Molecular simulation studies of separation of CH4/H2 mixture in metal-organic frameworks with interpenetration and mixed-ligand

Chemical Engineering Science 66 (2011) 3012–3019

Contents lists available at ScienceDirect

Chemical Engineering Science

0009-25

doi:10.1

n Corr

E-m

journal homepage: www.elsevier.com/locate/ces

Molecular simulation studies of separation of CH4/H2 mixture inmetal-organic frameworks with interpenetration and mixed-ligand

Bei Liu n, Changyu Sun, Guangjin Chen

State Key Laboratory of Heavy Oil Processing, China University of Petroleum, Beijing 102249, China

a r t i c l e i n f o

Article history:

Received 28 January 2011

Received in revised form

31 March 2011

Accepted 4 April 2011Available online 15 April 2011

Keywords:

Separations

Adsorption

Diffusion

Simulation

Metal-organic framework

Natural gas

09/$ - see front matter & 2011 Elsevier Ltd. A

016/j.ces.2011.04.004

esponding author. Tel.: þ86 10 89733252; fa

ail address: [email protected] (B. Liu).

a b s t r a c t

In our previous work, we have investigated the adsorption selectivity of CH4/H2 in three pairs of

isoreticular metal-organic frameworks (IRMOFs) with and without interpenetration to study the effect

of interpenetration on gas mixture separation through Monte Carlo simulation. In addition, the self-

diffusivities and the diffusion mechanism of single H2 and CH4 in these MOFs were examined by

molecular dynamics simulations. In this work, we extend our previous work to mixed-ligand MOFs to

investigate the effects of interpenetration as well as mixed-ligand on both equilibrium-based and

kinetic-based gas mixture separation. We found that methane adsorption selectivity is much enhanced

in the selected mixed-ligand interpenetrated MOFs compared with their non-interpenetrated counter-

parts, similar to what we found before for IRMOFs with single-ligand. At room temperature and

atmospheric pressure, molecular-level segregation was observed in the mixed-ligand MOFs, and the

extent of the effects of interpenetration is comparable for single-ligand and mixed-ligand MOFs. In

addition, we found that the diffusion selectivity in the interpenetrated MOFs is similar to the one in

their non-interpenetrated counterparts, while the permeation selectivity in the former is much higher

than that in the latter, which corroborates our expectation that interpenetration is a good strategy to

improve the overall performance of a material as a membrane in separation applications based only on

the single component diffusion results. Furthermore, the CH4 permeability of the selected MOF

membrane was also evaluated.

& 2011 Elsevier Ltd. All rights reserved.

1. Introduction

Metal-organic frameworks (MOFs), a new family of hybridporous materials that are formed by the coordination of metalions with organic linkers, have attracted considerable attentionnowadays. By a rational combination of different metals withdifferent organic linkers, these materials feature opportunities forfunctionality and structure. To date a large number of differentMOFs have been synthesized, which have shown various promis-ing applications in, for example, gas storage and separation, andso on (Eddaoudi et al., 2001; Ferey, 2008; Li et al., 2009; Muelleret al., 2006; Murray et al., 2009; Rowsell and Yaghi, 2005).

According to the structural characteristics, MOFs can becategorized into two types: those with non-interpenetratedframeworks (Kaye and Long, 2008; Kubota et al., 2005) and thosewith interpenetrated ones (Chen et al., 2007a; Kesanli et al.,2005). It is known that the loadings of the single gas componentat relatively low temperatures and pressures and the adsorptionseparation selectivity of gas mixtures are enhanced in

ll rights reserved.

x: þ86 10 89732126.

interpenetrated MOFs, due to the formation of additional smallpores and adsorption sites by the interpenetration of frameworks(Chen et al., 2006, 2007a, 2007b; Jung et al., 2006; Liu et al.,2008a; Ma et al., 2007; Ryan et al., 2008). These results indicatethat MOFs with interpenetration may serve as a good membranein separation applications. However, to draw a definite conclusionand design these interpenetrated MOFs for specific applications,we do need to know both adsorption and diffusion characteristicsof gas mixtures in these MOF pores quantitatively. To the best ofour knowledge, there is no experimental study measuring diffu-sivity of gas mixtures in interpenetrated MOFs to date, whiletheoretically, in our previous work, only the effect of interpene-tration on single H2 and CH4 diffusion were investigated (Liuet al., 2008b; Xue et al., 2009). Regarding the separation of gasmixtures based on diffusion selectivities and permeation selectiv-ities, Keskin and Sholl (2009) systematically investigated theseparation of CH4/H2, CO2/CH4, and CO2/H2 mixtures in eightMOFs, including one interpenetrated MOFs, i.e. IRMOF-9. Noinformation is available for mixture diffusion in other interpene-trated MOFs. In addition to MOFs with interpenetration, MOFswith multi-linkers or multi-ligands also exhibit great promise forgas storage and separation, as found by Deng et al. (2010)recently. Based on their adsorption separation results, we may

B. Liu et al. / Chemical Engineering Science 66 (2011) 3012–3019 3013

expect that MOFs with multi-linkers or multi-ligands can alsoserve as a good membrane in separation applications.

In this work, molecular simulation studies were carried out ineight MOFs with mixed-ligand and with or without interpenetration(Farha et al., 2010) to investigate the effects of interpenetration aswell as mixed-ligand on adsorption, diffusion, and separation of gasmixtures. CH4/H2 system was selected as the model mixture toseparate. The reason why we chose CH4/H2 is that firstly this isan important practical system that is involved in the processof purification of synthetic gas obtained from steam re-forming ofnatural gas (Mitchell et al., 2004). Secondly, adsorption separation ofCH4/H2 in several interpenetrated IRMOFs with single-ligand wasalready studied in our previous work (Liu et al., 2008a), which couldbe used for comparison for studying the effect of mixed-ligand ongas mixture separation. The adsorption selectivities of CH4/H2

system in the selected MOFs were studied in detail. In addition,the diffusion, the permeation selectivities of CH4/H2 system as wellas the CH4 permeability through the selected MOF membranes werecalculated. The potential of this kind of materials in equilibrium-based and kinetic-based separation applications was evaluated inthis work. The knowledge obtained is expected to apply to a broadrange of interpenetrated MOFs for separation of various gas mixturesystems of practical importance and accelerate the development ofappropriate interpenetrated MOF adsorbents and membranes.

2. Models and computational method

2.1. MOF structures

In this work, four pairs of mixed-ligand MOFs with andwithout interpenetration were selected, and their structures wereconstructed from their corresponding experimental XRD data(Farha et al., 2010). L5-L1, -L2, -L3, and -L4 (correspond tomaterials 1, 3, 5, and 7 in Farha et al. (2010)) are pillaredpaddlewheel interpenetrated MOFs, which are formed by thetetracarboxylic acid ligand (4,40,400,400 0-benzene-1,2,4,5-tetrayl-tetrabenzoic acid, L5) with ligand 4,4-bipyridine (L1), 4,40-Azo-pyridine (L2), di-3,6-(4-pyridyl)-1,2,4,5-tetrazine ligand (L3), andN,N0-di-(4-pyridyl)-1,4,5,8-naphthalenetetracarboxydiimide (L4),respectively. The linear L1, L2, L3, or L4 ligand produces a pillaredpaddlewheel structure that is interpenetrated where the strutresides directly in the middle of the diamond-shaped cavitiesformed by two of the L5 ligands (Farha et al., 2010). L6-L1, -L2, -L3, and -L4 (correspond to materials 2, 4, 6, and 8 in Farha et al.(2010)) are non-interpenetrated paddlewheel MOFs formed byligand L6 (bearing two large bromine atoms instead of hydrogenatoms (as in L5)) with ligand L1, L2, L3, and L4, respectively.Among these materials, L5-L1, -L2, -L3, and -L4 are the inter-penetrated counterparts of L6-L1, -L2, -L3, and -L4, respectively.

Table 1Structural properties for the MOFs studied in this work.

Material Structure Unit cell (A)

L6-L1 Pillared paddlewheel a¼11.2038, b¼13.975, c¼15.848

L6-L2 Pillared paddlewheel a¼11.711, b¼15.6181, c¼16.0362

L6-L3 Pillared paddlewheel a¼11.6151, b¼15.648, c¼18.163

L6-L4 Pillared paddlewheel a¼10.1617, b¼16.451, c¼22.313

L5-L1 Paddlewheel/interpenetration a¼14.008, b¼11.521, c¼15.701

L5-L2 Paddlewheel/interpenetration a¼15.654, b¼15.9467, c¼11.6268

L5-L3 Paddlewheel/interpenetration a¼15.674, b¼18.118, c¼11.5857

L5-L4 Paddlewheel/interpenetration a¼22.898, b¼15.668, c¼22.389

a Obtained from the XRD crystal data (Farha et al., 2010).b Calculated in this work. Details of calculation are given in Section 2.5.

The guest-free crystal structures of these eight MOFs can be foundin Farha et al. (2010) and some details of the structures of theseMOFs are summarized in Table 1.

2.2. Force field

Force field plays an important role in molecular simulations.For describing the adsorption and diffusion of mixtures of CH4

and H2 molecules in the selected MOFs, we used the followingmodels. CH4 was modeled as a single Lennard–Jones (LJ) interac-tion site model and the potential parameters were taken from theTraPPE force field (Martin and Siepmann, 1998). H2 was modeledas a rigid diatomic molecule with bond length of 0.74 A, and eachatom H was represented as a LJ interaction site using the potentialparameters developed by Yang and Zhong (2005). Electrostaticinteractions were not included, as previous simulations haveshown that the effects of these interactions on the adsorptionof hydrogen in MOFs are very small at room temperature(Garberoglio et al., 2005). The above potential models have beensuccessfully used to model adsorption, diffusion, and separationof methane and hydrogen in MOFs (Duren and Snurr, 2004; Liuet al., 2008a, 2008b; Surble et al., 2006; Xue et al., 2009; Yang andZhong, 2005). For the MOFs studied here, the site-site LJ potentialwas used to calculate the interactions between adsorbate mole-cules and adsorbents. In our simulations, all the LJ cross interac-tion parameters were determined by the Lorentz–Berthelotmixing rules. An atomistic representation was used for MOFsstudied. The dispersive interactions of all of the atoms in MOFsare modeled by the Universal Force Field (UFF) of Rappe et al.(1992), which has been successfully employed to depict theadsorption (Babarao and Jiang, 2008a; Garberoglio et al., 2005;Krungleviciute et al., 2007), diffusion (Liu et al., 2008b; Skoulidas,2004; Skoulidas and Sholl, 2005; Xue et al., 2009), and separation(Babarao et al., 2007; Babarao and Jiang, 2008b; Keskin and Sholl,2007; Liu et al., 2008a) of several light gases and their mixtures inMOFs. The potential parameters used are listed in Table 2.

2.3. Monte Carlo simulation

Grand-canonical Monte Carlo (GCMC) simulations wereemployed to calculate the adsorption of mixtures in MOFsstudied. The Peng–Robinson equation of state was used to relatethe bulk experimental pressure with chemical potential requiredin the GCMC simulations. The simulation box contained 12 unitcells for L6-L1, -L2, -L3, -L4 (3�2�2), L5-L1 (2�3�2), and L5-L2, -L3, (2�2�3), while 8 (2�2�2) unit cells were adopted forL5-L4. Similar to most simulation works about MOFs-relatedsystems (Duren et al., 2009; Han et al., 2009; Liu and Zhong,2010), the selected MOFs in this work were treated as rigidframeworks, with atoms frozen at their crystallographic positions

Cell angle (deg.) qcrysa(g/cm3) Vpore

b(cm3/g) Porosity b(%)

a¼b¼g¼90 0.669 1.15 76.6

a¼g¼90, b¼90.205 0.582 1.36 79.0

a¼g¼90, b¼93.202 0.546 1.48 81.1

a¼b¼g¼90 0.562 1.43 80.5

a¼g¼90, b¼96.679 1.197 0.27 32.0

a¼b¼g¼90 0.995 0.52 52.0

a¼b¼g¼90 0.934 0.63 59.2

a¼b¼g¼90 0.911 0.61 56.0

Table 2LJ potential parameters for CH4, H2, and the MOFs used in this work.

LJ Parameters CH4 H2_H MOF_Zn MOF_O MOF_C MOF_H MOF_N MOF_Br

s (A) 3.73 2.72 2.46 3.12 3.43 2.57 3.26 3.73

e/kB (K) 148.0 10.0 62.40 30.19 52.84 22.14 34.72 126.31

B. Liu et al. / Chemical Engineering Science 66 (2011) 3012–30193014

during the simulations. It has been shown that the flexibility ofthe framework has a negligible influence on the adsorption ofgases (Vlugt and Schenk, 2002). Therefore, the treatment of rigidframework is reasonable. A cutoff radius of 12.8 A was applied toall the LJ interactions. For each state point, GCMC simulationconsisted of 1.5�107 steps, to guarantee equilibration, followedby 1.5�107 steps to sample the desired thermodynamic proper-ties. The statistical uncertainty was estimated by dividing eachrun into 10 blocks and calculating the standard deviation from theblock averages. The standard deviation is within 75% for everysimulation. A detailed description of the simulation methods canbe found in Frenkel and Smit (2002) and Dubbeldam et al. (2004).

2.4. Molecular dynamics simulation

In this work, equilibrium molecular dynamics (MD) simula-tions were carried out in the canonical (NVT) ensemble toinvestigate the effects of interpenetration on the diffusion beha-viors of CH4/H2 mixture in the selected MOFs. The whole MDsimulations were performed under room temperature, and theNose–Hoover chain (NHC) thermostat as formulated by Martynaet al. (1996) was used to maintain the constant temperaturecondition. All the MOFs were treated as rigid with atoms frozenat their crystallographic positions during simulations. Althoughthe effect of the dynamics of MOFs may be significant on gasdiffusivity (Amirjalayer et al., 2007), this effect becomes signifi-cant only when the guests are large and/or strong guest-hostinteractions exist in the system. The velocity Verlet algorithm wasused to integrate Newton’s equations of motion. The time stepused in the MD simulations was taken as 1.0 fs and the totalsimulation time is 20.0 ns. All the LJ interactions were calculatedusing the cut and shifted potential with a 12.8 A cutoff radius, andperiodic boundary conditions were applied in all three dimen-sions. At least 10 independent simulations were performed foreach loading to estimate the statistical error. During each simula-tion, the trajectory of the system was saved every 100 steps tosubsequently calculate the self-diffusion coefficient Ds by mean-square displacements (MSDs) method using a so-called order-N

algorithm (Skoulidas, 2004; Skoulidas and Sholl, 2005). It waschecked that MD simulations conducted in microcanonical (NVE)ensemble gave the equivalent results.

2.5. Definitions of pore volume Vpore, porosity, adsorption selectivity,

diffusion selectivity, and permeation selectivity

The pore volume Vpore can be determined using the proceduredescribed by Myers and Monson (2002) and Duren et al. (2004):

Vpore ¼ 1=m�

Z Vpore

0expð�UðrÞ=kBTÞdr

where U is the interaction energy between a single helium atomand the framework, and m is the mass of the framework. A singlehelium molecule is chosen as the probe molecule and thesimulation is carried out at 298.15 K. 298.15 K is always chosenas the reference temperature for the experimental determinationof the helium void volume, then this value is also used inthe simulations. Using the Widom particle insertion method

(Frenkel and Smit, 2002), the pore volume can be readilycomputed from Monte Carlo sampling. The force field for He–Heinteractions is taken from Talu and Myers (2001) with s(A)¼2.64and e/kB(K)¼10.9. The interactions between He and the atoms ofthe MOF structures were determined using the Lorentz–Berthelotmixing rules. The pore volume data obtained are shown inTable 1. Porosity j, is then given by Vpore/Vtotal, where Vtotal isthe total volume of the unit cell of the framework.

In separation processes a good indication of the ability forseparation is the selectivity of a porous material for differentcomponents in mixtures. The adsorption selectivity for compo-nent A relative to component B is defined by Sads¼(xA/xB)(yB/yA),where xA and xB are the mole fractions of components A and B inthe adsorbed phase, and yA and yB are the mole fractions ofcomponents A and B in the bulk phase, respectively.

As proposed by Krishna and van Baten (2007) and modified byKeskin and Sholl (2009), the diffusion selectivity of component A

from component B was calculated as the ratio of self-diffusivitiesin a binary mixture, DA,self, evaluated directly at their correspond-ing adsorbed compositions (xA, xB):Sdiff¼DA,self (xA, xB)/DB,self(xA, xB).In this study, all mixture self-diffusivities were reported asaverage diffusivities using Di,self¼(Di,self, xþDi,self, yþDi,self, z)/3.

Predicting the permeation selectivity is specifically importantfor assessing MOFs in membrane-based separation processes. Thepermeation selectivity of MOF membranes can be approximatedas the multiplication of adsorption selectivity and diffusionselectivity (Keskin and Sholl, 2009): Sperm(A/B)¼Sads(A/B)� Sdiff(A/B)

3. Results and discussion

3.1. Adsorption selectivity

3.1.1. Effect of interpenetration on adsorption separation

As a first step, we performed molecular simulations to calcu-late the adsorption selectivity of methane from the binarymixture of CH4/H2 in the eight selected MOFs to investigate theeffect of interpenetration on adsorption selectivity. All simula-tions were carried out at 298 K and the bulk phase composition isspecified in terms of fugacity.

Fig. 1 shows that the adsorption selectivities of CH4 in theMOFs with interpenetration (L5-L1, -L2, -L3, and -L4) are muchhigher than those in their corresponding non-interpenetratedcounterparts (L6-L1, -L2, -L3, and -L4). Although a change fromL5 moiety (aryl-H moiety) to L6 moiety (aryl-Br furnished on thetetraacid ligand moiety), i.e. the presence of the Br functionalgroups in L6 ligand, should increase the amount of adsorption inthe order CH44H2, resulting in an increase in the adsorptionselectivities of CH4/H2 in the L6-based MOFs as compared withthe L5-based MOFs, this is not true as seen from Fig. 1, indicatingthat interpenetration is the main factor that significantlyimproves the adsorption selectivity for CH4/H2 system. A compar-ison with other typical porous materials shows that L5-basedmixed-ligand interpenetrated MOFs are promising candidates formaking highly selective adsorbents. For example, at room tem-perature and moderate pressure, the selectivity of CH4 is 14.6,22.6, and 20.1 in interpenetrated IRMOF-9, -11, and -13,

B. Liu et al. / Chemical Engineering Science 66 (2011) 3012–3019 3015

respectively (Liu et al., 2008a), 3.7 in IRMOF-10 (Liu et al., 2008a),5.6 in IRMOF-12 (Liu et al., 2008a), 5.1 in IRMOF-14 (Liu et al.,2008a), 5.0 in MOF-5 (Yang and Zhong, 2006a), 13.3 in Cu-BTC(Yang and Zhong, 2006a), �5 in IRMOF-8 (Keskin and Sholl,2009), �12 in COF-102 (Keskin and Sholl, 2009), �7 in ZIF-60(Guo et al., 2010), and �12 in ZIF-67 (Guo et al., 2010).

3.1.2. Effect of mixed-ligand on adsorption separation for

non-interpenetrated MOFs

In order to investigate the effect of mixed-ligand on theadsorption separation performance of MOFs, the correspondingsingle-ligand MOFs are required for comparison. In this work, L6-L1 and L6-L3 were chosen as the starting mixed-ligand materialsand three MOFs, IRMOF-10 (Eddaoudi et al., 2002), MOF-single(the MOF synthesized by Farha et al. (2008), which is denoted asMOF-single here), and IRMOF-16 (Eddaoudi et al., 2002) wereselected to mimic the corresponding single-ligand MOFs con-structed by L1, L6, and L3, respectively. Though the ligands inthese three MOFs are slightly different with the ligands in L6-L1and L6-L3 (we could not find MOFs with exactly the same ligandas the ones in L6-L1 and L6-L3), we think the results obtained arestill meaningful and can be used for future reference for studyingthe effects of mixed-ligand on adsorption separation of MOFs. Forclarity, the structures of ligands in these MOFs are shown in Fig. 2.

The adsorption selectivity of methane from CH4/H2 in two setsof MOFs, i.e. (a) L6-L1, MOF-single, and IRMOF-10 and (b) L6-L3,

Fig. 1. Adsorption selectivities for CH4 from an equimolar binary mixture of

CH4/H2 as a function of the total bulk fugacity at 298 K.

Fig. 2. Structures of ligands

MOF-single, and IRMOF-16 are given in Fig. 3. Fig. 3a and b showsthat the adsorption selectivities in the MOFs with mixed-ligandare in between the two corresponding single-ligand MOFs. Ofcourse, the adsorption separation behaviors shown in Fig. 3 arenot only the result of the effect of mixed-ligand, but the interplayof many influencing factors, such as pore size and pore topology,etc. It would be desirable if we can take advantage of the single-ligand by tuning the way of mixing them.

Furthermore, the occupying situation of methane and hydro-gen in the gas mixture was studied in detail. Fig. 4 shows thecenter of mass (COM) distributions of these gases in L6-L1, MOF-single, and IRMOF-10 at 0.1 MPa, as examples. Here we show theCOM distributions of each component for clarity.

As can be seen from Fig. 4a, strongest adsorption for methaneoccurs in the diamond-shaped cavities formed by L6 ligands andmost of methane molecules are in these cavities. However,hydrogen is preferably adsorbed in the regions between thecavities due to the competitive adsorption between CH4 and H2,as shown in Fig. 4d. We could say that molecular-level segrega-tion occurs in this case. As to MOF-single and IRMOF-10 (Fig. 4b,c, e, and f), we did not find molecular-level segregation.

This kind of molecular-level segregation has been found forCO2-related mixtures in some MOFs because of the distribution ofthe electrostatic potential in the pores (Wu et al., 2010; Yang andZhong, 2006b). In addition, Dubbeldam et al. (2008) reported anunusual molecular-level segregation of alkane isomers in onemixed-ligand MOF, MOF-1. They suggested that by tuning the‘‘width’’ and ‘‘length’’ of the linker, as well as the distancebetween the boxes, it is possible to design and creation of highlyselective adsorption sites in MOFs (Dubbeldam et al., 2008). Wethink these findings also apply to our study, that is, by choosingthe appropriate ligands and tuning the way of mixing them, it ispossible to design MOFs with good adsorption separation perfor-mance for CH4/H2 mixture.

3.1.3. Effect of mixed-ligand on adsorption separation for

interpenetrated MOFs

To study the effect of mixed-ligand on the adsorption separa-tion performance for interpenetrated MOFs, we compared theresults obtained in this work with our previous work (Liu et al.,2008a). A similar trend was found, that is, the adsorptionselectivity of CH4/H2 mixtures is greatly enhanced by the inter-penetration of frameworks for all the MOFs considered, eitherwith single-ligand or mixed-ligand. The increment is about 4–7times compared to their non-interpenetrated counterparts. How-ever, the values in interpenetrated MOFs with mixed-ligandstudied in this work are generally higher than the ones ininterpenetrated MOFs with single-ligand. We may say that by

in the selected MOFs.

40L6-L1MOF-singleIRMOF-10

L6-L3MOF-singleIRMOF-16

30

20

10

S ads

CH

4/H

2

S ads

CH

4/H

2

00.0 0.5 1.0 1.5 2.0

40

30

20

10

00.0

Total fugacity of the bulk fluid phase f [MPa]Total fugacity of the bulk fluid phase f [MPa]

0.5 1.0 1.5 2.0

Fig. 3. Adsorption selectivities for CH4 from an equimolar binary mixture of CH4/H2 as a function of the total bulk fugacity at 298 K in (a) L6-L1, MOF-single, and IRMOF-10

and in (b) L6-L3, MOF-single, and IRMOF-16.

Fig. 4. The COM distributions of CH4 in (a) L6-L1 (the left picture is a sideview of the diamond-shaped cavities formed by L6. The cavities are pillared by L1. The right

picture is the view of the cavities along L1), (b) MOF-single, and (c) IRMOF-10 and H2 in (d) L6-L1, (e) MOF-single, and (f) IRMOF-10 at 0.1 MPa (Zn, gray; O, red; C, light

blue; N, dark blue; Br, green; and H, white). Brighter colors indicate a higher gas COM distribution density. (For interpretation of the references to color in this figure

legend, the reader is referred to the web version of this article.)

B. Liu et al. / Chemical Engineering Science 66 (2011) 3012–30193016

adopting the strategy of generating interpenetration and usingmixed-ligand, high adsorption selective MOFs could be designed.

In addition, our previous work (Liu et al., 2008a) found that theselectivity distribution of methane is heterogeneous in the mate-rial, with highest selectivity occurs in the small pores and lowestselectivity in the center of the large pores for interpenetratedIRMOFs with single-ligand. This is also true for the interpene-trated MOFs studied in this work with mixed-ligand. Fig. 5 showsthe center of mass (COM) distributions of methane and hydrogenin L5-L3 at 0.1 MPa, as an example. Clearly, from Fig. 5 we can seethat larger selectivity should occur in the small pores formed byinterpenetration, while smaller selectivity occurs in thelarger pores.

3.1.4. IAST predictions

It has been commonly recognized that ideal adsorbed solutiontheory (IAST) (Myers and Prausnitz, 1965) can give good predic-tions of CH4/H2 mixture adsorption in many single-ligand MOFs

(Keskin and Sholl, 2009; Liu et al., 2008a; Yang and Zhong, 2006a).IAST calculations were then performed in this work to checkwhether it is applicable for mixed-ligand MOFs (both with andwithout interpenetration). The calculated adsorption selectivitiesof CH4 from equimolar mixtures CH4/H2 in L5-L2, L5-L3, L6-L2,and L6-L3 with GCMC and IAST are shown in Fig. 6 as an example.In all the cases, good agreement between GCMC simulation andIAST calculation was obtained, indicating that IAST is applicableto predict the adsorption behavior of CH4/H2 mixtures in themixed-ligand MOFs.

3.2. Diffusion selectivity and permeation selectivity

Nowadays, studies on the performance of MOFs as membranesfor separation applications have attracted considerable attention.Therefore, the diffusion selectivity and permeation selectivity ofL5-L2 were further simulated as an example To draw a definiteconclusion whether interpenetration is a good strategy toimprove the performance of a material as a membrane in

Fig. 5. The COM distribution of CH4 and H2 in L5-L3 (Zn, gray; O, red; C, light blue;

N, dark blue; and H, white). Brighter colors indicate a higher gas COM distribution

density. (For interpretation of the references to color in this figure legend, the

reader is referred to the web version of this article.)

Fig. 6. Comparison of IAST and GCMC for CH4 selectivity as a function of pressure

from equimolar binary mixture of CH4/H2 at 298 K in L5-L2, L5-L3, L6-L2, and

L6-L3.

Fig. 7. Adsorption selectivity, diffusion selectivity, and permeation selectivity for

CH4 from an equimolar binary mixture of CH4/H2 in L5-L2 and L6-L2 as a function

of the total bulk fugacity at 298 K. The results in L5-L2 are given in open symbols

and those in L6-L2 are given in close symbols.

B. Liu et al. / Chemical Engineering Science 66 (2011) 3012–3019 3017

separation applications, the diffusion selectivity and permeationselectivity of L6-L2 were also simulated for comparison, and theresults for both MOFs are shown in Fig. 7.

Fig. 7 shows that diffusion selectivity of CH4/H2 is less thanunity in both L5-L2 and L6-L2, indicating that the stronglyadsorbed component CH4 diffuses slower than the weaklyadsorbed component H2. A slight increase in diffusion selectivitieswas found with increasing pressure and this can be attributed tothe reason that at higher loadings CH4 reduces the diffusivity ofthe faster diffusing component, H2, in adsorbed mixture, whichcauses higher diffusion selectivities toward CH4. In our previouswork (Xue et al., 2009), we found the relative diffusivity of CH4

and H2 (based on the self-diffusivity of the single CH4 and H2

component) in the interpenetrated IRMOFs is much higher thanthose in their corresponding non-interpenetrated counterpartsand concluded that interpenetration may significantly enhancethe dynamic selectivity for CH4/H2. By examining the truemixture diffusion, however, we found that the diffusion selectiv-ities of CH4/H2 in L5-L2 and L6-L2 are comparable. In order to

understand membrane-based separation process, a detailedunderstanding of both molecular adsorption and diffusion of gasmixtures is required. Furthermore, in our previous work (Liuet al., 2008b; Xue et al., 2009) we found that in IRMOFs withsingle-ligand, interpenetration reduces gas diffusivity at roomtemperature. A similar trend was observed in this work for L5-L2and L6-L2 with mixed-ligand based on the self-diffusivities of twocomponents in the mixture.

Permeation selectivities of L5-L2 and L6-L2 membranes werepredicted using Sperm(A/B)¼Sads(A/B)� Sdiff(A/B). This approximateexpression for MOF membranes was already validated by Keskinand Sholl (2009) and has been used to predict the permeationselectivity of MOF and zeolite membranes for various gas mix-tures (Keskin, 2010; Keskin and Sholl, 2009; Krishna and vanBaten, 2010). Fig. 7 shows that the permeation selectivities forCH4 in both L5-L2 and L6-L2 are smaller than the correspondingadsorption selectivities because of the low diffusion selectivity.The same trend was also observed by Keskin and Sholl (2009) forother MOF membranes . Because of its much higher adsorptionselectivity, interpenetrated L5-L2 still shows higher permeationselectivity than its non-interpenetrated counterpart, L6-L2, indi-cating that interpenetration is a good strategy to improve theperformance of a material as a membrane in separation applica-tions. It is useful to compare the performance of L5-L2 with othernanoporous membranes. Separation of equimolar mixture ofCH4/H2 has been performed by many groups at room temperatureand moderate pressures. For example, the permeation selectivityof CH4 is �4 in interpenetrated IRMOF-9 (Keskin and Sholl, 2009),�1 in IRMOF-1, -8, -10, and -14 (Keskin and Sholl, 2009), �3 inCOF-102 (Keskin and Sholl, 2009), �8 in SAPO-34 membranes(Poshysta et al., 2000), �2 in microporous SSF membrane (Vieira-Linhares and Seaton, 2003), and �13 in carbon nanotubes (Chenand Sholl, 2006). The comparison shows that L5-L2 is a promisingcandidate for making highly selective membranes.

As discussed by Krishna and van Baten (2010), from a mem-brane process development point of view, except for permeationselectivity, the gas permeability of the membrane is another pointthat needs to be considered. Membranes with high gas selectivityand high gas permeability are desired materials for separationpurpose. Therefore, in this work the CH4 permeability through theL5-L2 membrane at 298 K was also evaluated and compared withother typical nanoporous materials. Method suggested by Krishna

Fig. 8. Comparison of L5-L2 membrane with other nanoporous membranes for

CH4/H2 separation. Data for materials CHA, LTA, MFI, ZIF-8, and CNT were taken

from Krishna and van Baten (2010) at 300 K.

B. Liu et al. / Chemical Engineering Science 66 (2011) 3012–30193018

and van Baten (2010) was used to calculate this permeability.

PA ¼j� DA,self � cA=fA

where PA is the permeability of the component A (mol/m/s/Pa), jis the porosity of the material, DA,self is the self-diffusivity ofcomponent A in the mixture (m2/s), cA is the concentration ofcomponent A at the upstream face of the membrane (mol/m3),and fA is the bulk phase fugacity of the component A (Pa). Similarto what Krishna and van Baten (2010) did for CO2-relatedmixtures, the Robeson plot ((2008) for a chosen upstream totalfugacity 1 MPa was constructed in this work for CH4/H2, in whichthe permeation selectivities are plotted against the CH4 perme-ability, PCH4

, expressed in Barrers, as shown in Fig. 8. This figureshows that L5-L2 is among the best MOFs and zeolites for CH4/H2

separation, further corroborating that interpenetration is a goodstrategy to make the material as a membrane in separationapplications.

4. Conclusions

This work shows that methane adsorption selectivity ismuch enhanced in the selected mixed-ligand interpenetratedMOFs compared with their non-interpenetrated counterparts,and the trend of the increment is similar to what we foundbefore for IRMOFs with single-ligand. At low pressures molecular-level segregation occurs for CH4/H2 mixture in the mixed-ligandMOFs, which suggests the possibilities for designing highselective MOFs.

With respect to diffusion selectivity, we found that the one inthe interpenetrated MOFs is comparable with that in their non-interpenetrated counterparts. In addition, we found that permea-tion selectivity of gases through interpenetrated MOF membranesis higher than the one in their non-interpenetrated counterparts,indicating that interpenetration is a good strategy to improvethe performance of a material as a membrane in separationapplications.

Acknowledgments

The financial supports of the NSFC (nos. 21006126, 20925623),the Research Funds of China University of Petroleum, Beijing

(BJBJRC-2010-01), the Research Fund for the Doctoral Program ofHigher Education (20100007120009) and the National BasicResearch Program of China (2009CB219504) are greatlyappreciated.

References

Amirjalayer, S., Tafipolsky, M., Schmid, R., 2007. Molecular dynamics simulation ofbenzene diffusion in MOF-5: importance of lattice dynamics. Angew. Chem.Int. Ed. 46, 463.

Babarao, R., Hu, Z., Jiang, J., Chempath, S., Sandler, S.I., 2007. Storage and separationof CO2 and CH4 in silicalite, C-168 schwarzite, and IRMOF-1: a comparativestudy from Monte Carlo simulation. Langmuir 23, 659.

Babarao, R., Jiang, J., 2008a. Molecular screening of metal-organic frameworks forCO2 storage. Langmuir 24, 6270.

Babarao, R., Jiang, J., 2008b. Diffusion and separation of CO2 and CH4 in silicalite,C168 schwarzite, and IRMOF-1: a comparative study from molecular dynamicssimulation. Langmuir 24, 5474.

Chen, B., Liang, C., Yang, J., Contreras, D.S., Clancy, Y.L., Lobkovsky, E.B., Yaghi, O.M.,Dai, S., 2006. A microporous metal-organic framework for gas-chromato-graphic separation of alkanes. Angew. Chem. Int. Ed. 45, 1390.

Chen, H.B., Sholl, D.S., 2006. Predictions of selectivity and flux for CH4/H2

separations using single walled carbon nanotubes as membranes. J. Membr.Sci. 269, 152.

Chen, B., Ma, S., Hurtado, E.J., Lobkovsky, E.B., Zhou, H.C., 2007a. A triplyinterpenetrated microporous metal-organic framework for selective sorptionof gas molecules. Inorg. Chem. 46, 8490.

Chen, B., Ma, S., Zapata, F., Fronczek, F.R., Lobkovsky, E.B., Zhou, H.C., 2007b.Rationally designed micropores within a metal-organic framework for selec-tive sorption of gas molecules. Inorg. Chem. 46, 1233.

Deng, H., Doonan, C.J., Furukawa, H., Ferreira, R.B., Towne, J., Knobler, C.B., Wang,B., Yaghi, O.M., 2010. Multiple functional groups of varying ratios in metal-organic frameworks. Science 327, 846.

Dubbeldam, D., Calero, S., Vlugt, T.J.H., Krishna, R., Maesen, T.L.M., Smit, B., 2004.United atom force field for alkanes in nanoporous materials. J. Phys. Chem. B108, 12301.

Dubbeldam, D., Galvin, C.J., Walton, K.S., Ellis, D.E., Snurr, R.Q., 2008. Separationand molecular-level segregation of complex alkane mixtures in metal-organicframeworks. J. Am. Chem. Soc. 130, 10884.

Duren, T., Sarkisov, L., Yaghi, O.M., Snurr, R.Q., 2004. Design of new materials formethane storage. Langmuir 20, 2683.

Duren, T., Snurr, R.Q., 2004. Assessment of isoreticular metal-organic frameworksfor adsorption separations: a molecular simulation study of methane/n-butanemixtures. J. Phys. Chem. B 108, 15703.

Duren, T., Bae, Y.S., Snurr, R.Q., 2009. Using molecular simulation to characterisemetal-organic frameworks for adsorption applications. Chem. Soc. Rev. 38,1237.

Eddaoudi, M., Moler, D.B., Li, H., Chen, B., Reineke, T.M., O’Keeffe, M., Yaghi, O.M.,2001. Modular chemistry: Secondary building units as a basis for the design ofhighly porous and robust metal-organic carboxylate frameworks. Acc. Chem.Res. 34, 319.

Eddaoudi, M., Kim, J., Rosi, N., Vodak, D., Wachter, J., O’Keeffe, M., Yaghi, O.M.,2002. Systematic design of pore size and functionality in isoreticular MOFsand their application in methane storage. Science 295, 469.

Farha, O.K., Mulfort, K.L., Hupp, J.T., 2008. An example of node-based postassemblyelaboration of a hydrogen-sorbing, metal-organic framework material. Inorg.Chem. 47, 10223.

Farha, O.K., Malliakas, C.D., Kanatzidis, M.G., Hupp, J.T., 2010. Control overcatenation in metal-organic frameworks via rational design of the organicbuilding block. J. Am. Chem. Soc. 132, 950.

Ferey, G., 2008. Hybrid porous solids: past, present, future. Chem. Soc. Rev. 37,191.

Frenkel, D., Smit, B., 2002. Understanding Molecular Simulations: From Algorithmsto Applications, second ed. Academic Press, San Diego, CA.

Garberoglio, G., Skoulidas, A.I., Johnson, J.K., 2005. Adsorption of gases in metalorganic materials: Comparison of simulations and experiments. J. Phys. Chem.B 109, 13094.

Guo, H., Shi, F., Ma, Z., Liu, X., 2010. Molecular simulation for adsorption andseparation of CH4/H2 in zeolitic imidazolate frameworks. J. Phys. Chem. C 114,12158.

Han, S.S., Mendoza-Cortes, J.L., Goddard, W.A., 2009. Recent advances on simula-tion and theory of hydrogen storage in metal-organic frameworks andcovalent organic frameworks. Chem. Soc. Rev. 38, 1460.

Jung, D.H., Kim, D., Lee, T.B., Choi, S.B., Yoon, J.H., Kim, J., Choi, K., Choi, S., 2006.Grand canonical Monte Carlo simulation study on the catenation effect onhydrogen adsorption onto the interpenetrating metal-organic frameworks.J. Phys. Chem. B 110, 22987.

Kaye, S.S., Long, J.R., 2008. Matrix isolation chemistry in a porous metal-organicframework: photochemical substitutions of N2 and H2 in Zn4O[(Z6-1,4-benzenedicarboxylate)Cr(CO)3]3. J. Am. Chem. Soc. 130, 806.

Kesanli, B., Cui, Y., Smith, M.R., Bittner, E.W., Bockrath, B.C., Lin, W., 2005. Highlyinterpenetrated metal-organic frameworks for hydrogen storage. Angew.Chem. Int. Ed. 44, 72.

B. Liu et al. / Chemical Engineering Science 66 (2011) 3012–3019 3019

Keskin, S., Sholl, D.S., 2007. Screening metal-organic framework materials for mem-brane-based methane/carbon dioxide separations. J. Phys. Chem. C 111, 14055.

Keskin, S., Sholl, D.S., 2009. Efficient methods for screening of metal organicframework membranes for gas separations using atomically detailed models.Langmuir 25, 11786.

Keskin, S., 2010. Molecular simulation study of CH4/H2 mixture separations usingmetal organic framework membranes and composites. J. Phys. Chem. C 114,13047.

Krishna, R., van Baten, J.M., 2007. Using molecular simulations for screening ofzeolites for separation of CO2/CH4 mixtures. Chem. Eng. J. 133, 121.

Krishna, R., van Baten, J.M., 2010. In silico screening of zeolite membranes for CO2

capture. J. Membr. Sci. 360, 323.Krungleviciute, V., Lask, K., Heroux, L., Migone, A.D., Lee, J.-Y., Li, J., Skoulidas, A.,

2007. Argon adsorption on Cu3 (benzene-1, 3, 5-tricarboxylate)2(H2O)3

metal�organic framework. Langmuir 23, 3106.Kubota, Y., Takata, M., Matsuda, R., Kitaura, R., Kitagawa, S., Kato, K., Sakata, M.,

Kobayashi, T.C., 2005. Direct observation of hydrogen molecules adsorbed ontoa microporous coordination polymer. Angew. Chem. Int. Ed. 44, 920.

Li, J., Kuppler, R.J., Zhou, H., 2009. Selective gas adsorption and separation inmetal-organic frameworks. Chem. Soc. Rev. 38, 1477.

Liu, B., Yang, Q., Xue, C., Zhong, C., Chen, B., Smit, B., 2008a. Enhanced adsorptionselectivity of hydrogen/methane mixtures in metal-organic frameworks withinterpenetration: a molecular simulation study. J. Phys. Chem. C 112, 9854.

Liu, B., Yang, Q., Xue, C., Zhong, C., Smit, B., 2008b. Molecular simulation ofhydrogen diffusion in interpenetrated metal-organic frameworks. Phys. Chem.Chem. Phys. 10, 3244.

Liu, D., Zhong, C., 2010. Understanding gas separation in metal–organic frame-works using computer modeling. J. Mater. Chem. 20, 10308.

Ma, S., Sun, D., Ambrogio, M., Fillinger, J.A., Parkin, S., Zhou, H.C., 2007. Framework-catenation isomerism in metal-organic frameworks and its impact on hydro-gen uptake. J. Am. Chem. Soc. 129, 1858.

Martin, M.G., Siepmann, J.I., 1998. Transferable potentials for phase equilibria. 1.United-atom description of n-alkanes. J. Phys. Chem. B 102, 2569.

Martyna, G., Tuckerman, M.E., Tobias, D.J., Klein, M.L., 1996. Explicit reversibleintegrators for extended systems dynamics. Mol. Phys. 87, 1117.

Mitchell, M.C., Gallo, M., Nenoff, T.M., 2004. Computer simulations of adsorptionand diffusion for binary mixtures of methane and hydrogen in titanosilicates.J. Chem. Phys. 121, 1910.

Mueller, U., Schubert, M., Teich, F., Puetter, H., Schierle-Arndt, K., Pastre, J., 2006.Metal-organic frameworks—prospective industrial applications. J. Mater.Chem. 16, 626.

Murray, L.J., Dinca, M., Long, J.R., 2009. Hydrogen storage in metal-organicframeworks. Chem. Soc. Rev. 38, 1294.

Myers, A.L., Monson, P.A., 2002. Adsorption in porous materials at high pressure:theory and experiment. Langmuir 18, 10261.

Myers, A.L., Prausnitz, J.M., 1965. Thermodynamics of mixed-gas adsorption. AIChEJ. 11, 121.

Poshysta, J.C., Tuan, V.A., Pape, E.A., Noble, R.D., Falconer, J.L., 2000. Separation oflight gas mixtures using SAPO-34 membranes. AIChE J. 46, 779.

Rappe, A.K., Casewit, C.J., Colwell, K.S., Goddard III, W.A., Skiff, W.M., 1992. UFF, afull periodic table force field for molecular mechanics and molecular dynamicssimulations. J. Am. Chem. Soc. 114, 10024.

Robeson, L.M., 2008. The upper bound revisited. J. Membr. Sci. 320, 390.Rowsell, J.L.C., Yaghi, O.M., 2005. Strategies for hydrogen storage in metal-organic

frameworks. Angew. Chem. Int. Ed. 44, 4670.Ryan, P., Broadbelt, L.J., Snurr, R.Q., 2008. Is catenation beneficial for hydrogen

storage in metal-organic frameworks? Chem. Commun. 35, 4132.Skoulidas, A.I., 2004. Molecular dynamics simulations of gas diffusion in metal-

organic frameworks: argon in CuBTC. J. Am. Chem. Soc. 126, 1356.Skoulidas, A.I., Sholl, D.S., 2005. Self-diffusion and transport diffusion of light gases

in metal-organic framework materials assessed using molecular dynamicssimulations. J. Phys. Chem. B 109, 15760.

Surble, S., Millange, F., Serre, C., Duren, T., Latroche, M., Bourrelly, S., Llewellyn, P.L.,Ferey, G., 2006. Synthesis of MIL-102, a chromium carboxylate metal-organicframework, with gas sorption analysis. J. Am. Chem. Soc. 128, 14889.

Talu, O., Myers, A.L., 2001. Molecular simulation of adsorption: Gibbs dividingsurface and comparison with experiment. AIChE J. 47, 1160.

Vieira-Linhares, A.M., Seaton, N.A., 2003. Non-equilibrium molecular dynamicssimulation of gas separation in a microporous carbon membrane. Chem. Eng.Sci. 58, 4129.

Vlugt, T.J.H., Schenk, M., 2002. Influence of framework flexibility on the adsorptionproperties of hydrocarbons in the zeolite silicalite. J. Phys. Chem. B 106, 12757.

Wu, D., Xu, Q., Liu, D., Zhong, C., 2010. Exceptional CO2 capture capability andmolecular-level segregation in a Li-modified metal-organic framework. J. Phys.Chem. C 114, 16611.

Xue, C., Zhou, Z., Liu, B., Yang, Q., Zhong, C., 2009. Methane diffusion mechanism incatenated metal-organic frameworks. Mol. Sim. 35, 373.

Yang, Q., Zhong, C., 2005. Molecular simulation of adsorption and diffusion ofhydrogen in metal-organic frameworks. J. Phys. Chem. B 109, 11862.

Yang, Q., Zhong, C., 2006a. Molecular simulation of carbon dioxide/methane/hydrogen mixture adsorption in metal-organic frameworks. J. Phys. Chem. B110, 17776.

Yang, Q., Zhong, C., 2006b. Electrostatic-field-induced enhancement of gas mixtureseparation in metal-organic frameworks: a computational study. Chem. Phys.Chem. 7, 1417.