Separation of CO2–CH4 mixtures in the mesoporous MIL-100(Cr) MOF: experimental and modelling approaches

This article is published as part of the Dalton Transactions themed issue entitled:

Coordination chemistry in the solid state

Guest Editor Russell E. Morris

Published in Issue 14, Volume 41 of Dalton Transactions

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Separation of CO2–CH4 mixtures in the mesoporous MIL-100(Cr) MOF:experimental and modelling approaches†

Lomig Hamon,a Nicolas Heymans,b Philip L. Llewellyn,c Vincent Guillerm,d Aziz Ghoufi,e Sébastien Vaesen,b

Guillaume Maurin,f Christian Serre,d Guy De Weireld*b and Gerhard D. Pirngruber*a

Received 3rd November 2011, Accepted 19th January 2012DOI: 10.1039/c2dt12102f

Carbon dioxide is the main undesirable compound present in raw natural gas and biogas. Physisorptionbased adsorption processes such as pressure swing adsorption (PSA) are one of the solutions toselectively adsorb CO2 from CH4. Some hybrid crystalline porous materials that belong to the family ofmetal–organic frameworks (MOFs) show larger CO2 adsorption capacity compared to the usual industrialadsorbents, such as zeolites and most activated carbons, which makes them potentially promising for suchapplications. However, their selectivity values have been most often determined using only single gasadsorption measurements combined with simple macroscopic thermodynamic models or by means ofmolecular simulations based on generic forcefields. The transfer of this systematic approach to all MOFs,whatever their complex physico-chemical features, needs to be considered with caution. In contrast, directco-adsorption measurements collected on these new materials are still scarce. The aim of this study is toperform a complete analysis of the CO2–CH4 co-adsorption in the mesoporous MIL-100(Cr) MOF (MILstands for Materials from Institut Lavoisier) by means of a synergic combination of outstandingexperimental and modelling tools. This solid has been chosen both for its fundamental interests, given itsvery large CO2 adsorption capacities and its complexity with a combination of micropores and mesoporesand the existence of unsaturated accessible metal sites. The predictions obtained by means of GrandCanonical Monte Carlo simulations based on generic forcefields as well as macroscopic thermodynamic(IAST, RAST) models will be compared to direct the co-adsorption experimental data (breakthroughcurve and volumetric measurements).

Introduction

Carbon dioxide and methane are commonly present in fuel gasessuch as natural gas and biogas. However, CO2, one of the maingreenhouse gases, is also undesirable because it contributes todecreasing the heating value of such gases. Physisorption basedadsorption processes such as the pressure swing adsorption

(PSA) might be one of the solutions to separate CO2 from CH4.Zeolites, carbon molecular sieves and silica gel are actually thebest performing adsorbents for such a separation.1 The develop-ment of new porous materials is of main interest not only toincrease the adsorption capacities but also to improve the adsorp-tive separation capability with the aim to improve the pro-ductivity of the separation process and the purity of the products.The relatively new class of hybrid crystalline porous materials,the metal–organic frameworks (MOFs), might be an alternativeto zeolites and activated carbons in the gas separation technol-ogies. With the ambition to adapt or design adsorption-basedprocesses involving such solids, their CO2–CH4 mixture adsorp-tion performances need to be determined by either experimentalmeasurements or predictions issued from both microscopic andmacroscopic models.2

The MIL-1003a and the MIL-1013a materials show, togetherwith MOF-177,4a PCN-144b and MOF-210,4c the best CO2 andCH4 storage capacities reported so far for MOF materials. Theyoutperform those obtained for zeolites and most activated car-bons.4d Different synthesis routes,5 their catalytic properties,6 thenew properties obtained by combination with other materials7

and the adsorption properties (adsorption capacities, Henry con-stants, differential enthalpies)3b,8 of these two large pore solids

†Electronic supplementary information (ESI) available. See DOI:10.1039/c2dt12102f

aIFP Energies Nouvelles, Direction Catalyse et Séparation, Rond-pointde l’échangeur de Solaize, 69360 Solaize, France. E-mail: [email protected]; Fax: +33437702006; Tel: +33437702733bService de Thermodynamique, Université de Mons, 20 Place du Parc,7000 Mons, Belgium. E-mail: [email protected]; Fax: +3265 374209; Tel: +32 65 374205cLaboratoire Chimie Provence, UMR CNRS 6264-Universités d’Aix-Marseille I, II & III, Centre de Saint-Jérôme, 13397 Marseille cedex 20,FrancedInstitut Lavoisier, UMR CNRS 8180-Université de Versailles St Quentinen Yvelines, 45 Avenue des Etats-Unis, 78035 Versailles, FranceeInstitut de Physique de Rennes, CNRS-University of Rennes 1, UMR6251, 35042 Rennes, FrancefInstitut Charles Gerhardt, UMR 5253 CNRS-UM2-ENSCM, Universitéde Montpellier II, Place E. Bataillon, 34095 Montpellier cedex 05,France

4052 | Dalton Trans., 2012, 41, 4052–4059 This journal is © The Royal Society of Chemistry 2012

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have already been studied. Beyond their already known CO2

adsorption capacities, here we focus on their separation proper-ties, which have been not addressed so far, especially for theMIL-100(Cr), which shows the highest differences in the differ-ential adsorption enthalpies between CO2 and CH4 suggesting alarge selectivity for CO2.

3b Compared to the MIL-101 solid,MIL-100 has been less studied, most probably because of itssmaller pore volume and pore size. Nevertheless, its affinity forCO2 and CH4 is actually higher than that of theMIL-101 material.

Indeed, MIL-100(Cr) is built-up from trimers of Cr3O, whichare linked by 1,3,5-benzenetricarboxylic acids generating super-tetrahedral units: octahedral Cr are bound by 4 oxygen atomsfrom tricarboxylic groups, 1 μ3-O shared by three Cr octahedra,and 1 terminal site. The supertetrahedra, also called buildingblocks, are of 6.6 Å in diameter and form two types of differentmesoporous cages of 25 and 29 Å in diameter. The smallestcages are composed of 20 supertetrahedra forming a dodecahe-dron by joining the centres of these building blocks. The dodeca-hedron has 12 pentagonal and 4 hexagonal faces withpentagonal windows of 4.8 × 5.8 Å2. The largest cages are com-posed of 28 supertetrahedra and are accessible through 12 penta-gonal and 4 hexagonal faces.

The aperture of the hexagonal windows is 8.6 × 8.6 Å2 (seeFig. 1). The structure of the MIL-100(Cr) is an extended MTNzeolite-topology with a BET surface area of 1720 m2 g−1.3b Thisvalue is significantly lower than the theoretical accessible surfacearea (2000 m2 g−1) estimated using the method reported in theESI,† due probably to the presence of residual species within thepores. For an outgassed MIL-100(Cr) sample, i.e. MIL-100(Cr)in the dehydrated form, the terminal site can be empty or filledby a fluorine atom, according to the electroneutrality of thematerial: the average is one fluorine per chromium trimer. Thereare 0, 1, or 2 fluorines per trimer with a distribution of 37%,45%, or 18%, respectively.3c

The purpose of this study is to show the importance of collect-ing co-adsorption measurements to accurately evaluate the separ-ation performance of such a complex material, instead ofperforming only predictions based on single gas adsorption iso-therm measurements. The complexity of this material relies on

the presence of coordinatively unsaturated sites (cus sites Cr3+)and the coexistence of micropores/mesopores leading to a largepore volume. However such mixture measurements are usuallycomplicated and subject to interrogation and the accuracy isquestionable.9 We thus measure the CO2–CH4 co-adsorption at303 K for different pressures. The results are validated by com-paring two methods: breakthrough curves and volumetricmeasurements. These reliable experimental data are further ana-lysed using both molecular simulations (Grand Canonical MonteCarlo, GCMC) and thermodynamic models (Ideal Adsorbed Sol-ution Theory, IAST, and Real Adsorbed Solution Theory, RAST).

Moreover, in the literature, most of the selectivity valuesreported so far for a series of MOFs have been deduced fromsingle gas adsorption data combined with simple macroscopicmodels or predicted by molecular simulations. Here, we suggesttesting (i) different macroscopic models and (ii) molecular simu-lations coupled with a generic forcefield to predict the co-adsorp-tion data that will be compared to our own co-adsorptionmeasurements. This will establish the validity of the differentmodelling tools for accurately reproducing the co-adsorptiondata for such complex adsorbents as the MIL-100(Cr). So, weprovide for the first time a complete joint experimental/simu-lation study to characterize the CO2–CH4 separation ability ofthe MIL-100(Cr).

Experimental section

Synthesis

MIL-100(Cr) was prepared using a scaled up method inspired bythe already reported method, using a large scale mixture of met-allic chromium (260 mg, 5 mmol), trimesic acid (750 mg,3,6 mmol), a 5 M aqueous solution of hydrofluoric acid (2 mL,10 mmol) and deionised water (24 mL, 6,625 mol). The slurrywas then introduced in a 125 mL Teflon liner and further intro-duced in a metallic PARR bomb. The system was heated fromroom temperature up to 493 K using a 12 h heating ramp, andkept at 493 K for 96 h, before being cooled to room temperaturein 24 h. The unreacted metallic chromium was removed by suc-cessive decanting operations. The resulting light green productwas filtered off, washed three times with hot water (reflux), thentwice in ethanol (reflux) to remove the excess of unreactedorganic ligand and then filtered again. This synthesis has beenrepeated three times in order to obtain around 10 grams ofMIL-100(Cr). X-Ray powder diffractogram (Brüker D5000, λCu≈ 1.5406 Å) of the overall sample does not show any metallicchromium impurity (see Fig. S1†).

Nitrogen sorption measurements (77 K) after outgassing thesample overnight under secondary vacuum at 473 K (Fig. S2†)gave a BET surface area of 1720 m2 g−1 with a total porevolume of 0.793 cm3 g−1. This latter value is again significantlylower than the predicted pore volume (0.99 cm3 g−1) consideringan ideally activated material (see ESI† for the methodology).

Volumetric measurements

The principle of volumetric co-adsorption measurements10 isbased on classic pure compound manometric apparatus:11 theadsorbed quantity is calculated by subtracting the gas quantity

Fig. 1 The structure of the MIL-100(Cr): (a) trimer of chromium octa-hedra; (b) supertetrahedron and (c) view of a mesoporous cage.

This journal is © The Royal Society of Chemistry 2012 Dalton Trans., 2012, 41, 4052–4059 | 4053

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present after adsorption from the gas quantity present beforeadsorption in the installation. For calculating the gas quantities,an appropriate equation of state is used.

In this home-built apparatus,12 a cylindric piston replaces the“classic” cell and enables a change in the total volume. Thisallows the pressure to be maintained at a set point value for theco-adsorption equilibrium measurements. The gas compositionwas analyzed by a gas chromatograph coupled with a TCDdetector. More details about the co-adsorption apparatus andexperimental procedure are given in ESI.†

Breakthrough curves measurements

Breakthrough curve measurements were carried out using acolumn with a length of 8 cm and an internal diameter of1.05 cm, packed with 1.8 g of MIL-100(Cr) powder. Thecolumn was placed into an oven and was outgassed at 503 Kwith a helium flow of 1 NL h−1. After cooling the column to303 K, the helium flow was increased to 2 or 4 NL h−1 and thepressure was raised to the desired value (1, 5 or 10 bar) bymeans of a back pressure regulator. The breakthrough experimentwas triggered by switching from helium to the feed. The detectorwas a mass spectrometer (see ESI†). The normalized intensitiesmeasured by the mass spectrometer Ii are proportional to themolar flow rate in the column effluent. The stoichiometric time(or first moment) of the breakthrough front of component i, Fi(t)∼ Ii(t),

μ1;i ¼ð

1� FiðtÞFi;0

� �dt ¼

ð1� IiðtÞ

Ii;0

� �dt ð1Þ

is proportional to the amount retained in the column. In order toobtain the adsorbed amount, it must be corrected for the amountretained in the interstitial volume of the column. The finalequation for the adsorbed amount of component i, qi, is

qi ¼μ1;i � Fi;0

m� ρgas �

Fi;0

Ftot� Vcol

m� 1

ρgrain

!ð2Þ

Fi,0 is the molar feed flow rate of component i, Ftot the totalmolar feed flow rate, ρgas the feed gas density at the conditionsof the experiment, Vcol the volume of the column, m the adsor-bent mass, and ρgrain the crystallographic density of MIL-100(Cr). ρgas was calculated from the GERG equations of state.13a

Note also that the time t must be corrected for the dead time ofthe system, which was obtained in blank experiments.

The adsorption selectivity was calculated via

αij ¼ qiqj� Fj

Fið3Þ

GCMC simulations

The crystal structure of the MIL-100(Cr) was built from theatomic coordinates previously reported from X-ray diffractionstudies.3b In this structure, as mentioned in the introduction, eachoctahedral Cr is bonded to 4 oxygen atoms from carboxylates,1 μ-O and 1 terminal site. Taking into account the experimentalmolar ratio F–Cr about 30%,3c 1 fluorine atom per Cr3O trimer

was added to the exposed Cr sites. The constructed model wasthen energy minimized in the space group P1 using the Forciteprogram implemented in the Materials Studio software,14a inwhich the framework atoms were represented by the DREIDINGforcefield.14b In order to avoid time consuming density func-tional theory calculations on such a large system, the partialcharges carried by each atom of the framework were extracted asa first approximation from the electronegativity equalizationmethod.15a This protocol has been recently revealed to be suffi-ciently accurate for screening a series of MOFs for carbondioxide capture.15b These charges are reported in Table S1,† thelabels of the atoms being described in Fig. S5.† One can observethat they are similar to those previously calculated by Babaraoet al. on the MIL-101(Cr) solid using quantum calculations.15c

Regarding the adsorbates, a single uncharged Lennard-Jones(LJ) interaction site model was used to depict the CH4 moleculewith interatomic potential parameters taken from the TraPPE for-cefield.16a The CO2 molecule was represented by the conven-tional rigid charged linear triatomic model with three charged LJinteraction sites (C–O bond length of 1.149 Å) located on eachatom as developed by Harris and Yung.16b The interactionsbetween the adsorbates and the surface of the MOFs weredescribed by a combination of site–site LJ and Coulombic poten-tials, except for CH4 where only a site–site LJ potential was con-sidered. All the LJ cross interaction parameters betweenadsorbate–adsorbate and adsorbate–MOF were determined bythe Lorentz–Berthelot mixing rule.

Grand Canonical Monte Carlo simulations (GCMC) were thenconducted to explore the adsorption behaviours of the singlecomponents and their binary mixtures (gas compositions 50 : 50,25 : 75 and 75 : 25) using the simulation code CADSS (ComplexAdsorption and Diffusion Simulation Suite). The adsorbatesinvolve translational, rotational and insertion/deletion trial moveswith frequencies of 0.2, 0.2 and 0.6, respectively. The simulationbox consisted of 1 unit cell for the MIL-100(Cr). A cutoff radiusof 12.0 Å was applied to the LJ interactions, while the long-range electrostatic interactions were handled by the Ewald sum-mation technique. Periodic boundary conditions (PBC) wereconsidered in all three dimensions. Peng–Robinson equation ofstate13b was used to convert the pressure to the correspondingfugacity used in the GCMC simulations. For each state point,GCMC simulations consisted of 1 × 109 steps to ensure a con-vergence of the adsorbed amount.

Thermodynamic simulations

The ideal adsorbed solution theory (IAST) was presented byMyers and Prausnitz.17 It describes the equilibrium between aperfect gas phase and an ideal adsorbed phase. In this model, themixture adsorption equilibrium is predicted on the basis of purecomponent isotherms only. In this work, the multi-sites Lang-muir equation is chosen for pure component isothermrepresentation.

The basic equation for IAST has the following form:

pyi ¼ xipi0ðπÞ ð4Þ

In this equation p is the mixture pressure, yi and xi are the gasphase and the adsorbed phase molar fractions for component i

4054 | Dalton Trans., 2012, 41, 4052–4059 This journal is © The Royal Society of Chemistry 2012

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respectively and pi0 is the equilibrium gas phase pressure of the

pure component i corresponding to mixture temperature andspreading pressure (π), i.e. in the standard state. If the adsorbedphase is non ideal (Real Adsorbed Solution Theory, RAST), it isnecessary to take into account the non ideality of the adsorbedphase by the mean of the activity coefficients, γi(π), which arefunctions of spreading pressure:

pyiφi ¼ xipi0ðπÞγiðπÞ ð5Þ

In eqn (5), the non ideality of the gas phase is also taken intoaccount. The Peng–Robinson equation of state13b is then used todetermine the fugacity coefficient ϕi.

The excess Gibbs free energy given by Siperstein and Myers18

is used to determine activity coefficients γi(π), which takeaccount of the spreading pressure dependence of the excessterms in binary mixture:

g ex ¼ αx1x2ð1� e�CψÞ ð6Þwith ψ = πA/RTwhere A is the specific surface area.

The binary parameters are determined using binary exper-imental data by minimizing the difference between the exper-imental and calculated partial adsorbed amounts.

More details about the IAST, RAST and parameter determi-nation are given in ESI.†

Results and discussion

Volumetric experiments

It should be noted that the experimental excess amounts havebeen converted into absolute values, using the pore volumesmeasured for the sample outgassed at the correspondingtemperature.

Fig. 2 shows the adsorbed quantities as a function of thepressure for gas phase molar fraction of CO2–CH4 mixture25 : 75, 50 : 50, 75 : 25 at 3 pressures (1, 5 and 10 bar). The lessadsorbed component is always CH4. At low pressure, asexpected from previous calorimetry experiments, the adsorbedamount of CO2 is much higher than of CH4, which clearlyshows that carbon dioxide is preferentially adsorbed overmethane. CO2 most probably adsorbs at low coverage by strongcoordination with the cus Cr3+ sites, which is consistent with a

very high differential adsorption enthalpy at zero coverage of−63 kJ mol−1. It is then followed by a filling in the residual por-osity correlated with a rapid decrease of the adsorption enthalpy.In the case of CH4, the interactions between the probe moleculesand the surface are relatively moderate with a differential adsorp-tion enthalpy at zero coverage of −20 kJ mol−1. The slightdecrease of the adsorption enthalpy going with the increase ofthe CH4 coverage suggests a heterogeneous surface with weakinteractions between the non polar CH4 with metallic centres andorganic ligands (see Fig. S5†).

The CO2–CH4 adsorption selectivity is defined by the follow-ing expression: SCO2/CH4 = (xCO2/xCH4)/(yCO2/yCH4), where xCO2and xCH4 are the molar fractions of CO2 and CH4 in the adsorbedphase, respectively, while yCO2 and yCH4 are the molar fractionsof CO2 and CH4 in the gas phase, respectively.

Fig. 3 reports the selectivities for the CO2–CH4 mixture withdifferent gas phase compositions at 3 pressures, covering thevery low-quality of natural gas such as landfill gases. It showsthat the selectivities are comparable for these three examined gasphase compositions. For each mixture, the initial decrease in theprofiles shown in Fig. 3 can be attributed to the decrease of theconcentration of the strongest energetic adsorption sites that arenot anymore available for interacting with CO2 at higher press-ures. The resulting selectivity for the CO2–CH4 mixture at lowpressure is around 6–8. This selectivity is on the whole compar-able to the experimental values in Cu-BTC (5–10),19a as well asthe simulated data obtained for both the dehydroxylated (5–7)19b

and hydroxylated (6–10) forms of the UiO-66(Zr),19c,b and forthe flexible MIL-53(Al) (4–7).2f However, the adsorbed amountsare higher than in other potential MOFs promising for the CO2–

CH4 separation, while they are similar to the best CO2 storagecapacity for certain MOFs.4

Breakthrough curve measurements

Fig. 4 shows the breakthrough curves of an equimolar CO2–CH4

mixture at 1, 5, 10 and 20 bar. The less adsorbed componentCH4 always breaks first and its breakthrough curve exhibits a so-called roll-up, which means that the flow rate at the column exitexceeds the feed flow rate for some period of time.

The explanation for this phenomenon is that CH4 is firstadsorbed and thereby concentrated in the adsorbent, but thendesorbed by CO2 whose concentration front advances slower

Fig. 2 Experimental absolute adsorption isotherms for CO2 (fullsymbols) and CH4 (open symbols) in the MIL-100(Cr) at 303 K for thegas phase molar fractions of CO2(blue)–CH4(red) mixture of 25 : 75(square), 50 : 50 (circle), 75 : 25 (triangle).

Fig. 3 Experimental CO2 selectivities in the MIL-100(Cr) at 303 K forthe gas phase molar fractions of CO2–CH4 mixture of 25 : 75 (greensquare), 50 : 50 (blue circle), 75 : 25 (red triangle).

This journal is © The Royal Society of Chemistry 2012 Dalton Trans., 2012, 41, 4052–4059 | 4055

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through the column than that of CH4. The desorption of the CH4

that was concentrated in the adsorbent by incoming CO2 makesthe CH4 flow rate rise above the feed flow rate. The net amountof adsorbed CH4 at the end of the breakthrough experiment is,therefore, the amount that was initially adsorbed (before break-through of CH4) minus the amount desorbed by CO2 (the areaabove F/F0 = 1). This results in a relatively large error bar.

The amount of adsorbed CH4 was, therefore, also evaluatedfrom integration of the desorption curve and from a breakthroughcurve of CH4–CO2 on a column that was initially equilibratedwith CO2. In this way the roll-up of CH4 can be avoided. Aver-aging these results yields a more reliable value of the adsorbedquantity of CH4.

Fig. 4 reveals that there is a second peak in the roll-up of CH4.This might be caused by the thermal wave that accompanies theconcentration front of CO2, because of the high exothermicity ofCO2 adsorption. The temperature increase further enhances thedesorption of CH4.

Since not all the experiments were carried out at the samefeed flow rate, the time axis in Fig. 4 is normalized by thecontact time (contact time = Vcol/volumetric flow rate): τ = time/contact time. We can observe that the adimensional stoichio-metric breakthrough time of CO2 decreases with increasingpressure. The reason is that the CO2 isotherm is concave and theslope of the isotherm decreases with the pressure increase. Inother words, the more the pressure increases, the less theadsorbed amount is proportional to the pressure.

The breakthrough curve of CO2 becomes also more dispersedas the pressure increases. This corresponds to a progressive shifttowards the linear part of the CO2 isotherm as the pressureincreases. Therefore, the compressive effect of a concave iso-therm on the breakthrough front diminishes. On the other hand,the molecular diffusion coefficient decreases because it is inver-sely proportional to the pressure. As a result of both effects thedispersion increases.

Fig. 5 shows the binary adsorption isotherms, which areextracted from the breakthrough curve experiments and the

corresponding CO2 selectivity is presented in Fig. 6a. The selec-tivity decreases from 1 to 5 bar as already shown by volumetricmeasurements and then increases again for the highest pressures.The selectivities are higher in the case of data extracted frombreakthrough curves, which might be explained by the uncertain-ties of such measurements.

Indeed, for both volumetric and breakthrough curve methods,the uncertainty on the adsorbed amounts is estimated between0.1 and 0.3 mmol g−1. This value strongly influences the deter-mination of the CO2 selectivity because of the accumulation ofthe uncertainties. That is why the error bars on Fig. 6a are solarge.

The CO2–CH4 breakthrough curve experiments have beenconducted with different molar ratios of CO2–CH4 at 5 bar andthe selectivity evaluated as a function of the composition. Thedata points at 5 bar fit well into the selectivities obtained atdifferent pressures if the partial pressure of CO2 is chosen as thex-axis (see Fig. 6b). This indicates that the selectivity is mainlygoverned by the partial pressure of CO2. As expected, the higherselectivity at low partial pressure of CO2 and its sharp decreaseat higher partial pressure (∼4 bar) correspond, in the same waythan in volumetric measurements, to the strong interaction ofCO2 with the cus sites of MIL-100(Cr) at low coverage only.Finally, the gradual increase of selectivity at higher pressures is aphenomenon observed on most adsorbents20 and can be attribu-ted to stronger adsorbate–adsorbate interactions for CO2 than forCH4.

Fig. 4 Breakthrough curves of a 50 : 50 CO2–CH4 mixture overMIL100-Cr at 303 K and different pressures: (a) 1 bar, (b) 5 bar, (c) 10bar, (d) 20 bar.

Fig. 5 Adsorption isotherms of CO2 (circle) and CH4 (triangle) inMIL-100 (Cr) at 303 K for an equimolar gas phase mixture in: isothermsobtained from breakthrough experiments (open symbols) and volumetricmeasurements (full symbols).

Fig. 6 (a) Experimental CO2 selectivities for an equimolar bulkmixture in MIL-100(Cr) at 303 K obtained from breakthrough exper-iments (open symbols) and volumetric measurements (full symbols); (b)CO2 selectivity data obtained at different pressures and compositionsfrom breakthrough experiments as a function of the partial pressure ofCO2.

4056 | Dalton Trans., 2012, 41, 4052–4059 This journal is © The Royal Society of Chemistry 2012

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Thermodynamic models and GCMC simulations

The first step in the co-adsorption thermodynamic models is thedetermination of pure experimental isotherms (see ESI andFig. S6). The multisite Langmuir models reproduce the exper-imental data within 1% for carbon dioxide and 4% for methane.The resulting parameters can be found in Table S2.†

The experimental and IAST simulated results agree verypoorly for the less adsorbed component, CH4 (Fig. 7). The devi-ation factors are indeed 4% for CO2 and 39% for CH4. It isnecessary to keep in mind that the studied material is rather acomplex system for the reasons mentioned above. Indeed, theadsorbent exhibits a crystalline structure with different adsorp-tion sites and pore sizes and CH4 interacts weakly with highenergetic sites contrary to CO2. Thus, such a system is not reallyideal and does not correspond to the hypothesis of the idealadsorbed solution. In this context, much attention should be paidto the selectivity values of some MOFs extracted from the idealadsorption solution theory without experimental co-adsorptionmeasurement. The use of a more elaborated theory as the RASTprovides an improvement in the modeling of the adsorption equi-librium. The deviation factors with RAST are 3.7% and 9.2% forCO2 and for CH4, respectively. This predicted adsorbed amountof CH4 is lower but remains within the experimental uncertaintyvalues.

In a highly selective system, a good precision of the adsorbedamount for the less adsorbed species using the adsorbed solutiontheory is difficult to obtain. In this case, the p0 value determinedfor the less adsorbed compound is always greater than themixture pressure. These values exceed the range of the exper-imental single component isotherm (for example, at 10 bar andfor a 50 : 50 mixture, p0(CH4) is hgher than 100 bar). As areminder, the values p0 are used to determine the adsorbed quan-tity (see ESI for the methodology). The real adsorption of pureCH4 is not known at such high pressures and its extrapolationstrongly depends on the choice of the isotherm model. Theimprovement obtained with RAST can be explained by the factthat this model considers an additional term (eqn (6)).

Still, we have to conclude that the MIL-100(Cr) system is toocomplex to be accurately predicted from pure component data bymacroscopic co-adsorption models. For such systems, we alwaysneed binary mixture adsorption data in required temperature andpressure ranges to use RAST and describe their behavior in thewhole composition range.

At the microscopic scale, Grand Canonical Monte Carlo simu-lations are the most adapted techniques to predict the adsorption/coadsorption performance of porous adsorbents. Fig. S8† com-pares the simulated absolute adsorption isotherms for the pureCO2 and CH4 on the MIL-100(Cr) to those from experimentalmeasurements. While the calculations reproduce relatively wellthe adsorbed amounts for both gases in the intermediate range ofpressure ∼10–15 bar, some deviations are observed at highpressures, where the simulated values overestimate the exper-imental data. Such a discrepancy is not unexpected as the pres-ence of residual trimesic acid or inorganic species within thepores, not totally removed during activation, might limit theavailable space. In contrast to that, molecular simulations arecarried out in perfect and infinite MIL-100(Cr) crystals whoseaccessible surface area and pore volume are almost 20% largerthan the experimental data as mentioned above. This has beenalready pointed out in a series of MOFs for differentadsorbates.21

In addition, although the low domain of pressure of theadsorption isotherm is well described for CH4, there is a signifi-cant discrepancy for CO2. This deviation cannot be assigned tothe set of charges used if we refer to the conclusions drawn pre-viously on the MIL-101(Cr)–CO2 system, which clearly statedthat the simulated data are only slightly affected by the chargescarried by the MOF framework.15c This observation suggeststhat the generic forcefield that was considered here and pre-viously by others15c for treating MOFs containing coordinativeunsaturated sites fails to correctly describe the interactionsbetween quadrupolar adsorbate molecules and the cus sites thattake place at the initial stage of the adsorption. To address such aproblem, Chen et al., has very recently proposed to directlyimplement a potential energy surface calculated by a hybrid DFTmethod in the GCMC scheme for the Cu-BTC cus MOF typesolid.22 However, while this approach is very accurate, it can beeasily considered for such a large unit cell crystal structure andanother route would be necessary to be envisaged, which is outof scope of this paper.

Fig. 8 compares the simulated absolute isotherms for the threegas mixture compositions to those obtained by volumetricmeasurements. One observes: that the experimental trend is wellreproduced with CO2 preferentially adsorbed compared to CH4

in the whole range of pressure. However, while the calculatedadsorbed amounts match well the experimental data for CH4,there is a significant deviation for CO2, the simulations

Fig. 7 Experimental absolute adsorption isotherms (symbol), IAST (dotted line) and RAST (full line) of CO2 (blue lines) and CH4 (red lines) in theMIL-100(Cr) at 303 K, for the gas phase mole fractions of CO2–CH4 mixture (a) 75 : 25, (b) 50 : 50 and (c) 25 : 75.

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underestimating the experimental loading. This latter point iscaused again by the failure of the generic forcefield to accuratelydescribe the interactions between quadrupolar molecules and thecus sites.

Conclusions

A complete analysis of the CO2–CH4 co-adsorption in the micro-porous–mesoporous MIL-100(Cr) MOF has been performed bycombining experimental and modelling tools. The resultingselectivity for the CO2–CH4 mixture is around 6–8 at lowpressure and decreases when the pressure increases. This selec-tivity is on the whole comparable to the experimental valuesalready reported in the literature for some MOFs.

The predictions obtained by macroscopic thermodynamic(IAST) model have been compared to direct co-adsorptionexperimental data (breakthrough curve and volumetric measure-ments). The predicted selectivities strongly differ because theMIL-100(Cr) has very large CO2 adsorption capacities and lowerones for CH4 due to the existence of unsaturated accessiblemetal sites, which interact predominantly with CO2 molecules.The use of a more elaborated theory as the RAST combined withbinary mixture adsorption data provides a significant improve-ment in the modeling of the co-adsorption equilibrium. Wefurther emphasize that molecular simulations based on ageneric forcefield fail to reproduce the co-adsorption datacollected on such a MOF containing coordinatively unsaturatedsites. This study shows the necessity of collecting co-adsorption measurements to accurately evaluate the separationperformance of complex materials rather than simply performingpredictions based on single gas adsorption isothermmeasurements.

From an application point of view, it is quite unlikely thatMIL-100(Cr) itself will be used for CO2 capture applications,notwithstanding its attractive adsorption capacity and selectivity.The reason is that there are serious environmental concernsabout the toxicity of Cr and the use of HF in the synthesis ofMIL-100(Cr). The Fe-analogue of MIL-100 is an environmen-tally more viable alternative, but the activation of MIL-100(Fe)is more difficult and the solid is therefore less suited for funda-mental studies.

Acknowledgements

The French authors acknowledge the financial support of theFrench ANR “NOMAC” (ANR-06-CO2-008) and the UEthrough the FP6-STREP “DeSANNS” (SES6-020133). Theauthors from Universities of Mons, Versailles, Montpellier andMarseille acknowledge the financial support of the EuropeanCommunity’s Seventh Framework Programme (FP7/2007-2013)“Macademia” under grant agreement no. 228862.

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Fig. 8 Experimental absolute adsorption isotherms (full symbol), GCMC (open symbol) for CO2 (blue) and CH4 (red) in the MIL-100(Cr) at 303 K,for the gas phase mole fractions of CO2–CH4 mixture of (a) 75 : 25, (b) 50 : 50 and (c) 25 : 75.

4058 | Dalton Trans., 2012, 41, 4052–4059 This journal is © The Royal Society of Chemistry 2012

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