CO2. All the selectivity and permeability calculations for ZIF-90/ polymer (ZIF-65/polymer) composite membranes were performed at a feed pressure of 2 bar and permeate pressure of vacuum to be consisted with the experimental data of pure polymers. Predictions of the Maxwell model indicated that as the volume fraction of ZIF-65 or ZIF-90 increases in composite membranes, the permeability of H2 is significantly improved in the case of polyester, polyaniline, and polyimide. For example, increasing the volume fraction of ZIF-90 from 0 to 0.3 improves the permeability of H2 from 31.4 to 71.6 barrer in polyimide/ZIF-90 membranes. Parts b and c of Figure 7 show that liquid crystalline polyester, polyaniline, and polyimide can exceed the Robeson’s upper bound if the volume fraction of ZIF particles is higher than 0.2. Since the selectivity of these polymers is higher (or very close) than those of ZIF-90 and ZIF-65, no selectivity improvement was observed. In contrast to the cases of these polymers, both the H2 selectivity and H2 permeability of PTMSP increased when ZIFs are used as filler particles. Pure PTMSP is highly permeable (23300 barrer) with a low H2 selectivity (0.53). Since ZIF-90 and ZIF-65 exhibit better H2 selectivity under the same conditions (6 and 9, respectively), adding these as filler particles in PTMSP improved its H2 selectivity. The H2 permeabilities of PTMSP and ZIFs are very close (∼24000); therefore, a very slight permeability increase can be achieved.

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ASSOCIATED CONTENT

S Supporting Information *

Atomic representations of ZIF-65 and ZIF-90, partial charges of ZIF-65 and ZIF-90 structures, single component and mixture self-diffusivities of H2 and CO2 in ZIF-65 and ZIF-90 at 25 °C. 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].

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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REFERENCES

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4. CONCLUSION In this study, we introduced atomically detailed models for transport of single gases and gas mixtures through pure ZIF membranes and ZIF/polymer composite membranes. We computed single gas permeance, mixed gas permeance, ideal selectivity, mixture selectivity, adsorption selectivity, and diffusion selectivity of ZIF membranes for H2/CO2 separations, and compared performances of ZIF membranes with those of zeolite, polymer, and MOF membranes. Our results indicated that characterizing the properties of ZIF membranes using mixed gas feeds rather than single-component gases is crucial, since ideal and mixture selectivities are different from each other, especially at high loadings. All our membrane calculations assumed that surface resistances were negligible, so the membrane boundary conditions were defined by the appropriate adsorption isotherm. Detailed tests of this assumption for silicalite and carbon nanotube membranes have indicated that it is accurate unless membrane thicknesses are much less than 1 μm.66 In this work, we considered ZIF membranes having thickness of 20 μm to be consistent with the synthesized ZIF membranes. The work we presented here has focused on ZIF-90 because at present this is the only ZIF for which experimental data exists for both pure membrane and composite membranes. Motivated 3098



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