Molecular Simulations of MOF Membranes and Performance Predictions of MOF/Polymer Mixed Matrix Membranes for CO2/CH4 Separations.

Efficient separation of CO2 from CO2/CH4 mixtures using membranes has economic, environmental and industrial importance. Membrane technologies are currently dominated by polymers due to their processing abilities and low manufacturing costs. However, polymeric membranes suffer from either low gas permeabilities or low selectivities. Metal organic frameworks (MOFs) are suggested as potential membrane candidates that offer both high selectivity and permeability for CO2/CH4 separation. Experimental testing of every single synthesized MOF material as membranes is not practical due to the availability of thousands of different MOF materials. A multilevel, high-throughput computational screening methodology was used to examine the MOF database for membrane-based CO2/CH4 separation. MOF membranes offering the best combination of CO2 permeability (>106 Barrer) and CO2/CH4 selectivity (>80) were identified by combining grand canonical Monte Carlo and molecular dynamics simulations. Results revealed that the best MOF membranes are located above the Robeson's upper bound indicating that they outperform polymeric membranes for CO2/CH4 separation. The impact of framework flexibility on the membrane properties of the selected top MOFs was studied by comparing the results of rigid and flexible molecular simulations. Relations between structures and performances of MOFs were also investigated to provide atomic-level insights into the design of novel MOFs which will be useful for CO2/CH4 separation processes. We also predicted permeabilities and selectivities of the mixed matrix membranes (MMM) in which the best MOF candidates are incorporated as filler particles into polymers and found that MOF-based MMMs have significantly higher CO2 permeabilities and moderately higher selectivities than pure polymers.

Introduction

There is a rapidly increasing demand for the development of efficient CO2 separation technologies due to the climate change problems. Separation of CO2 from natural gas is a global challenge with energetic and environmental importance. CO2 does not only reduce the energy content of the natural gas, which is mainly composed of CH4, but also causes pipeline corrosion. Membrane-based separation of CO2 from CH4 has emerged as an alternative to the current energy-intensive technologies such as cryogenic distillation and chemical absorption.[1] Membrane-based separation units are easy to operate, control and scale-up. Polymeric membranes such as polyimide and polyamide have been widely utilized for CO2/CH4 separation due to their relatively low manufacturing costs, good processing abilities into different configurations and existence of well-documented research studies.[2] However, polymeric membranes have a trade-off between permeability and selectivity. High permeability and high selectivity are desired to achieve efficient and economic membrane-based gas separation. A selective membrane provides high purity thus requires less complex units while a membrane with high gas permeability requires less surface area and smaller capital cost. Another challenge in using polymeric membranes for commercial CO2/CH4 separation is the plasticization problem in which CO2 permeability increases with pressure while the CO2/CH4 selectivity decreases.[3] In order to eliminate these problems, zeolites have been considered as alternatives to polymeric membranes for membrane-based CO2/CH4 separation. Zeolite membranes offer significantly higher CO2/CH4 selectivities than the polymer membranes but their low CO2 permeabilities, high costs and difficulties in reproducibility are the main problems.[3] A zeolite membrane, SAPO-34, was reported to exceed the Robeson’s upper bound by displaying both high selectivity and high permeance for CO2/CH4 mixtures.[4−7] Techno-economic analysis also showed that SAPO-34 membranes can surpass the benchmark technology distillation for natural gas treatment.[8]

Metal organic frameworks (MOFs) have appeared as a new group of porous materials that offer huge potential as membranes.[3,9−11] MOFs are composed of metal complexes combined by organic linkers to form highly porous frameworks. One of the most important features of MOFs is their structural tunabilities that can be obtained by altering the combination of metals and linkers used during synthesis. The ability of tuning the MOF structures offers a wider variety of pore sizes and functionalities than zeolites. High surface areas, large porosities, uniform pores, reasonable mechanical and thermal stabilities make MOFs ideal candidates for membrane-based CO2 separations. Several excellent reviews have addressed a variety of novel methods to fabricate continuous, defect-free MOF membranes for CO2 separation.[3,10,12,13] Many thin-film MOF membranes exhibit high CO2 permeabilities and low to moderate CO2/CH4 selectivities.[9] Most of these membranes were fabricated using the prototype MOFs, such as MOF-5 (IRMOF-1)[14−18] and CuBTC (HKUST-1).[19−21] Zeolitic imidazolate frameworks (ZIFs) including ZIF-8, ZIF-69, ZIF-78, ZIF-90 have been widely used to make membranes.[22−24] For example, Venna and Carreon[25] fabricated reproducible, thin ZIF-8 membrane and reported that its CO2/CH4 selectivity ranges from ∼6.5 to 10, comparable with SAPO-34 membranes. Caro’s group tested ZIF-90 membranes for separation of equimolar CO2/CH4 mixture at 1 bar, 498 K and reported high CO2 permeance, 1.26 × 10–8 mol/(m2 × s × Pa) (corresponds to 753 Barrer) and CO2/CH4 selectivity of 4.7, which was reported to be among the MOF membranes having high separation performance.[26] In addition to pure ZIF-8 membranes, several mixed matrix membranes (MMMs) in which ZIF-8 is used as filler particles in various types of polymers have been fabricated to improve permeability and selectivity of polymer membranes. A recent review addressed the CO2 capture, CO2/CH4, CO2/H2, and CO2/N2 separations using ZIF-8-based MMMs by summarizing the fabrication techniques and special features of each membrane.[27] MOF-based MMMs are highly promising since they combine the two advantages of polymers and MOFs, easy processability and high gas permeability.

The number of MOFs is increasing rapidly and this large material space offers a great potential to be used as novel membranes for CO2/CH4 separation. Many MOFs might exhibit high CO2/CH4 separation potential but they have not been identified and tested yet. Experimental fabrication and testing of even a single MOF membrane require a long time, extensive efforts and resources. Similarly, choosing the best MOF filler to make MMMs is challenging because many MOFs and polymers are available resulting in infinite number of MOF/polymer combinations. Therefore, only a small fraction of MOFs has been experimentally examined as membranes and/or as fillers in MMMs to date and molecular simulations that screen many MOFs to identify the best materials have a vital role in directing experimental efforts.[28] Computational screening studies generally focus on adsorption-based H2/CH4, CO2/N2, and CO2/CH4 separations and grand canonical Monte Carlo (GCMC) simulations are used to compute gas adsorption in MOFs.[29−32] The number of studies on screening MOF membranes is very limited since assessing selectivity and permeability of a MOF membrane requires calculation of gas diffusivities in the MOFs’ pores using equilibrium molecular dynamics (MD) simulations, which is computationally very demanding compared to the GCMC simulations. Watanabe and Sholl[33] used molecular simulations to compute CO2/N2 separation performances of 179 MOFs and reported ideal selectivities in the range of 2–26 300 and CO2 permeabilities in the range of 2–6 × 107 Barrer. Daglar and Keskin[34] examined 3806 MOF membranes for CO2/N2 separations and identified the best MOF membranes having CO2/N2 selectivity >350 and CO2 permeability >106 Barrer. Qiao et al.[35] used molecular simulations to screen a large number of hypothetical MOFs, which are computer-generated materials, for membrane-based separation of CO2/N2/CH4 mixture. The top 24 hypothetical MOFs were identified and their CO2 selectivities were reported to be in the range of 260–10 500 at 10 bar and 298 K. The same group also carried out molecular simulations for separation of ternary CO2/N2/CH4 mixture using real MOFs at 10 bar, 298 K and reported CO2 selectivities of MOFs in the range of 700–8100 and CO2 permeabilities >1000 Barrer for the 7 best MOF materials.[36] Our group recently used high-throughput screening methods to examine >3500 MOF membranes for H2/CH4 separation[37] and H2/CO2 separation.[38] Results showed that many MOF membranes outperform polymer and zeolite membranes in terms of H2 selectivity and H2 permeability. An important point to note is that previous computational works were performed using rigid framework assumption, where the crystallographic positions of MOF atoms were fixed. Significant computational time is saved due to this assumption, however flexibility of MOFs might affect gas diffusion and eventually change the predicted performances of MOF membranes.[39,40] Therefore, the effect of flexibility on CO2/CH4 separation performance of at least some of the most promising MOF membranes deserves to be examined.

With these motivations, we applied a multilevel, high-throughput computational screening methodology showing increasing computational expense and complexity at each level to study the most recent MOF database reported in the literature.[41] This database has been only studied for membrane-based CO2/N2 separation[34] and CO2/H2 separation[38] but not for CO2/CH4 separation. In the first-level of screening, we calculated CO2 permeabilities and CO2/CH4 selectivities of MOF membranes using single-component gas adsorption and diffusion data obtained from the GCMC and MD simulations performed at infinite dilution. Predicted separation performances of MOF membranes were compared with polymeric and zeolite membranes. The top 8 MOF membranes exhibiting CO2 permeabilities >106 Barrer and CO2/CH4 selectivities >80 were identified. In the second-level of calculations, we carried out GCMC and MD simulations for the top MOF membranes considering equimolar CO2/CH4 mixtures. Impacts of adsorption and diffusion on the separation performance of the top membranes were investigated in detail. In the third level of calculations, framework flexibility was considered and its impact on the membrane properties of MOFs was studied by comparing the results of rigid and flexible MD simulations. Relations between structures and performances of MOFs were also investigated to provide atomic-level insights into the design of novel MOFs which will be useful for CO2/CH4 separation processes. Finally, the potential of using top MOFs as filler particles in polymer membranes was examined by computing gas permeability and selectivity of MOF/polymer MMMs for separation of CO2/CH4 mixture. The results presented in this study will be beneficial in guiding the selection of the best MOF membranes and MOF-based MMMs for natural gas purification process.

Molecular Simulations

The most recent MOF database[41] reported in the literature was used in this work. Solvent molecules were removed from the structures as described in the literature[41] and Zeo++ software[42] (version 0.2) was utilized to calculate pore limiting diameters (PLDs), the largest cavity diameters (LCDs), porosities and surface areas of MOFs. More details of these calculations are available in our earlier studies.[32,34] This MOF database was refined to only include materials with nonzero accessible surface areas and PLDs > 3.75 Å to let the permeation of both CO2 (3.3 Å) and CH4 (3.73 Å) through the membranes. We also excluded the MOFs for which molecular simulations resulted in gas diffusivities <10–8 cm2/s, which is the limit of MD to accurately characterize molecular diffusion. As a result, we ended up with 3794 MOFs having various structural properties.

Molecular simulations were initially performed to calculate the Henry’s constants (K0) and self-diffusivities (D0) of CO2 and CH4 at infinite dilution using the RASPA simulation code.[43] The adsorbate–adsorbate interactions were switched-off and 30 gas molecules were inserted into each MOF to imitate infinite dilution. The Widom particle insertion method was used to calculate K0 of each gas at 298 K.[44] For the Monte Carlo simulations, the number of initialization and production cycles was set to 5000 and 10 000, respectively. The mean square displacement of gas molecules was computed and its slope with respect to time obtained from the MD simulations was used to calculate D0 of each gas component. MD simulations were performed in the NVT ensemble using the Nosé–Hoover thermostat[44] for 106 cycles with a time step of 1 fs. Lennard-Jones (LJ) potential was used to define intermolecular interactions between the gases and MOFs. CO2 molecule was modeled as a three-site rigid molecule and its partial point charges were positioned at the center of each site.[45] CH4 was modeled as a single-sphere. Potential parameters and charges of gases are given in Table S1 of Supporting Information (SI). The Universal Force Field (UFF)[46] was used to define the potential parameters of MOFs. Charge equilibration method (QEq)[47,48] existing in RASPA was employed to assign partial point charges to MOF atoms and electrostatic interactions between MOFs and CO2 were calculated using the Ewald summation.[49] The good agreement between simulations and experiments for adsorption and diffusion properties of CO2 and CH4 in various MOFs was shown in our earlier studies[32,50,51] and validated the appropriateness of the selected force fields for MOFs and gas molecules. The UFF was developed a long time ago and it has the advantage of being adaptable to many chemical environments. However, it may not be suitable for certain materials such as MOFs having open metal sites. For example, Dzubak et al.[52] reported that common force fields (FFs) typically underestimate CO2 adsorption in Mg-MOF-74 which have open metal sites and presented a novel methodology that gives accurate FFs for CO2 adsorption in this MOF from high-level quantum chemical calculations. There have been more recently parametrized FFs which have been shown to be more appropriate for MOFs.[53,54] For example, Bristow et al.[54] developed a transferable potential form suitable to describe majority of ligand and metal combinations for MOFs. In contrast to UFF, in which general parameters were not fitted for MOFs and fixed generic charges were employed, their FF was fitted explicitly to the periodic frameworks and it was shown to accurately reproduce structural parameters of several MOFs. We used UFF in our molecular simulations for two reasons: (a) We previously showed the good agreements between simulations employing UFF and experiments for adsorption and diffusion of CO2 and CH4 in various MOFs, validating the appropriateness of UFF for MOFs as explained above. (b) We preferred a generic FF that is applicable to all types of MOFs in our high-throughput molecular simulations since it is not possible to perform high-level quantum chemical calculations for each MOF having open metal site in large scale material screening studies. Therefore, molecular simulations using the generic UFF may be underestimating CO2 adsorption and CO2 separation performances of MOFs having open metal sites.

Gas permeabilities of MOFs at infinite dilution (Pi0) were calculated using Pi0 = Ki0 × Di0. Ideal CO2/CH4 selectivities of MOF membranes were calculated as the ratio of gas permeabilities, Smem0 = PCO0/PCH0. Top 8 MOFs having high membrane selectivities, Smem, CO0 > 80 and high CO2 permeabilities, PCO0 > 106 Barrer were identified at the end of first-level of calculations. In the second-level of calculations, we computed adsorption of binary CO2/CH4:50/50 mixtures in top 8 MOFs. Binary mixture simulations were performed at two different pressures, 1 and 10 bar, at 298 K. In contrast to the first-level of calculations, both gas–gas and gas–MOF interactions were taken into account in the mixture simulations. Intermolecular interactions were truncated at a cutoff distance of 13 Å. A total of 15 000 cycles was used, where 5000 cycles were used for initialization and 10 000 cycles were used to obtain the ensemble averages. GCMC simulations of equimolar CO2/CH4 mixtures performed at 1 and 10 bar, at 298 K were used to define the initial states of mixture MD simulations. After 10 000 initialization and 10 000 equilibration cycles, 107 cycles were used to obtain mean square displacement of gases in the NVT ensemble using a time step of 1 fs. Gas diffusivities were computed using at least two trajectories. More details about using these simulations can be found in the literature.[44,55] Mixture permeabilities through MOF membranes were computed using Pimix = cimix × Dimix/fi where ci, Di and fi correspond to adsorbed gas loading, self-diffusivity and feed side partial pressure of the gas, respectively. Permeate side of the membrane was assumed to be vacuum.[56] Mixture selectivities were computed as the ratio of gas permeabilities using Smemmix = PCOmix/PCHmix. It is important to note that we previously validated the accuracy of this computational methodology by showing the good agreement between our predictions and experimentally measured permeances/permeabilities of single-component CO2 and CH4 gases through MIL-53-Al,[57] Ni-MOF-74,[34,37,38,57] IRMOF-1,[34,37,57] ZIF-69,[57] ZIF-78,[57] ZIF-90,[34,37,57] ZIF-95[34,37] membranes and even for the equimolar mixture permeability of CO2 and CH4 through ZIF-69 membranes.[57]

In the third-level of calculations, flexible MD simulations were performed using the Forcite module of Materials Studio 17.2[58] to study the influence of flexibility on the predicted membrane performances of MOFs. Due to the computational expense of the flexible MD simulations, only 2 of the top 8 MOFs were simulated and these MOFs were selected based on their pore sizes to represent a narrow-pored MOF (LOYMET, PLD:3.98 Å) and a large-pored MOF (KIPJUQ, PLD: 7.29 Å). Before starting the flexible MD simulations, the number of gas molecules that was computed using mixture GCMC simulations were loaded into the MOFs by the Fixed Loading task of the Sorption module. The force fields used in RASPA were employed in the Sorption module of Materials Studio. Both the equilibration and production steps were set to 5 × 106. van der Waals interactions were summed with atom-based interaction method with cubic spline truncation, cutoff distance of 13 Å and spline width of 1 Å were used in the Fixed Loading simulations. Partial charges for the framework atoms were assigned using QEq[48] charge method as implemented in the Materials Studio. Electrostatic interactions were summed with the Ewald summation method with an Ewald accuracy of 10–3 kcal/mol. Further information on performing these simulations using Materials Studio can be found in the literature.[59] The lowest energy frame obtained at the end of the fixed loading simulation was used for the flexible MD simulations which were performed in NVT ensemble with a step size of 1 fs up to a total of 10 ns by removing the fixed constraints on each coordinate of the MOF atoms. Initial velocities of gas molecules were randomly assigned. Similar to the rigid simulations, UFF and Nosé–Hoover thermostat were used in the flexible MD simulations. We validated the generic FF parameters used in flexible MD simulations of MOFs by comparing the experimental and simulated gas permeabilities in our previous work.[60] A recent work[61] also showed that results obtained with the UFF description of MOF flexibility is quantitatively comparable with the Density-Functional Tight-Binding (DFTB) predictions. To evaluate the differences between the results of rigid and flexible MD simulations, the changes in pore sizes of the MOFs were investigated. Crystal structures of MOFs were recorded at different time points during the flexible MD simulations using Materials Studio and pore sizes of materials were computed using Zeo++.

Finally, we examined the potential of MOF-based MMMs by estimating their gas permeabilities and selectivities. The top 8 MOFs were used as filler particles in 8 different types of polymers including the widely used ones such as cellulose acetate,[62] Matrimid,[63] polysulfone,[64] SPEEK-3 (sulfonated aromatic poly(ether ether ketone)),[65] Pebax (poly(ether-b-amide-6),[66] 6FDA-DAM (6FDA: 2,2-bis (3,4-carboxyphenyl) hexafluoropropane dianhydride and DAM: diaminomesitylene),[67] PIM-1 (polymer of intrinsic microporosity)[68] and PIM-6FDA-OH (6FDA: hexafluoroisopropylidene bisphthalic dianhydride).[69] These polymers were selected considering availability of the experimental permeability data for CO2/CH4 mixture. We previously studied numerous permeation models such as Maxwell, Bruggeman, Lewis-Nielson, Pal by comparing permeabilities obtained from these models with the available experimental data for CO2 and CH4 permeabilities of many MOF-based MMMs and concluded that Maxwell is the most appropriate model among the ones using the ideal morphology concept to estimate separation performances of MOF/polymer MMMs.[70] Therefore, we used the Maxwell model[71] to predict gas permeabilities of the MOF-based MMMs (PMMM) using the following expression:where n is the geometry shape factor taken as 0.3 assuming sphere-like MOF particles,[72] ϕ is the volume fraction of the MOF particles in the polymer matrix, PMOF is the gas permeability of MOF, PP is the gas permeability of polymer collected from the literature, and PMMM is the gas permeability of the MOF-based MMM. Since the Maxwell model was reported to be valid at low filler loadings,[72] we used ϕ as 0.2 in this work. If the permeability of polymer was measured at a feed pressure lower than 5 bar (Pebax and 6FDA-DAM), permeability of MOF computed at 1 bar was used for the Maxwell model, for all other polymers, permeability of MOF calculated at 10 bar was used.

Results and Discussions

We first computed K0 and D0 values of CO2 and CH4 in 3794 MOFs as shown in Figure a. K0 can be considered as the representative of the gas affinity of materials and as it gets higher, interaction of gas molecules with the adsorption sites of MOFs increases leading to stronger adsorption. K0 values vary between 10–7 and 10–1 mol/kg/Pa for CO2 and between 10–7 and 10–4 mol/kg/Pa for CH4. Higher K0 values of CO2 can be explained by the existence of three interaction sites of CO2 molecule compared to the single-sphere representation of CH4 in addition to the quadrupolar moment of CO2, which causes electrostatic interactions with the MOFs that are absent in the case of nonpolar CH4 molecules. The values of D0 vary between 10–8 and 10–4 cm2/s for CO2 and between 10–8 and 10–3 cm2/s for CH4. Since CH4 molecules are weakly adsorbed in MOFs and lighter compared to CO2 molecules, they are able to move faster. Strongly adsorbing gas molecules need to overcome a larger interaction energy barrier to move through the pores whereas diffusion of the weakly adsorbed gas molecules is easier.[73] Therefore, there is an inverse relationship between K0 and D0 of gases as shown in Figure a. This relationship is less linear for CH4 molecules because in some MOFs, PLDs are very close to the kinetic diameter of CH4, which leads to very slow diffusion of CH4 even though K0 is low. It is important to note that MOFs for which gas diffusivities were calculated to be less than 10–8 cm2/s (the limit of MD simulations to accurately access gas diffusivity on the nanosecond scale) were eliminated in our work. The MOFs having high diffusion selectivities due to the presence of very slow diffusing gas molecules might be highly selective membranes, but we eliminated them to remove the uncertainties resulting from the time scale limitation of MD simulations.

Figure 1

(a) Self-diffusivity of gases (D0) as a function of Henry’s constants (K0) calculated at infinite dilution. (b) Comparison of K0, D0, and P0 values of gases.

The relationship between K0 and D0 determines gas permeabilities (Pi0 = Ki0 × Di0) as shown in Figure b and drives the membrane-based separation performances of MOFs. K0 always favors CO2 molecules whereas D0 mostly favors CH4 molecules. As a result, gas permeabilities of MOFs are generally close to each other but mostly higher for CO2 than CH4 as shown in Figure b. Kim et al.[73] discussed that zeolite membranes should have well-balanced adsorption–diffusion properties for the effective CO2/CH4 separation: If the zeolites have very small KCO0 values, CO2 permeability and selectivity is too low. If structures have very large KCO0 values, they have strong adsorption sites that significantly hinder gas diffusion. They showed that optimal zeolite membranes with the highest CO2 permeabilities (>105 Barrer) have 10–5< KCO0 < 10–4 mol/kg/Pa. We showed the combined effects of K0 and D0 on gas permeabilities of MOF membranes in Figure S1. Analyzing MOFs exhibiting high CO2 permeabilities (>106 Barrer) showed that 1787 highly permeable MOFs have 10–6 < KCO0 < 10–1 mol/kg/Pa whereas 702 of them have 10–5 < KCO0 < 10–4 mol/kg/Pa. This comparison shows that MOFs we examined in this work have a wider range of KCO0 values than the zeolites. The highest CO2 permeability, 6.72 × 108 Barrer, belongs to the MOF having KCO0of 1.85 × 10–2 mol/kg/Pa, indicating the strong affinity of MOF toward CO2.

We examined adsorption selectivity (Sads0 = KCO0/KCH0), diffusion selectivity (Sdiff0 = DCO0/DCH0) and membrane selectivity (also known as perm-selectivity) calculated at the infinite dilution (Smem0 = PCO0/PCH0 = (KCO0 × DCO0)/(KCH0 × DCH0)) in Figure . Sads0 is always higher than 1 which means all the MOFs selectively adsorb CO2 over CH4. While Sads0 ranges from 1.2 to 7.82 × 104, Sdiff0 tends to favor CH4. MOFs shown in Figure are color-scaled according to their Sdiff0 values, ranging from 3.86 × 10–4 to 58. Red, green and blue points show MOFs having strong, moderate and low Sdiff0 values for CH4 over CO2, respectively. Small numbers of MOFs shown with purple points (395 MOFs) have Sdiff0 values equal to or higher than unity, indicating that diffusivity favors CO2 over CH4 in these materials. When both adsorption and diffusion favor the same gas molecule, CO2, membrane selectivity becomes higher than the adsorption selectivity. In fact, those are the highly desired membrane materials for selective separation of CO2 from CH4. For the other 3399 MOFs, CH4 has higher diffusivity through the MOFs’ pores, therefore Sdiff0 values are less than unity as shown with red, green and blue points in Figure . In this case, Smem0 could not reach as high values as Sads0 because diffusion selectivity favoring CH4 compensates adsorption selectivity favoring CO2. 429 MOFs have Smem0 lower than 1. For these MOFs, it can be concluded that CO2 adsorption is not strong enough to dominate the fast CH4 diffusivity. These MOFs are shown below the red dashed line in Figure as CH4 selective MOF membranes and CO2 can be obtained in the retentate stream rather than the permeate when this type of membrane is used. We note that the maximum CH4 selectivity of these membranes was calculated to be 12.5 indicating that they are at most moderately CH4 selective. Eleven MOFs were predicted to have Smem0 of exactly 1 which means these membranes are not useful for selective separation of CO2 from CH4. A large number of MOFs (3354) was computed to have Smem0 larger than 1 and these CO2 selective MOF membranes are shown above the red dashed line in Figure . As we discussed in Figure b, some MOFs have similar CO2 and CH4 permeabilities, therefore their CO2 selectivities are low. For example, 1598 MOFs have Smem0 between 1 and 2 indicating that they do not have a very strong preference for CO2. These are the MOFs for which adsorption selectivity for CO2 is almost the same with diffusion selectivity that prefers CH4 and as a result the membrane is almost nonselective. The remaining 1756 MOFs have Smem0 between 2 and 1643 and these are the potential membrane candidates.

Figure 2

Adsorption, diffusion and membrane selectivities of MOFs calculated for CO2 over CH4 separation at infinite dilution. The diagonal line is given to guide the eye, the dashed line shows the gas preference of the membrane.

For an efficient membrane-based gas separation process, not only the purity (selectivity) but also the amount of gas transported through the membrane (permeability) is critical because the required surface area of membrane is the dominant factor determining the cost of the separation process. Figure represents the membrane selectivity (Smem0) as a function of CO2 permeability (PCO0) together with the famous Robeson’s upper bound, which is established based on the single-component CO2 permeability and ideal CO2/CH4 selectivity of polymeric membranes.[74] In contrast to the well-known trade-off of polymeric membranes between the gas permeability and selectivity, permeability of MOF membranes usually increases as the selectivity increases. Predicted CO2 permeability of MOFs varies between 102 and 108 Barrer, significantly higher than the corresponding permeabilities of polymeric membranes. Therefore, the upper bound was extended with a dashed line in Figure . There are 1995 MOFs that can exceed Robeson’s upper bound due to their high permeabilities, or their high selectivities or both and these are shown with blue points. The most promising MOF membranes that will be further examined in the second-level of screening were selected as the materials that offer PCO0 > 106 Barrer and Smem0 > 80. 1483 MOFs that are over the upper bound have PCO0 higher than 106 Barrer while 8 of these MOFs have Smem0 higher than 80. These 8 MOFs, which are shown with red in Figure , are identified as the top membrane materials. We would like to note that all the MOFs we considered in our work are real, synthesized MOFs, they are not hypothetical materials. However, none of the top MOFs has been tested as membranes yet.

Figure 3

Selectivity and permeability of MOF membranes computed at infinite dilution. The black solid line represents the Robeson’s upper bound. MOFs that can exceed the bound are shown with blue and the top 8 MOF membranes are shown with red symbols.

In the second-level of screening, we computed adsorption and diffusion of equimolar CO2/CH4 mixtures for the top 8 MOFs and predicted mixture permeabilities and selectivities of these top MOF materials. Figure a compares permeability and selectivity predictions obtained at the first-level of screening (using single-component gas data at infinite dilution) and predictions obtained at the second-level (using equimolar mixture data at 1 and 10 bar). As shown in Figure a, both CO2 permeabilities and CO2/CH4 selectivities obtained from the mixture simulations performed at practical operating pressures are lower than the ones obtained from the single-component gas simulations performed at infinite dilution. This difference can be attributed to the competitive adsorption and collaborative diffusion between gas species in the mixture. At infinite dilution, a gas molecule can prefer the most favorable adsorption site since the intermolecular interactions between the gases are turned-off. However, at mixture conditions, gas–gas interactions exist and adsorbates compete with each other for the same adsorption sites. Moreover, at infinite dilution, self-diffusivity of a gas molecule is not affected by the diffusivity of another gas molecule. On the other hand, at mixture conditions, fast diffusing gas species (CH4) can fasten the slow diffusing molecules (CO2) and slow diffusing molecules can hinder the transport of other gas species. In order to better illustrate the mixture adsorption and diffusion effects, we compared all three selectivities computed at infinite dilution with the ones computed at mixture conditions in Figure b. Almost for all the MOFs, Sads is higher at infinite dilution than the mixture case since there is no competitive adsorption at infinite dilution. The diffusivity of CO2 increases due to the presence of fast CH4 molecules and diffusivity of CH4 decreases because of the presence of slow diffusing CO2 molecules. As a result, Sdiff values in mixture are higher than those in the infinite dilution as shown in Figure b. For example, one of the best performing MOF membranes is SAJFEO at infinite dilution with PCO0 of 2 × 108 Barrer and Smem0 of 535. At mixture conditions, permeability and selectivity of this MOF membrane were computed as 3.4 × 105 Barrer and 128, respectively. These dramatic decreases in the membrane properties can be explained by the significant decrease in the adsorption selectivity and increase in the diffusion selectivity. Adsorption selectivity decreased from 12266 at the infinite dilution to 210 whereas diffusion selectivity increased from 0.04 at infinite dilution to 0.61 at 1 bar. The increase in diffusion selectivity could not compensate the decrease in adsorption selectivity. As a result, predicted separation performance of the membrane (permeability and selectivity) was lower at the mixture case compared to the infinite dilution case. Here, the important point is that mixture permeabilities and selectivities of the top 8 MOF membranes were still high enough to locate them above the Robeson’s upper bound as shown in Figure a. We also note that in this figure there are two additional upper bounds named as mixture upper bounds which have been established for separation of CO2/CH4 mixtures having different compositions.[75] Permeabilities and selectivities obtained from the mixture calculations showed that top MOF membranes exceed the mixture upper bounds. These results suggest that initial screening of MOF membranes based on the membrane properties computed at infinite dilution is efficient to quickly identify the most promising materials and more detailed and computationally expensive mixture simulations should be performed for the top membrane candidates to unlock their actual separation performances at practical operation conditions.

Figure 4

(a) Separation performance of the top 8 MOF membranes computed at infinite dilution (blue), 1 bar (red), and 10 bar (green). Results of flexible simulations for the two MOFs are also shown at 10 bar (green, crossed). (b) Comparison of adsorption (full symbols), diffusion (empty symbols) and membrane (crossed symbols) selectivities computed at infinite dilution and mixture conditions at 1 bar (circles) and 10 bar (stars).

Details on the separation performance of the top 8 MOF membranes at two different feed pressures, 1 and 10 bar, are given in Table . As the pressure increases, gas uptakes increase but this increase is more pronounced for CH4 leading to a decrease in the adsorption selectivities. For most MOFs, diffusivity of both gas molecules decrease with increased pressure as higher loadings hinder the gas diffusion. CH4 diffusivity is more affected than CO2 diffusivity because spherical CH4 molecules are larger and bulkier in size than the linear CO2 molecules. As a result, higher Sdiff values were calculated at 10 bar compared to 1 bar for all MOFs. The increase in Sdiff dominated the decrease in Sads therefore, higher Smem values were observed at 10 bar compared to 1 bar.

Table 1

Performances of the Top 8 MOF Membranes for Separation of Equimolar CO2/CH4 Mixture at 1 and 10 bara

MOF	LCD (Å)	PLD (Å)	Volume fraction	NCO2 (mol/kg)	NCH4 (mol/kg)	DCO2 (cm2/s)	DCH4 (cm2/s)	PCO2 (Barrer)	PCH4 (Barrer)	Sads	Sdiff	Smem
1 bar
SAJFEO	6.63	6.00	0.60	6.31	0.03	6.16 × 10–6	1.01 × 10–5	3.39 × 105	2.64 × 103	210.33	0.61	128.28
NURVAZ	6.58	6.00	0.60	6.29	0.03	5.52 × 10–6	1.49 × 10–5	3.02 × 105	3.89 × 103	209.67	0.37	77.61
LOYMET	5.37	3.98	0.37	1.43	0.01	1.10 × 10–6	2.30 × 10–6	1.47 × 104	1.93 × 102	158.89	0.48	76.34
KIPKEB	7.31	7.00	0.46	2.65	0.03	3.14 × 10–6	1.23 × 10–5	7.74 × 104	3.44 × 103	88.33	0.25	22.52
KIPJUQ	7.29	6.98	0.46	2.43	0.02	1.78 × 10–6	1.31 × 10–5	4.75 × 104	2.87 × 103	121.50	0.14	16.59
RIPRUF	6.48	4.09	0.59	4.17	0.08	5.86 × 10–6	3.87 × 10–5	2.34 × 105	2.97 × 104	52.13	0.15	7.89
RIPRIT	6.46	4.22	0.60	4.10	0.09	5.73 × 10–6	4.36 × 10–5	2.22 × 105	3.71 × 104	45.56	0.13	5.99
XAXSOG	7.71	5.92	0.63	4.42	0.11	4.65 × 10–6	4.51 × 10–5	1.73 × 105	4.17 × 104	40.18	0.10	4.14
10 bar
LOYMET	5.37	3.98	0.37	1.63	0.03	7.21 × 10–7	2.53 × 10–7	1.10 × 103	7.09 × 10°	54.33	2.85	154.59
SAJFEO	6.63	6.00	0.60	8.11	0.07	4.02 × 10–6	3.73 × 10–6	2.84 × 104	2.27 × 102	115.86	1.08	125.09
NURVAZ	6.58	6.00	0.60	8.01	0.08	4.10 × 10–6	3.37 × 10–6	2.86 × 104	2.35 × 102	100.13	1.21	121.63
KIPJUQ	7.29	6.98	0.46	3.04	0.03	7.33 × 10–7	1.71 × 10–6	2.45 × 103	5.63 × 101	101.33	0.43	43.45
KIPKEB	7.31	7.00	0.46	3.37	0.04	1.49 × 10–6	2.89 × 10–6	4.66 × 103	1.08 × 102	84.25	0.51	43.35
RIPRIT	6.46	4.22	0.60	6.08	0.28	7.95 × 10–6	1.31 × 10–5	4.57 × 104	3.47 × 103	21.71	0.61	13.17
RIPRUF	6.48	4.09	0.59	6.16	0.22	6.97 × 10–6	1.95 × 10–5	4.11 × 104	4.11 × 103	28.00	0.36	10.00
XAXSOG	7.71	5.92	0.63	7.53	0.32	2.83 × 10–6	8.62 × 10–6	1.79 × 104	2.32 × 103	23.53	0.33	7.73

All selectivities were calculated for CO2 over CH4.

All simulations that we discussed so far were carried out using rigid framework assumption. It is known that some MOFs may show inherent flexibility upon various stimuli including pressure, temperature or loading. This flexibility might affect the pore properties of MOFs and change their separation performances.[76] We previously examined the effect of flexibility on the CO2/CH4 separation performance of bio-MOFs and showed that flexibility has a significant impact on the permeability and selectivity of MOFs having narrow pore diameters close to the size of adsorbates.[60] Therefore, we carried out computationally demanding flexible MD simulations in the third-level of our calculations for 2 top MOFs, one representing a narrow-pored material (LOYMET) and another representing a large-pored MOF (KIPJUQ). We note that these simulations required significant computation time and resources therefore, we were able to perform them only for 2 representative MOFs. Since the selected 2 MOFs do not have significantly different structural features than the other top materials, similar results are expected for the remaining top MOFs. Results of flexible MD simulations were compared with the results of rigid simulations in Table . Gas diffusivities computed using flexible simulations were less than the ones obtained from rigid simulations. Therefore, both permeabilities and selectivities of MOFs were predicted to be lower in flexible case compared to the rigid case as shown in Figure a. The decreases in gas permeabilities and selectivities were more pronounced for LOYMET than KIPJUQ since PLD of the former is narrower. For example, membrane selectivity of LOYMET decreased from 155 to 32 while selectivity of KIPJUQ decreased from 43 to 22 when the flexibility was considered. The changes in pore sizes of MOFs were examined using the snapshots taken at different time points of flexible MD simulations by considering the frameworks with and without the adsorbate molecules. As shown in Figure S2a, pore sizes of LOYMET significantly decreased and its PLD became smaller than the kinetic diameter of CH4 molecule. As a result, diffusivities of both gas molecules were computed to be very slow, in the orders of ∼108 cm2/s. On the other hand, pore sizes of KIPJUQ in the flexible case were still larger than the kinetic diameters of both gases, even when the pores were filled with the adsorbates, resulting in higher CO2 and CH4 diffusivities compared to the ones observed in LOYMET. Although gas permeabilities and selectivities of flexible MOFs were found to be lower than the ones computed for rigid MOFs, MOF membranes were still located over the mixed gas upper bound. In other words, the overall assessment about the separation performance of the top MOF membranes did not change even if the structures were flexible.

Table 2

Comparison of Rigid and Flexible Simulations

	Rigid						Flexible
MOF	DCO2 (cm2/s)	DCH4 (cm2/s)	PCO2 (Barrer)	PCH4 (Barrer)	Sdiff	Smem	DCO2 (cm2/s)	DCH4 (cm2/s)	PCO2 (Barrer)	PCH4 (Barrer)	Sdiff	Smem
LOYMET	7.21 × 10–7	2.53 × 10–7	1096	7	2.85	154.59	1.91 × 10–8	3.27 × 10–8	29	0.9	0.58	31.74
KIPJUQ	7.33 × 10–7	1.71 × 10–6	2448	56	0.43	43.45	1.43 × 10–7	6.50 × 10–7	478	21	0.22	22.34

We so far compared separation performance of MOF membranes with polymers and zeolites and concluded that MOFs can outperform traditional membranes for CO2/CH4 separations due to their high gas permeabilities. It is also useful to compare our results with other simulation studies where MOFs are examined. Large numbers of hypothetical MOFs, which are not experimentally synthesized but computer-generated materials, were screened for membrane-based separation of ternary CO2/N2/CH4:10/70/20 mixtures using molecular simulations.[35] The best 5 MOFs were computed to have CO2 permeabilities and CO2/CH4 selectivities in the range of 1500–6780 Barrer and 460–8970, respectively at 10 bar, 298 K. We predicted CO2 permeabilities and CO2/CH4 selectivities of MOFs in the range of 1090–45700 Barrer and 7.7–155, respectively for separation of equimolar CO2/CH4 mixture at the same pressure and temperature. The lower gas permeabilities and higher membrane selectivities of hypothetical MOFs compared to the real MOFs we considered in this work are due to the narrow pore sizes of the hypothetical MOFs. Hypothetical MOFs were selected to have PLDs between 3 and 4 Å. Since the kinetic diameter of CH4 is close to 4 Å, hypothetical MOFs act as molecular sieves resulting in high CO2/CH4 selectivities. In this work, we especially focused on MOFs having PLDs > 3.75 Å to guarantee the adsorption and diffusion of both CO2 and CH4 molecules in the pores. In another study focusing on separation of a ternary mixture of CO2/N2/CH4, dominated by N2 in contrast to our equimolar CO2/CH4 binary mixture, the top 7 MOFs were identified using molecular simulations at 10 bar, 298 K.[36] The top MOFs were again selected to have narrow pores in the range of 2.9 < PLD < 3.26 Å and they were computed to have lower permeabilities (1170 < PCO < 5090 Barrer, 0.18 < PCH < 2.61 Barrer) and higher selectivities (704 < Smem < 8155) compared to the ones we calculated for separation of equimolar CO2/CH4 mixtures.

We also investigated the impacts of structural belongings on the separation performances of MOFs. Figure a shows that porosity of MOFs increases as the LCD increases as expected. We marked the location of the top 8 MOF membranes in Figure a. These best membrane candidates have low porosities between 0.4 and 0.6 and narrow pore sizes, LCDs between 5 and 8 Å and PLDs between 4 and 7 Å. Five of the MOFs overlapped in the figure since they have almost the same porosities, 0.6. Figure b shows that permeabilities of CO2 and CH4 significantly vary at small LCDs (<10 Å) leading to selective membranes whereas permeabilities of gases become similar as the LCD increases (>10 Å). As shown in Figure (a), MOFs with LCDs > 15 Å generally have porosities larger than 0.75 so that both gas molecules can easily adsorb and diffuse in the pores. This eliminates the capability of the pores to sieve the larger gas molecule and leads to lower membrane selectivities. As a result, Figure suggests that membrane materials with small porosities and narrow pore sizes are desired for effective separation of CO2/CH4.

Figure 5

(a) Porosity and LCD of MOFs. Stars represent the top 8 MOF membranes. (b) Gas permeabilities of MOFs as a function of their LCDs.

MOFs have been widely used as fillers in MMMs to improve the CO2 permeability and CO2/CH4 selectivity of polymers.[77] Motivated from this, we examined the impact of using the top MOFs as fillers in polymer membranes on the CO2 permeability and CO2/CH4 selectivity of MOF-based MMMs. We collected available experimental CO2/CH4 mixture permeation data for 8 different polymeric membranes as given in Table S2. This data was then combined with the gas permeability data of the top 8 MOFs obtained from our molecular simulations using Eq. . As a result, permeability and selectivity of 64 different MOF-based MMMs were predicted and shown in Figure together with the data of polymer membranes. The arrows represent how the performance (permeability and selectivity) of the polymer membrane changes when the MOF filler is incorporated. Gas permeabilities of the 8 top MOFs are very high compared to the corresponding permeabilities of polymers, cellulose acetate, Matrimid, polysulfone, Pebax, SPEEK-3, and 6-FDA-DAM. For example, PCO (PCH) of Matrimid is 7 (0.4) Barrer while the lowest PCO (PCH) among the top 8 MOFs is 1095 (7) Barrer. As shown in previous works,[72,78] when the permeability of filler is very high compared to that of polymer, achievable permeability of the MMM becomes limited. This is because Eq. reduces to PMMM = PP × 1.75 at a volume fraction of 0.2 if PMOF ≫ Pp. Therefore, regardless of the identity of the MOF used in a given polymer, similar gas permeabilities and selectivities were obtained for the MMMs and a single data point was used in Figure to represent the MMMs of each polymer except PIM-1 and PIM-6FDA-OH. Incorporation of MOFs into polymers either provides a permeability improvement without significantly affecting the selectivity as in the cases of cellulose acetate, Matrimid, SPEEK-3, Pebax, 6-FDA-DAM and polysulfone or causes a change in both permeability and selectivity as in the cases of PIM-1 and PIM-6FDA-OH. For example, PCO of Matrimid increased from 7 to 12 Barrer but its selectivity remained around 18 when MOFs are used as fillers. Since CO2 and CH4 permeabilities of MOFs are very high compared to the permeabilities of Matrimid, addition of MOFs increases gas permeabilities without changing the selectivity. For PIM-6FDA-OH, while 6 MOFs caused an increase both in permeability and selectivity, LOYMET significantly increased selectivity with a slight increase in permeability and XAXSOG increased only the permeability. Similarly, for PIM-1, NURVAZ and SAJFEO increased permeability and selectivity. When LOYMET was used as the filler, selectivity of PIM-1 increased at the expense of a reduction in permeability due to the lower CO2 permeability of LOYMET than that of PIM-1. Other 5 MOFs increased the polymer’s permeability without a significant change in selectivity. It is important to highlight the importance of MOF/polymer matching for the separation performance of MOF-based MMMs: While LOYMET provided the highest increase both in permeability and selectivity of PIM-6FDA-OH, the same MOF decreased the permeability of PIM-1. Overall, Figure shows that MOFs can even carry the polymer over the upper bound by increasing both the CO2 permeability and selectivity if the polymer is close to the upper bound. For example, PIM-6FDA-OH is located just below the upper bound and using LOYMET as a filler significantly improved its CO2 selectivity from 15 to 22 while increasing its CO2 permeability from 557 to 960 Barrer. These results suggest that the top MOFs we identified in this work are not only good membrane candidates, but they are also highly promising for making MOF-based MMMs. We would like to note that performances of MOF membranes and MOF/polymer membranes were evaluated based on the Robeson’s upper bound. It is important to note that this bound has not been updated since 2008. Several polymer membranes have been developed in the past decade and it is possible that the new polymer membranes may shift the upper bound.

Figure 6

Predicted separation performances of MOF-based MMMs (open symbols) together with separation performances of polymeric membranes (closed symbols).

We finally would like to discuss the assumptions used throughout our computational analysis. All our molecular simulations were performed on defect free, perfect, single-crystals of MOFs. In practical applications, MOF membranes may have defects which may significantly affect their separation performances. Therefore, gas permeabilities and selectivities we predicted in this work should be considered as the most optimistic performances that can be expected from an ideal MOF membrane. We only focused on the separation of binary CO2/CH4 mixture; however, natural gas may include H2S and water vapor as impurities that need to be removed. Our molecular simulations cannot provide information about the MOF membranes’ stabilities under the presence of these impurities. A recent study showed some MOFs may decompose after H2S exposure[11] whereas another one reported that some ZIFs degrade in the presence of humid CO2.[79] Molecular simulation studies also showed that the presence of H2O may decrease CO2 adsorption and selectivity of MOFs due to the competitive adsorption between H2O and CO2.[80] Similarly, compatibility and stability may be a problem for the MMMs based on the selected MOF–polymer combination. Our MMM calculations did not account for the interactions between the polymer and MOF particles, size distribution and orientation of the MOF fillers in the polymer matrices and simply predicted the separation performances of ideal MOF-based MMMs. However, particle size of the MOF fillers may lead to different concentrations of the nonselective pathways due to the interaction with the polymer and this may have an important effect on the overall separation performance of the MMM. The main motivation of our calculations was to screen very high number of materials to identify a small number of promising MOFs and the issues discussed above can be examined for the top membrane candidates by further experimental efforts.

Conclusion

In this work, we combined GCMC and MD simulations to screen 3794 MOF membranes for CO2/CH4 separation. In the first-level of screening, we computed gas permeabilities and selectivities of MOFs at infinite dilution to efficiently identify the promising materials. The top 8 MOFs that have CO2 permeabilities greater than 106 Barrer and CO2/CH4 selectivities higher than 80 were identified as the best candidates and further studied at the second-level of calculations by performing mixture simulations at two different pressures. Results showed that separation performances of MOF membranes computed at infinite dilution are overestimated compared to the ones computed at practical operating conditions considering binary gas mixtures. We also showed that the top MOF membrane candidates identified using the simulations at infinite dilution are still located above the upper bound based on their gas permeabilities and selectivities computed using the mixture simulations, indicating the efficiency and validity of our screening approach. We finally performed computationally demanding flexible MD simulations for the two MOFs and showed that these materials are still above the mixed gas upper bound and promising membrane candidates although lower permeabilities and selectivities were estimated compared to the rigid simulations. Materials having narrow pore sizes and low porosities were found to be potential candidates for membrane-based separation of CO2/CH4 mixtures. We finally investigated permeabilities and selectivities of 64 different types of MMMs composed of 8 polymers and 8 MOF fillers and showed that incorporation of MOFs significantly enhances CO2 permeabilities of all polymers and even enhances CO2/CH4 selectivities of some polymers. All these results suggest that MOFs can be used as membranes and MMMs for efficient separation of CO2/CH4 mixtures. Results of molecular simulations showed that using highly permeable MOFs as pure membranes may be more effective than using them as fillers in polymers since permeability of the MMM is limited when the permeability of filler is very high compared to polymer. The computational screening approach that we used in this work would advance the design and development of MOF membranes and MOF/polymer MMMs by identifying the best MOF candidates and contribute to the sustainable chemistry and engineering in the field of natural gas purification.