Understanding CO2/CH4 Separation in Pristine and Defective 2D MOF CuBDC Nanosheets via Nonequilibrium Molecular Dynamics

The separation of CO2/CH4 gas mixtures is a key challenge for the energy sector and is essential for the efficient upgrading of natural gas and biogas. A new emerging field, that of metal–organic framework nanosheets (MONs), has shown the potential to outperform conventional separation methods and bulk metal–organic frameworks (MOFs). In this work, we model the CO2/CH4 separation in both defect-free and defective 2D CuBDC nanosheets and compare their performance with the bulk CuBDC MOF and experimental data. We report the results of external force nonequilibrium molecular dynamics (EF-NEMD) for pure components and binary mixtures. The EF-NEMD simulations reveal a pore blocking separation mechanism, in which the CO2 molecules occupy adsorption sites and significantly restrict the diffusion of CH4. The MON structure achieves a better selectivity of CO2 over CH4 compared to the bulk CuBDC MOF which is due to the mass transfer resistance of the methane molecules on the surface of the nanosheet. Our results show that it is essential to consider the real mixture in these systems rather than relying solely on pure component data and ideal selectivity. Furthermore, the separation is shown to be sensitive to the presence of missing linker defects in the nanosheets. Only 10% of missing linkers result in nonselective nanosheets. Hence, the importance of a defect-free synthetic method for CuBDC nanosheets is underlined.

■ INTRODUCTION CO 2 /CH 4 gas mixtures are present in natural gas and biogas. 1,2 Removing carbon dioxide from methane is important as it will result in a more energy dense product, given that methane is rich in calorific energy while carbon dioxide has no heating value. Furthermore, CO 2 is known to cause pipe corrosion in industry in the presence of water as it forms acidic solutions. 3 Current technologies for carbon dioxide removal include the usage of liquid solvents. However, they are energy demanding and costly. 1 Polymeric membranes are also commercially used, but they can suffer from drawbacks such as low permeability and selectivity and insufficient chemical and thermal stability. 4 A trade-off between selectivity and permeability exists for polymeric membranes. Increasing the value of one would decrease the value of the other, which is described as Robeson's upper bound. 5,6 A class of porous, crystalline nanomaterials named metal−organic frameworks (MOFs) has been studied extensively over the past years. 7−9 MOFs are composed of metal nodes connected by organic ligands. They are easily tunable by altering these building blocks, which results in a wide range of topologies and pore openings. 10 They demonstrate high surface areas, pore volumes, and high gas uptake that make them great candidates for a range of applications, including gas separations. 11−14 There are reports in the literature that their 2D MOF nanosheet (MON) counterparts outperform them by demonstrating higher selectivity and high permeability. 14 −16 In contrast with isotropic, 3D bulk MOFs, MONs are anisotropic, free-standing 2D MOF structures. 17 One of the dimensions (thickness) of the MONs is within the nanoscale while the other dimensions are in the microscale. The orders of magnitude difference in one dimension results in their characterization as 2D. In recent years, there has been an increasing number of publications on MON fabrication and utilization for gas separations. In 2017, Peng et al. synthesized Zn 2 (Bim) 3 MOF nanosheets for the separation of CO 2 /H 2 mixtures with a separation factor of up to 166. 18 Thermoswitchable 2D nanosheets of various thickness were synthesized by Wang et al. for the separation of CO 2 /H 2 mixtures, and a separation factor ranging from 34 to 235 was observed. 19 In 2015, Rodenas et al. reported that 2D CuBDC nanosheets were incorporated into polyimide (PI) matrix for the formation of 30−50 μm thick mixed matrix membranes (MMM) which achieved a separation of CO 2 over CH 4 with a selectivity 8 times higher than the isotropic 3D bulk CuBDC MOF and 30−80% higher than the polymer solely. 20 The thickness of the nanosheets ranged from 5 to 25 nm, and the other dimensions were in the microscale. The researchers observed an unexpected increase in selectivity with increasing pressure drop which was attributed to the polymer's swelling from CO 2 adsorption. Despite the high selectivity value of 80 observed for the MMM when the 2D nanosheet was used as the filler, the permeability values were very low (around 10 barrer), limiting the overall performance under Robeson's upper bound. Yang et al. resynthesized CuBDC nanosheets, but they incorporated them in 6FDA-DAM and PIM-1 polymers for the formation of 40 nm thick MMM. 21 2− 4 wt % CuBDC nanosheet loading was dispersed into the polymers. For the 6FDA-DAM polymer, when 2 wt % MON was added, the selectivity increased from 30 to 37 for an equimolar CO 2 /CH 4 gas mixture. When a 4 wt % was reached, the selectivity increased to 43. The same loading range was applied to PIM-1, and an initial increase from 17 to 24 was observed while no further increase was possible which was attributed to defects. In this study a permeability of around 10000 barrer was observed for carbon dioxide which was an overall performance above Robeson's upper bound, and the separation mechanism was assumed to be a molecular sieving effect. The differences observed in selectivity and permeability when pairing CuBDC nanosheets with different polymers for the formation of MMM give rise to the question: What is the contribution of the CuBDC MONs to the separation?
The implementation of MONs in MMM is a rapidly growing field. 17 MONs can be synthesized in a top-down or bottom-up approach. In the top-down method, the 3D bulk MOF is sliced while in the bottom-up approach the building components of the MOF follow a self-assembly process to form an anisotropic 2D nanosheet. Both methods in theory should result in the same structure, but the latter one is preferred to reduce the prevalence of defects. There are no defect-free MOFs, however. A variety of defect types are possible, which might occur as the result of the synthesis process. In 2013, Wu et al. proved that in a UiO-66 sample 10% of the linkers were missing. By controlling the synthesis conditions, the researchers could tune the linker vacancies and increase the CO 2 uptake in the MOF. 22 Defects can be both desirable and undesirable, depending on the application. 23,24 For decades, researchers have been modeling ideal crystals, and only a few papers have addressed the presence of defects. Thornton et al. investigated CO 2 adsorption in both defectfree and defective UiO-66 MOF. The researchers concluded that at high pressures the uptake is enhanced with increasing defect concentration, but the mechanical stability was reduced. 25 In 2015, Sarkisov explored the impact of a number of different types of defects in IRMOF-1 for argon adsorption and geometric characteristic changes of the structure. The study showed that up to 20% of missing linkers had no impact on the adsorption isotherm. 26 While molecular simulations on bulk MOFs have advanced considerably, 27,28 computational work on 2D MOFs for gas separations is more scarce. 29 Equilibrium molecular dynamics (EMD) combined with grand canonical Monte Carlo (GCMC) simulations can be used to calculate the uptake and the permeability of gases (and gas mixtures) in framework structures. 30−32 However, these simulations are typically performed by using the 3D bulk MOF, assuming that the 2D MOF nanosheet will have similar adsorption and diffusion properties. Thus, surface effects are (c) CuBDC nanosheet structure. The coloring scheme is as follows: red, oxygen atoms; orange, copper atoms; gray, carbon atoms; black, hydrogen atoms.
Langmuir pubs.acs.org/Langmuir Article neglected, missing the mass transfer resistance on the surface and the pore window of the MOF. 33 In addition, the different possible directions of growth for a 2D MOF nanosheet or different surface saturations may not be considered. An additional major drawback of this approach is the absence of a driving force, such as a pressure gradient, which will be present when the separation is performed in an industrial context. For a more thorough study, nonequilibrium molecular dynamics (NEMD) is better suited. NEMD can directly calculate gas permeabilities by using explicitly a MOF nanosheet structure under a pressure gradient and allow for adsorption, desorption, and diffusion phenomena to occur. There are different NEMD methods, such as external force NEMD (EF-NEMD), the piston approach or moving walls, and the dual control volume grand canonical molecular dynamics (DCV-GCMD). These methods have been applied in several scientific fields, 34−36 such as water purification from heavy metals with MOF membranes. 37 In 2016, Richard et al. compared the results from EF-NEMD to moving walls for water transport through a hydrophilic silica nanochannel and concluded that both methods provided similar results. 38 Frentrup et al. used EF-NEMD to calculate CO 2 and He permeabilities through a polymeric membrane, PIM-1, and good agreement with the experiments was observed. 39 In 2019, Velioglu and Keskin implemented an EF-NEMD for the separation of a H 2 /CH 4 mixture with MOF nanosheets and compared their results to EMD and GCMC simulations with the former method achieving a better agreement with the experimental data. 40 To the best of our knowledge, this work is the first computational study evaluating the impact of defects in 2D MOF nanosheets by using a NEMD method for a gas separation application. More specifically, in this work we use EF-NEMD simulations for CO 2 /CH 4 separation with CuBDC nanosheets and compare the results to experimental work. 20,21 Only the MOF nanosheet contribution in the separation is evaluated, while the nanosheets were dispersed in polymers during the experimental work. NEMD simulations confirm that the separation is selective toward CO 2 and reveal that it is achieved through a pore blocking mechanism, wherein the CO 2 molecules occupy the majority of the adsorption sites and they diffuse slower than CH 4 molecules inside the nanosheet. The performance of the 2D CuBDC nanosheets was found to be better than the 3D bulk MOF material. The performance of the nanosheets depends strongly on the synthetic quality of the material, with the material found to be nonselective at missing linker defect concentrations as low as 10% and selective toward methane for defect concentrations of 20%.
■ METHODOLOGY Structure Generation. Copper terephthalate also known as CuBDC was first synthesized by Mori et al., but no structure was provided. 41 It was not until 2014 when Carson et al. resynthesized the MOF with a solvent exchange technique 42 and reported a structure that can now be found in the Cambridge Structural Database. 43 CuBDC consists of copper paddlewheel metal nodes connected with 1,4-benzenedicarboxylate organic ligands which form 1D pore channels with 5.2 Å diameter as shown in Figure 1a. Rodenas et al. used a bottom-up technique to synthesize 2D CuBDC nanosheets which were expanded in the direction of the 1D channels (xdirection), and 5−25 nm thick nanosheets were produced. 20 In this work we study the bulk MOF, 5 nm thick nanosheets to represent the MON, and defective CuBDC MONs. The CuBDC structure reported by Carson et al. 42 was used as the starting point for simulations of the 3D bulk MOF, while the structure was expanded in the x-direction as indicated by the experimental work 20 to generate 5 nm thick CuBDC nanosheets. A 2 nm vacuum was added on either side of the 5 nm thick nanosheet (Figure 1c), which is sufficient to eliminate finite size effects in this case ( Figure S10).
Unsaturated atoms of the MON surface after expansion were saturated with hydrogen atoms. A number of other common surface saturations were also investigated (acetate, carboxylic acid, and hydroxyl groups). The surface saturation was found to have a negligible impact on the separation (see the Supporting Information), and thus only the hydrogen saturation is presented and discussed in subsequent sections. The software used was CrystalMaker. 44 Defective MONs were also generated. The defects were in the form of missing linkers. Using the already generated CuBDC nanosheet structure of Figure 1c, we removed sequentially BDC linkers to generate defective CuBDC MONs. Defective systems were generated where 5%, 10%, and 20% of the organic ligands were missing from the structure. In the case of 5% and 10% defect concentrations, it is possible to vary the location of the defects ( Figure S17). For every BDC ligand removed, four hydroxy groups were added to saturate the broken bonds following the methodology applied by Ghosh et al. 45 Example defective structures can be seen in Figure 2.
Charge Generation. Mulliken charges were used and generated at the DFT level using the Gaussian and plane wave method (GPW) for the CuBDC bulk MOF, the MON, and the defective structures. 46 The generalized gradient functional PBE and the Goedecker−Teter−Hutter pseudopotentials were applied. 47,48 The basis set used was DZVP-MOLOPT-SR-GTH. 49 A cutoff energy of 600 Ry was used for the plane wave basis. Periodic boundary conditions in every direction were used to take into account the crystalline nature of the nanosheet. The calculations were completed with the Quickstep code of CP2K software. 50,51 It has been previously shown that the choice of calculation method for partial atomic charges can have an effect on the simulated adsorption isotherm. 52 To evaluate the impact of partial charges, EF-NEMD simulations of CH 4 −CO 2 mixture diffusion were undertaken by using the semiempirical EQeq charge method. 53 Simulated permeabilities and selectivity from each partial charge method were found to be within margin of error of each other (Figures S15 and S16).
EF-NEMD Simulations. In this work EF-NEMD was applied to model CO 2 /CH 4 separation with bulk CuBDC MOF, ideal and defective CuBDC nanosheets, to mimic the experimental setup. 20 For all simulations the UFF4MOF force field was used for the MOF atoms, and all MOF structures were fully flexible. 54 The elementary physical model 2 (EPM2) was used to model carbon dioxide 55 and TraPPE for methane. 56 All simulations were performed by using the GROMACS software package. 57 The topology file needed for GROMACS was generated by using OBGMX software. 58 While there are no open metal sites (OMS) inside the nanosheet, there are OMS on the surface, and the interaction of CO 2 with these sites will not be captured accurately by the force fields used in this work. 59−61 It has been shown that simulated isotherms of carbon dioxide in MOFs with OMS can be estimated with good accuracy if the density of the OMS is Langmuir pubs.acs.org/Langmuir Article relatively low. 62,63 The researchers found that the OMS−guest molecule interaction is important when the ratio of the two approaches is 1:1. In the present work, the ratio of OMS:CO 2 molecules is 1:3.7, and the OMS−CO 2 interaction is likely to be less influential than CO 2 −MOF, CO 2 −CO 2 , and CH 4 − CO 2 interactions. Nevertheless, the accurate and CPU-efficient modeling of CO 2 −OMS systems in NEMD simulations remains a challenge for future work. EF-NEMD simulations for an equimolar mixture of CO 2 / CH 4 were completed for the nanosheets (ideal and defective) and the bulk MOF. For the ideal nanosheet only, pure component simulations were also completed. In every case, the system was initially prepared following the same procedure. Gas molecules were randomly inserted into the simulation box, which also contained the framework structure. For all pure component calculations, 90 molecules were used for each species. In the case of all mixture simulations, 90 CO 2 and 90 CH 4 molecules were inserted. An energy minimization of the system was performed with a 100 kJ mol −1 nm −1 maximum force allowed to avoid any unphysical insertions. A 500 ps NVT equilibration followed to saturate the nanosheet and prepare the system for a NEMD simulation. A time step of 1 fs was used. The temperature was 298 K, and the v-rescale thermostat 64 was used for the entire system with a coupling time constant of 1 ps. A cutoff of 1.2 nm was used for the nonbonded interaction. From this equilibration step, it was estimated that the gas loading corresponded to 1.6 bar pressure based on grand canonical Monte Carlo (GCMC) calculations for an equimolar CO 2 /CH 4 mixture (refer to the Supporting Information for GCMC details). The same pressure was used to estimate the loading of the bulk MOF from GCMC and an energy minimization and NVT equilibration followed with the same parameters. For the defective nanosheets the same number of guest molecules as the ideal nanosheet structure was used for the equimolar mixture, as a negligible change in uptake was observed from GCMC calculations for defect concentrations up to 20% ( Figure S3).
After the equilibration step, for every case EF-NEMD was run for 10 ns in the NVT ensemble by using a time step of 1 fs. The Nose−Hoover thermostat was applied with a coupling time constant of 1 ps. For the nonbonded interactions, a cutoff of 1.5 nm was applied. To prevent the structures (nanosheet and bulk) from drifting due to the rescaling of the velocities (a phenomenon which is known as the flying ice cube which is related to the thermostat and is an MD artifact 65 ), the centerof-mass translation velocity of the structure was removed.
The first 2 ns of each trajectory was ignored, allowing the system to reach steady state, and the last 8 ns was used for data analysis. Three trajectories were analyzed for every EF-NEMD simulation. An external force f i in the x-direction which is perpendicular in the stacking direction and parallel to the 1D pore channels of the structure was applied as shown in Figure  3. This force ranges from 0.024 to 0.11 kJ mol −1 Å −1 for the nanosheet and 0.017−0.077 kJ mol −1 Å −1 for the bulk MOF and was applied on every guest molecule of the system, causing a pressure drop ΔP from 4.5 to 20 bar, calculated from eq 1 N is the total number of molecules where f i was applied on, and A box is the surface area of the simulation box. The same method for the calculation of the pressure drop was applied by Richard et al. 38 Guest molecules were allowed to reflux as periodic boundary conditions were applied in every direction. Guest molecules leaving the box from the right would re-enter from the left, and because of the pressure drop across the structure (nanosheet or bulk), a steady-state flux occurred. A similar approach was correspond to 5%, 10%, and 20% missing linker structures, respectively. The coloring scheme is as follows: red, oxygen atoms; orange, copper atoms; gray, carbon atoms; black, hydrogen atoms. Figure 3. A force f i is applied on every guest molecule in the xdirection. The green color corresponds to CO 2 molecules while the red and the gray correspond to CH 4 molecules and MOF atoms, respectively. Langmuir pubs.acs.org/Langmuir Article followed by Frentrup et al. 39 The flux of each species J i was measured from eq 2. (2) N i LR and N i RL are the number of molecules crossing the crosssectional area A cs in the center of the structure from left to right and from right to left, respectively. The total simulation time is represented as t. The permeability K i of each species for the nanosheet simulations can then be calculated from Darcy's law shown in eq 3.
L is the thickness of the nanosheet which is equal to 5 nm. However, to ensure that the permeability K i can be calculated via eq 3, a linear correlation between the flux J i and the pressure drop ΔP needs to be confirmed. In every case a linear response was achieved (refer to the Supporting Information for further details).
In line with the experimental work 20 the selectivity S CO 2 /CH 4 of the nanosheet for the mixture of gases can then be calculated as the ratio of the permeabilities of the two species, shown in eq 4.
If only pure components are studied, the selectivity is described as ideal.
To compare the performance of the bulk material with the nanosheet, the ratio of the fluxes for the two species in both materials was calculated via eq 2.
■ RESULTS AND DISCUSSION CH 4 and CO 2 Diffusion in the Defect-Free Nanosheet. The permeabilities of pure CO 2 and CH 4 are summarized in Figure 4 for six different pressure drops. The permeability of methane is significantly higher compared to the permeability of pure carbon dioxide simulations, and it remains almost constant for the entire pressure drop range studied. The average ideal selectivity of carbon dioxide over methane for all the pressure drops is calculated at 0.36, which is below 1 and indicates that the nanosheet is not selective for carbon dioxide, and this is in direct contrast with the experiments. 20 There have been reports in the literature where the ideal selectivity has been misleading. For example, in 2007 Keskin and Sholl studied the CO 2 /CH 4 gas mixture separation with MOF-5 membranes where the ideal selectivity was strong for methane while the selectivity of the binary mixture was weak in favor of carbon dioxide. They concluded that the study of the mixture is crucial and the single component simulations are insufficient. 66 In addition, Kadioglu and Keskin in 2017 examined 139 different MOF membranes for He/CH 4 separation and concluded that the ideal selectivity (pure components) might be an overestimation compared to the selectivity of binary mixtures. 67 When pure components are studied instead of binary mixtures, the two gases do not compete for the available adsorption sites and diffusion pathways.
To more fully understand the competition and interactions between the two components in the structure, we undertook EF-NEMD simulations of an equimolar mixture of CO 2 /CH 4 . The estimated flux of each species for the equimolar mixture is lower than the calculated flux for the pure components as it can be seen in Figure S4 when compared to Figures S7 and S8. The permeability of each species is presented in Figure 5. The permeability of methane in the mixture is almost 86% lower than in pure component studies and is lower than the permeability of carbon dioxide which showed only a slight drop. The average selectivity of CO 2 over CH 4 for all the pressure drops studied is equal to 1.88 compared to 0.36 for the pure component simulations; that is, an inversion in selectivity is observed for the mixture compared to the ideal selectivity predicted from the pure component behavior. The study of pure components might be computationally cheaper, but when the application of interest involves gas mixtures, it is recommended that mixture simulations are performed.
To understand the separation mechanism for the mixture of CO 2 /CH 4 with CuBDC nanosheets, the density and the velocity profiles were calculated for an 8 ns EF-NEMD run, averaged across three trajectories. Figures 6 and 7 correspond to 20 bar pressure drop.
An accumulation of methane molecules near the surface of the nanosheet is observed (Figure 6), corresponding to the entrance into the pores of the framework. This is due to the mass transfer resistance of the MON in response to the imposed pressure gradient combined with the restriction of access to the MON due to adsorbed CO 2 . The majority of the carbon dioxide molecules are located within the MON (between 2.3 and 7.3 nm) presenting peaks every ∼0.5 nm where a slightly increased pore volume (and number of adsorption sites) is available. The density of carbon dioxide molecules is significantly higher than the density of methane    Figure 7, the average velocity in direction x for all the molecules of each species within the MON is analyzed. Methane presents a higher velocity-x over carbon dioxide molecules, especially for higher pressure drops; that is, once inside the framework, methane can diffuse more quickly. Considering the density profile and the average velocity of the molecules within the MON, we conclude that a pore blocking mechanism is in place. The preferential adsorption and lower interframework velocity of carbon dioxide combine to significantly retard the permeability of methane through the MON.
The selectivity of the CuBDC MONs for the equimolar mixture of CO 2 /CH 4 is the ratio of the permeabilities of the two species, shown in eq 4, and can be calculated from NEMD. In Figure 8, we present the simulated selectivity of CO 2 over CH 4 for a pressure drop range from 4.5 to 20 bar. The average selectivity in this pressure range is 1.88, which is significantly lower than the selectivity of ∼80 presented in the experimental work of Rodenas et al., in which the permeability values were around 10 barrer. 20 The experimental work of Yang et al. showed a selectivity as low as 17 in favor of carbon dioxide, which is also higher than the simulated value, but the observed permeability values were of the same order of magnitude as some of the simulated values (around 10 4 barrer). 21 It should be noted that the present work only considers the nanosheet contribution in the separation, while the experimental setups of both Rodenas et al. and Yang et al. included a polymer matrix.
In this study the selectivity shows a slight tendency to drop with increased pressure drop, which is in agreement with literature studies, 68 while Rodenas et al. reported an unexpected and out of trend increase in the selectivity with increasing pressure drop. The simulation results indicate that the presence of the MON cannot account for the experimentally observed increase in the selectivity on its own, and we speculate that this phenomenon might occur because of the MOF−polymer interface.
Comparison of the Nanosheet to the Bulk Material. Synthesizing anisotropic 2D MOFs is more challenging than the synthesis of isotropic 3D bulk MOFs. 17 To achieve an anisotropic growth, more advanced techniques than the conventional methods need to be applied. 20 A significant amount of time and consumables is used in fabrication of MONs. Hence, a question arises: Are 2D MOFs better for gas separations when compared to their 3D bulk MOF counterparts? We performed EF-NEMD for the bulk CuBDC structure for the equimolar mixture of CO 2 /CH 4 . To directly compare the two materials, the ratio of the fluxes was calculated for both the MON and the bulk CuBDC MOF, as shown in Figure 9. The ratio of the fluxes is slightly higher for the MON and equal to 1.88 if averaged in the pressure drop range shown (4.5−20 bar). The average value of the selectivity for the bulk MOF is 1.27. The slightly better performance of the MON can be attributed to the surface effect and to the mass resistance that the guest molecules face at the entrance of the pore window. While the accumulation of guest molecules on the surface will also occur in the bulk MOF in reality, the effect will be much more pronounced in the MON, as MONs have a significantly higher external surface area to volume ratio compared to bulk MOFs. 17 Equimolar CO 2 /CH 4 Mixture Separation with Defective CuBDC Nanosheets. The effectiveness of the CuBDC nanosheets in the separation of the CO 2 /CH 4 mixture can be    Langmuir pubs.acs.org/Langmuir Article reduced by the presence of defects (missing linkers). In Figure  10, the selectivity of the ideal structure is compared to the selectivity of defective structures for a range of pressure drops. For the 5 and 10% defect concentrations (for which linkers may be removed at different locations to achieve the required defect concentration), the defect location was not found to strongly influence the calculated selectivity ( Figure S18). With an increasing percentage of defects, the selectivity drops ( Figure 10) due to changes in the permeability of each species.
While the permeability of carbon dioxide reduces slightly, the permeability of methane molecules increases considerably as it can be seen in Figure 11. With only 10% of linkers removed, the two species have almost equal permeability (i.e., the MON becomes nonselective), while for 20% there is an inversion in selectivity (i.e., the selectivity drops below one, and the MON will selectively remove methane from the mixture instead of CO 2 ). To fully understand why the presence of defects makes the nanosheets nonselective, the density and the velocity profile of each species are studied. In Figure 12, the density profile is presented. High CO 2 peaks can be observed at the positions of the missing linkers. The overall gas uptake in the defective structures does not change noticeably ( Figure S3); however, the position of the adsorption sites does. There is an accumulation of carbon dioxide molecules in the cavities created by the missing linkers. In every case, one high peak at the entrance of the nanosheet is observed for methane molecules, and the occupied adsorption sites within the nanosheet are significantly lower when compared to carbon dioxide.
In Figure 13, the average velocity in the x-direction is presented for every species inside the nanosheet. Methane molecules present an increasing velocity with increasing percentage of defects, while the carbon dioxide molecules have an almost constant average velocity. We conclude that the cavities created around the defect sites reduce the effectiveness Figure 10. Selectivity of carbon dioxide over methane of the ideal structure compared to defective structures for a range of pressure drops.

■ CONCLUSIONS
Some metal−organic framework nanosheets have shown great promise for gas separations, outperforming their bulk MOF counterparts by showing higher selectivity. Such an example is CuBDC, for which the nanosheets have systematically demonstrated a higher selectivity when compared to the CuBDC bulk MOF for gas separation of CO 2 over CH 4 in experiments. 20,21 In this work, we have applied external-force nonequilibrium molecular dynamics for the separation of equimolar CO 2 /CH 4 mixture with defect-free CuBDC nanosheets, defective nanosheets, and bulk CuBDC MOF. These studies confirm that if the application of interest is a gas separation process, then the study of a mixture instead of the pure components is vital. The ideal selectivity might be misleading as it is calculated from pure component simulations where the gas components do not compete for the adsorption sites and the diffusion pathways. Our study has shown that the separation mechanism in place is a pore blocking effect. The majority of the adsorption sites are occupied by CO 2 molecules which interact strongly with the framework atoms and have a lower velocity through the MON, restricting the permeability of CH 4 molecules in the nanosheet. The nanosheet performs better for separating CO 2 over CH 4 when compared to the bulk MOF which can be attributed to the surface effect and the mass transfer resistance which causes the accumulation of methane molecules on the pore window of the MON. The simulated selectivity is lower than the experimental values, but the permeability values agree in order of magnitude in the lowpressure drop area. The simulations accounted only for the nanosheet contribution while the experimental work was conducted with the MONs dispersed in polymers. Finally, we have demonstrated that the effectiveness of the nanosheets is very sensitive to the presence of defects in the system which confirms the hypothesis of Yang et al. that defects in the nanosheets would have an impact on the selectivity. 21 Just 10% of linkers missing results in a nonselective MON, while for 20% concentration, the MON becomes selective toward methane, strongly suggesting that the synthesis process needs to reduce the presence of missing linkers as much as possible in order for CuBDC to be used effectively for light gas separations.
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