Metal organic frameworks (MOFs) have received significant attention as a new family of nanoporous materials in the last decade. Variations in geometry, size, and chemical functionality of these materials have led to several thousands of different MOF structures. MOFs typically have high porosities, large surface areas, and reasonable thermal and mechanical stabilities. These properties make them ideal adsorbents for adsorption-based gas separations. It is not practically possible to test the adsorption-based gas separation potential of all available MOFs using purely experimental techniques. Molecular simulations can guide experimental studies by providing insights into the gas adsorption and separation mechanisms of MOFs. Several molecular simulation studies have examined adsorption-based CO2 separation using MOFs due to the importance of CO2 capture for clean energy applications. These simulations have been able to identify the MOF having the most promising CO2 separation properties prior to extensive experimental efforts. The aim of this chapter is to address current opportunities and challenges of molecular simulations of MOFs for adsorption-based CO2 separations and to provide an outlook for prospective simulation studies.
- molecular simulation
We have witnessed the quick growth of a new group of nanoporous materials named as metal organic frameworks (MOFs) in the last decade. MOFs are crystalline nanoporous materials composed of metal complexes that are linked by organic ligands to create highly porous frameworks [1, 2]. MOFs become strong alternatives to more traditional nanoporous materials such as zeolites due to their fascinating physical and chemical properties. MOFs typically have very large surface areas (500–6000 m2/g), high pore volumes (1–4 cm3/g), wide range of pore sizes from micro- to mesoscale (1–98 Å), and reasonable thermal and mechanical stabilities. The most important characteristic of MOFs is that their physical, chemical, and structural properties can be tuned during synthesis. This controllable synthesis leads to a large diversity of materials having different geometry, pore size, and chemical functionality [3, 4]. As a result, thousands of MOFs have been reported in the Cambridge Crystallographic Database . The family of MOFs can be divided into subgroups such as isoreticular MOFs (IRMOFs), zeolitic imidazolate frameworks (ZIFs), zeolite-like MOFs (ZMOFs), and covalent organic frameworks (COFs).
MOFs have been examined for a variety of chemical applications including gas storage [6, 7], gas sensing , gas separating membranes , mixed matrix membranes , catalysis , and biomedical applications [12, 13]. Among these applications, gas separation has received a significant interest because the pore sizes of MOFs can be tuned to selectively separate gases at the molecular level. Gas separation using MOFs has been generally studied in two categories: equilibrium-based gas separations and kinetic-based gas separations . In equilibrium-based gas separations, MOFs are used as adsorbents and in kinetic-based separations, MOFs are used as membranes. Adsorption-based gas separation is governed by the thermodynamic equilibrium. Gas components are reversibly adsorbed into the pores of the adsorbent. An ideal adsorbent material must have a good combination of adsorption selectivity and working capacity in addition to high stability, high void volume, and well-defined pore sizes. High porosities, large surface areas, different pore sizes and shapes, and reasonable stabilities of MOFs suggest that these materials can be ideal adsorbents in equilibrium-based gas separation applications. Several experimental studies have been carried out for adsorption-based gas separations using MOFs [15–17].
Two criteria are widely investigated to assess the potential of MOF adsorbents: adsorption selectivity and working capacity. Adsorption selectivity is determined by the adsorption affinity of the MOF for one gas species relative to another. High adsorption selectivity means a high-purity product and hence lower energy requirements. Working capacity is defined as the difference between the adsorbed amounts of gas at the adsorption and desorption pressures. High working capacity means easy regeneration of the adsorbent material. For an efficient and economic adsorption-based gas separation, both high selectivity and high working capacity are desired. Therefore, experimental studies on MOF adsorbents generally examine selectivity and working capacity of the materials .
Most of the experimental studies have focused on CO2 separation. Because of the growing environmental concerns, removal of CO2 from natural gas (CO2/CH4), flue gas (CO2/N2), and other gases (CO2/H2) becomes an important issue. Experimentally measured selectivity and gas uptake capacity of several MOFs for separation of CO2 from CH4 and N2 have been summarized in the literature . Currently available adsorbents such as activated carbons, carbon molecular sieves, and zeolites are not highly selective for CO2 separation, especially for separation of CO2 from flue gas . A good comparison of CO2 separation performances of different nanoporous materials such as MOFs, zeolites, and activated carbons is available in a recent review . It is shown that CO2/N2 selectivity changes from low in zeolites to moderate in carbon-based absorbents and becomes high in MOFs. Therefore, research on adsorption-based gas separations has focused on identifying highly selective MOF adsorbents with high CO2 capacities that can replace traditional adsorbents.
Considering the very large number of available MOFs, it is not possible to test thousands of different MOFs as adsorbents using purely experimental methods. Molecular simulations play an increasingly important role in understanding the potential of MOFs in adsorption-based gas separations. Among molecular simulation methods, grand canonical Monte Carlo (GCMC) simulations have been widely used to accurately predict adsorption isotherms of various gases in MOFs . Gas selectivities calculated from simulated adsorption isotherms are generally found to be in good agreement with the experiments . In most studies, single-component gas adsorption isotherms are computed using GCMC simulations; mixture adsorption isotherms are then predicted based on pure gas adsorption data using ideal adsorbed solution theory (IAST). IAST is a well-developed technique to describe adsorption equilibria for gas components in a mixture using only single-component adsorption data at the same temperature and on the same adsorbent . GCMC simulations can be also performed to obtain mixture adsorption data directly. This data is then used to predict adsorption selectivity and working capacity of the MOF. Results of molecular simulations provide molecular-level insights which can be used to design new MOFs with better separation performances. In the early years of these studies, simulations examined only one or a few MOFs at a time. With the development of new computational approaches and with the quick increase in the number of synthesized MOFs, molecular simulations have started to screen a large numbers of materials. The results of large-scale MOF screening studies are highly useful to direct experimental efforts, resources, and time to the most promising MOF materials.
This chapter aims to address the importance of molecular simulations to evaluate the potential of MOFs in adsorption-based CO2 separations. Section 2.1 introduces details of GCMC simulations to study CO2 adsorption in MOFs. Section 2.2 describes evaluation criteria used to assess CO2 separation potential of MOF adsorbents. Studies on large-scale computational screening of MOF adsorbents are discussed in Section 2.3. Structure-separation performance relations obtained from molecular simulations of MOFs are summarized in Section 2.4. Section 3 closes by addressing the opportunities of using molecular simulations for examining the potential of MOF adsorbents in CO2 separations.
2. Molecular simulations for CO2 separation using MOFs
2.1. GCMC simulations for CO2 adsorption
GCMC is a well-known method to estimate the adsorption equilibria of gases in nanoporous materials. This simulation mainly mimics an adsorption experiment. In an experimental setup, the adsorbed gas is in equilibrium with the gas in the reservoir at fixed temperature, volume, and chemical potential . GCMC simulations are run at an ensemble where the temperature, volume, and chemical potential are kept constant and the number of gas molecules is allowed to fluctuate during the simulation at the imposed temperature and chemical potential. The output of a GCMC simulation is the number of adsorbed gas molecules per unit cell of the MOF structure at predetermined temperature and pressure. These simulations provide single-component adsorption isotherms, binary mixture adsorption isotherms, and isosteric heat of adsorptions which are directly comparable with the output of adsorption experiments. In GCMC simulations where only a single-component gas such as CO2 is studied, four different types of moves are considered including translation, rotation, insertion, and deletion of a molecule. In mixture GCMC simulations where a binary gas mixture is considered such as CO2/H2, CO2/CH4, and CO2/N2, another trial move, exchange of molecules is also performed in order to speed up the equilibrium. The adsorbed amounts of each gas component are calculated by specifying pressure, temperature, and composition of the bulk gas mixture in GCMC simulations.
In a typical GCMC simulation of CO2 adsorption in an MOF, CO2 is the adsorbate and MOF is the adsorbent. Adsorbate molecules interact with the MOF atoms and with other adsorbates through dispersive and electrostatic interactions. These interactions are defined using a force field. A force field is the functional form and parameter sets are used to calculate the potential energy of a system of atoms in molecular simulations . There are several potentials such as Lennard-Jones (LJ)  and Morse  potentials. In almost all molecular simulations of gases in MOFs, Lennard-Jones (LJ) potential is used. Results of a GCMC simulation may vary depending on the force field choice. General-purpose force fields such as universal force field (UFF)  and DREIDING force field  have been widely employed for simulations of MOFs. At the early stages of the molecular simulation studies of MOFs, efforts have been made to develop new force fields specific to MOF-gas interactions using quantum-level calculations [31, 32]. Some studies refined the force field parameters to match the predictions of molecular simulations with the available experimental measurements of gas adsorption in MOFs [32–36]. However, considering the large number and variety of MOFs, it is challenging to develop a new force field or refine an existing one for every single MOF. Therefore, generic force fields such as UFF and DREIDING are mostly preferred in molecular simulations of CO2 adsorption in MOFs, especially for large-scale computational screening of MOFs. The reliability of the molecular simulation studies, of course, hinges on the accuracy of the force fields used. Schmidt et al.  computed CO2 adsorption isotherms in a very large number of MOFs using ab initio force fields to probe the accuracy of common force fields. They concluded that there are significant quantitative differences between gas uptakes predicted by generic force fields such as UFF and ab initio force fields, but the force fields predict similar ranking of the MOFs, supporting the further use of generic force fields in large-scale material screening studies.
The LJ potential parameters of CO2 are generally taken from the force field developed by Potoff and Siepmann . A rigid linear triatomic molecule with three charged LJ interaction sites located at each atom is used for CO2 molecules. Partial point charges centered at each LJ site approximately represent the first-order electrostatic and second-order induction interactions. Charge-quadrupole interactions between MOF atoms and CO2 molecules significantly contribute to the adsorption of CO2. It was shown that if these interactions are not taken into account, adsorption isotherms of CO2 molecules in MOFs can be significantly underestimated . In order to compute the electrostatic interactions between CO2 molecules and MOF, partial point charges must be assigned to the MOF atoms. Several different methods are available in the literature to assign partial charges such as density-derived electrostatic and chemical charge (DDEC) method , connectivity-based atom contribution (CBAC) method , extended charge equilibration (EQeq) method , and quantum mechanical methods based on the ChelpG  density functional theory (DFT) calculations. Charges obtained from different methods generally do not agree well with each other. This is acceptable because atomic charges are not experimentally observable and the methods used to derive them depend on the physical phenomenon the charges are intended to be reproduced . A simulated CO2 adsorption isotherm is generally compared with the experimentally measured one to tune the charges if necessary. After atomic models, force fields and charges are defined for CO2 molecules and MOF atoms, GCMC simulations can be carried out to obtain the adsorbed gas amounts. Results of these simulations are directly used to calculate the adsorption-based gas separation potential of MOFs based on several criteria as discussed below.
2.2. Evaluation of MOF adsorbents for CO2 separation
In adsorption-based gas separation processes such as pressure swing adsorption (PSA), selectivity and working capacity of the adsorbent are the two important parameters that define the efficiency of the process [45, 46]. Adsorption selectivity is described as the ratio of mole fractions of gases in the adsorbed phase normalized by the bulk composition of the gas mixture:
Here, x stands for the molar fraction of the adsorbed phase obtained from the GCMC simulations, while y represents the molar fraction of the bulk gas phase. Eq. (1) defines the adsorption selectivity of an MOF adsorbent with respect to component 1, meaning that if selectivity is greater than 1, then the adsorbent is selective for component 1 over 2. Selectivities for CO2/CH4, CO2/H2, and CO2/N2 mixtures are calculated using the results of binary mixture GCMC simulations where 1 is CO2 and 2 is the other gas component in Eq. (1). The bulk gas compositions of CO2/CH4, CO2/H2, and CO2/N2 mixtures are generally set to 50/50, 15/85, and 15/85, respectively, in molecular simulations to represent industrial operating conditions.
Working capacity (ΔN) is described as the difference between the loading amounts of the strongly adsorbed gas at the corresponding adsorption (Nads) and desorption (Ndes) pressures . It is defined in the unit of mol gas per kg of MOF adsorbent. GCMC simulations are performed at specific adsorption and desorption pressures to calculate the working capacity as shown in Eq. (2).
Bae and Snurr  recently suggested some other adsorbent evaluation criteria in addition to selectivity and working capacity. The CO2 uptake of an MOF under adsorption conditions (Ndes), sorbent selection parameter (Ssp), and regenerability (R%) are also considered as adsorbent evaluation criteria to assess the potentials of MOFs in CO2 separation processes such as natural gas purification, landfill gas separation, and CO2 capture from power-plant flue gas. The CO2 uptake of an MOF under adsorption conditions (Nads) is the direct output of GCMC simulations. Sorbent selection parameter (Ssp) is defined as the combination of adsorption selectivity and working capacity. It is used to compare performances of different nanoporous materials in adsorption-based separation processes and is defined as shown in Eq. (3). Here, subscripts 1 and 2 indicate the strongly adsorbed component and the weakly adsorbed component, respectively. In CO2-related mixtures, CO2 is generally the strongly adsorbed component (1), whereas other gases such as CH4 and N2 are weakly adsorbed (2).
Regenerability (R%) is defined as the ratio of working capacity to the amount of the adsorbed gas at the adsorption pressure and it is an important parameter to evaluate the practical usage of an adsorbent for cyclic PSA and vacuum swing adsorption (VSA) processes:
At that point, it is important to mention that none of these criteria are perfect but they are complementary with each other to assess adsorbent potential of MOFs under practical conditions. Bae and Snurr  calculated adsorption selectivity, working capacity, gas uptake capacity, sorbent selection parameter, and regenerability values of several MOFs for adsorption-based separation of CO2/CH4:10/90, CO2/CH4:50/50, and CO2/N2:10/90 mixtures. Although mixtures are considered, they used the experimental single-component adsorption isotherm data from the literature and obtained mixture amounts under adsorption and desorption conditions at the partial pressure of the specific component. In order to investigate the effect of mixture data, Ozturk and Keskin  calculated the same separation properties of MOFs using both single-component and mixture GCMC data. They showed that selectivity calculated from single-component GCMC simulations can be enormously different than the selectivity calculated from mixture GCMC simulations due to strong competition effects between different gas species. Therefore, it is better to characterize adsorbent materials based on their performance for mixed-gas feeds to reflect the real operation conditions .
Llewellyn et al.  recently suggested a new criterion named as adsorbent performance indicator (API) as shown in Eq. (5) to initially highlight porous materials of potential interest for PSA processes. This indicator takes into account working capacity (represented as WC in Eq. (5)), adsorption energy (ΔHads,1) of the most adsorbed species, and selectivity (Sads). It additionally uses weighting factors to reflect the specific requirements of a given process.
They calculated APIs of seven MOFs for two different CO2/CH4 separation scenarios using the experimental gas adsorption data . Results showed that API can be more versatile than previously discussed comparison criteria for an initial indication of potential adsorbent performance.
2.3. Performance of MOFs in CO2 separations
It is beyond the scope of this chapter to give a complete account of all GCMC studies of MOFs for CO2 separation. Several molecular simulation studies examined a single MOF or a few MOFs at a time [50–59]. Most of these studies focused on adsorption-based separation of CO2 using the two most widely studied MOFs, MOF-5 and CuBTC [60–64]. This section will focus on molecular simulation studies that examine a family of MOFs for adsorption-based CO2 separations and large-scale computational screening studies to provide a relation between structure and separation performance of MOFs.
IRMOFs are isoreticular MOFs. The “IR” stands for isoreticular, which essentially means that the molecular system is “stitched together” into a netlike structure through strong chemical bonds. Molecular simulations were used to compare the separation of CO2/N2 mixtures in two different classes of nanoporous materials, traditional zeolites (MFI, LTA, and DDR) and MOFs (IRMOF-1, -11, -12, -13, -14, CuBTC, and MIL-47 (V)) . Results showed that although MOFs perform much better for gas storage than zeolites, their CO2 separation performance is comparable to zeolites with adsorption selectivities in the range of 5–35. Krishna and van Baten  used configurational-bias Monte Carlo (CBMC) simulations to examine zeolites and IRMOF-1, MOF-177, rho-ZMOF, CuBTC, ZnMOF-74, and MgMOF-74 for separation of CO2/CH4, CO2/N2, and CO2/H2 mixtures using PSA units. The best CO2 capture performance was obtained with MgMOF-74 that offers strong electrostatic interactions of CO2 molecules with the exposed metal cation sites. Selectivity of MgMOF-74 was reported as ∼300, 50, and 10 for CO2/H2, CO2/N2, and CO2/CH4 separations, respectively. Traditional zeolite adsorbents such as NaX and NaY show higher adsorption selectivities for these gas separations but these two zeolites suffer from relatively low working capacities that are important in PSA units. For CO2/N2 and CO2/H2 separation in PSA units, MgMOF-74 was found to offer the best combination of high adsorption selectivity and high working capacity. Han et al.  used GCMC simulations with first-principles-based force fields to report the effects of interpenetration on the CO2/H2 separation of MOFs. Non-interpenetrating IRMOF-1, -7, -8, -10, -14, -16, MOF-177, and MOF-200 and interpenetrating IRMOF-9, -13, -62, and SUMOF-4 were considered for comparison. For example, IRMOF-9 and IRMOF-13 are interpenetrating versions of IRMOF-10 and -14, respectively. The interpenetration of MOFs at low pressure remarkably enhanced the selectivity of CO2 over H2 by creating new adsorption sites for CO2. However, selectivity of the interpenetrating and non-interpenetrating MOFs was reversed at higher pressures. Since interpenetration lowers the pore volume of MOFs, it significantly reduced CO2 uptake at high pressures. The decrease in the H2 uptake resulting from interpenetration was found to be marginal. Therefore, selectivity of the interpenetrating MOFs was reported to be lower than that of non-interpenetrating MOFs at high pressures.
Zeolitic imidazolate frameworks (ZIFs) are composed of tetrahedral networks that resemble those of zeolites with transition metals connected by imidazolate ligands. Zeolites are known with the Al(Si)O2 unit formula, whereas ZIFs are recognized by M(Im)2, where M is the transition metal and Im is the imidazolate-type linker. Battisti et al.  calculated CO2/CH4, CO2/H2, and CO2/N2 adsorption selectivity in the zero-pressure limit for nine ZIFs, ZIF-2, -3, -4, -5, -6, -7, -8, -9, and -10 using GCMC simulations. These ZIFs were characterized by pores of medium to small size compared to other MOFs. Therefore, they were able to store at most half of the amount of gases than other MOFs. ZIF-7 and ZIF-9 were shown to be promising due to their high adsorption selectivities of 280 and 15 for CO2/H2 and CO2/N2 separations, respectively. Atci and Keskin  used GCMC simulations to predict the performance of 15 different ZIFs (ZIF-1, -2, -3, -6, -8, -10, -60, -65, -67, -68, -69, -70, -79, -81, and -90) in both adsorption-based and membrane-based separations of CH4/H2, CO2/CH4, and CO2/H2 mixtures. Adsorption selectivity, working capacity, membrane selectivity, and gas permeability of ZIFs were predicted using GCMC and molecular dynamics simulations. Figure 1 compares adsorption selectivities and working capacities (shown as delta loadings) of ZIFs calculated at an adsorption pressure of 10 bar and desorption pressure of 1 bar with the data for zeolites and MOFs . Several ZIFs were identified to outperform traditional zeolites and widely studied MOFs in CO2/CH4 and CO2/H2 separations. Keskin’s group  also calculated adsorption of both single-component gases (CH4, CO2, H2, and N2) and binary gas mixtures (CO2/CH4, CO2/N2, and CO2/H2) using GCMC simulations and predicted the ideal and mixture adsorption selectivities of ZIFs. They showed that the adsorption selectivity calculated from mixture GCMC simulations can be significantly higher than the ideal adsorption selectivity calculated from single-component adsorption isotherms. This result highlighted the importance of using mixture selectivity to assess the performance of MOF adsorbents.
The calculated adsorption selectivity of ZIFs may vary significantly depending on the force field parameters used in molecular simulations . Generic force fields generally tend to overestimate gas adsorption capacities; hence, adsorption selectivities of ZIF-68 and ZIF-69 compared to the tailored-force fields. However, the difference between predicted adsorption selectivities of different force fields is not high enough to change the assessment about the separation performance of the material. Both generic and tailored-force fields were able to identify the promising adsorbent materials that exhibit high adsorption selectivities. In other words, generic force fields can be safely used to screen large number of MOFs to differentiate between the promising and non-promising materials.
MOFs are also referred as porous coordination networks (PCNs) in the literature and several synthesized materials have been named as PCNs . Ozturk and Keskin  studied 20 different PCNs (PCN-6, 6’, 9-Co, 9-Mn, 9-Fe, 10, 11, 13, 14, 16, 16’, 18, 19, 20, 26, 39, 46, 80, 131’, and 224-Ni) using molecular simulations to identify the most promising adsorbent and membrane candidates for CO2/H2, CO2/CH4, and CO2/N2 mixtures. PCN-9-Co, -9-Mn, -14, and -16 were found to be strong adsorbents for CO2 capture, especially for CO2/CH4 separations because of their high working capacities. They also developed a simple model that can predict adsorption selectivities of PCNs for CO2/H2 mixtures without performing extensive molecular simulations. The model was based on the structural and chemical properties of the materials that can be simply measured or computed, such as pore volume, surface area, and the inverse of difference of heat of adsorption of components in the mixture. Predictions of the model for adsorbent selectivities were found to be in good agreement with the direct results of detailed molecular simulations.
Covalent organic frameworks (COFs) are not strictly MOFs but similar materials. They are formed by building units linked into a periodic framework but in contrast to MOFs, all components are organic in COFs. Zhong’s group  examined a diverse set of 46 COFs to predict their separation performance for industrial gas mixtures, CO2/H2 and CO2/CH4, using PSA process. Results show that COFs outperform most commonly used zeolites and widely studied MOFs in the separation of CH4/H2 while they have a comparable performance in separating CO2/H2 and CO2/CH4. The same group then studied the performance of 151 MOFs with large chemical and topological diversity for CO2/CH4 separation for temperature swing adsorption (TSA) process . The thermal regeneration energy was used as an evaluation criterion in addition to adsorption selectivity, working capacity, and regenerability. Cu-TDPAT and IRMOF-1-2Li MOFs were reported as the most promising candidates for CO2/CH4 separation in TSA processes based on the ranking of the materials according to the four evaluation criteria. Cu-TDPAT was identified as the best adsorbent candidate because of its high thermal stability and water-stable property.
2.3.5. Large-scale screening of MOFs
In 2012, Sholl’s group  used GCMC simulations to calculate adsorption of CO2 and N2 in 500 different MOFs. This was the largest set of structures for which this information has been reported until 2012. Adsorption selectivities of MOFs were calculated using Henry’s constant at infinite dilute loading. More detailed calculations such as quantum chemistry methods and binary mixture GCMC simulations were then carried out to assess adsorption selectivities of highly promising MOFs. Watanabe and Sholl  later on screened a larger number of MOFs for CO2/N2 separation. They first analyzed pore characteristics of 1163 MOFs using a simple steric model developed by Haldoupis et al. . Adsorption selectivity of the selected 201 MOFs was calculated using single-component GCMC simulations at infinite dilute loading. Selectivities were plotted as a function of largest cavity diameter (LCD) of MOFs as shown in Figure 2. This figure demonstrates that MOFs are promising materials for CO2/N2 separations. There is a significant number of MOFs with high selectivities of 100–1000. A small number of materials have extremely high adsorption selectivities, greater than 1000. Selectivities of the top 10 promising MOFs were also computed considering CO2/N2:15/85 mixture and results showed that CO2/N2 selectivities of MOFs remained high even for binary gas mixtures with the composition of dry flue gas.
Lin et al.  screened hundreds of thousands of hypothetical zeolite and ZIF structures for CO2 capture from flue gas. They determined the optimal process conditions of each material by minimizing the electric load imposed on a power plant by a temperature-pressure swing capture process using that material followed by compression. This minimum load was called as parasitic energy and it was introduced as a metric to compare different materials. Results of that study showed that parasitic energy for ZIFs is higher than for zeolites. Wilmer et al.  drastically expanded the scope of previous MOF screening studies by examining over 130,000 hypothetical MOFs. They used molecular simulation to calculate adsorption selectivity, working capacity, regenerability, and sorbent selection parameter of MOFs for CO2/CH4 and CO2/N2 separations. Single-component GCMC simulations to obtain the pure component CO2, CH4, and N2 adsorption data are required to calculate the five adsorbent evaluation criteria. The resulting simulation data exhibited sharply defined structure-property relationships as we will discuss in Section 2.4. These type of relationships were not apparent when smaller collections of MOFs were studied in the previous works, indicating that screening large number of MOFs is important to understand the effect of structure on the gas separation performance of MOFs.
2.3.6. Breakthrough calculations
We so far discussed the molecular simulation studies in the literature that mimic a classical adsorption experiment. Other than isotherm experiments, breakthrough experiments are also carried out on nanoporous adsorbents in order to investigate the materials’ kinetics. However, these experiments are labor-intensive and can present a range of technical challenges to achieve accurate results. Krishna and Long  suggested a new metric, breakthrough time (τbreak), that is based on the analysis of the transient response of an adsorber to a step input of a gaseous mixture. This metric determines the frequency of required regeneration of an adsorbent. High value of τbreak is desirable in practice because it reduces the frequency of required regeneration. Breakthrough calculations were done for separation of CO2/H2, CO2/CH4, and CO2/CH4/H2 mixtures using five MOFs, MgMOF-74, CuBTTri, MOF-177, BeBTB, and Co(BDP) and results were compared with traditional zeolites. MgMOF-74 emerged as the best material from the viewpoints of both frequency of regeneration and productivity. The advantage of MgMOF-74 over traditionally used NaX zeolite was found to be evident at pressures exceeding 10 bar. Krishna and van Baten  later studied breakthrough characteristics of an adsorber packed with a number of zeolites (MFI, JBW, AFX, and NaX) and MOFs (MgMOF-74, MOF-177, and CuBTTri-mmen) for CO2 capture from a CO2/N2 mixture. These calculations demonstrated that high capacities could have a dominant influence on the overall performance of PSA units. MgMOF-74 was again identified as a promising adsorbent with a CO2 capture capacity more than twice that of other materials investigated. For separation of CO2/H2, CO2/CH4, and CH4/H2 mixtures, Jiang’s group  recently studied seven different rht-MOFs namely Cu-TDPAT, PCN-61,-66,-68, NOTT-112, NU-111, and NU-110. These MOFs have the same rht topology with different ligands. The breakthrough profiles for CO2-containing mixtures were predicted from the simulation results. Due to the presence of small ligands, unsaturated metals, and amine groups, Cu-TDPAT was found to exhibit the highest adsorption capacity and separation performance among the seven rht-MOFs. Upon substituting the phenyl rings in Cu-TDPAT by pyridine rings, Cu-TDPAT-N was designed and the breakthrough time for CO2 in Cu-TDPAT-N was found to be extended by twofold. This result shows the importance of understanding structure-separation performance relations for MOFs as we discuss below.
2.4. Structure-performance relations
High-throughput computational screening is a very useful approach to identify promising MOF materials for gas separation applications and to uncover structure-property relations . With the development of new computational methodologies, it is now easier to perform large-scale computational screening studies where the properties of thousands of MOF candidates can be evaluated and compared. When this type of large-scale MOF screening is performed, a large amount of data is produced and used to investigate correlations between MOFs’ structural properties and their gas separation performances.
Maurin’s group  used molecular simulations to examine separation performance of 105 MOFs with a large chemical and topological diversity for CO2 capture from flue gas under industrial operating conditions. They developed a quantitative structure-property relationship (QSPR) model from this extended series of MOFs to rationalize the resulting CO2/N2 selectivity. The difference of isosteric heats of adsorption between CO2 and N2 at infinite dilution (ΔQst0) and porosity (ϕ) were found to be the main features of the MOFs that strongly impact the CO2/N2 adsorption selectivity at 1 bar. Figure 3 shows the interplay map of these two factors on the calculated CO2/N2 adsorption selectivity. Results of QSPR analysis suggested that increasing ΔQst0 and simultaneously decreasing ϕ seems to be an appropriate route to enhance the CO2/N2 selectivity of MOFs. Motivated from this structure-performance relation, a new functionalized MOF, UiO-66(Zr)-(SO3H)2, was computationally designed and predicted to exhibit a high CO2/N2 selectivity as shown in Figure 3.
The CO2 separation potential of a new class of porous aromatic frameworks (PAFs) with diamond-like structure was studied by molecular simulations . It was discussed that selectivity might be only determined by the difference of the gas-material interactions of the mixtures at a pressure close to zero. The CO2/H2, CO2/N2, and CO2/CH4 selectivities and the difference of isosteric heats (ΔQst0) were calculated at the pressure close to zero. The ΔQst0 was found to be linear with the logarithm of the selectivity no matter what the gas mixtures and materials were. This result suggested that at zero pressure the selectivity is only dependent on the values of ΔQst0 and is independent of the type of the gases and the materials. With the increase of ΔQst0, the selectivity increases correspondingly, which means that the ΔQst0 can be used instead of the selectivity to screen out the promising nanoporous materials for gas separation. Finding a correlation between adsorption selectivity and ΔQst0 is useful. However, it is difficult to design new MOF materials that have a priori chosen Qst value. It is easier to design materials based on measurable structural properties such as porosity, pore size, or surface area. Wilmer et al.  studied a very large number of hypothetical MOFs and showed clear correlations between purely structural characteristics such as pore size, surface area, and pore volume as well as chemical characteristics such as functional groups with five adsorbent evaluation criteria listed in Section 2.2. For example, it was shown that adsorption selectivity correlates well with the maximum pore diameter for flue gas separation. Adsorption selectivity also correlates with the heat of adsorption of CO2 for flue gas and natural gas separation. Certain chemical functional groups, particularly those with fluorine and chlorine atoms, were frequently found among the best performing MOF adsorbents. These type of structure-property relationships can be used as a guide for experimental MOF synthesis studies.
In a recent study, in silico screening of 4764 MOFs was performed for adsorption-based CO2/CH4 and CO2/N2 separations . Quantitative relations between the metal type and adsorbent properties such as selectivity, working capacity, and regenerability were investigated for the first time in the literature. A wide variety of metals exists in MOFs such as alkalis, alkalines, lanthanides (Ln), and transition metals. Figure 4 shows the probabilities of different metals in the selected MOFs based on their selectivity and working capacity for CO2/CH4 and CO2/N2 separations. For instance, the probability of K is about 0.8 for CO2/N2 separation, meaning that 80% of K-based MOFs show high selectivity and working capacity. Combining selectivity, working capacity, and regenerability, however, alkali- and alkaline-MOFs possess the lowest performance for CO2 separation. Among 4764 MOFs, about 1000 were found to contain Ln metals, 50% contain Ln as open metal sites. These open metal sites have high adsorption affinity for CO2; therefore, MOFs with Ln metals have the highest CO2 separation performance. The 30 best candidates identified for CO2/CH4 and CO2/N2 separations have Ln metals. These results can be used to synthesize MOFs having predetermined metal atoms to enhance the CO2 separation performance of materials.
As can be seen from this literature review, current studies have generally focused on establishing relations between adsorption selectivity and a single chemical or structural property such as difference of isosteric heat of adsorption of gases or metal type. However, separation performances of materials are determined by the interplay of various factors and cannot be easily correlated to only one or two properties. All physical and chemical properties of MOFs including pore size, shape, porosity, surface area, topology, metal and organic linker type must be considered to better understand structure-performance relations. Deriving structure-performance relations for MOFs is a new and developing research area and more studies in this area will be valuable to synthesize new MOFs with useful physical and chemical properties to achieve targeted gas separations.
3. Conclusion and outlook
Molecular simulations are very useful to quickly evaluate the potential of new MOF materials in adsorption-based gas separation processes. The outcome of molecular simulations can be used as a guide to design and develop new materials with enhanced separation properties. There is a continuous growth in the number of molecular simulation studies of MOFs for adsorption-based CO2 separations. However, there are still several open areas in which future studies will be valuable. Opportunities and challenges related with these open research areas are discussed below:
3.1. Computational design of new materials
Strategies to improve the ability of MOFs to selectively adsorb CO2 are reviewed in detail in the literature . Some of these strategies are control of pore size, using materials with open metal sites, introduction of alkali-metal cations into MOFs, interpenetration, and using materials with polar functional groups [45, 88]. Among these, rational design of functionalized materials is a feasible way to improve the CO2 separation efficiency of MOFs. GCMC simulations were recently used to study the effect of amine functionalization on the CO2/CH4 separation performance of MIL-53 . Results showed that CO2/CH4 separation factor of −(NH2)4 amine-functionalized MIL-53 is the best and predicted separation performance of −NH2 and −NHCO functionalized MIL-53 surpasses that of the original one. Future molecular simulation studies examining the effects of functionalization on the separation performance of MOFs will be very useful to establish guidelines for the experimental design and development of new materials.
3.2. Considering impurities in CO2-related mixtures
As discussed in Section 2.3., most molecular simulation studies of MOFs focus on the separation of CO2 from its binary mixtures such as CO2/CH4 and CO2/N2. However, in reality, these gas mixtures include some impurities. Water and the other minor components mostly H2O, O2, SO2, and NOx cannot be ignored in assessing the performance of MOFs especially for post-combustion CO2 capture. However, the number of molecular simulation studies examining the effects of trace gases on the CO2/N2 and CO2/CH4 separation performance of MOFs is limited. Bahamon and Vega  recently used GCMC simulations to study 11 materials including zeolites and MOFs for separation of CO2 from N2, including water as an impurity. Sun et al.  studied 12 materials including MOFs, ZIFs, and zeolites for removal of SO2 and NOx from flue gas using GCMC simulations. The influences of water and SO2 on CO2 adsorption and separation in UiO-66(Zr) MOFs with different functional groups were evaluated using a combination of GCMC and DFT simulations . Babarao et al.  considered small amounts of O2, H2O, and SO2 impurities typically found in flue gas and evaluated the CO2/N2 selectivity of four PCNs in the presence of these impurities. Zhong’s group  used molecular simulations to investigate the effect of trace amount of water on CO2 capture in natural gas upgrading process in a diverse collection of 25 MOFs. These studies concluded that the effect of H2O impurities on the CO2 selectivity is highly specific to the chemistry of the framework and needs to be evaluated on an individual case-by-case basis. The CO2 selectivity of MOFs was generally reported to decrease in the presence of water. Future studies on GCMC simulations of MOFs considering impurities in CO2-related mixtures must be conducted to evaluate the potential use of MOFs in industrial CO2 capture processes.
3.3. Multi-scale modeling
While CO2 separation using MOF adsorbents has been extensively investigated in different MOFs, their performance under practical process conditions is scarcely examined. A multi-scale modeling study was recently carried out to examine CO2 capture from flue gas by vacuum swing adsorption (VSA) process using rho-ZMOFs as adsorbents . The full adsorption process was simulated and optimized and results showed that the operating spaces of rho-ZMOFs are similar to that of traditional 13X zeolite. Further studies that employ multi-scale modeling approaches will be useful to design and develop MOF-based industrial CO2 separation processes. A related point is to test the long-term stability of MOF adsorbents under industrial operating conditions. An ideal MOF adsorbent must have good thermal and mechanical stability. Several MOFs are sensitive to atmospheric moisture and lose their crystal structures when exposed to water. This may be a significant problem when MOFs are used as adsorbents in flue gas separations since flue gas contains water. Molecular simulation studies that can provide information about the long-term stability of MOF adsorbents will be useful to evaluate the real performance of MOFs.