Diffusion of Binary CO2/CH4 Mixtures in the MIL-47(V) and MIL-53(Cr)Metal−Organic Framework Type Solids: A Combination of NeutronScattering Measurements and Molecular Dynamics SimulationsFabrice Salles,† Herve Jobic,*,‡ Thomas Devic,§ Vincent Guillerm,§ Christian Serre,§ Michael M. Koza,∥

Gerard Ferey,§ and Guillaume Maurin*,†

†Institut Charles Gerhardt Montpellier − UMR CNRS 5253, UM2, ENSCM-Universite Montpellier 2, Place E. Bataillon, 34095Montpellier Cedex 05, France‡Institut de Recherches sur la Catalyse et l’Environnement de Lyon, UMR 5256 CNRS, Universite Lyon 1, 2 avenue Albert Einstein,69626 Villeurbanne cedex, France§Institut Lavoisier, UMR CNRS 8180, Universite de Versailles Saint-Quentin-en-Yvelines, 45 avenue des Etats-Unis, 78035 Versaillescedex, France∥Institut Laue Langevin, BP 156, 38042 Grenoble cedex, France

*S Supporting Information

ABSTRACT: The dynamics of CO2 and CH4 in a mixture ofdifferent compositions has been explored in two metal−organicframeworks, namely, MIL-47(V) and MIL-53(Cr), by combiningmolecular dynamics (MD) simulations and quasi-elastic neutronscattering (QENS) measurements. The experimental and simulatedself-diffusion coefficient (Ds) values for CH4 are in very goodagreement in the whole range of the CO2 explored loadings. It isclearly stated that CH4 which shows a fast diffusivity at low loadingbecomes significantly slower in both metal−organic frameworks(MOFs) when CO2 molecules are introduced within the porositiesof these materials. Further, compared to its behavior in a singlecomponent, CH4 tends to diffuse slightly faster in the presence ofCO2. The MD simulations revealed that this speeding up isconcomitant with a mutual speeding up or a slowing down of the slower CO2 molecules in MIL-47(V) and MIL-53(Cr),respectively. Analysis of the MD trajectories emphasizes that both gases in the mixture follow individually a 1D-type diffusionmechanism in both MOFs, where the CO2 molecules diffuse close to the pore wall while the motions of CH4 are restricted in thecentral region of the tunnel.

■ INTRODUCTION

The elimination of carbon dioxide from a gas mixturecontaining methane is of great economic and technologicalimportance in the treatment of low-quality natural gas such asbiogas and landfill gases. The industrial feasibility of such aselective CO2 capture has been extensively demonstrated usingeither amine-based chemisorption or physisorption techniquessuch as the pressure swing adsorption (PSA) that involves theuse of porous media.1 In this latter process, the conventionaladsorbents including the porous zeolites and activated carbonsare widely employed. However, throughout the past decade, theassociated research on porous metal−organic frameworks(MOFs) has established that this relatively new class ofmaterials can show great promises over the other families ofporous solids for mixture separation.2−5 The interest of theseMOF type materials strongly relies on their high versatility,allowing a possible modulation of not only their chemicalfeatures including the nature of both the inorganic subunits and

the organic moieties associated to form the structures but alsoof their possible connectivity and topology.2,6−9 Owing to theirmany fascinating characteristics, above their prospectiveapplications in different fields related to catalysis, biology/medicine, and physics,2,9−22 a few of these materials exhibitperformances of great importance for the CO2/CH4 separationpurpose with a relatively high selectivity combined to apotential regeneration in mild conditions that are expected tolead to a higher productivity and a lower energetic cost for theindustrial process.8,16,23−46 As typical examples, it has beendemonstrated that while certain MOFs with ultrahigh porosity,such as MIL-101, MOF-177, or UMCM-2, are able to adsorblarge amounts of CO2 and CH4

47,48 some others including afew functionalized MOFs such as the UiO-66(Zr)s series, the

Received: April 1, 2013Revised: May 6, 2013Published: May 8, 2013

Article

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flexible MIL-53(Al)-NH2, the SIFSIX, and the ZIFs solidssignificantly outperform the CO2/CH4 selectivity of the mostcommonly employed NaY Faujasite type adsorbent in PSAapplications.49−58 These latter conclusions have been primarilybased on studies which explored only the thermodynamicaspect of the separation process and which emphasized that theselective capture of CO2 can be driven either by interactionswith specific adsorption sites or by steric hindrance. However,above the thermodynamic consideration, the kinetics can alsosignificantly impact such separation processes. Indeed, it is ofinterest to probe the dynamics of the confined CO2 and CH4species in MOFs for gaining preliminary fundamental insightinto the mechanisms in play. While the diffusion of the singlegases has been intensively investigated in MOFs,59−67 only avery few experimental and simulated data have been reportedso far on the mobility of the binary mixtures.36,54,57,68−72 Muchof the work on this topic has been addressed computationallywith significant contributions from Keskin and Sholl67,69−72

who explored the dynamics of a series of gas mixtures in someMOFs for further evaluating their separation performances asmembranes. Krishna et al.54 have also investigated the impact ofthe pore size and topology of various MOFs on the diffusivityof several binary mixtures. In addition, following previousstudies on zeolites,73,74 the only experimental investigationsemanate from us coupling quasi-elastic neutron scattering(QENS) measurements and molecular dynamics (MD)simulations to probe the codiffusion of CO2/CH4 and xyleneisomers in the 3D pore UiO-66(Zr)57 and in the 1D pore MIL-47(V),75 respectively.In light of this lack of available literature, much effort is still

required to get a complete picture of the separation processesthat are in play in some of the most promising MOFs. To thatpurpose, based on previous successful QENS−MD combinedstudies on the molecular motions of pure and mixed fluids(hydrogen, benzene, short and long linear alkanes, carbondioxide, water, ...) confined in diverse MOFs,57,59−66,75 here wepropose to adopt this joint experimental/modeling approach toexplore the codiffusion of CO2 and CH4 within the porosity oftwo MOFs, namely, MIL-47(V) and MIL-53(Cr).76,77 TheseMOF type solids have been selected as recent thermodynamicstudies have revealed that for distinct reasons both solids can berelatively attractive for the separation of the gas mixture ofinterest. Indeed, MIL-47(V) which is built up from chainscorner sharing VO6 octahedra interconnected by terephthalatelinkers defining a 1D type diamond-shaped pore system (Figure1) shows a moderate selectivity toward CO2 due to the absenceof specific adsorption sites at its pore wall surface combined toa relatively high working capacity which makes this materialpromising in the area of separation.76,78 At a variance, MIL-53(Cr) which is isostructural to MIL-47(V) with the μ2-Overtices substituted by the μ2-OH groups has been shown to behighly CO2 selective in a specific pressure range, a phenomenonattributed to the breathing behavior of this solid that can switchfrom its initial large pore (LP) form to a narrow pore (NP)version upon CO2/CH4 adsorption, the pore dimensions of thislatter structure being able to only trap CO2 while CH4 isexpulsed.16

In the present work, we aim to (i) determine the loadingdependence of the self-diffusivity for CH4 in the presence ofCO2 in the MIL-47(V) and MIL-53(Cr), (ii) compare bothprofile and absolute diffusion coefficient values with thoseobtained for the single component, and further (iii) address themicroscopic codiffusion mechanism for both diffusive species

through a detailed analysis of both QENS spectra and MDtrajectories.

■ MATERIALS AND METHODSMaterial. Deuterated MIL-53(Cr) and MIL-47(V) samples

were synthesized and activated according to the publishedprocedures,61,65,79 using d4-terephthalic acid (Eurisotop,France) and hydrogenated solvent. After activation, thehydrogen atoms of the hydroxyl groups in MIL-53(Cr) wereexchanged with deuterium by stirring in deuterated waterovernight at room temperature.

Quasi-Elastic Neutron Scattering Measurements. Theneutron experiments were performed at the Institut Laue-Langevin (Grenoble, France) using the time-of-flight (TOF)spectrometer IN6. The main characteristics of this instrumentare an intermediate elastic resolution (of the order of 80 μeV,full-width at half-maximum, for an incident energy of 3.12meV) but a very high flux which is obtained by vertical andhorizontal focusing. After scattering from the sample, theneutrons pass through a box filled with helium toward a bank ofdetectors covering a range of scattering angles 10° < θ < 115°.The TOF spectra were grouped into several Q-space regions,avoiding the Bragg peaks of the MILs. The correspondingelastic wave-vector transfers, Q, ranged from 0.25 to 1.6 Å−1.The Bragg peaks of the MOF were determined on thespectrometer by comparing the intensities of the elastic peaks ateach angular position with those obtained from a standardvanadium plate (vanadium was also used to measure theinstrumental resolution). Since the scattering from thehydrogen atoms of the terephthalate linker is incoherent, theframework was deuterated as previously mentioned to reducethe signal between the Bragg peaks.The MOFs were activated by pumping under slow heating

up to 473 K (final pressure below 10−3 Pa). The solids werethen transferred inside a glovebox into slab-shaped aluminumcontainers, which could be connected to a gas inlet systemallowing in situ adsorption. After measuring the scattering ofthe empty materials, and after a preliminary adsorption of CH4,three and five successive concentrations of CO2 were

Figure 1. View of the MIL-47(V) structure along the chain (z axis),highlighting the 1D pore system. The MIL-53(Cr) structure isobtained by substituting the μ2-O by μ2-OH groups. The vanadium,oxygen, carbon, and hydrogen atoms are represented in green, red,gray, and white, respectively.

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investigated at 230 K for MIL-47(V) and MIL-53(Cr),respectively, to explore the self-diffusion for CH4. Theinvestigated loadings correspond to 0.5 CH4 and 0.6, 1.7, and2.8 CO2 molecules per unit cell (u.c.) for MIL-47(V) and to 0.8CH4 and 0.8, 1.4, 1.8, 2.8, and 3.3 CO2 molecules/u.c. for MIL-53(Cr). These amounts adsorbed were determined byvolumetry and then compared to the adsorption isothermsmeasured independently.16 The groupings of spectra weretreated by standard correction programs, subtracting the signalsof the empty MILs, and the TOF axis was converted to energytransfer.Computational Method. Microscopic Model and Force

Field. The structure models for MIL-47(V) and MIL-53(Cr)were built up from the crystallographic coordinates available inthe literature.76,77 MIL-47(V) was considered as a rigidframework consistently with the unchanged position of thewhole Bragg peaks (see Figure S1, Supporting Information)observed during the QENS experiments upon coadsorption.This assumption has been previously validated for a series ofsingle guest molecules diffusing within the porosity of thismaterial.60−62,64−66 MIL-53(Cr) was treated in a firstapproximation as being rigid in its large pore (LP) form,while the impact of the flexibility has been further evaluated.The partial charges carried by each atom of the MILframeworks were taken from our previous DFT calculations.61

The 12-6 Lennard-Jones (LJ) interatomic potential parametersfor MIL-53(Cr) were extracted from our previous inves-tigation80 and were transferred to MIL-47(V) solid except thatthe vanadium atom was treated by the UFF force field.81 Such aparametrization has already been successfully employed toreproduce the dynamic behavior of CO2 and CH4 as singlecomponent in the considered MOFs.61,63,64 For the MDsimulations conducted with a flexible MIL-53(Cr) framework,we implemented our own force field that was shown toaccurately capture the breathing of this material upon theadsorption of a series of single gas molecules.80 While CO2 wastreated using the EPM2 model developed by Harris andYung,82 CH4 was described by our previous force field that wassuccessfully employed to deal with the thermodynamicsproperties of this adsorbate in different MOFs.61,83 In thesemicroscopic representations, CO2 and CH4 are represented bya three and five-point charged LJ model, respectively,considered as rigid in our simulations. Note that these twomodels have already been coupled to successfully describe thecoadsorption behavior of these gases at various compositions inMIL-53(Cr) and in the zeolite NaY.16,84 The adsorbate/adsorbent LJ interatomic potential parameters were thenestimated using the Lorentz−Berthelot mixing rule.Molecular Dynamics Simulations. Molecular dynamics

(MD) simulations were performed using the DL_POLY_2.19program85 in the NVT ensemble at 230 K with the Berendsenensemble. As mentioned above, complementary simulationswere realized with a flexible framework for MIL-53(Cr). In thislatter case it was evidenced that both calculated trends andabsolute values of Ds for CO2 and CH4 (Figure S2, SupportingInformation) are very similar to those obtained when rigidframeworks are considered. Indeed, the flexibility of the LPform has therefore only a weak impact on the diffusionmechanism occurring in MIL-53(Cr), as already observed forthe diffusivity of the single gas CO2 in the same solid.63

All these calculations were run considering a simulation cellbox consisting of 32 unit cells to get good statistics and thecritical size to maintain a consistent cutoff distance of 12 Å to

be applied to the LJ interactions (rc < L/2, L = the smallestlength of box). Each simulation was conducted for 10 ns (i.e.,107 steps with a time step of 1 fs) after 1 ns of equilibration.The electrostatic interactions were handled using the Ewaldsummation technique.86 The SHAKE-RATTLE and the usualVelocity Verlet algorithms were used to constrain rigid bondsand to integrate the equations of motion, respectively. As thediffusive species were maintained as rigid, the QUATERNIONalgorithm was employed to treat their motions.From these simulations, the self-diffusivity Ds for CH4 and

CO2 in binary mixture components was extracted for thedifferent loadings mentioned below. They were determined foreach investigated concentration (c) using the Einstein relation87

reported in eq 1.

∑= ⟨ − ⟩→∞ =

D ct

r t r o( ) lim16

[ ( ) ( )]t j

N

j js1

2

(1)

In this equation, ⟨...⟩ denotes an ensemble average; r(t) are thepositions of the tagged guest molecule; while N corresponds tothe number of adsorbate molecules in the simulation volume.Further, to improve the statistics of the calculation, multipletime origins as described elsewhere87 were used with an averagevalue over five independent trajectories.The MD simulations were performed only in the LP form of

MIL-53(Cr) loaded first by 0.8 CH4/u.c. using CanonicalMonte Carlo simulations, the CO2 molecules being successivelyadded in a range of [1−6 molecules/u.c.] to be consistent withthe experimental conditions. The structure behavior of MIL-53(Cr) upon coadsorption of CO2 and CH4 was shown to berather complex and both dependent on the total pressure andthe CO2/CH4 ratio.

16 The consideration of only the LP form ofthe MIL-53(Cr) for our diffusion investigation is justified asfollows. One can imagine that the gas molecules in the mixturecan be distributed as (i) CO2 and CH4 molecules both in theLP, (ii) only CH4 or CO2 molecules in the LP, (iii) CO2 andCH4 molecules both in the NP, (iv) only CH4 molecules in theNP, and (v) only CO2 molecules in the NP. The scenario (iii)can be straightforwardly eliminated as our previous thermody-namic studies of different mixture CO2/CH4 compositions haveclearly established that CH4 cannot coexist with CO2 in a NPform. Similarly, one can exclude the presence of only CH4 in aNP form as the neutron diffraction patterns (see Figure S3,Supporting Information) show the same Bragg peaks as thosecharacteristics of the NP in the presence of a CO2/CH4mixture. The existence of a narrow pore form filled by CH4would lead to a set of additional peaks in the diffractogramsassigned to the more open narrow pore structure previouslyevidenced for the Al analogue upon adsorption of CH4 only atvery low temperature.88 Further, Grand Canonical Monte Carlo(GCMC) simulations realized on a large simulation box (144unit cells) clearly emphasized that the situation (ii) can beneglected, as whatever the CO2/CH4 composition a maximumof ∼10% of the configurations stored during the GCMC runsshow their LP pores containing only a unique type ofadsorbates. Finally, the case (v) should occur as the Braggpeaks present in the neutron diffractograms are characteristicsof such a situation as mentioned above; however, as these CO2molecules present in these structures do not see any CH4 intheir vicinity, they are not expected to impact their diffusivities.Indeed, to summarize, only the case (i) needs to be consideredwith both CO2 and CH4 coexisting in the LP form.

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Regarding MIL-47(V), we considered an initial loading of 0.5CH4/u.c., and CO2 was incrementally inserted in the samerange of concentration as for MIL-53(Cr) to be againconsistent with the mixtures experimentally explored.In addition, to make a comparison between the self-

diffusivity of CH4 and CO2 in pure and mixture components,complementary MD simulations have been realized in bothMIL-47(V) and MIL-53(Cr) for the single componentsconsidering loadings ranging from 0.5 to 4 CH4/u.c. andfrom 1 to 6 CO2/u.c., respectively.

■ RESULTS AND DISCUSSIONSince CH4 is an incoherent scatterer, the self-diffusioncoefficient (Ds) can be experimentally determined. In contrast,CO2 is a coherent scatterer, and only the transport diffusion canbe experimentally followed.89 It follows that the QENS study ofthe CH4−CO2 mixtures only provides the Ds(CH4) evolutionas a function of the CO2 loading since the scattering fromhydrogen is much larger than the one from other atoms,leading to a scattering dominated by CH4. From these data, it isthen possible to evaluate the impact of the CO2 concentrationon the diffusivity for CH4. The diffusion of the CH4 moleculescan be first experimentally characterized from the shape of thespectra: the larger the broadening of the peak, the larger thediffusivity. The QENS spectra were fitted with a translationalmotion convoluted with isotropic rotation and with theinstrumental resolution. Comparison between experimentaland calculated profiles shows that one-dimensional diffusion forCH4 in both MILs fits better the experimental spectra thanthree-dimensional diffusion. This observation was alreadyreported for pure CH4 in both MIL-47(V) and MIL-53(Cr).61

The anisotropy of diffusion in these 1D systems is taken intoaccount by performing a powder average of the scatteringfunction.90

Regarding MIL-47(V), the comparison between experimen-tal and fitted QENS spectra obtained for CH4 in the case ofmixtures (Figure 2) shows that the signal becomes narrowerwhen the CO2 loading increases. This is also evident in a plot ofthe width of the translational component versus Q2 (Figure S4,Supporting Information). It leads to a decrease of the resultingdiffusion coefficients for CH4 plotted as a function of the CO2loading (Figure 3). First, the rapid mobility for CH4 as a singlecomponent at a loading of 0.5 molecule/u.c. is reported (3 ×10−8 m2 s−1), as it was measured in our previous study on thesame sample.61 From this point, when the CO2 loadingincreases, the experimental Ds(CH4) in the mixture monoto-nously decreases from 2 × 10−8 to 7 × 10−9 m2 s−1 for loadingsvarying from 0.6 to 2.8 CO2/u.c., respectively. It means that therapid mobility of CH4 disappears in the presence of CO2molecules in pores, as was observed in the case of the singlecomponent when CH4 loading increases.61 The added CO2molecules act therefore in a similar way as CH4: the increase ofloading imposes a decrease of Ds(CH4) in both the singlecomponent and mixture. As shown in Figure 3, this trend isvery well reproduced by our simulations, and the calculatedDs(CH4) values that vary from 6 × 10−8 to 8 × 10−9 m2 s−1 in asimilar range of explored CO2 loadings [1−3 molecules/u.c.]are also in excellent agreement with the experimental data. Oneshould notice that such a behavior of Ds(CH4) in the presenceof CO2 is consistent with what has been found for the NaYzeolite in similar conditions.73

To further compare the Ds(CH4) values in both single andmixture components, we reported in Figure 4 the self-diffusion

coefficients normalized by the highest Ds values (obtained atthe lowest investigated loading of CH4 in the case of bothsingle and mixture components, i.e., 0.5 CH4/u.c.). The

Figure 2. Comparison between experimental (crosses) and fitted(solid lines) QENS spectra obtained for CH4 in MIL-47(V) uponincreasing CO2 loadings: (a) CH4 alone (0.5 molecule/u.c.); sameloading of CH4 with (b) 0.6 CO2 /u.c.; (c) 1.7 CO2 /u.c.; and (d) 2.8CO2 /u.c. (T = 230 K, Q = 0.35 Å−1). The small contribution of therotation to the profiles is illustrated in (a) by the green line.

Figure 3. Evolution of the self-diffusion coefficients for CH4 in mixtureas a function of the added CO2 loading. Circles and trianglescorrespond to data for MIL-47(V) and MIL-53(Cr), respectively,while empty and full symbols are attributed to simulated andexperimental data, respectively.

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experimental data for CH4 as a single component are takenfrom ref 61, while the calculated values are issued from thiswork. Both experimental and simulated normalized values forMIL-47(V) (Figure 4a) show that the decrease of Ds(CH4) isless pronounced in the case of a mixture than for a purecomponent in the range of the QENS explored loading. Indeed,it can be established that CO2 tends to enhance the diffusivityfor CH4 leading for a given total number of molecules to Dsvalues larger than those in the single gas for the major part ofthe investigated loadings. This diffusion behavior is similar tothat previously evidenced in the narrow window MOF typeUiO-66(Zr),57 while it deviates from other findings for thesame mixture in various zeolites such as LTA, CHA, DDR, andNaY, where the diffusivity of CH4 remains almost unchanged oreven decreases in the presence of CO2.

73,74 At high loading, thesimulated Ds for CH4 converges toward similar values in pureand mixture cases as they are mainly governed by stericconsideration which becomes similar in both situations. Theself-diffusivities for CO2 have also been simulated for bothsingle and binary mixture cases (Figure 5). A similar decreasingprofile for Ds as a function of the loading is obtained for bothpure and mixture components consistent with what has beenpreviously reported in several zeolites.73,74 One can also noticethat the resulting Ds values are about 1 order of magnitudelower than for CH4 in the whole range of the investigatedloading. This observation emphasizes that the mobility of the

faster CH4 is indeed enhanced by the slower CO2 molecules inthe binary mixture for which the diffusivity is either not affectedor only slightly sped up (Figure 5). Such a dynamic behaviordeviates with that we recently observed in the same MIL-47(V)solid for a mixture of xylene isomers, the slowly diffusing p-xylene molecules tending to retard the faster m-xylenespecies.75

Further, to shed some light onto the microscopic diffusionmechanism for the binary mixture, the MD trajectories werecarefully analyzed. The resulting 2D probability density plotsshow that both CO2 and CH4 follow individually a 1D-typediffusion whatever the mixture composition (Figure 6). While

this dynamic behavior is similar to that previously obtained inthe pure component for CH4,

61 this is no longer true for CO2.While this species has been shown to follow a purely 3Ddiffusion mechanism in a single component,64 here in thepresence of CH4, the CO2 molecules mainly diffuse close to thepore wall, while CH4 is more distributed in the central zone ofthe tunnel consistent with a stronger MIL-47(V)/CO2interaction as previously evidenced from our thermodynamicsinvestigation.78 Such a diffusion mechanism was further

Figure 4. Evolution of the normalized Ds(CH4) as a function of thetotal loading for MIL-47(V) (a) and MIL-53(Cr) (b). For MIL-47(V)(respectively, MIL-53(Cr)), circle (respectively, triangle up) andtriangle down (respectively, square) symbols correspond to data for amixture and single component, respectively. Simulated and exper-imental results are reported with empty and full symbols, respectively.The Ds(CH4)° correspond to the maximum values of the self-diffusioncoefficients obtained for both the single (at 0.35 (0.5) and 0.67 (0.5)CH4/u.c. for experimental (simulated) values in MIL-53 and MIL-47,respectively) and mixture (at 0.8 (0.8) and 0.5 (0.5) CH4/u.c. forexperimental (simulated) values in MIL-53 and MIL-47, respectively)conditions.

Figure 5. Evolution of Ds(CO2) as a function of the total loading inMIL-47(V) and MIL-53(Cr) for a single component (full square andtriangle up, respectively) and binary mixture (empty circle and triangledown, respectively).

Figure 6. 2D density plots issued from the MD simulations for a CO2(green)/CH4 (red) mixture in MIL-47(V): case of 0.5 CH4/u.c. with 1and 3 CO2/u.c. represented along the xz axis (a,b) and case of 0.5CH4/u.c. with 3 CO2/u.c. orientated along the xy axis (c).

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confirmed by the analysis of the QENS data: the use of a 1Ddiffusion model gives a better fit than 3D models.Regarding MIL-53(Cr), the experimental Ds(CH4) values

have been first computed from the QENS spectra. Startingfrom the initial CH4 loading, when the CO2 loading increases,the width of the spectra decreases similarly to the diffusion ofmixtures in MIL-47(V) (Figure 7). Again, it is thus possible to

extract the diffusion coefficients for CH4 molecules as afunction of the CO2 loading which are reported in Figure 3.The experimental values range from 1.8 × 10−8 to 2 × 10−9 m2

s−1 for loading varying from 0.8 to 3.3 CO2/u.c. and with aninitial CH4 loading equal to 0.8 CH4/u.c. Again, the rapidmobility for CH4 which was previously measured at low CH4concentration (2 × 10−8 m2 s−1) further vanishes when CO2molecules are incorporated within the porosity, as it wasobserved in the case of pure CH4 diffusion. Similarly to MIL-47(V), one observes that the profile of the normalized Ds(CH4)obtained for the mixture does not differ from the onedetermined for the pure component.61 One further observesthat the diffusivity for CH4 is only slightly influenced by theCO2 molecules present in the pores (Figure 4b). Here again,these experimental findings were further compared to thoseextracted from the MD simulations assuming that theintegrality of the CO2 and CH4 molecules coexist in the LPform of MIL-53(Cr) (see Computational Section forjustification). The simulated Ds(CH4) profile reproduces verywell the decreasing experimental trend when adding CO2molecules (Figure 3): the so-obtained self-diffusion coefficientswhich vary from 1.6 × 10−8 to 2.2 × 10−9 m2 s−1 when the CO2loading increases in the range [1−4] CO2/u.c. are in very goodagreement with the QENS data. Figure 5 which reports thesimulated Ds(CO2) in the LP form of MIL-53(Cr) for pure andbinary mixture components shows: (i) that CO2 diffusessignificantly slower than CH4 (up to 3 times) and (ii) theexistence of a maximum for Ds(CO2) as a function of theloading, a trend that drastically deviates with the monotonousdecreasing trend obtained for MIL-47(V). Such a behavior ishere triggered by the presence of a specific interaction betweenCO2 and the μ2-OH groups present at the MIL-53(Cr) surface:the relatively slow diffusivity for CO2 at low loading is ascribedto these relatively strong host/guest interactions. Once the μ2-OH adsorption sites are occupied, they are screened for

additional adsorbate molecules which can consequently diffusewithout being inhibited. Finally, at higher loading, thisthermodynamic consideration is partially counterbalanced bya steric effect leading to a drop of the self-diffusivity. (iii) Theself-diffusivity values are slightly larger in a mixture in the rangeof the CO2 loading explored experimentally (up to ∼3 CO2molecules/u.c.), while they remain very similar for the highestCO2 concentration. Indeed, the predicted enhancement of theCH4 diffusivity in the presence of a CO2 uptake below 3molecules/u.c. (Figure 4b), which confirms the experimentalQENS observation, occurs concomitantly with a slowing downof the slowly diffusive CO2 species. This behavior deviates withthe behavior obtained in MIL-47(V) for which the CO2molecules are shown to diffuse slightly faster.A careful analysis of the MD trajectories further confirmed

that whatever the explored composition of the gas mixture CO2diffuses in the vicinity of the μ2-OH groups following a 1Ddiffusion mechanism (Figures 8c and 8d for low and high

loadings). At low loading, CO2 shows a jump-like diffusionbehavior along the direction of the tunnel between μ2-OHgroups as illustrated in Figure 9 which reports the positions of

Figure 7. Normalized QENS spectra showing the narrowing of theprofile measured for CH4 in MIL-53(Cr) upon increasing CO2loadings: (blue line) CH4 alone (0.8 molecule/u.c.); (red line) CH4with 0.8 CO2/u.c.; (green line) CH4 with 1.4 CO2/u.c.; (brown line)CH4 with 1.8 CO2/u.c.; (black line) CH4 with 2.8 CO2/u.c.; thedashed line corresponds to the resolution function (T = 230 K, Q =0.42 Å−1).

Figure 8. 2D density plots issued from the MD simulations for a CO2(green)/CH4 (red) mixture in MIL-53(Cr) at low and high loadingscorresponding to 0.8 CH4/u.c. as initial filling and 1 and 3 CO2/u.c.represented along the xz (a,c) and xy (c,d), respectively.

Figure 9. Snapshots illustrating the jump-diffusion-type mechanism forCO2 in MIL-53(Cr) by following the center of mass of the CO2molecule passing from one μ2-OH to another along the tunnel atdifferent times (from left to right: t = 0, 5, 20, 40, 50, and 70 ps).

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the diffusive species along the channel at different simulationtimes. However, this situation evolves toward a morecontinuous dynamics when the CO2 concentration increases.These diffusive species further tend to maintain the CH4

molecules in the region close to the center of the pore whichalso adopts a 1D-type diffusion mechanism in a similar way asfor MIL-47(V) as discussed above. These microscopicmechanisms for both gases are again consistent with the useof a 1D model to fit the QENS data.Such a diffusion mechanism evidenced for CO2 and CH4 in

the mixture slightly deviates with those we previouslyelucidated for their single components. Indeed, in the gasmixture, the possible jump sequence identified for CH4 in thepure component along the direction of the tunnel with the μ2-OH groups acting as a steric barrier is no longer valid since theCH4 molecules have no access to the μ2-OH. Regarding CO2 ina mixture, we still observe a 1D diffusion as already evidencedfor the single component;63 however, here one notices that atlow loading an additional possible jump of the moleculesbetween μ2-OH groups can occur, while at higher concen-tration the mechanism becomes more continuous similarly tothe pure CO2.Finally regarding the gas separation applications, one

observes that the diffusivities for both species in mixtures atlow loading, i.e., 3 ×10−8 and 6 × 10−9 m2 s−1 for CH4 andCO2, respectively, are finally significantly faster than the valuespreviously reported in the conventional NaY Faujasite at similarranges of loading and temperature61 (CH4: 6 × 10−9 m2 s−1 andCO2: 3 × 10−10 m2 s−1). Indeed, such a conclusion emphasizesthat the kinetics will not be a drawback for the use of such aMOF type material in physisorption-based processes.

■ CONCLUSION

Our joint experimental/modeling approach first evidenced thatin both MIL-47(V) and MIL-53(Cr) CH4, which ischaracterized by a fast diffusivity at a low loading below 1molecule/u.c. in a single component, diffuses significantlyslower in the presence of CO2 molecules, and the self-diffusioncoefficient continuously decreases when the CO2 concentrationincreases. We further observed that compared to the singlecomponent situation, CO2 tends to slightly enhance thediffusivity for CH4 in both MOFs, the simulations allowingus to mention that concomitantly the slowest CO2 species areeither sped up or slowed down in MIL-47(V) and MIL-53(Cr),respectively. A careful analysis of the MD trajectories led to theconclusions that in mixture both gases follow individually a 1D-type diffusion mechanism, CO2 diffusing mainly close to thepore wall, while the motions of CH4 primarily occur in thecentral zone of the tunnel. Finally it was established that themagnitude of the self-diffusion coefficients for both species iswithin the same order of magnitude as those observed for theconventional NaY Faujasite adsorbent, which clearly empha-sizes that the separation process in such MOFs will not belimited by kinetics.

■ ASSOCIATED CONTENT

*S Supporting InformationFigures S1−S4. This material is available free of charge via theInternet at http://pubs.acs.org.

■ AUTHOR INFORMATIONCorresponding Author*E-mail: guillaume.maurin@univ-montp2.fr; herve.jobic@ircelyon.univ-lyon1.fr.NotesThe authors declare no competing financial interest.

■ ACKNOWLEDGMENTSWe thank the Institut Laue-Langevin for allocating neutronbeam time on the IN6 spectrometer. This work was supportedby the ANR CO2 Program “NoMAC”.

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