High-Throughput Computational Screening of the Metal Organic Framework Database for CH4/H2 Separations.

Metal organic frameworks (MOFs) have been considered as one of the most exciting porous materials discovered in the last decade. Large surface areas, high pore volumes, and tailorable pore sizes make MOFs highly promising in a variety of applications, mainly in gas separations. The number of MOFs has been increasing very rapidly, and experimental identification of materials exhibiting high gas separation potential is simply impractical. High-throughput computational screening studies in which thousands of MOFs are evaluated to identify the best candidates for target gas separation is crucial in directing experimental efforts to the most useful materials. In this work, we used molecular simulations to screen the most complete and recent collection of MOFs from the Cambridge Structural Database to unlock their CH4/H2 separation performances. This is the first study in the literature, which examines the potential of all existing MOFs for adsorption-based CH4/H2 separation. MOFs (4350) were ranked based on several adsorbent evaluation metrics including selectivity, working capacity, adsorbent performance score, sorbent selection parameter, and regenerability. A large number of MOFs were identified to have extraordinarily large CH4/H2 selectivities compared to traditional adsorbents such as zeolites and activated carbons. We examined the relations between structural properties of MOFs such as pore sizes, porosities, and surface areas and their selectivities. Correlations between the heat of adsorption, adsorbility, metal type of MOFs, and selectivities were also studied. On the basis of these relations, a simple mathematical model that can predict the CH4/H2 selectivity of MOFs was suggested, which will be very useful in guiding the design and development of new MOFs with extraordinarily high CH4/H2 separation performances.

Introduction

We have witnessed the very quick growth of metal organic frameworks (MOFs) in the last decade. MOFs are crystalline nanoporous materials composed of metal complexes connected with organic linkers.[1] They are crystalline structures with exceptional physical properties such as very large surface areas (up to 6000 m2/g), high pore volumes (1–4 cm3/g), a large variety of pore sizes (1–98 Å), and reasonable chemical stabilities. The most exciting feature of MOFs compared to traditional porous materials is their chemical and topological tunability. The controllable synthesis of MOFs led to a large diversity of materials having different geometry and chemical functionality.[2] The number of synthesized MOFs has been rapidly increasing and already reached to several thousands. Theoretically unlimited numbers of MOFs can be synthesized by changing the organic linkers and metals.[3] MOFs have been studied for a wide range of applications, including gas storage and gas separation,[4] catalysis,[5] sensing,[6] and drug storage and delivery.[7] Among these, gas storage and separation can be considered as the most mature ones because high porosities, large surface areas, and varieties in pore sizes and shapes make MOFs highly promising adsorbent candidates.

The existence of large numbers of MOFs generates both an opportunity and a challenge for the material search. It is an excellent opportunity to have thousands of candidates that can achieve various gas separations. On the other hand, it is challenging to identify and select the best MOF for a target gas separation application. Experimental synthesis and testing of a material for a gas separation generally takes several weeks. Testing thousands of MOFs using purely experimental techniques is simply impractical. Computational methods play a critical role in examining a large number of MOFs in a time-effective manner to identify the most promising materials for desired applications.[8] Computer simulations have been successful in providing molecular-level information about gas adsorption in MOFs.[9] High-throughput molecular simulation studies generally focused on hypothetical MOFs. Storage of CH4,[10,11] H2,[12−14] and CO2[15,16] in hypothetical MOFs was examined. A recent study[17] used molecular simulations to screen hypothetical MOFs for CO2/CH4 and N2/CH4 separations. Although hypothetical MOFs are very useful in producing structure–property relations as we will discuss later, the main drawback is that there is no guarantee for experimental synthesizability of these hypothetical materials. An experimental synthesis protocol should be designed to make these materials, and this is often very complicated.

Computer simulations require the experimental crystal structures of real MOFs. When an MOF is experimentally synthesized, it is deposited into Cambridge Structural Database (CSD),[18] the world’s essential database for crystal structures. Previously, a challenge was that structures in the CSD were not labeled as MOF, and there was no simple way to search specifically for MOFs, which is now possible as we will explain below. Another challenge is that the crystal structure files of MOFs deposited into the CSD generally have several problems such as existence of solvent molecules in the pores that must be removed before molecular simulations to make pores available for gas adsorption. Some other MOF structures have disordered and/or missing atoms that should be “corrected” before the molecular simulations. Recent studies aimed to build an MOF library. For example, Goldsmith et al.[19] started with 20 000 MOFs from the CSD, excluding ∼16 000 because of the problematic crystal structures such as missing hydrogen atoms and disorders. They then computed theoretical H2 storage capacity for ∼4000 structures. Snurr’s group[20] also started with 20 000 MOFs and ended up with 4764 MOFs by excluding highly disordered and difficult-to-correct materials. In this way, they constructed a very useful database, computation-ready experimental MOFs (CoRE MOFs), and examined CH4 storage in these MOFs using molecular simulations. Li et al.[21] recently started with the CoRE MOF database, discarded MOFs with zero accessible surface areas, and examined 2054 MOFs for CO2/H2O separation. Jiang’s group[22] also used the CoRE MOF to study CO2/N2 and CO2/CH4 separations using molecular simulations.

Jimenez’s group[23] very recently reported the most complete collection of MOFs maintained and updated, for the first time, by the CSD. They discussed that a small number of nonMOF structures are present in the CoRE MOF, whereas some MOF structures are missing. In their collection, they included all MOFs and integrated the library with CSD to allow subsequent addition of new MOFs. To the best of our knowledge, this complete MOF library has not been screened for any gas separation application to date. In this work, we performed high-throughput molecular simulations to identify the adsorption-based CH4/H2 separation performances of this complete collection of MOFs. Separation of CH4 from H2 is industrially and economically important because H2 purification from various process streams constitutes the largest commercial use of pressure swing adsorption (PSA).[24] Highly efficient adsorbents are strongly needed for PSA. Various porous materials, such as single-walled carbon nanotubes,[25] carbons,[26] titanosilicates,[27] and zeolites,[28] have been studied for this separation using molecular simulations. Predicted CH4/H2 selectivities of these traditional adsorbents are not sufficiently high for practical applications; therefore, MOFs have been recently considered as alternatives to achieve high CH4/H2 selectivities. Molecular simulations were performed for isoreticular MOFs (IRMOFs),[29,30] mixed-ligand interpenetrated MOFs,[31] and zeolitic imidazolate frameworks (ZIFs)[32,33] for adsorption-based CH4/H2 separation. Either a single or a few different types of MOFs were examined in these simulations. Wu et al.[34] computed selectivities of 105 different MOFs, and our research group[35] studied 250 MOF structures for CH4/H2 separations using molecular simulations. These studies showed that MOFs have higher adsorption selectivities than zeolites. This literature review shows that current studies on MOF adsorbents for the separation of CH4/H2 mixtures have investigated only a very small fraction of the MOFs reported in the CSD. Considering the large variety and number of available MOFs, there may be many existing MOFs with better separation performances. Furthermore, structure–performance relations which greatly guide the design and development of new materials can only be generated if a large number and diversity of MOFs are studied.

With these motivations, we performed the first high-throughput molecular simulation study in the literature, which unlocks the potential of all existing MOFs in the world for adsorption-based CH4/H2 separation. Adsorption data of CH4/H2 mixtures obtained from the grand canonical Monte Carlo (GCMC) simulations were used to calculate several adsorbent selection metrics such as adsorption selectivity, working capacity, adsorbent performance score (APS), sorbent selection parameter, and regenerability of MOFs. Top performing MOF adsorbents were identified based on the combination of these metrics. The types of the metal sites available in the highly promising MOFs were also identified. Separation performances of MOFs were compared with traditional adsorbents, such as zeolites, carbon-based materials, and silica gels to assess the potential of MOFs for CH4/H2 separations. We examined the relations between structural properties such as pore sizes, porosities, and surface areas of MOFs and their selectivities to provide the structure–performance relationships that can serve as a map for experimental synthesis of new MOFs with better gas separation performances. Relations between the heat of adsorption, adsorbility, and selectivities were also explored. On the basis of these correlations, a simple mathematical model was suggested, which can accurately predict MOFs’ selectivities based on easily computable properties.

Computational Details

MOFs

We used the most complete collection of MOFs available and the only collection integrated within the CSD.[23] This collection comprises 69 666 MOFs with a wide range of chemical and structural properties. The nondisordered MOF subset contains 54 808 structures, and we started with it. The bound and unbound solvents in MOFs were removed using a Python script available in the literature.[23] We computed physical properties of MOFs such as accessible surface area, accessible pore volume, pore-limiting diameter (PLD), and the largest cavity diameter (LCD) using Zeo++ software.[36] We then refined the collection to only have the MOFs that have nonzero accessible gravimetric surface areas and PLDs greater than 3.75 Å so that both CH4 and H2 molecules can be adsorbed into the pores. After this refinement, we ended up with 4350 different MOFs that span in a wide range of chemical functionalities. Figure S1 shows the distribution of PLDs and LCDs for all MOFs together with the kinetic diameters of H2 and CH4 molecules. PLDs and LCDs of MOFs are in the range of 3.75–31 and 4.0–33.6 Å, respectively. 3842 MOFs have LCDs greater than PLDs, and 508 MOFs have almost identical PLDs and LCDs. We also showed the relation between porosity, surface area, and LCD in Figure S2. The surface areas (porosities) of MOFs range from 27.7 to 7091.7 m2/g (0.28 to 0.91). Only a small number of MOFs (32) have accessible surface areas <100 m2/g. Majority of MOFs (3540) have surface areas between 100 and 2000 m2/g, 646 MOFs have surface areas between 2000 and 4000 m2/g, and 132 MOFs have very large surface areas (>4000 m2/g). A large number of MOFs (3566) have porosities between 0.5 and 0.7. 461 MOFs have mediocre porosities (0.3–0.4), and 323 MOFs have very large porosities (>0.8). As the porosity increases, surface areas and LCDs also increase as shown in Figure S2. MOFs with high LCDs (18–33.6 Å) have high porosities (0.65–0.91) and high surface areas (most of them larger than 1000 m2/g). All these computed structural properties of MOFs together with their CSD names are given in the Supporting Information.

Molecular Simulations

GCMC simulations have been widely used to compute gas adsorption isotherms in porous materials.[37] We performed GCMC simulations as implemented in the RASPA simulation code.[38] Both single-component and mixture GCMC simulations were performed. All the GCMC simulations were performed at room temperature. Three different types of moves were considered for single-component GCMC simulations including translation, reinsertion, and swap of a molecule. In the binary mixture GCMC simulations, another trial move, identity exchange of molecules, was also performed. We considered equimolar bulk mixtures in the simulations. The Lorentz–Berthelot mixing rules were employed. The cutoff distance for truncation of the intermolecular interactions was set to 13 Å. The simulation cell lengths were increased to at least 26 Å along each dimension, and periodic boundary conditions were applied in all simulations. For each MOF, simulations were carried out for 10 000 cycles with the first 5000 cycles for initialization and the last 5000 cycles for taking ensemble averages. The Peng–Robinson equation of state was used to convert the pressure to the corresponding fugacity. The isosteric heat of adsorption (Qst), difference in the partial molar enthalpy of adsorbate between the bulk and adsorbed phases, and the Henry’s constants of gas molecules were also calculated at the limit of zero coverage (infinite dilution) using the Widom particle insertion method.[37] More details of these simulations can be found in the literature.[37,39]

Single-site spherical Lennard-Jones 12-6 potential was used to model H2[40] and CH4[41] molecules that are given in Table S1. The potential parameters of MOF atoms were taken from the universal force field.[42] These potentials and force fields were selected based on the results of our previous simulation studies.[43−45] In our previous studies, we showed very good agreement between our simulation results and experimentally measured CH4 and H2 adsorptions in many MOFs.[45,46] For example, we validated the accuracy of our CH4 simulations by comparing with 267 experimental adsorption data of CH4 in a very large number of MOFs at a variety of pressures and temperatures.[45] Similarly, we showed the good agreement between simulated H2 uptake and the experimentally reported data of a variety of MOFs including many subfamilies such as BioMOFs, covalent organic frameworks, coordination polymers, IRMOFs, porous coordination networks, and ZIFs.[46] Good agreements between our simulations and experiments for full CH4 and H2 adsorption isotherms can be seen in both of these studies. As examples, we showed a comparison of the adsorption isotherms of CH4 and H2 in some prototypical MOFs, IRMOF-1, CuBTC, UiO-66, and ZIF-8 in Figure S3. Comparison of our simulated adsorption isotherms of CH4 and H2 with the experiments for various different MOFs can also be seen in Table S2. We also showed the good agreement between experimentally reported CH4/H2 selectivities and simulated ones for several ZIFs[47] and MOFs.[35] These results validated the accuracy of our molecular simulations and the choice of the force fields. MOFs were assumed to be rigid in their reported crystallographic structures in simulations. This assumption has been used in all high-throughput molecular simulation studies of MOFs to save significant computational time. The main aim of this work is to demonstrate the potential value of a material using efficient computational screening approach prior to experiments. Furthermore, because the gas molecules we studied are relatively small compared to the MOFs’ pore sizes, flexibility is expected to have a negligible effect on the gas adsorption.

Adsorbent Evaluation Metrics

Results obtained from molecular simulations of equimolar CH4/H2 mixtures were used to predict separation performances of MOFs. Several adsorbent evaluation metrics have been defined and used to date. In this study, we considered five commonly used metrics, adsorption selectivity (Sads), working capacity (ΔN), adsorbent performance score (APS), sorbent selection parameter (Ssp), and regenerability (R %). Mathematical definitions of these metrics can be seen in Table . Adsorption selectivity, Sads, is the most widely used metric to evaluate adsorbents, and it is simply defined as the ratio of compositions of the adsorbed gases (x) in the adsorbent normalized by the ratio of bulk phase compositions (y) of components. In Table , subscript 1 represents the strongly adsorbed gas (CH4) and subscript 2 represents the weakly adsorbed gas (H2). Working capacity (ΔN) is defined as the difference between the gas uptakes (N) at the adsorption and desorption pressures in the unit of mol gas per kg adsorbent.[48] It is used for the strongly adsorbed component of the gas mixture, which is CH4 in this work. APS was recently defined by Chung et al.[16] as the product of selectivity and working capacity to easily identify the top performing adsorbent materials. The sorbent selection parameter (Ssp) includes the ratio of working capacities.[49] Regenerability (R %) is an important metric in cyclic PSA processes[35] because it determines the percent regeneration of the adsorption sites while desorption step is ongoing.[48] All these metrics were computed for equimolar CH4/H2 mixtures at room temperature at an adsorption pressure of 10 bar and desorption pressures of 1 bar because most of the PSA separations in industry are performed under these conditions. Previous molecular simulation studies reported that selectivities of MOFs do not significantly change with the temperature.[50]

Table 1

Adsorbent Evaluation Metrics Used in the Ranking of MOFs

parameter	formula
selectivity
working capacity	ΔN = Nads – Ndes
adsorbent performance score	APS = Sads(1/2) × ΔN1
sorbent selection parameter
percent regenerability

It is important to highlight two important aspects of our work in terms of using performance evaluation metrics to assess MOF adsorbents:

Some high-throughput molecular simulation studies[17,21] calculated the adsorption selectivity of MOFs using the ratio of Henry’s constants of single-component gases computed at zero loading and reported ideal selectivities, whereas a smaller number of studies[16] used mixture adsorption data to compute mixture selectivities. Ideal selectivity at infinite dilution represents the intrinsic separation capacity of a material when there is no interaction between gas species. Ideal selectivity may significantly differ from the mixture selectivity when interactions (competitive or cooperative) between two gas molecules exist.[51] The deviation between ideal and mixture selectivities becomes more pronounced as the pressure increases because of the multicomponent mixture effects that are dominant at high pressures.[35] Therefore, in this work, we calculated “mixture selectivity” of all MOFs using the adsorbed loadings of each gas species at the adsorption pressure of interest to represent real operating conditions.

Selectivity has been generally considered as the most critical factor to rank MOFs for CH4/H2 separations in the previous molecular simulation studies that we summarized above.[29−35] Other parameters that can be used to compare adsorbents also exist but rarely studied. For example, Rege and Yang[49] proposed the PSA selection parameter to compare two adsorbents for gas separation on the basis of their equilibrium adsorption capacities, and Llewellyn et al.[52] defined an adsorbent performance indicator to evaluate adsorption-based gas separation performances of MOFs. In our recent study,[53] we showed that R % is a very important metric to screen materials in identifying the most promising adsorbents. For example, it was shown that several MOFs with high CO2 selectivities exhibit very low R %, limiting their practical usage as adsorbents.[53] To efficiently rank the very large number of MOFs considered in this study, we first eliminated MOFs having R % < 85% and then ranked the remaining materials based on their APSs, which take both the selectivity and the working capacity into account, as previously used by Snurr’s group for ranking the MOFs for CO2/H2 separations.[16] As a result, the top MOFs identified in this work have the best combinations of high selectivities, high working capacities, and high regenerabilities.

Results and Discussion

Separation Performances of MOFs

Although gas separation is tied with gas mixtures, large-scale MOF screening studies in the literature mostly focus on ideal selectivity calculated at low pressures.[17,21] In this work, we computed both the ideal and mixture selectivities. Figure compares ideal and mixture selectivities of 4350 MOFs computed at two different pressures, 1 and 10 bar. Ideal selectivities computed from single-component GCMC simulations and mixture selectivities computed from binary mixture GCMC simulations were found to be greater than one. This means all MOFs are CH4 selective in adsorption because H2 has weaker interactions with the MOF atoms compared to CH4. The deviation between ideal and mixture selectivities increases as the pressure increases from 1 to 10 bar because at high pressures, most of the adsorption sites are occupied and gas molecules compete with each other for the same sites. The more strongly adsorbing CH4 molecules exclude the weakly adsorbing H2 molecules in the pores. As a result, mixture selectivities are always higher than the ideal selectivities as shown in Figure . A significant number of MOFs (3915) have mixture selectivities between 10 and 1000, whereas a small number of MOFs (15) have mixture selectivities > 1000 at 1 bar. Similarly, most MOFs (3939) exhibit mixture selectivities between 10 and 1000, whereas only three MOFs have very high mixture selectivities, >1000 at 10 bar. Results shown in Figure suggest that ideal selectivity can make a preliminary estimate for the separation performance of MOFs if the MOF has a low selectivity, less than 10. However, for MOFs that are promising with mixture selectivities greater than 100, ideal selectivity significantly underestimates the mixture selectivity. This means it is not accurate to screen MOFs based on ideal selectivity for the identification of the most promising materials. Therefore, we used the mixture selectivity throughout this manuscript and simply referred it as selectivity in the remaining sections.

Figure 1

Comparison of ideal and mixture selectivities of MOFs at (a) 1 and (b) 10 bar. The red line represents x = y to guide the eye.

Figure shows both the CH4/H2 selectivity and CH4 working capacity of MOF adsorbents computed at an adsorption pressure of 10 bar and a desorption pressure of 1 bar. Selectivities of MOFs are in the range of 1.4–2028, whereas working capacities vary from 0.001 to 7.3 mol/kg. Most MOFs have a trade-off between selectivity and working capacity. Materials with high selectivities (>500) generally suffer from low working capacities (<1 mol/kg). Therefore, we color-coded the figure with APSs to separate low- and high-performance regions within the MOF search space. Four different regions were defined intuitively arbitrary to provide a reference for quantitatively defining a number of promising MOFs. The purple region represents the MOFs with high selectivities (>100) but low working capacities (<0.5 mol/kg) and the MOFs with high working capacities (>3 mol/kg) but low selectivities (<10). A large number of MOFs having moderate selectivity (10–100) and working capacity (1–2 mol/kg) combination also exist in this region. The blue region represents a group of promising MOFs with APSs in the range of 100–300. The most promising MOFs are in the green and red regions. 30 MOFs were identified out of 4350 as the top performing structures with APSs greater than 300. For example, an MOF with the CSD name of QUQQID was found to have the highest APS (802 mol/kg) with a high CH4 working capacity of 3.15 mol/kg and a high CH4/H2 selectivity of 255. Other exceptionally promising MOFs shown with red color in Figure are UTEXIB, PARMIG, and ADIQEL. They exhibit high selectivities of 1520, 517, and 394 and high working capacities of 0.43, 1.04, and 1.30 mol/kg, respectively.

Figure 2

Selectivities and working capacities of MOFs color-coded according to their APSs.

To assess the potential of MOFs for CH4/H2 separations, we compared them with traditional adsorbents. The selectivity and working capacity of widely studied zeolites CHA, LTA, and ITQ-29 (which is the pure silica version of LTA, in other words, the same structure) were previously reported at 10 bar, 300 K using molecular simulations. The working capacities of LTA-Si, ITQ-29, and CHA were approximately 0.8, 1, and 1.1 mol/kg, respectively, whereas their selectivities were computed as 6.5, 8.2, and 13.[28] MOFs have significantly higher selectivities and working capacities than these zeolites. Infinite dilution selectivities of several adsorbents such as activated alumina, silica gel, coal carbon, and coconut carbon were reported in the literature as 13, 14.3, 34.1, and 58.3, respectively.[54] We computed CH4/H2 selectivities of MOFs under the same conditions and found that a significant number of MOFs (1647) have selectivities greater than 60. Wu et al.[34] identified CUK-2 as the MOF with the highest CH4/H2 selectivity (267.1) at infinite dilution among the 105 MOFs they considered. In this work, we identified 236 MOFs that have higher selectivities than CUK-2 under the same conditions. This comparison suggests that MOFs outperform traditional adsorbents and that they can be better adsorbent candidates than zeolites in CH4/H2 separations.

Ranking MOF Adsorbents

Although selectivity has been used as the primary assessment metric, there are several other parameters such as Ssp and R % to define the performance of the MOF adsorbent. We showed Ssp values of 4350 MOFs in Figure as a function of selectivity. Ssp values change between 0.8 and 1.1 × 106, whereas most of the MOFs (3039) have Ssp values between 300 and 7500. The selectivity of these MOFs ranges from 17 to 833. It is important to note that MOFs which have been widely studied as adsorbents in the literature such as CuBTC (FIQCEN), UiO-66 (RUBTAK), IRMOF-8 (SAHYIK), and IRMOF-1 (EDUSIF) generally suffer from low Ssp values of 97.3, 82.6, 30.9, and 29.4, respectively, meaning that there are many other MOFs with better separation potential than these widely studied ones. The most promising MOFs are located at the top right corner of Figure , which have both high Ssp and high selectivity such as UTEXIB (Ssp: 1.1 × 106, S: 1519.9) and WEHJAW (Ssp: 2.4 × 105, S: 1873.9). The relation between R % and selectivity of MOFs is shown in Figure a. MOFs show a very wide range of R %, from 0.05 to 90.3%, and the red line represents 85%, which is desirable for practical PSA applications. The selectivities of the easily regenerable MOFs, the ones above the red line, significantly vary. For example, the MOF with the highest R % (YEYGAM, 90.3%) has a low selectivity, 2.4, at 10 bar. On the other hand, there are several MOFs with high selectivities (>2000), but they suffer from very low R % (<5%). The most promising MOFs that offer both high R % (>85%) and high selectivity are represented by red stars in Figure a. For example, CAYSIE, OXUPUT, and CAYSOK have selectivities of 44, 47, and 49 and R % of 87, 86, and 86%, respectively. In Figure b, R % of MOFs is plotted as a function of their APSs and the top 20 regenerable MOFs with the highest APSs are shown with red stars.

Figure 3

Sorbent selection parameters and selectivities of MOFs.

Figure 4

R % of MOFs as a function of (a) selectivities and (b) APSs. Red dashed lines show R % = 85%. Red stars represent the most promising MOFs with the highest (a) selectivities and (b) APSs above the red line.

Results so far suggested that considering selectivity is not enough to decide if an MOF is promising for gas separation applications because an MOF with high selectivity might have a low ΔN and/or R %, which will make the separation process economically inefficient. Therefore, we used the following ranking strategy to rank MOFs: we first focused on the MOFs with R % > 85. Among these MOFs, we identified the top 20 MOFs according to their selectivities and APSs and listed their performance evaluation metrics in Tables and 3. Eight of the MOFs, which are RORVAX, PIBXOP, KEWZOD, KINNEC, JOVXUP, SIKGEA, FEHCOM, and ROHKAC, were found to be common in both tables and are represented in bold. These MOFs can be considered as the best adsorbent candidates for CH4/H2 separations in terms of all adsorbent evaluation metrics. It is important to note that in addition to having high scores in performance evaluation metrics, MOFs should also be stable to find place in real applications. We searched for the stability information of these eight MOFs. KEWZOD[55] and JOVXUP[56] were reported to be stable at high temperatures. FEHCOM[57] was reported to keep its structural integrity after the complete removal of guests, and guest-free ROHKAC[58] was reported to be thermally stable up to ∼250 °C. PIBXOP was reported to be very stable in common organic solvents.[59] RORVAX was found to be the only promising MOF, which was reported to lose its porosity after solvent removal.[60] We could not find any information about the stability of KINNEC[61] and SIKGEA.[62] Among the MOFs discussed in Figures and 3, UTEXIB[63] was identified as a robust structure with a thermal stability of up to 450 °C, whereas no information was available for QUQQID[64] and WEHJAW.[65] Stabilities of the most promising materials identified in this work are most likely to be examined under practical gas separation experiments in future studies.

Table 2

Top Performing MOFs (20) Ranked Based on Selectivitya

MOFs	SCH4/H2	ΔNCH4 (mol/kg)	R (%)	APS (mol/kg)
CAYSOK	48.59	1.65	86.31	80.31
OXUPUT	47.36	0.38	85.53	18.09
CAYSIE	43.96	1.55	86.68	68.04
YOVTOS	37.95	1.46	85.99	55.36
CAYYEG	36.30	1.44	86.31	52.44
SAZQEQ	34.32	1.32	87.27	45.46
QANSEE	32.92	1.22	88.55	40.07
SUTWOT	31.44	2.39	85.09	75.24
FEHCOM	31.18	3.68	86.51	114.60
ROHKAC	30.49	3.55	86.01	108.08
KINNEC	30.24	4.51	85.16	136.50
JOVXUP	30.01	4.53	85.02	136.07
KEWZOD	29.96	4.57	85.00	136.95
RORVAX	29.89	6.33	85.16	189.16
SIKGEA	29.85	4.25	85.30	126.94
HOWHEI	29.70	3.03	85.04	89.85
PIBXOP	28.94	4.84	85.75	140.16
RINPUZ	28.67	3.11	86.28	89.04
PACZUQ	28.33	1.73	85.47	49.10
CATDEH	28.10	1.08	87.90	30.34

MOFs written in bold are common in Tables and 3.

Table 3

Top Performing MOFs (20) Ranked Based on APSa

MOFs	SCH4/H2	ΔNCH4 (mol/kg)	R (%)	APS (mol/kg)
RORVAX	29.89	6.33	85.16	189.16
QUQQAV	27.13	5.65	86.11	153.35
VOCXUH	27.59	5.25	85.50	144.83
PIBXOP	28.94	4.84	85.75	140.16
KEWZOD	29.96	4.57	85.00	136.95
KINNEC	30.24	4.51	85.16	136.50
JOVXUP	30.01	4.53	85.02	136.07
METPAC	27.97	4.67	85.64	130.69
SIKGEA	29.85	4.25	85.30	126.94
JUCKEZ	27.24	4.56	85.20	124.24
FIRNUR	24.08	5.14	86.29	123.71
QUQQUP	22.72	5.32	87.17	120.81
AFEHUO	27.06	4.43	86.56	119.98
FEHCOM	31.18	3.68	86.51	114.60
JUCKID	25.65	4.31	86.09	110.61
KUTPEW	25.84	4.24	85.68	109.47
ROHKAC	30.49	3.55	86.01	108.08
DABWUA	26.62	3.92	85.24	104.36
EYEYAJ	24.92	4.15	85.58	103.46
CUFFOZ	24.35	4.22	85.32	102.87

MOFs written in bold are common in Tables and 3.

Structure–Performance Relations

Understanding the relation between structural properties of MOFs and their performances for target gas separation is highly useful not only to easily select the promising materials among many available ones but also to guide the further design and synthesis of new MOFs with exceptionally high gas separation properties. For example, Fernandez and Woo[66] reported a large-scale, quantitative structure–property relationship analysis for hypothetical MOFs and examined the effects of pore sizes and void fraction on the simulated CH4 storage capacities. Snurr’s group[67] examined structure–property relations of a large number of hypothetical MOFs for their CO2 separation performances from CH4 and N2. Although these relations provide an insight into the structural properties that would lead to the design of new MOFs with high separation performance, it is not certain that the relations found for hypothetical MOFs will be valid for real MOFs. The strength of this study is that every MOF we considered is real and experimentally synthesized.

The selectivities of adsorbents are generally correlated with the difference of isosteric heats of adsorption values of the two gas species that are aimed to be separated. On the basis of the Langmuir adsorption theory, Yang et al.[68] suggested a correlation, ln S = 0.8558 + ΔQst0/(R × T), to show the relation between the difference of heat of adsorption values of gases at infinite dilution loading (ΔQst0) and selectivity (S). Here, R is the ideal gas constant and T is the temperature. This correlation was proposed to be suitable for all the physical adsorption-based separation of gas mixtures in porous materials. We tested its validity for all the MOFs for the first time in the literature. The selectivities of MOFs computed at three different pressures, at infinite dilution (using the ratio of Henry’s constants of each competing gas molecule), 1, and 10 bar, are shown in Figure as a function of ΔQst0 together with the line obtained from the Yang’s correlation. Predictions of the correlation are in a very good agreement with the infinite dilution selectivities as shown in Figure a because this correlation is based on ΔQst0 computed at zero pressure. The correlation was found to predict the mixture selectivities of MOFs well at low ΔQst0 values (≤15 kJ/mol) at 1 bar and at lower ΔQst0 values (≤12 kJ/mol) at 10 bar as shown in Figure b,c. Yang’s correlation generally overestimates selectivities of MOFs as ΔQst0 increases. This can be explained with the following discussion: the correlation considers zero-coverage enthalpies, in other words, it only accounts for adsorbent–gas interactions. As the pressure increases, gas–gas interactions play a much important role in adsorption, but the correlation does not include these effects. Therefore, deviations between selectivities and ΔQst0 become more observable at higher pressures. Results shown in Figure suggest that Yang’s correlation can be used for a rough initial screening of MOFs for CH4/H2 separations. Inspired from the solubility theory,[69] inverse of the adsorbility (1/ΔAD) was recently defined as (1/ΔAD = ϕ/ΔQst0).[34]Figure shows that as 1/ΔAD decreases, the selectivity increases. 1/ΔAD correlates well with the selectivity of MOFs both at 1 and 10 bar. This means the inverse of the adsorbility can be used to make an accurate estimation about the selectivities of MOFs at practical operating pressures.

Figure 5

Relation between ΔQst0 and selectivities of MOFs at (a) infinite dilution, (b) 1, and (c) 10 bar. The red line shows the slope of Yang’s correlation defined in the text.

Figure 6

Relation between selectivities and the inverse of adsorbility of MOFs at (a) 1 and (b) 10 bar. The red line shows the correlation.

Among many structural/chemical parameters, ΔQst0 is not the easiest one to obtain because it requires either a computational study or an experimental measurement. To establish an easier-to-use structure–performance relation, we examined the correlations between selectivities of MOFs and their easily measurable/computable structural properties such as pore sizes, porosities, and surface areas. Correlations between APS values of MOFs and structural properties were also examined; however, much weaker correlations were found compared to the ones between selectivities and structural properties. Figure shows that as the LCDs of MOFs decrease, the selectivities increase because small cavities are more favorable adsorption sites for gas molecules because of the strong confinement of the gas molecules. Although the relation is not perfect, Figure suggests that MOFs with LCDs larger than 15 Å exhibit lower selectivities, <30. Relation between porosities and selectivities of MOFs is also given in Figure . MOFs with high porosities can easily adsorb both CH4 and H2 molecules, resulting in a nonselective adsorption. Therefore, selectivity is generally low for MOFs having high porosities. Figure shows the relation between surface areas of MOFs and their CH4/H2 selectivities. It is clear that there is not a strong correlation between surface areas and selectivities; however, some useful interpretations can be made. Selectivities generally tend to decrease as the surface areas increase. MOFs with very large surface areas (>5000 m2/g) generally exhibit selectivities less than 10.

Figure 7

Relation between the LCDs and selectivities of MOFs at (a) 1 and (b) 10 bar.

Figure 8

Relation between porosities and selectivities of MOFs at (a) 1 and (b) 10 bar.

Figure 9

Relation between accessible surface areas and selectivities of MOFs at (a) 1 and (b) 10 bar.

Results so far indicated that selectivities usually do not present very good correlations with a commonly used single property such as pore size, ϕ, Sacc, and ΔQst0 but an interplay of these factors.[34,70] Correlation coefficients (R2 values) between selectivity and five parameters that we discussed so far ΔQst0, 1/ΔAD, LCD, ϕ, and Sacc are given in Figure S4 for both 1 and 10 bar. At 1 bar, selectivity shows strong correlations with 1/ΔAD (R2 = 0.82) and ΔQst0 (R2 = 0.78), but there is not a strong correlation between Sacc or LCDs of MOFs and selectivities (R2 < 0.4). Because porosity and ΔQst0 are already included in 1/ΔAD, we concluded that at 1 bar selectivity is only dependent on 1/ΔAD as discussed in Figure . At 10 bar, selectivities have a strong correlation with 1/ΔAD (R2 = 0.74) and ΔQst0 (R2 = 0.67) and a weak correlation with LCD (R2 = 0.41). On the basis of these results, we propose a simple model that can reasonably predict the CH4/H2 selectivity of MOFs as follows, Sads = a × (1/ΔAD) + c × (LCD), where a, b, c, and d are the coefficients given in Table S3. Selectivity predictions of this model are compared with the results of direct GCMC simulations shown in Figure . The deviation of model predictions from the simulated selectivities was calculated as the percent error, error % = |Ssimulated – Spredicted|/Ssimulated × 100. Blue points in Figure represent the MOFs for which the deviations between model predictions and simulations are less than 30%. The selectivities of 2243 MOFs (52% of the MOFs we considered) are predicted well with the suggested model, leading to high R2 of 0.91. However, the model is not able to make accurate predictions for the complete set of MOFs. Black data points show the MOFs for which the deviation between the model predictions and simulation results is larger than >30%. Considering the large variety in chemistry, topology, and physical properties of MOFs, it is somehow natural that establishing a simple mathematical model that works for all the available MOFs is impractical. When we analyzed the MOFs for which the deviations are high, it occurred that these are the MOFs that do not follow the general structure–performance relations. For example, Figures and 7 suggested that as 1/ΔAD and LCD decrease, selectivities increase, and this is what the model uses in making selectivity predictions. There is an MOF which has a high LCD (11 Å), but it exhibits high selectivity (2027) in contrast to the general LCD–selectivity relation we discussed. As a result, the model significantly underpredicts the selectivity of this material (80). To summarize, our suggested model can be used to make reasonable selectivity predictions for 70% of the MOFs, which follow the general structure–performance correlations, within <40% error.

Figure 10

Comparison of model predictions with the simulation results of MOF selectivities at 10 bar. Blue points represent MOFs for which the deviations between model predictions and simulations are less than 30%.

We finally examined the effect of the metal type of MOFs on their gas separation performances. It was discussed that metal sites are the primary adsorption sites for gas molecules,[71] but their effects on the gas separation abilities of MOFs are not known. The frequency of metals and semimetals present in MOFs is given in Table . There are 67 types of metals in 4350 MOFs, and the most frequently used one is Zn. 26% of the MOFs contain Zn, and Cu follows this with 17%. MOFs (774) contain more than one type of metal (2, 3, and 4). In Figure , metal types of the 1101 MOFs which have R % > 85% are labeled. Zn (33%), Cu (16%), and Co (11%) are the most observed metals in these easily regenerable MOFs. Other metals seen in highly selective MOFs that are located at the right of that figure are Cr, Mn, Pr, and U. It is challenging to quantify the effect of the metal type on selectivity, but our results suggest that MOFs with Zn, Cu, Co, and Mn appear to be more promising in terms of high CH4/H2 selectivity and high R %.

Table 4

Frequency of Metals in 4350 MOFsa

Ag	0.063	Na	0.018
Al	0.006	Nd	0.012
As	0.000	Ni	0.060
Au	0.005	Np	0.000
B	0.025	Os	0.000
Ba	0.004	Pb	0.009
Be	0.001	Pd	0.005
Bi	0.003	Pr	0.007
Ca	0.004	Pt	0.004
Cd	0.106	Rb	0.001
Ce	0.007	Re	0.002
Co	0.105	Rh	0.005
Cr	0.007	Ru	0.006
Cs	0.003	Sb	0.005
Cu	0.167	Sc	0.001
Dy	0.011	Si	0.012
Er	0.007	Sm	0.006
Eu	0.016	Sn	0.003
Fe	0.037	Sr	0.003
Ga	0.003	Tb	0.011
Gd	0.012	Tc	0.000
Ge	0.001	Te	0.000
Hf	0.001	Th	0.000
Hg	0.006	Ti	0.002
Ho	0.003	Tl	0.000
In	0.024	Tm	0.003
Ir	0.002	U	0.006
K	0.010	V	0.007
La	0.010	W	0.012
Li	0.005	Y	0.003
Lu	0.002	Yb	0.006
Mg	0.010	Zn	0.259
Mn	0.048	Zr	0.006
Mo	0.008

MOFs (774) have more than one type of metal.

Figure 11

Metal types of the most promising MOFs. Stars represent the most selective MOFs with R % > 85%.

Conclusions

Considering the rapid increase in the number of synthesized MOFs, high-throughput computational screening studies play an important role in the identification of MOFs with high gas separation performance. In this study, we screened the recent MOF database to show the ultimate performance limits of MOFs for CH4/H2 separations. Our results showed that MOFs can outperform traditional adsorbent materials such as zeolites, activated alumina, silica gel, and carbon-based materials in CH4/H2 separations because of their higher selectivities and working capacities. The top 20 materials that combine high selectivity, high working capacity, and high regenerability were identified and listed. We also examined the relations between structural properties of 4350 MOFs and their gas separation performances to guide the future experimental synthesis efforts toward the structural properties that are likely to result in materials with better CH4/H2 separation abilities. A simple model was also suggested to predict the CH4/H2 selectivity of MOFs based on easily measurable/computable structural properties. The ultimate choice of the MOF should, of course, also include other parameters such as stability, cost, and synthesis conditions of the MOFs. We believe that our results will trigger experimental efforts to accelerate the design of new MOFs with better separation capacities.