ARTICLE pubs.acs.org/JPCC
Adsorption, Diffusion, and Separation of CH4/H2 Mixtures in Covalent Organic Frameworks: Molecular Simulations and Theoretical Predictions Seda Keskin* Department of Chemical and Biological Engineering, Koc- University Rumelifeneri Yolu, Sariyer, 34450, Istanbul, Turkey
bS Supporting Information ABSTRACT: Grand canonical Monte Carlo and equilibrium molecular dynamics simulations were used to compute adsorption isotherms and self-diffusivities of CH4/H2 mixtures at various compositions in three representative covalent organic frameworks (COFs). Several properties of COFs such as adsorption selectivity, working capacity, diffusion selectivity, gas permeability, and membrane selectivity were evaluated and were compared with metal organic frameworks (MOFs), zeolites, zeolite imidazolate frameworks (ZIFs), and carbon nanotubes. Results showed that COF-6 outperforms traditional zeolites CHA, LTA, and ITQ-29 and MOFs IRMOF-1, CuBTT, and MOF-177 in adsorption-based CH4 selectivity. Membrane selectivities of COF-5, COF-6, and COF-10 were found to be higher than those of zeolites and similar to ZIFs and MOFs. Adsorption isotherms and diffusivities of CH4/H2 mixtures in the pores of COF-6 were computed using both atomically detailed simulations and theoretical correlations. Results showed that theoretical correlations based on single component adsorption and diffusion data can be used to accurately predict mixture adsorption and diffusion of gases in COFs.
’ INTRODUCTION Metal organic frameworks (MOFs) are a new class of nanoporous materials that are formed by coordination of metal ions with organic linkers. MOFs have emerged as new alternatives for gas storage and gas separation applications because of their high porosities, tailorable physical and chemical characteristics during their synthesis, large surface areas, and low densities. Thousands of distinct MOF materials have been synthesized to date, and many comprehensive reviews exist for experimental synthesis and characterization of MOFs.15 Since the number of the different types of MOFs that have been synthesized is enormous, molecular modeling of these materials has played an important role in providing information about the performance of MOFs for specific applications.68 A new subclass of MOFs named as covalent organic frameworks (COFs) has been characterized and synthesized very recently.914 Porous and crystalline COFs are composed solely from light elements (H, B, C, N, and O) that are known to form strong covalent bonds in well-established and useful materials such as diamond, graphite, and boron nitride. COFs have rigid structures and exceptional thermal stabilities up to 600 C.14,15 They exhibit lower densities compared to MOFs because of the absence of heavy metals in their structures. They have permanent porosity with specific surface areas surpassing those of wellknown zeolites and porous silicates. Recent studies showed that COFs rank among the highest performing materials in terms of gas storage capacities because of their low framework densities, high surface areas, and open-pore structures.16 r 2011 American Chemical Society
Single component adsorption of gases in COFs has been examined by several experimental studies in the literature. Adsorption isotherms of N2 in COF-1 and COF-5;9 Ar in COF-6, COF-8, and COF-10;11 H2 in COF-11 Å, COF-14 Å, COF-16 Å, and COF-18 Å;15 N2 in COF-18 Å;10 Ar in COF-102, COF-103, and COF-202;14,17 and Ar, H2, CH4, and CO2 in several COFs16 were measured experimentally. The large number of different COF structures indicates that purely experimental means for selecting optimal COFs for targeted applications is inefficient at best. Molecular level simulations provide a means to complement experimental methods for screening COFs. A few molecular modeling studies examined single component adsorption of gases in COFs: Garberoglio et al. computed adsorption of Ar, H2, and CH4 in COF-102, COF-103, COF-105, and COF-108 using grand canonical Monte Carlo (GCMC) simulations.18 Babarao and Jiang calculated adsorption of CO 2 in COF-6, COF-8, COF-10, COF-102, COF-103, COF-105, and COF-108 using the same technique.19 Han et al. used GCMC simulations to predict H2 adsorption in COF-1, COF-5, COF-102, COF-103, COF-105, and COF-108.20 Yang and Zhong investigated CH4, H2, and CO2 adsorption in COF-8 and COF-10 using GCMC simulations.21 Klontzas et al. studied gravimetric and volumetric H2 uptake of lithium functionalized COF-105 with molecular simulations.22 Mendoza-Cortes et al. studied CH4 uptake of Received: October 12, 2011 Revised: December 12, 2011 Published: December 19, 2011 1772
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The Journal of Physical Chemistry C several COFs,23 and Assfour and Seifert computed adsorption of H2 in the same set of materials using GCMC simulations.24 An accurate description of mixture adsorption and diffusion is crucial in many applications that are envisioned for COFs such as membranes and adsorption-based separations. However, there is very limited information on mixture adsorption in COFs. The only study to date about mixture adsorption in COFs is by Liu et al. and they used GCMC simulations to evaluate binary adsorption isotherms of CH4, H2, and CO2 gases in a series of COFs including widely studied COF-102, COF-103, COF-105, and COF-108 and compared adsorption selectivities of these COFs with isoreticular MOFs.25 A more striking case is that no experimental information is available about diffusion of single gases or gas mixtures in the pores of COFs. Two molecular simulation studies calculated diffusion of single component gases in two COFs: Garberoglio and Vallauri computed single component self-diffusivity of H2 and CH4 in COF-10 as a function of temperature using equilibrium molecular dynamics (EMD) simulations.26 Krishna and van Baten used EMD simulations to determine the single component self-diffusivity and MaxwellStefan diffusivity of H2, Ar, CO2, CH4, ethane, propane, n-butane, n-pentane, and n-hexane in BTP-COF.27 Understanding multicomponent diffusion in nanopores of COFs is of paramount importance for advancing many applications of these materials. One major objective of this study is to provide the first information about diffusion of binary gas mixtures in a COF material using both molecular simulations and theoretical correlations. In this study, molecular simulations were used to calculate adsorption and diffusion of single component gases, CH4 and H2, as well as CH4/H2 mixtures at various compositions in three representative COFs—COF-5, COF-6, and COF-10—at room temperature. Adsorption isotherms of CH4/H2 mixtures were computed using GCMC simulations and ideal adsorbed solution theory,28 whereas transport rates of CH4/H2 mixtures were computed using EMD simulations and KrishnaPascheks’ correlations.29 The accuracy of theoretical correlations for predicting multicomponent adsorption and diffusion of adsorbed gases in COFs was tested for the first time in the literature by comparing with the results of detailed molecular simulations. Adsorption selectivity, kinetic-based selectivity, and membrane selectivity of COFs for separation of CH4/H2 mixtures were computed on the basis of molecular simulation results. This type of calculation is vital to understand whether it is better to use COFs as adsorbents or as membranes in gas separations. Gas permeability, working capacity, and selectivity of COFs were calculated and were compared with other nanoporous materials such as MOFs, zeolites, ZIFs, and carbon nanotubes.
’ DETAILS OF MOLECULAR SIMULATIONS Grand canonical Monte Carlo (GCMC) and equilibrium molecular dynamics (EMD) simulations were used to study adsorption and diffusion of CH4/H2 mixtures in COFs, respectively. The atomic positions of COF-5, COF-6, and COF-10 were obtained from the experimental data, and rigid structures were used.9,11 All three COFs are two-dimensional structures having pores only in the z direction. The pore sizes of COF-5, COF-6, and COF-10 are 27, 8.6, and 31.7 Å, respectively. These three materials have similar topologies with slight differences in their organic linkers. Unit cell representations (1 1 1 and 3 3 3) of COFs are shown in Figure S.1 of the Supporting
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Figure 1. Comparison of molecular simulation results of this study with the experimental measurements (ref 16) for H2 and CH4 uptake of COFs. Continuous (dotted) lines present the molecular simulations employing Dreiding (UFF) force field.
Information, and unit cell parameters are given in Table S.1 of the Supporting Information. The choice of force field is crucial for an accurate description of framework atoms. Both the universal force field (UFF)30 and the DREIDING31 force field were used in GCMC simulations of this study. The resulting single component adsorption isotherms from GCMC simulations were compared with the available experimental adsorption isotherm data in Figure 1. The results of GCMC simulations employing DREIDING force field agree well with the experimental data, whereas simulations employing UFF overpredict adsorption isotherms of H2 and CH4. Therefore, the DREIDING force field was used in all molecular simulations throughout this work. Spherical Lennard-Jones (LJ) 12-6 potentials were used to model H2 (ε/k = 34.2 K, σ = 2.96 Å) and CH4 (ε/k = 148 K, σ = 3.73 Å) molecules.32,33 In the literature, two different types of fluidfluid potential models for H2 have been used to study adsorption in MOFs: single-site and two-site LJ models. The single-site spherical 12-6 Lennard-Jones (LJ) model is the most commonly used and the Buch potential32 is known to reproduce the experimental bulk equation of state accurately.34 The Lorentz Berthelot mixing rules were employed to calculate the fluidsolid and fluidfluid LJ cross interaction parameters. The intermolecular potentials were truncated at 13 Å for adsorption and diffusion simulations. A minimum 2 2 2 unit cell simulation box was used for GCMC simulations. For EMD simulations, the size of the simulation volume was increased up to 6 6 6 to contain enough particles at the lowest loadings. Periodic boundary conditions were applied in all simulations. Conventional GCMC was employed to compute the single component and mixture adsorption isotherms. The temperature and the fugacity of the adsorbing gases were specified, and the number of adsorbed molecules was calculated at equilibrium. Simulations at the lowest fugacity for each system were started from an empty COF matrix. Each subsequent simulation at higher fugacity was started from the final configuration of the previous run. Simulations consisted of a total of 2 107 trial configurations with the last half of the configurations used for 1773
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data collection. A configuration is defined as an attempted translation or creation or deletion of an adsorbate molecule. For the case of mixture simulations, there is also an attempted swap of the particle species. Single component self-diffusivities, corrected diffusivities, and mixture self-diffusivities of each species were calculated using EMD simulations. The details of using EMD simulations to obtain these diffusion coefficients have been described in previous studies of zeolites, carbon nanotubes, and MOFs.3538 The selfdiffusivity Dself,i describes the motion of individual tagged particles, and in an isotropic three-dimensional material, it is related to the mean-squared displacement of tagged particles by the Einstein relation * + 1 1 Ni 2 ½r il ðtÞ r il ð0Þ ð1Þ Dself , i ¼ lim t f ∞ 6t N t l¼1
∑
where N is the number of molecules, ril(t) is the three-dimensional position vector of molecule l of species i at time t, and the angular brackets denote the ensemble average.39 The corrected diffusivity includes information on the collective motion of multiple adsorbed molecules that is relevant to net mass transport and can be calculated using the following expression:39,40 Do, i ¼ lim
tf∞
Ni 1 Æð ½r il ðtÞ r il ð0ÞÞ2 æ 6N t l ¼ 1
∑
ð2Þ
Because all the COFs considered in this work have onedimensional pores in the z direction, the term 1/6 reduces to 1/2 both in self-diffusivity and in corrected diffusivity descriptions.The Nose-Hoover thermostat in NVT-ensemble was used in EMD simulations.41 For the single component corrected (self) diffusivities, 20 (10) independent EMD simulations were performed because having a large number of independent trajectories is vital in order to accurately compute the corrected diffusivities. After creating initial states with the appropriate loadings using GCMC, each system was first equilibrated with EMD for about 20 ps prior to taking data. Mixture self-diffusivities were computed at various adsorbed loadings of CH4/H2 mixtures obtained from binary GCMC simulations.
Figure 2. Single component and binary mixture adsorption isotherms of CH4 and H2 in (a) COF-5, (b) COF-6, and (c) COF-10 at room temperature. The symbols are the results from GCMC simulations, and the lines are the predictions of ideal adsorbed solution theory.
’ RESULTS AND DISCUSSION Single component and mixture adsorption isotherms of CH4 and H2 in COFs at 298 K are shown in Figure 2. The adsorption isotherms of CH4/H2 mixtures were calculated for 10% and 50% CH4 in the bulk phase. In all calculations, the bulk phase composition was specified in terms of fugacity because the differences between fugacity and pressure for CH4 and H2 for the conditions considered here are small. As should be expected from the single component isotherms, adsorption favors CH4 over H2 in the mixtures because the more strongly adsorbing CH4 molecules exclude H2 molecules in the pores. The amount of adsorbed CH4 (H2) in the mixture increases (decreases) as the amount of CH4 increases in the bulk phase. Keskin and Sholl42 previously showed that ideal adsorbed solution theory (IAST) gives accurate predictions for the adsorbed mixtures of CH4/H2 in COF102. IAST28 is well-known to give accurate predictions for mixture adsorption isotherms on the basis of adsorption isotherms of pure gases in many nanoporous materials except in materials characterized by strong energetic or geometric heterogeneity.43,44 Single component adsorption isotherms of CH4 and H2 for all COFs were fitted using a dual-site Langmuir isotherm to apply IAST. 1774
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Figure 3. Adsorption selectivity of COFs for CH4/H2 mixtures as a function of fugacity at room temperature.
The results of IAST predictions for CH4/H2 mixtures are also shown in Figure 1. The predictions of IAST agree well with the mixture GCMC simulations for all compositions and for all COFs indicating that IAST can accurately predict mixture adsorption isotherms of CH4/H2 in COFs. A good indication of the ability for separation in an equilibriumbased separation process is the adsorption selectivity of a nanoporous material for different components in the mixtures. The adsorption selectivity for CH4 relative to H2 is defined as
SadsðCH4 =H2 Þ
xCH4 x H2 ¼ yCH 4 y H2
Figure 4. Adsorption-based CH4 selectivity vs delta CH4 loadings at 298 K. The composition of the CH4/H2 mixture is equimolar. Data for other materials were taken from refs 42 and 45.
ð3Þ
where x and y are the molar fractions of the adsorbed and bulk phases, respectively. The adsorption selectivities of COF-5, COF-6, and COF-10 for CH4/H2 mixtures with 10% and 50% CH4 in the bulk phase are shown in Figure 3. Adsorption selectivity favors CH4 at low pressures since CH4 is energetically preferred over H2. At higher pressures, the adsorption selectivity of COF-5 and COF-6 for CH4 over H2 slightly decreases because entropic effects come into play that favor H2 adsorption. Adsorption selectivity of COF-10 is almost constant in the whole pressure range because entropic effects are unimportant even at high loadings because of very large pores of COF-10. The adsorption selectivity of COF-10 (∼5) for CH4 is very similar to that of IRMOFs, whereas COF-5 and COF-6 exhibit higher selectivities (∼20 and ∼35) than IRMOF-1, IRMOF-8, IRMOF-10, and IRMOF-14.42 Relatively smaller pores of COF-6, compared to COF-5 and COF-10, provide a stronger confinement of CH4 molecules. The degree of confinement of H2 molecules in COFs having small pores and COFs having large pores can be thought of as being similar because in both cases the molecule is small relative to the pore size giving similar adsorption strength for H2. The stronger confinement of CH4 in COF-6 than in COF-5 and COF-10 results in higher CH4 selectivity. As discussed by Krishna and van Baten,45 adsorption selectivity and working capacity (also known as delta loading) govern the costs of separation in adsorption-based separation processes. The working capacities of COFs were calculated at room
Figure 5. Single component self-diffusivities of CH4 and H2 in COF-5, COF-6, and COF-10 at 298 K as a function of total adsorbed loading.
temperature for equimolar CH4/H2 mixtures at a total gas phase fugacity of 10 bar and at a desorption pressure of 1 bar. Figure 4 compares the adsorption selectivities and delta CH4 loading capacities of COFs with widely studied zeolites and MOFs. The most desirable materials for adsorption-based separation should be located in the top right-hand corner of Figure 4. The results of molecular simulations showed that there is generally a tradeoff between adsorption selectivity and working capacity. For example, traditional zeolites such as LTA, CHA, and ITQ-29 exhibit good CH4 selectivity but low working capacity whereas MOF-177 and IRMOFs have high working capacity but low CH4 selectivity. Although COF-6 exhibits higher CH4 selectivity than all other materials considered in Figure 4, its delta loading capacity is very low. Among the COFs studied in this work, COF-5 has the best CH4 selectivity/delta loading combination (10 and 2 mol CH4/kg COF, respectively). As our earlier molecular simulation studies concluded, CPO-27-X (X = Zn, Mg) materials and CuBTC exhibit high selectivity and high loading capacity.45,46 1775
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Figure 6. Single component and mixture self-diffusivities of H2 and CH4 in COF-6 at 298 K. Closed symbols represent single component self-diffusivities of each species computed using EMD simulations. Open triangles, circles, and diamonds show the self-diffusivities of gases in adsorbed mixtures with composition of 25, 50, and 75% CH4, respectively. The symbols are the results of EMD simulations, and the lines are the predictions of Krishna and Paschek (KP) correlations.
Single component self-diffusivities of CH4 and H2 computed from EMD simulations are shown in Figure 5 as a function of total adsorbed loading in COF-5, COF-6, and COF-10. The selfdiffusivities of CH4 and H2 in COFs have the same trend with many other MOFs showing a moderate decrease with increasing adsorbate loading. This behavior is one of the most common forms of loading dependent self-diffusivity observed in nanoporous materials, and this loading dependence arises as a natural consequence of steric hindrance between diffusing molecules. The magnitudes of self-diffusivities of CH4 and H2 are in the following order: COF-10 > COF-5 > COF-6. This is consistent with the decreasing pore sizes of the materials. The self-diffusivity of H2 (CH4) in the most widely studied MOF, IRMOF-1, at an adsorbed loading of 10 molecules/unit cell was computed as 2 103 cm2/s (3 104 cm2/s) from EMD simulations,38 whereas H2 (CH4) diffusivities in COF-10 and COF-5 were computed as 102 and 7 103 cm2/s (103 and 2 103 cm2/s), respectively. This is due to the larger pores of COF-10 and COF-5 (31.7 Å and 27 Å) compared to IRMOF-1 (12 Å). The selfdiffusivities of H2 and CH4 are smaller in COF-6 because of its narrower pores (8.7 Å), and EMD simulations were computed up to three molecules/unit cell since both molecules reach saturation at that loading in COF-6. The magnitude of H2 diffusivity is greater than that of CH4 in all three COFs as in silica zeolites and MOFs because of the differences in size and weight of these two molecules.37,38 In most practical applications, gases exist as mixtures rather than as single components. The relative transport rates of components of a mixture inside the material of interest are crucial in determining the overall performance of this material in applications such as gas separations. Therefore, mixture self-diffusivities of CH4 and H2 in COF-6 were investigated in detail using both EMD simulations and theoretical correlations. Both pure component and mixture self-diffusivities of CH4 and H2 in COF-6 computed from EMD simulations are shown in Figure 6. The self-diffusivities of each species in adsorbed CH4/H2 mixtures
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were examined at three different compositions: 25/75, 50/50, and 75/25. Figure 6 shows that self-diffusivities of CH4 in CH4/H2 mixtures are larger than the pure component CH4 self-diffusivity at the same loading. This observation is natural since the fast diffusing H2 molecules in the mixture speeds up the slowly diffusing CH4 molecules. For example, the self-diffusivity of pure CH4 is 1.5 104 cm2/s at a loading of two CH4 molecules per unit cell of COF-6. The self-diffusivity of CH4 increases to 2.15 104 cm2/s at a total loading of two molecules consisting of one CH4 and one H2 molecule per unit cell. Also, the overall number of CH4 molecules in the presence of H2 is smaller than the number of molecules in the pure CH4 case. Because H2 molecules are smaller than CH4 molecules in size, there will be more space for motion of CH4, which can cause faster diffusion of CH4 in the presence of H2. As the fraction of H2 (CH4) in the mixture increases, the increase (decrease) in the diffusion of CH4 (H2) is more profound. For example, increasing the adsorbed concentration of H2 in the mixture from 25% to 75% increases the diffusivity of CH4 from 1.7 104 cm2/s to 3.9 104 cm2/s. Similarly, self-diffusivities of H2 in CH4/H2 mixtures are smaller than the pure component H2 self-diffusivity at the same loading because CH4 acts to slow the diffusion of H2 through the pore. The prediction of transport properties in mixtures from data taken from single component studies has been a long-standing goal in describing mass transport in nanoporous materials. Krishna and Paschek (KP)29 introduced the following correlation in order to predict the self-diffusion coefficients in a mixture from single component data: Di, self ¼
1 θj 1 θi þ corr þ corr D̵ i D̵ ii D̵ ij
ð4Þ
Dj, self ¼
1
ð5Þ
θj 1 θi þ corr þ corr D̵ j D̵ ji D̵ jj
This correlation was tested in carbon nanotubes,47 MFI zeolite,48 and CuBTC MOF,44 and the predictions of the correlation were found to be in a good agreement with the results of direct EMD simulations for mixture diffusion. In this correlation, Di,self is the self-diffusivity of species i in a binary mixture with species j, D9i is the pure component corrected diffusivity (also known as Do,i), and D9ijcorr are the self-exchange and binary-exchange difD9corr ii fusivities which reflect the correlation effects in a mixture,48 and θi is the fractional loading of species i. The fractional loading was defined as θi ¼
Θi Θi, sat
ð6Þ
where Θi and Θi,sat represent the loading of species i and the saturation loading of species i, respectively. To apply eqs 4 and 5, first, single component self (Dself,i(θ)) and corrected diffusivities (D9i(θ)) of CH4 and H2 computed from EMD simulations at various fractional loadings were fitted to continuous functions. corr Then, D 9ii (θ) values at each loading of interest were derived 1776
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Figure 7. Adsorption selectivity, diffusion selectivity, and membrane selectivity of COFs for CH4/H2 mixtures at 298 K. The composition of the bulk gas mixture is CH4/H2:10/90.
from the following equation: Dself , i ðθÞ ¼
48
1 1 θ þ corr D̵ i ðθÞ D̵ ii ðθÞ
ð7Þ
Figure 8. Comparison of CH4 selectivity of COF membranes with MOF membranes (data taken from ref 42), zeolite, and CNT membranes (data taken from ref 45). The feed composition is CH4/H2:10/ 90 for COFs and IRMOFs and CH4/H2:50/50 for others.
and COF-10, the performances of these materials as membranes can be predicted. Previous studies showed that selectivity of a MOF membrane can be approximated as the multiplication of adsorption selectivity and diffusion selectivity42,45,49
SmixtureðCH4 =H2 Þ
In a similar way, the binary-exchange coefficients, D9corr ij , were corr estimated using D9corr 9jj , loadings, and fractional loadings of ii , D each species48 θi =θi þ θj θj =θi þ θj Θj, sat D̵ corr D̵ corr ½Θi, sat D̵ corr ij ðθÞ ¼ ½Θj, sat ii ðθÞ jj ðθÞ
ð8Þ In application of eq 7, it is important to remember that the selfand corrected diffusivities were actually evaluated at the total fractional loading and not at the pure component fractional loading.44 Mixture self-diffusivity predictions of KP correlation are shown as lines in Figure 6 and are compared with direct EMD simulation results for three different compositions of adsorbed CH4/H2 mixtures in COF-6 at room temperature. The predictions for mixture self-diffusivities are in a good agreement with the results of EMD simulations. This good agreement indicates that it is possible to accurately predict transport rates of adsorbed gas mixtures in COF-6 using only the single component adsorption and diffusion data obtained from molecular simulations. An important issue that cannot be directly addressed with current results is the generality of the conclusion that the properties of adsorbed mixtures in all COFs can be predicted from single component data. Similar levels of agreement can be expected for CH4/H2 mixtures in other COFs since COF-6 does not have any structural characteristics that suggest it defines a potential energy surface for these adsorbed species that differs greatly in character from other COFs. This idea is supported by the observation that qualitative aspects of molecular diffusion in COFs have been found to be similar to diffusion in noncationic zeolites, and KP correlation has been shown to work well in a variety of noncationic zeolites.38 Since both adsorption and diffusion data for CH4/H2 mixtures were obtained from molecular simulations for COF-5, COF-6,
xCH4 xH2 DCH4 , self ðxCH4 , xH2 Þ ¼ yCH 3 D 4 H2 , self ðxCH4 , xH2 Þ yH2
ð9Þ
The validation of this approximate expression for MOF membranes was previously shown by Keskin and Sholl.42 In this approximate expression, the diffusion selectivity is defined as the ratio of self-diffusivities in a binary mixture evaluated directly at their corresponding adsorbed compositions. Equation 9 approximates a membrane’s selectivity at a specified feed pressure and composition on the basis of a single GCMC simulation and an EMD simulation performed at the loadings determined from this GCMC calculation. Figure 7 shows adsorption selectivity, diffusion selectivity, and membrane selectivity of COFs for CH4/H2 mixtures at 298 K. In all COFs, the adsorbed mixture is CH4 dominant as Figure 2 suggested. Because it is statistically not very accurate to measure mixture self-diffusivities when one of the components is strongly adsorbed in the mixture, all EMD simulations shown in Figure 7 were performed at a bulk gas composition of CH4/H2:10/90. The selectivity greater (less) than 1 indicates that COF is selective for CH4 (H2). As discussed before, adsorption selectivity favors CH4 over H2 because of energetic effects, and yet, it was compensated by the low diffusion selectivities toward CH4 since strongly adsorbed species (CH4) diffuse more slowly than the weakly adsorbed species (H2). As a result, membrane selectivity of COFs for CH4 over H2 is smaller than adsorption selectivity, which was also observed in the earlier studies of MOF and ZIF membranes.42,50 For example, adsorption selectivity of COF-6 for CH4 is 20.45 at 10 bar, 298 K, whereas diffusion favors H2 with a selectivity of 2.92. The combined effect of adsorption and diffusion preferences resulted in CH4 selective COF-6 membrane with a selectivity of 7. Selectivities of COF membranes were compared to well-studied MOF, carbon nanotube, and zeolite membranes in Figure 8. In contrast to ZIF-8, LTA, and CHA, COF-5 and COF-6 are CH4 1777
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the best selectivity/permeability properties among the materials considered in Figure 9.
Figure 9. Comparison of CH4 selectivity and permeability of COF membranes with other nanoporous membranes. Data for materials except COFs were taken from refs 45 and 50.
selective membranes. COF-5 and COF-6 outperform MOF-177, IRMOF-1, IRMOF-10, and COF-10 in terms of CH4 selectivity. The selectivity of COF-10 is similar to IRMOFs. Figure 8 underlines the fact that although topologies of the materials are similar, their performances as membranes can be different. For example, COF-5 and COF-10 are very similar structures. At low feed pressures, the former is CH4 selective with a selectivity of 5, whereas the latter is slightly H2 selective with a selectivity of 1.7. For an efficient membrane-based separation process, both high gas selectivity and high gas permeability are desired. High gas selectivity without high gas permeability has limited value for membrane-based gas separations since this type of membrane will require a large surface area and, thus, high capital cost. Therefore, mixture gas permeabilities through COF membranes were computed using the following equation:49 Pi ¼
ϕ 3 Di, self 3 ci fi
ð10Þ
In this expression, Pi is the permeability of the species i (mol/m/s/Pa), ϕ is the fractional pore volume of the material, Di,self is the self-diffusivity of species i in the mixture (m2/s), ci is the concentration of species i at the upstream face of the membrane (mol/m3), and fi is the bulk phase fugacity of the species i (Pa). A more commonly used unit for reporting permeability in the membrane community is Barrers; therefore, predicted gas permeabilities through COF membranes are reported in Barrers in Figure 9. To assess the performance of COF membranes among many different nanoporous materials, selectivity/permeability data of zeolite, MOF, and carbon nanotube (CNT) membranes are also included in this figure. Zeolites which have narrow windows separating large cages such as ZIF-8, LTA, and CHA give H2 selective permeation because of their molecular sieving properties. Gas permeabilities of COF membranes are 3 (12) orders of magnitude higher than ZIF-8, LTA, and CHA (ZIF-3, ZIF-10, CuBTT, MOF-177, MFI) because of their larger pore volumes. CNTs offer the highest CH4 permeation as previously predicted by molecular simulations because of the rapid transport of gases through the pores because of the specific potential energy surface of CNTs.51 After CNTs and MFI, COF-6 shows
’ CONCLUSIONS This study aimed to make predictions for adsorption, transport, and separation of CH4/H2 mixtures in three representative COF materials using atomically detailed simulations. The first examination of diffusion of an adsorbed gas mixture in a COF material was also presented. The main conclusion from this examination was that it is possible to predict mixture behavior from single component data with a high degree of accuracy for CH4/H2 mixtures in COF-6. This conclusion has important implications for predicting the possible utility of COFs in chemical separations especially in applications that rely on mass transport of adsorbed species. It was shown that by using IAST and KP correlations, it is possible to rapidly examine a large range of potential operating conditions for chemical mixtures as soon as information on each species in the COF of interest is known. If methods equivalent to the correlations explored here were not available, the performance of COFs for chemical mixtures could only be tested by accumulating detailed mixture diffusion and adsorption data at every state point relevant to the macroscopic process being examined. The results showed that COFs can be promising materials for membrane-based CH4/H2 separations compared to several IRMOF and zeolite membranes. All three COF materials studied in this work exhibited higher adsorption selectivity than membrane-based selectivity. Of course, finding examples of COFs where adsorption and diffusion do not compensate each other would be very interesting to see materials with higher membrane selectivities. At least two examples with this attractive combination of properties is known from studies of small pore MOFs demonstrating that it is possible to find COFs with these properties.52,53 In making predictions for membranes, idealized membranes from COF crystals were considered assuming that resistance to mass transfer is due to only intracrystalline diffusion. This approach has been used in previous studies of zeolite membranes54,55 and MOF membranes.5658 The aim of this type of calculation is identifying materials that have attractive intrinsic properties as defect-free crystals assuming that materials which do not have useful properties in this form are unlikely to lead to useful devices in practice. ’ ASSOCIATED CONTENT
bS
Supporting Information. Unit cell representations of COFs, tables summarizing structural properties of COFs, and the interaction potential parameters used in molecular simulations. This information is available free of charge via the Internet at http://pubs.acs.org
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT S.K. acknowledges TUBA (Turkish Academy of Sciences) supported-L’OREAL Turkey National Fellowship for Young Women in Science-2011. 1778
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