Computational Screening of Porous Coordination Networks for

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Computational Screening of Porous Coordination Networks for Adsorption and Membrane-Based Gas Separations Tugba Nur Ozturk†,‡ and Seda Keskin*,†,‡,§ †

Department of Computational Sciences and Engineering, ‡TUPRAS Energy Center, and §Department of Chemical and Biological Engineering, Koc University, Rumelifeneri Yolu, Sariyer, 34450 Istanbul, Turkey S Supporting Information *

ABSTRACT: Porous coordination networks (PCNs) are promising nanoporous materials in gas separation applications due to their tunable pore sizes, large surface areas, high porosities, and good thermal and mechanical stabilities. In this work, we investigated adsorption-based and membrane-based separation performances of 20 different PCNs for CH4/H2, CO2/H2, CO2/CH4, and CO2/N2 mixtures using molecular simulations. Several PCNs were identified to show higher selectivity than traditional zeolites and polymers in membranebased CO2 separations. We also developed simple models that can predict adsorption, diffusion, and permeation selectivities of PCNs for CH4/H2 and CO2/H2 mixtures based on the structural properties of materials such as pore volume, surface area, and pore diameter.

1. INTRODUCTION Separation of gas mixtures has social, environmental, industrial, and economical importance. Traditional gas separation techniques include distillation, absorption, adsorption, and membranes.1 Among these techniques, adsorption- and membrane-based gas separation methods have received significant attention from academy and industry since they are energy-efficient and environmentally friendly processes. Various materials such as polymers, zeolites, carbon molecular sieves, and metal−organic frameworks have been developed and tested as adsorbents and membranes to achieve highperformance gas separations.2,3 Porous coordination networks (PCNs), also known as metal−organic frameworks (MOFs), offer high potential for gas storage and separation due to their large surface areas, high porosities, tunable pore sizes, and good chemical and thermal stabilities.4 In the literature, several studies have focused on examining single-component gas uptake capacities of PCNs. Many experiments were carried out to examine H2 storage capacities of PCNs, including PCNs 6 and 6′,5 10 and 11,6 14,4 16,7 20,8 26,9 46,10 and 80.11 Adsorption isotherms of other gases such as CH4, CO, CO2, O2, and N2 were experimentally investigated in several PCNs including PCNs 6 and 6′,5 11,6 14,12 46,10 and 80.11 Adsorption-based gas separation performances of PCNs were generally assessed on the basis of results of single-component gas uptake studies. For example, Liu et al.13 examined singlecomponent adsorption of CO2 and N2 in PCN-72 and concluded that this material can be a promising adsorbent for CO2 capture from flue gas. Makal et al.14 studied singlecomponent gas adsorption capacities of PCNs 38 and 39 and showed that PCN-39 exhibits selective adsorption for H2 over CO, CO2, and N2. © XXXX American Chemical Society

Computational studies have been widely used to investigate gas adsorption properties of PCNs. Many research groups studied H2 uptake of PCNs 12-Si,15 61,16−18 and 68, 69, and 61018 by performing grand canonical Monte Carlo (GCMC) simulations. Parkes et al.19 investigated adsorption and diffusion of Kr in 16 MOFs including PCN-14 by performing GCMC and molecular dynamics simulations and suggested that MOFs are highly promising materials for industrial separation of noble gas from air. Using GCMC simulations, Lucena et al.20 studied PCN-14 for CH4 uptake; Zhuang et al.9 examined CH4, CO2, and N2 adsorption in PCN-26; Yuan et al.21 investigated step behavior in adsorption isotherms of Ar, CO2, and N2 in PCN53; and Ward and Getman22 predicted N2 uptake in PCN-53. PCNs 6 and 6′23 and 12424 were examined for capturing CO2 from CO2/CH4 mixtures; PCNs 6125,26 and 20026 were studied to separate CO2/N2 mixtures by GCMC simulations. Babarao et al.27 used a combination of first-principles calculations and GCMC simulations to investigate the influence of functional groups and flue gas impurities on postcombustion CO2 capture in PCNs 56−59 and reported that PCN-59 is a good adsorbent candidate to separate CO2 from a predehydrated flue gas mixture. As the literature summarized above suggests, various PCNs have been synthesized by different research groups and singlecomponent gas uptake capacities of these PCNs are generally determined by experimental methods or GCMC simulations. However, there has not been any experimental study related to binary gas adsorption and/or diffusion in PCNs. This lack of Received: April 7, 2014 Revised: May 22, 2014

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with a grid size of 0.4 Å. When the grid size was changed from 0.2 to 0.4 Å, the maximum change in calculated diffusion selectivities was 13.4% for one PCN and less than 5.5% for all other PCNs. In molecular simulations, the Dreiding force field39 was used for potential parameters of the framework atoms except metal atoms, which were not available from Dreiding and were taken from the Universal Force Field (UFF).40 The potential parameters used in simulations are listed in Table S2 in Supporting Information. We used single-site spherical LennardJones (LJ) 12−6 potential to model H241 and CH442 molecules. CO2 was represented as a rigid, three-site molecule with LJ potential, and partial point charges were located at the center of each site.43 N2 was modeled as a three-site molecule with two sites located at the two N atoms and the third site located at the center of mass with partial point charges.44 In order to compute the electrostatic interactions between gas molecules having quadrupole moments (CO2 and N2) and framework atoms, we assigned partial atomic charges to PCN atoms using the extended charge equilibration45 (EQeq) method. If the total charge of the PCN was not zero after the EQeq method was applied, the charge of hydrogen atom was resolved to make the total charge zero. Single-component GCMC simulations were performed to calculate the adsorbed amounts of H2, CH4, CO2, and N2 gases in PCNs. Adsorption isotherms of CH4/H2, CO2/H2, CO2/ CH4, and CO2/N2 were obtained from the binary mixture GCMC simulations. The adsorbed amounts of each gas component were calculated by specifying the bulk pressure, temperature, and composition of the bulk gas mixture in GCMC simulations. Four different types of moves were considered for single-component GCMC simulations: translation, rotation, insertion, and deletion of a molecule. In the binary mixture GCMC simulations, another trial move, exchange of molecules, was also performed. Lorentz−Berthelot mixing rules were employed. The cutoff distance for truncation of intermolecular (electrostatic) interactions was set to 13 (25) Å. Periodic boundary conditions were applied in all simulations. For GCMC simulations, a simulation box of 2 × 2 × 2 crystallographic unit cells was used. During the simulations, 1.5 × 107 steps were performed to guarantee the equilibration and 1.5 × 107 steps were performed to sample the desired properties. We used GCMC simulations to compute the isosteric heat of adsorption (Qst), the difference in partial molar enthalpy of adsorbate between bulk and adsorbed phase, as described in the literature.46 The Qst values of each gas component were calculated by single-component GCMC simulations at their corresponding partial pressures in the binary mixtures and are listed in Tables S3−S6 in Supporting Information. EMD simulations were performed to compute selfdiffusivities of each gas species in CH4/H2, CO2/H2, CO2/ CH4, and CO2/N2 mixtures. The initial states of EMD simulations with the appropriate adsorbate loadings were obtained from GCMC simulations, and each system was equilibrated for 20 ps prior to taking data. The Nosé−Hoover thermostat was applied to run EMD simulations at NVT ensemble.47 At least 20 independent EMD simulations with a length of 16 ns were performed to compute self-diffusivities of gases at a given loading. At the lowest loadings, the size of the simulation volume was increased to 4 × 4 × 5 to contain enough particles to increase the statistical accuracy of simulations.

information limits the assessment of PCNs’ potential in adsorption- and membrane-based gas separation applications. We recently used atomic simulations to examine the separation performance of PCNs 9-Co, 9-Fe, 9-Mn, and 26 for mixtures of CH4/H2, CO2/H2, CO2/CH4, and CO2/N2.28 Our results showed that these PCNs can outperform traditional zeolites and widely studied MOFs in gas separations, especially in CO2related separation processes, and PCN-26 was identified as a potential membrane material that can exceed the upper bound established for CO2/CH4 and CO2/N2 separations due to its high CO2 permeability and selectivity.28 Motivated from these initial results, we carried out a large-scale molecular simulation study in this work for 20 different PCNs, which represents the largest number of PCN materials studied in a molecular simulation work, to examine their potential for both adsorption- and membrane-based gas separations. We specifically focused on separation of CH4/H2, CO2/H2, CO2/CH4, and CO2/N2 mixtures. Separation of CH4 from H2 is crucial for the recovery of H2 from plants and refineries. CO2/CH4 separation, purification of natural gas from CO2, is important since CO2 reduces the energy content of natural gas and causes risk for pipeline corrosion due to its acidic nature. Separation of CO2 from H2 and N2 is required for precombustion processing of syngas mixtures and flue-gas treatment, respectively. In addition to computing adsorption, diffusion, and membrane selectivities of PCNs via molecular simulations, we also examined the structure−performance relationships of materials and developed simple selectivity models based on structural properties. We showed that these simple models can make accurate predictions for adsorption, diffusion, and membrane selectivities of PCNs without performing computationally demanding molecular simulations.

2. COMPUTATIONAL DETAILS In this study, adsorption- and membrane-based separation performance of 20 different PCNs (6 and 6′,5 9-Co,29 9-Mn and 9-Fe,30 10 and 11,6 13,31 14,4 16 and 16′,7 18,32 19,33 20,8 26,9 39,14 46,10 80,11 131′,34 and 224-Ni35) were examined for CH4/H2, CO2/H2, CO2/CH4, and CO2/N2 mixtures by grand canonical Monte Carlo (GCMC) and equilibrium molecular dynamics (EMD) simulations. The atomic positions of PCNs were taken from X-ray diffraction data of experiments, and the structures were assumed to be rigid in simulations. All the molecular simulations for PCNs in the literature used the rigid framework assumption because these simulations should be performed for multiple materials on time scales shorter than the same materials can be assessed experimentally, and the rigid framework assumption saves a significant amount of computational time. As presented in Figure 1, we found good agreement between the results of our molecular simulations in which rigid frameworks were used and available experimental data for single-component gas uptake (H2, CH4, and CO2) of several PCNs at various temperatures and pressures, indicating the validity of the rigid framework assumption. Structural properties of PCNs such as pore sizes [limiting pore diameter (LPD) and largest cavity diameter (LCD)], pore volumes, and surface areas were computed by the algorithm of Sarkisov and Harrison38 (Poreblazer), Mercury 5.35 software,37 and the method of Düren et al.,36 respectively. These structural properties are tabulated in Table S1 of Supporting Information. We used the default grid size of Poreblazer code, 0.2 Å, in all calculations. In order to test the effect of grid size on our predicted diffusion selectivities, we repeated our calculations B

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Figure 1. Comparison of our simulation data with experimental gas uptake data of PCNs for (a) H2, (b) CH4, and (c) CO2. Experimental data were collected at (a, c) 1−50 bar or (b) 1−65 bar and are taken from the literature.4−12

PCNs 9-Co and 9-Mn, where the composition of the CO2/H2 mixture was set to 1/99 to increase the statistical accuracy of EMD simulations.28

The results of GCMC and EMD simulations were used to predict separation performance of PCNs. In order to evaluate the adsorption-based separation performance of PCNs, adsorption selectivity (Sads), working capacity, sorbent selection parameter (Ssp) and percent regenerability (R%) were calculated for each material. Sads is defined as the ratio of adsorbed amounts of gases in a mixture normalized by the feed composition of the mixture, whereas working capacity is described as the difference between gas loadings at the corresponding adsorption and desorption pressures.28 Combination of Sads and working capacity is used to define Ssp to compare the performances of different nanoporous materials in adsorption-based separation processes.48 R% is defined as the ratio of working capacity to amount of adsorbed gas species at the adsorption pressure, to evaluate the practical usage of an adsorbent for cyclic adsorption processes.48 In order to evaluate the membrane-based separation performance of PCNs, diffusion selectivity (Sdiff), permeation selectivity (Sperm), and permeability were computed. Sdiff is computed as the ratio of self-diffusivities of each gas component in the binary mixture, and Sperm, also known as membrane selectivity, is defined as the multiplication product of adsorption and diffusion selectivity.49 Gas permeability is calculated from the adsorbed amount of gas, self-diffusivity, fractional pore volume of the material, and bulk fugacity of the gas species.50 Detailed descriptions, equations, and calculation procedures for all these properties can be found in our previous work.28 All these calculations were carried out at room temperature. For computing working capacity, Ssp, and R%, adsorption and desorption pressures were set to 10 and 1 bar, respectively since most of the adsorption-based separations in the industry are performed under these conditions. Permeation selectivity and permeability of membranes were calculated at a membrane feed pressure of 10 bar and permeate pressure of vacuum. Bulk gas compositions of the mixtures were set as CH4/H2 = 50/50, CO2/H2 = 15/85, CO2/CH4 = 50/50, and CO2/N2 = 15/85 in all calculations except for

3. RESULTS AND DISCUSSION In order to validate the accuracy of the molecular simulation parameters, we first compared the results of our simulations with the available experimental data4−12 for single-component gas adsorption of several PCNs. GCMC simulations were performed exactly at the same pressure and temperature as the experimental data to be consistent. Figure 1 shows simulated and experimental data for excess uptake of H2, CH4, and CO2 in various PCNs. There is reasonable agreement between experiments and simulations for all three gases and all PCNs at both low and high pressures, although there are some simulation results that deviate from experimental measurements by 10−20%, which is acceptable for the purpose of this work. For example, experiments6 measured H2 uptake of PCN-10 (PCN-11) as 2.4 (2.7) wt % at 1 bar and 298 K, while our simulations predicted a value of 2.3 (2.5) wt % under the same conditions. The quantity of adsorbed CH4 was measured as 179.1 cm3 STP/cm3 by experiments10 at 110 bar and 298 K in PCN-46, and our GCMC simulations predicted this value as 178 cm3 STP/cm3 under the same conditions. Similarly, good agreement was obtained for CO2, although simulations slightly overestimated the experimental CO2 adsorption isotherms at high pressures. For example, our simulations calculated the adsorbed quantity of CO2 as 13.4 mmol/g in PCN-80 at 10 bar and 296 K, whereas experiments11 reported this value as 11.4 mmol/g. Motivated by the good agreement between experiments and simulations for single-component gas uptakes, we used the same potential parameters to perform binary mixture GCMC and EMD simulations. In our recent work,28 we computed adsorption selectivity and working capacity of four PCNs for CH4/H2, CO2/H2, CO2/ CH4, and CO2/N2 mixtures and concluded that these four C

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Figure 2. Adsorption selectivity and working capacity of PCNs for (a) CH4/H2, (b) CO2/H2, (c) CO2/CH4, and (d) CO2/N2 mixtures. Adsorption and desorption pressures of PCN adsorbents were set to 10 and 1 bar, respectively. The compositions of the bulk gas mixtures are (a, c) 50/50 or (b, d) 15/85 at 298 K for PCNs, whereas for other materials, data were collected at 300 K at the same compositions from the literature.50

kg of PCN). Several PCNs (9-Fe, 11, 14, 16′, 18, 19, 26, 39, and 224-Ni) exhibit good adsorption selectivity (∼65−285) and high working capacities for CO2 (∼5−8.5 mol of CO2/kg of PCN) compared to other nanoporous materials. For CO2/CH4 separation, none of the PCNs show better adsorption selectivity compared to NaX, NaY, and rho-ZMOF, as can be seen from Figure 2c. Krishna and van Baten50 reported that the high CO2 selectivity of these three materials is due to strong electrostatic interactions between CO2 and extraframework cations. PCNs 9-Co and 13 are the best candidates to separate CO2 from CH4 in terms of selectivity (21 and 22, respectively). PCN-9-Co also exhibits high working capacity (5.4 mol of CO2/kg of PCN), but PCN-13 exhibits significantly lower working capacity (1.1 mol of CO2/kg of PCN) due to its smaller pore volume. Several PCNs such as 10, 11, 16, 16′, 46, and 224-Ni show high CO2 working capacity (∼7−14 mol of CO2/kg of PCN) and similar adsorption selectivity (∼5−15) compared to zeolites. We calculated CO2/ CH4 adsorption selectivity of PCNs 6 and 6′ as ∼4.4 and 3.9 at 10 bar and 298 K, whereas Babarao et al.23 computed these selectivities as ∼3.6 and 2.5 at 10 bar and 300 K, respectively. The slight difference between selectivities can be attributed to the different force fields and different partial charge assignment methods used in simulations. Figure 2d shows that PCNs 9-Co and 9-Mn are the best candidates for separation of CO2/N2 mixtures since they show high adsorption selectivity (∼470 and 280, respectively) and high working capacity (5.6 and 6.3 mol of CO2/kg of PCN, respectively). PCN-13 is another good adsorbent candidate for this separation due to its high adsorption selectivity (∼115). Other important parameters to evaluate new adsorbent materials are Ssp and R%. Tables S7−S10 in Supporting Information list the calculated Ssp and R% values of all PCNs for CH4/H2, CO2/H2, CO2/CH4, and CO2/N2 separations. Results showed that PCNs 9-Co, 9-Mn, 9-Fe, 13, and 131′ are

PCNs can be promising materials for adsorption-based gas separations. In this work, we extend our molecular simulations for 20 new PCNs and show their adsorption selectivity and working capacity in Figure 2, together with data for well-known zeolites and MOFs. Figure 2a suggests that PCN-13 is one of the best candidates to separate CH4/H2 mixtures among the materials considered in this work since it outperforms other PCNs, traditional zeolites, and MOFs due to its high CH4 selectivity (77) and high working capacity (2.2 mol of CH4/kg of PCN). PCN-131′ has the second highest CH4 selectivity, 61, among the materials we considered but its working capacity is low (∼1 mol of CH4/kg of PCN), which limits its practical usage. The PCN-9 series are also promising candidates to separate CH4 from H2 since they exhibit both high working capacity (>4 mol of CH4/kg of PCN) and high adsorption selectivity (>30). All other PCNs show similar selectivity and better working capacity compared to zeolites, which may be attributed to the larger pore volumes and pore sizes of PCNs. Figure 2b represents adsorption-based separation performances of PCNs for CO2/H2 mixture. The selectivity values for CO2/H2 mixture are higher than the other mixtures since CO2 is the most strongly adsorbed component whereas H2 is the most weakly adsorbed one in PCNs’ pores. This is due to the three-site representation of CO2 compared to single-site representation of H2 and to electrostatic interactions between CO2 and PCN atoms, which are absent for H2.28 PCNs 9-Co and 9-Mn exhibit very high CO2 selectivity (∼2300 and ∼1660, respectively) and high working capacity (5.5 and 6.1 mol of CO2/kg of PCN, respectively) compared to other materials. In fact, performances of these PCNs were found to be similar to that of zeolite NaX, one of the most promising adsorbent for CO2/H2 separation due to strong electrostatic interactions between CO2 molecules and extraframework cations of NaX.50 Adsorption selectivity of PCN-13 is also high (∼1030) but its working capacity is similar to that of zeolites (1.7 mol of CO2/ D

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Figure 3. Permeation selectivity and permeability of PCNs for (a) CH4/H2, (b) CO2/H2, (c) CO2/CH4, and (d) CO2/N2 mixtures. Feed and permeate pressures of PCN membranes were set to 10 bar and vacuum, respectively. Compositions of the bulk gas mixtures are (a, c) 50/50 and (b, d) 15/85 at 298 K for PCNs. Composition in panel b was set to 1/99 only for PCNs 9-Co and 9-Mn. For other materials, data were taken from the literature at 300 K at the same compositions.50 Lines in panels c and d represent Robeson’s upper bound.

potential candidates for CH4/H2 separations due to their high Ssp values (∼940−3400). PCNs 9-Co, 9-Mn, and 13 also exhibit high performance (Ssp values of 6 × 104 to 5 × 105) for CO2/H2 separation, although they suffer from low regenerability (∼35−50%). PCN-19 can be an ideal adsorbent for CO2/CH4 separation since it exhibits optimum Ssp and R% values of 226 and 75%, respectively. These values are higher than the values of the widely used MOF HKUST-1 (CuBTC), for which Ssp and R% values were reported as 21 and 66.7% at the adsorption (desorption) pressure of 1 bar (0.1 bar) for single-component adsorption data.48 For capturing CO2 from CO2/N2 mixture, performances of PCNs 9-Co and 9-Mn were found to be better (Ssp of ∼104) than those of ZIF-78, zeolite5A, and zeolite-13X, for which the Ssp values were computed as 396, 163, and 128, respectively, at adsorption (desorption) pressure of 1 bar (0.1 bar) for single-component adsorption data.48 Membrane-based separation performance of PCNs was investigated by comparing permeation selectivity and permeability of PCNs with those of zeolites and other MOFs. Permeation selectivity was simply defined as the multiplication of adsorption selectivity (calculated from GCMC results) and diffusion selectivity (calculated from EMD results).49 In most nanoporous materials, adsorption selectivity favors the more strongly adsorbed component whereas diffusion selectivity favors the weakly adsorbed component, because strongly adsorbed species diffuse more slowly than the weakly adsorbed species.49 In other words, high adsorption selectivities are generally compensated by low diffusion selectivities, and therefore membrane selectivities of materials are found to be much lower than their adsorption selectivities. This situation makes most materials promising for adsorption-based gas separations and much less efficient for membrane-based gas

separations. It would be very useful to identify materials where both adsorption and diffusion selectivities favor the same component and hence high membrane selectivities can be obtained. Figure 3a shows that some PCNs are CH4-selective membranes (PCNs 6, 9-Co, 9-Mn, 13, 14, 16′, 18, 19, 26, 39, 46, and 80), whereas some others are H2-selective (PCNs 6′, 9-Fe, 10, 11, 16, 20, 131′, and 224-Ni). All CH4-selective PCNs exhibit strong adsorption selectivity toward CH4, although their diffusion selectivity favors fast H2 molecules. Since the CH4/H2 adsorption selectivity values are higher (∼10−77) than the CH4/H2 diffusion selectivity values (∼0.08−0.48), these PCNs become CH4-selective membranes. On the other hand, H2-selective PCN membranes exhibit low CH4 adsorption selectivities and very high diffusion selectivities toward H2. Two PCNs, 10 and 11, were identified as strongly H2-selective membranes (25 and 7, respectively) because their narrow pore sizes limit the diffusion of large CH4 molecules (1 × 10−6 cm2/s in PCN-10 and 3 × 10−6 cm2/s in PCN-11) compared to small H2 molecules (4 × 10−4 cm2/s in PCN-10 and 7 × 10−4 cm2/s in PCN-11). PCN-131′ was also identified as a strongly H2-selective membrane with very low CH4 permeability due to its small pore volume and narrow pore sizes, as we discuss below. Figure 3b suggests that all PCNs are CO2-selective membranes except PCNs 6′, 20, and 224-Ni, which are weakly H2-selective. These PCNs are CO2-selective in adsorption, but slow diffusion of CO2 compared to H2 compensated their adsorption selectivities. For example, in PCN-20, the strongly adsorbed CO2 molecules diffuse slowly (∼10−5 cm2/s) compared to weakly adsorbed, light and small H2 molecules (∼10−3 cm2/s). Therefore, diffusion selectivity favors H2. Among CO2-selective PCNs, PCNs 11, 14, 16, and 16′ are E

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Figure 4. (a) Coefficient of correlation, R2, of CH4/H2 adsorption selectivity with Vpore, Asurface, and 1/ΔQ at different pressures. (b−d) Correlation between CH4/H2 adsorption selectivity and (b) Vpore, (c) Asurface, and (d) 1/ΔQ at 0.1 bar.

strong candidates for CO2/H2 separation due to their large CO2 permeabilities [(∼50−70) × 104 barrer]. In Figure 3c,d, we included Robeson’s upper line, which represents the selectivity/permeability trade-off of polymeric membranes for CO2/CH4 and CO2/N2 separations.51 Materials that can exceed these lines are highly promising for membranebased gas separations, and they can replace the traditional polymeric membranes in CO2 separations. Figure 3c shows that several PCNs (10, 11, 16, 16′, 19, and 131′) are located above Robeson’s upper bound due to their high CO2 selectivities. PCN-131′ exhibits significantly high permeation selectivity (∼105) for CO2/CH4 since diffusion selectivity strongly favors CO2 over CH4. Our classical EMD simulations of adsorbed CH4 in PCN-131′ indicated that CH4 cannot move along the pores on the nanosecond time scales (4 Å. Figure 5c suggests that eq 2 can be used to make accurate estimates for CH4/H2 diffusion selectivity of PCNs. Permeation selectivity (Sperm = SadsSdiff) of PCNs was then estimated by multiplication of the two values, adsorption selectivity predicted from eq 1 and diffusion selectivity predicted from eq 2. The results shown in Figure 5d indicate that predictions of the model are in good agreement with results of molecular simulations. The discrepancy between the model and simulations can be attributed to the weak prediction of the models for either adsorption selectivity or diffusion selectivity. For example, adsorption selectivity of PCN-13, which exhibits the highest permeation selectivity for CH4 over H2, was underestimated, and therefore its permeation selectivity was also underestimated by the model (28) compared to simulation results (37). Selectivities of PCNs 14 and 26 were calculated as 3.9 and 3.2 from simulations and predicted as 3.5 and 1.8 by our model. Another important aspect of the permeation model is that its predictions are qualitatively accurate; that is, the model accurately estimates which component is preferred in membrane permeation. For example, PCN-6′ is not a CH4-selective but a H2-selective membrane with a permeation selectivity of 2.3. Our model also identifies PCN-6′ as a H2-selective membrane with a permeation selectivity of 1.5. The good agreement between model predictions and simulation results suggest that we can make reasonable initial estimates about membrane selectivity of PCNs by use of these simple selectivity models. There was not a good correlation between adsorption selectivity and structural properties of PCNs for other mixtures, as shown in Figure S2 (Supporting Information), but the R2 values of CO2/H2 mixture were higher than those obtained for other CO2-related mixtures. We used the same models, eqs 1 and 2, with different sets of parameters as tabulated in Table S11 (Supporting Information), to predict adsorption, diffusion, and membrane selectivity of PCNs for CO2/H2 mixtures. Figure S3 (Supporting Information) shows that there is a reasonable agreement between model predictions and simulation results for both adsorption and permeation selectivities of CO2/H2 mixture. The model slightly underestimates permeation selectivity for PCN-11 (10) and PCN-19 (8) compared to the simulation results (15 and 9, respectively). This discrepancy is mainly caused by the diffusion selectivity model, which generally underestimated the EMD results. On the other hand, the model overestimates the permeation selectivity of PCN-13 (59) and PCN-18 (12) compared to the simulation results (49 and 9, respectively). Overall, when the high computational demand of molecular simulations is considered, especially H

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than the material’s pore size cannot permeate through the membrane. None of the PCNs considered in this work was reported to show flexibility/breathing effects during gas adsorption to the best of our knowledge. It is also important to note that the idea of our calculations is that once the potential value of a material has been demonstrated by molecular simulations, a more detailed calculation approach including framework flexibility can be used to increase the precision of the assessment.

4. CONCLUSION In this work, we examined adsorption- and membrane-based separation performances of 20 PCNs using molecular simulations to identify the most promising adsorbent and membrane candidates for CH4/H2, CO2/H2, CO2/CH4, and CO2/N2 mixtures. Several PCNs, such as the PCN-9 series and PCN-14, were identified as promising candidates for adsorption-based CH4/H2 separations since they exhibit both high adsorption selectivity and working capacity toward CH4. PCNs 9-Co, 9-Mn, 14, and 16 were found to be strong adsorbents for CO2 capture from CO2/H2, CO2/CH4, and CO2/N2 mixtures because of their high CO2 working capacities. Several PCN membranes were shown to exceed Robeson’s upper bound established for CO 2 /CH 4 and CO 2 /N 2 separations. We showed that both adsorption and diffusion favor the same component, CO2, over CH4 (N2) in PCNs 10, 11, and 131′ and make these PCNs highly CO2-selective in membrane-based CO2/CH4 (CO2/N2) separations.

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ASSOCIATED CONTENT

S Supporting Information *

Four figures showing potential energy barrier of CH4 in PCN131′, correlation between adsorption selectivity and pore volume, surface area, and inverse of isosteric heat of adsorption for PCNs, and comparison of model predictions and simulations for CO2/H2 adsorption and permeation selectivities and CH4/H2 adsorption selectivities of different nanoporous materials; 11 tables listing structural properties of PCNs, potential parameters of framework atoms, heat of adsorption values, Ssp and R% values of PCNs for four mixtures, and coefficients of selectivity models. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; phone 0090-212-338-1362. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support provided by the Koc University TUPRAS Energy Center is gratefully acknowledged. S.K. acknowledges and thanks the TUBA-GEBIP Programme.

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REFERENCES

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