CH4 Mixtures in the MIL-47(V) and MIL-53

Article pubs.acs.org/JPCC

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

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

ABSTRACT: The dynamics of CO2 and CH4 in a mixture of different compositions has been explored in two metal−organic frameworks, namely, MIL-47(V) and MIL-53(Cr), by combining molecular dynamics (MD) simulations and quasi-elastic neutron scattering (QENS) measurements. The experimental and simulated self-diffusion coefficient (Ds) values for CH4 are in very good agreement in the whole range of the CO2 explored loadings. It is clearly stated that CH4 which shows a fast diffusivity at low loading becomes significantly slower in both metal−organic frameworks (MOFs) when CO2 molecules are introduced within the porosities of these materials. Further, compared to its behavior in a single component, CH4 tends to diffuse slightly faster in the presence of CO2. The MD simulations revealed that this speeding up is concomitant 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 diffusion mechanism in both MOFs, where the CO2 molecules diffuse close to the pore wall while the motions of CH4 are restricted in the central region of the tunnel.

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INTRODUCTION

the organic moieties associated to form the structures but also of their possible connectivity and topology.2,6−9 Owing to their many fascinating characteristics, above their prospective applications in different fields related to catalysis, biology/ medicine, and physics,2,9−22 a few of these materials exhibit performances of great importance for the CO2/CH4 separation purpose with a relatively high selectivity combined to a potential regeneration in mild conditions that are expected to lead to a higher productivity and a lower energetic cost for the industrial process.8,16,23−46 As typical examples, it has been demonstrated that while certain MOFs with ultrahigh porosity, such as MIL-101, MOF-177, or UMCM-2, are able to adsorb large amounts of CO2 and CH447,48 some others including a few functionalized MOFs such as the UiO-66(Zr)s series, the

The elimination of carbon dioxide from a gas mixture containing methane is of great economic and technological importance in the treatment of low-quality natural gas such as biogas and landfill gases. The industrial feasibility of such a selective CO2 capture has been extensively demonstrated using either amine-based chemisorption or physisorption techniques such as the pressure swing adsorption (PSA) that involves the use of porous media.1 In this latter process, the conventional adsorbents including the porous zeolites and activated carbons are widely employed. However, throughout the past decade, the associated research on porous metal−organic frameworks (MOFs) has established that this relatively new class of materials can show great promises over the other families of porous solids for mixture separation.2−5 The interest of these MOF type materials strongly relies on their high versatility, allowing a possible modulation of not only their chemical features including the nature of both the inorganic subunits and © XXXX American Chemical Society

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

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dx.doi.org/10.1021/jp403225t | J. Phys. Chem. C XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry C

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flexible MIL-53(Al)-NH2, the SIFSIX, and the ZIFs solids significantly outperform the CO2/CH4 selectivity of the most commonly employed NaY Faujasite type adsorbent in PSA applications.49−58 These latter conclusions have been primarily based on studies which explored only the thermodynamic aspect of the separation process and which emphasized that the selective capture of CO2 can be driven either by interactions with specific adsorption sites or by steric hindrance. However, above the thermodynamic consideration, the kinetics can also significantly impact such separation processes. Indeed, it is of interest to probe the dynamics of the confined CO2 and CH4 species in MOFs for gaining preliminary fundamental insight into the mechanisms in play. While the diffusion of the single gases has been intensively investigated in MOFs,59−67 only a very few experimental and simulated data have been reported so far on the mobility of the binary mixtures.36,54,57,68−72 Much of the work on this topic has been addressed computationally with significant contributions from Keskin and Sholl67,69−72 who explored the dynamics of a series of gas mixtures in some MOFs for further evaluating their separation performances as membranes. Krishna et al.54 have also investigated the impact of the pore size and topology of various MOFs on the diffusivity of several binary mixtures. In addition, following previous studies on zeolites,73,74 the only experimental investigations emanate from us coupling quasi-elastic neutron scattering (QENS) measurements and molecular dynamics (MD) simulations to probe the codiffusion of CO2/CH4 and xylene isomers in the 3D pore UiO-66(Zr)57 and in the 1D pore MIL47(V),75 respectively. In light of this lack of available literature, much effort is still required to get a complete picture of the separation processes that are in play in some of the most promising MOFs. To that purpose, based on previous successful QENS−MD combined studies on the molecular motions of pure and mixed fluids (hydrogen, benzene, short and long linear alkanes, carbon dioxide, water, ...) confined in diverse MOFs,57,59−66,75 here we propose to adopt this joint experimental/modeling approach to explore the codiffusion of CO2 and CH4 within the porosity of two MOFs, namely, MIL-47(V) and MIL-53(Cr).76,77 These MOF type solids have been selected as recent thermodynamic studies have revealed that for distinct reasons both solids can be relatively attractive for the separation of the gas mixture of interest. Indeed, MIL-47(V) which is built up from chains corner sharing VO6 octahedra interconnected by terephthalate linkers defining a 1D type diamond-shaped pore system (Figure 1) shows a moderate selectivity toward CO2 due to the absence of specific adsorption sites at its pore wall surface combined to a relatively high working capacity which makes this material promising in the area of separation.76,78 At a variance, MIL53(Cr) which is isostructural to MIL-47(V) with the μ2-O vertices substituted by the μ2-OH groups has been shown to be highly CO2 selective in a specific pressure range, a phenomenon attributed to the breathing behavior of this solid that can switch from its initial large pore (LP) form to a narrow pore (NP) version upon CO2/CH4 adsorption, the pore dimensions of this latter structure being able to only trap CO2 while CH4 is expulsed.16 In the present work, we aim to (i) determine the loading dependence of the self-diffusivity for CH4 in the presence of CO2 in the MIL-47(V) and MIL-53(Cr), (ii) compare both profile and absolute diffusion coefficient values with those obtained for the single component, and further (iii) address the microscopic codiffusion mechanism for both diffusive species

Figure 1. View of the MIL-47(V) structure along the chain (z axis), highlighting the 1D pore system. The MIL-53(Cr) structure is obtained 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.

through a detailed analysis of both QENS spectra and MD trajectories.

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MATERIALS AND METHODS Material. Deuterated MIL-53(Cr) and MIL-47(V) samples were synthesized and activated according to the published procedures,61,65,79 using d4-terephthalic acid (Eurisotop, France) and hydrogenated solvent. After activation, the hydrogen atoms of the hydroxyl groups in MIL-53(Cr) were exchanged with deuterium by stirring in deuterated water overnight at room temperature. Quasi-Elastic Neutron Scattering Measurements. The neutron experiments were performed at the Institut LaueLangevin (Grenoble, France) using the time-of-flight (TOF) spectrometer IN6. The main characteristics of this instrument are an intermediate elastic resolution (of the order of 80 μeV, full-width at half-maximum, for an incident energy of 3.12 meV) but a very high flux which is obtained by vertical and horizontal focusing. After scattering from the sample, the neutrons pass through a box filled with helium toward a bank of detectors 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 corresponding elastic wave-vector transfers, Q, ranged from 0.25 to 1.6 Å−1. The Bragg peaks of the MOF were determined on the spectrometer by comparing the intensities of the elastic peaks at each angular position with those obtained from a standard vanadium plate (vanadium was also used to measure the instrumental resolution). Since the scattering from the hydrogen atoms of the terephthalate linker is incoherent, the framework was deuterated as previously mentioned to reduce the 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 were then transferred inside a glovebox into slab-shaped aluminum containers, which could be connected to a gas inlet system allowing in situ adsorption. After measuring the scattering of the empty materials, and after a preliminary adsorption of CH4, three and five successive concentrations of CO2 were B



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be applied to the LJ interactions (rc < L/2, L = the smallest length 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 Ewald summation technique.86 The SHAKE-RATTLE and the usual Velocity Verlet algorithms were used to constrain rigid bonds and to integrate the equations of motion, respectively. As the diffusive species were maintained as rigid, the QUATERNION algorithm was employed to treat their motions. From these simulations, the self-diffusivity Ds for CH4 and CO2 in binary mixture components was extracted for the different loadings mentioned below. They were determined for each investigated concentration (c) using the Einstein relation87 reported in eq 1.

investigated at 230 K for MIL-47(V) and MIL-53(Cr), respectively, to explore the self-diffusion for CH4. The investigated loadings correspond to 0.5 CH4 and 0.6, 1.7, and 2.8 CO2 molecules per unit cell (u.c.) for MIL-47(V) and to 0.8 CH4 and 0.8, 1.4, 1.8, 2.8, and 3.3 CO2 molecules/u.c. for MIL53(Cr). These amounts adsorbed were determined by volumetry and then compared to the adsorption isotherms measured independently.16 The groupings of spectra were treated by standard correction programs, subtracting the signals of the empty MILs, and the TOF axis was converted to energy transfer. 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 in the literature.76,77 MIL-47(V) was considered as a rigid framework consistently with the unchanged position of the whole Bragg peaks (see Figure S1, Supporting Information) observed during the QENS experiments upon coadsorption. This assumption has been previously validated for a series of single guest molecules diffusing within the porosity of this material.60−62,64−66 MIL-53(Cr) was treated in a first approximation 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 MIL frameworks were taken from our previous DFT calculations.61 The 12-6 Lennard-Jones (LJ) interatomic potential parameters for MIL-53(Cr) were extracted from our previous investigation80 and were transferred to MIL-47(V) solid except that the vanadium atom was treated by the UFF force field.81 Such a parametrization has already been successfully employed to reproduce the dynamic behavior of CO2 and CH4 as single component in the considered MOFs.61,63,64 For the MD simulations conducted with a flexible MIL-53(Cr) framework, we implemented our own force field that was shown to accurately capture the breathing of this material upon the adsorption of a series of single gas molecules.80 While CO2 was treated using the EPM2 model developed by Harris and Yung,82 CH4 was described by our previous force field that was successfully employed to deal with the thermodynamics properties of this adsorbate in different MOFs.61,83 In these microscopic representations, CO2 and CH4 are represented by a three and five-point charged LJ model, respectively, considered as rigid in our simulations. Note that these two models have already been coupled to successfully describe the coadsorption behavior of these gases at various compositions in MIL-53(Cr) and in the zeolite NaY.16,84 The adsorbate/ adsorbent LJ interatomic potential parameters were then estimated using the Lorentz−Berthelot mixing rule. Molecular Dynamics Simulations. Molecular dynamics (MD) simulations were performed using the DL_POLY_2.19 program85 in the NVT ensemble at 230 K with the Berendsen ensemble. As mentioned above, complementary simulations were realized with a flexible framework for MIL-53(Cr). In this latter case it was evidenced that both calculated trends and absolute values of Ds for CO2 and CH4 (Figure S2, Supporting Information) are very similar to those obtained when rigid frameworks are considered. Indeed, the flexibility of the LP form has therefore only a weak impact on the diffusion mechanism occurring in MIL-53(Cr), as already observed for the diffusivity of the single gas CO2 in the same solid.63 All these calculations were run considering a simulation cell box consisting of 32 unit cells to get good statistics and the critical size to maintain a consistent cutoff distance of 12 Å to

N

Ds(c) = lim

t →∞

1 ⟨∑ [rj(t ) − rj(o)]2 ⟩ 6t j = 1

(1)

In this equation, ⟨...⟩ denotes an ensemble average; r(t) are the positions of the tagged guest molecule; while N corresponds to the number of adsorbate molecules in the simulation volume. Further, to improve the statistics of the calculation, multiple time origins as described elsewhere87 were used with an average value 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 Canonical Monte Carlo simulations, the CO2 molecules being successively added in a range of [1−6 molecules/u.c.] to be consistent with the experimental conditions. The structure behavior of MIL53(Cr) upon coadsorption of CO2 and CH4 was shown to be rather complex and both dependent on the total pressure and the CO2/CH4 ratio.16 The consideration of only the LP form of the MIL-53(Cr) for our diffusion investigation is justified as follows. One can imagine that the gas molecules in the mixture can be distributed as (i) CO2 and CH4 molecules both in the LP, (ii) only CH4 or CO2 molecules in the LP, (iii) CO2 and CH4 molecules both in the NP, (iv) only CH4 molecules in the NP, and (v) only CO2 molecules in the NP. The scenario (iii) can be straightforwardly eliminated as our previous thermodynamic studies of different mixture CO2/CH4 compositions have clearly established that CH4 cannot coexist with CO2 in a NP form. Similarly, one can exclude the presence of only CH4 in a NP form as the neutron diffraction patterns (see Figure S3, Supporting Information) show the same Bragg peaks as those characteristics of the NP in the presence of a CO2/CH4 mixture. The existence of a narrow pore form filled by CH4 would lead to a set of additional peaks in the diffractograms assigned to the more open narrow pore structure previously evidenced for the Al analogue upon adsorption of CH4 only at very low temperature.88 Further, Grand Canonical Monte Carlo (GCMC) simulations realized on a large simulation box (144 unit cells) clearly emphasized that the situation (ii) can be neglected, as whatever the CO2/CH4 composition a maximum of ∼10% of the configurations stored during the GCMC runs show their LP pores containing only a unique type of adsorbates. Finally, the case (v) should occur as the Bragg peaks present in the neutron diffractograms are characteristics of such a situation as mentioned above; however, as these CO2 molecules present in these structures do not see any CH4 in their vicinity, they are not expected to impact their diffusivities. Indeed, to summarize, only the case (i) needs to be considered with both CO2 and CH4 coexisting in the LP form. C



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Regarding MIL-47(V), we considered an initial loading of 0.5 CH4/u.c., and CO2 was incrementally inserted in the same range of concentration as for MIL-53(Cr) to be again consistent with the mixtures experimentally explored. In addition, to make a comparison between the selfdiffusivity of CH4 and CO2 in pure and mixture components, complementary MD simulations have been realized in both MIL-47(V) and MIL-53(Cr) for the single components considering loadings ranging from 0.5 to 4 CH4/u.c. and from 1 to 6 CO2/u.c., respectively.

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RESULTS AND DISCUSSION Since CH4 is an incoherent scatterer, the self-diffusion coefficient (Ds) can be experimentally determined. In contrast, CO2 is a coherent scatterer, and only the transport diffusion can be experimentally followed.89 It follows that the QENS study of the CH4−CO2 mixtures only provides the Ds(CH4) evolution as a function of the CO2 loading since the scattering from hydrogen is much larger than the one from other atoms, leading to a scattering dominated by CH4. From these data, it is then possible to evaluate the impact of the CO2 concentration on the diffusivity for CH4. The diffusion of the CH4 molecules can be first experimentally characterized from the shape of the spectra: the larger the broadening of the peak, the larger the diffusivity. The QENS spectra were fitted with a translational motion convoluted with isotropic rotation and with the instrumental resolution. Comparison between experimental and calculated profiles shows that one-dimensional diffusion for CH4 in both MILs fits better the experimental spectra than three-dimensional diffusion. This observation was already reported for pure CH4 in both MIL-47(V) and MIL-53(Cr).61 The anisotropy of diffusion in these 1D systems is taken into account by performing a powder average of the scattering function.90 Regarding MIL-47(V), the comparison between experimental and fitted QENS spectra obtained for CH4 in the case of mixtures (Figure 2) shows that the signal becomes narrower when the CO2 loading increases. This is also evident in a plot of the width of the translational component versus Q2 (Figure S4, Supporting Information). It leads to a decrease of the resulting diffusion coefficients for CH4 plotted as a function of the CO2 loading (Figure 3). First, the rapid mobility for CH4 as a single component 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 the same sample.61 From this point, when the CO2 loading increases, the experimental Ds(CH4) in the mixture monotonously decreases from 2 × 10−8 to 7 × 10−9 m2 s−1 for loadings varying from 0.6 to 2.8 CO2/u.c., respectively. It means that the rapid mobility of CH4 disappears in the presence of CO2 molecules in pores, as was observed in the case of the single component when CH4 loading increases.61 The added CO2 molecules act therefore in a similar way as CH4: the increase of loading imposes a decrease of Ds(CH4) in both the single component and mixture. As shown in Figure 3, this trend is very well reproduced by our simulations, and the calculated Ds(CH4) values that vary from 6 × 10−8 to 8 × 10−9 m2 s−1 in a similar range of explored CO2 loadings [1−3 molecules/u.c.] are also in excellent agreement with the experimental data. One should notice that such a behavior of Ds(CH4) in the presence of CO2 is consistent with what has been found for the NaY zeolite in similar conditions.73 To further compare the Ds(CH4) values in both single and mixture components, we reported in Figure 4 the self-diffusion

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

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

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



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

faster CH4 is indeed enhanced by the slower CO2 molecules in the binary mixture for which the diffusivity is either not affected or only slightly sped up (Figure 5). Such a dynamic behavior deviates with that we recently observed in the same MIL-47(V) solid for a mixture of xylene isomers, the slowly diffusing pxylene molecules tending to retard the faster m-xylene species.75 Further, to shed some light onto the microscopic diffusion mechanism for the binary mixture, the MD trajectories were carefully analyzed. The resulting 2D probability density plots show that both CO2 and CH4 follow individually a 1D-type diffusion whatever the mixture composition (Figure 6). While

Figure 4. Evolution of the normalized Ds(CH4) as a function of the total loading for MIL-47(V) (a) and MIL-53(Cr) (b). For MIL-47(V) (respectively, MIL-53(Cr)), circle (respectively, triangle up) and triangle down (respectively, square) symbols correspond to data for a mixture and single component, respectively. Simulated and experimental results are reported with empty and full symbols, respectively. The Ds(CH4)° correspond to the maximum values of the self-diffusion coefficients 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. for experimental (simulated) values in MIL-53 and MIL-47, respectively) conditions.

experimental data for CH4 as a single component are taken from ref 61, while the calculated values are issued from this work. Both experimental and simulated normalized values for MIL-47(V) (Figure 4a) show that the decrease of Ds(CH4) is less pronounced in the case of a mixture than for a pure component in the range of the QENS explored loading. Indeed, it can be established that CO2 tends to enhance the diffusivity for CH4 leading for a given total number of molecules to Ds values larger than those in the single gas for the major part of the investigated loadings. This diffusion behavior is similar to that previously evidenced in the narrow window MOF type UiO-66(Zr),57 while it deviates from other findings for the same mixture in various zeolites such as LTA, CHA, DDR, and NaY, where the diffusivity of CH4 remains almost unchanged or even decreases in the presence of CO2.73,74 At high loading, the simulated Ds for CH4 converges toward similar values in pure and mixture cases as they are mainly governed by steric consideration which becomes similar in both situations. The self-diffusivities for CO2 have also been simulated for both single and binary mixture cases (Figure 5). A similar decreasing profile for Ds as a function of the loading is obtained for both pure and mixture components consistent with what has been previously reported in several zeolites.73,74 One can also notice that the resulting Ds values are about 1 order of magnitude lower than for CH4 in the whole range of the investigated loading. This observation emphasizes that the mobility of the

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 1 and 3 CO2/u.c. represented along the xz axis (a,b) and case of 0.5 CH4/u.c. with 3 CO2/u.c. orientated along the xy axis (c).

this dynamic behavior is similar to that previously obtained in the pure component for CH4,61 this is no longer true for CO2. While this species has been shown to follow a purely 3D diffusion mechanism in a single component,64 here in the presence of CH4, the CO2 molecules mainly diffuse close to the pore wall, while CH4 is more distributed in the central zone of the tunnel consistent with a stronger MIL-47(V)/CO 2 interaction as previously evidenced from our thermodynamics investigation.78 Such a diffusion mechanism was further E



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additional adsorbate molecules which can consequently diffuse without being inhibited. Finally, at higher loading, this thermodynamic consideration is partially counterbalanced by a steric effect leading to a drop of the self-diffusivity. (iii) The self-diffusivity values are slightly larger in a mixture in the range of the CO2 loading explored experimentally (up to ∼3 CO2 molecules/u.c.), while they remain very similar for the highest CO2 concentration. Indeed, the predicted enhancement of the CH4 diffusivity in the presence of a CO2 uptake below 3 molecules/u.c. (Figure 4b), which confirms the experimental QENS observation, occurs concomitantly with a slowing down of the slowly diffusive CO2 species. This behavior deviates with the behavior obtained in MIL-47(V) for which the CO2 molecules are shown to diffuse slightly faster. A careful analysis of the MD trajectories further confirmed that whatever the explored composition of the gas mixture CO2 diffuses in the vicinity of the μ2-OH groups following a 1D diffusion mechanism (Figures 8c and 8d for low and high

confirmed by the analysis of the QENS data: the use of a 1D diffusion 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. Starting from the initial CH4 loading, when the CO2 loading increases, the width of the spectra decreases similarly to the diffusion of mixtures in MIL-47(V) (Figure 7). Again, it is thus possible to

Figure 7. Normalized QENS spectra showing the narrowing of the profile measured for CH4 in MIL-53(Cr) upon increasing CO2 loadings: (blue line) CH4 alone (0.8 molecule/u.c.); (red line) CH4 with 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.; the dashed line corresponds to the resolution function (T = 230 K, Q = 0.42 Å−1).

extract the diffusion coefficients for CH4 molecules as a function 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 an initial CH4 loading equal to 0.8 CH4/u.c. Again, the rapid mobility for CH4 which was previously measured at low CH4 concentration (2 × 10−8 m2 s−1) further vanishes when CO2 molecules are incorporated within the porosity, as it was observed in the case of pure CH4 diffusion. Similarly to MIL47(V), one observes that the profile of the normalized Ds(CH4) obtained for the mixture does not differ from the one determined for the pure component.61 One further observes that the diffusivity for CH4 is only slightly influenced by the CO2 molecules present in the pores (Figure 4b). Here again, these experimental findings were further compared to those extracted from the MD simulations assuming that the integrality of the CO2 and CH4 molecules coexist in the LP form of MIL-53(Cr) (see Computational Section for justification). The simulated Ds(CH4) profile reproduces very well the decreasing experimental trend when adding CO2 molecules (Figure 3): the so-obtained self-diffusion coefficients which vary from 1.6 × 10−8 to 2.2 × 10−9 m2 s−1 when the CO2 loading increases in the range [1−4] CO2/u.c. are in very good agreement with the QENS data. Figure 5 which reports the simulated Ds(CO2) in the LP form of MIL-53(Cr) for pure and binary mixture components shows: (i) that CO2 diffuses significantly slower than CH4 (up to 3 times) and (ii) the existence of a maximum for Ds(CO2) as a function of the loading, a trend that drastically deviates with the monotonous decreasing trend obtained for MIL-47(V). Such a behavior is here triggered by the presence of a specific interaction between CO2 and the μ2-OH groups present at the MIL-53(Cr) surface: the relatively slow diffusivity for CO2 at low loading is ascribed to these relatively strong host/guest interactions. Once the μ2OH adsorption sites are occupied, they are screened for

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 loadings corresponding 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.

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

Figure 9. Snapshots illustrating the jump-diffusion-type mechanism for CO2 in MIL-53(Cr) by following the center of mass of the CO2 molecule passing from one μ2-OH to another along the tunnel at different times (from left to right: t = 0, 5, 20, 40, 50, and 70 ps). F



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the diffusive species along the channel at different simulation times. However, this situation evolves toward a more continuous 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 which also adopts a 1D-type diffusion mechanism in a similar way as for MIL-47(V) as discussed above. These microscopic mechanisms for both gases are again consistent with the use of 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 previously elucidated for their single components. Indeed, in the gas mixture, the possible jump sequence identified for CH4 in the pure component along the direction of the tunnel with the μ2OH groups acting as a steric barrier is no longer valid since the CH4 molecules have no access to the μ2-OH. Regarding CO2 in a mixture, we still observe a 1D diffusion as already evidenced for the single component;63 however, here one notices that at low loading an additional possible jump of the molecules between μ2-OH groups can occur, while at higher concentration the mechanism becomes more continuous similarly to the pure CO2. Finally regarding the gas separation applications, one observes that the diffusivities for both species in mixtures at low loading, i.e., 3 ×10−8 and 6 × 10−9 m2 s−1 for CH4 and CO2, respectively, are finally significantly faster than the values previously reported in the conventional NaY Faujasite at similar ranges of loading and temperature61 (CH4: 6 × 10−9 m2 s−1 and CO2: 3 × 10−10 m2 s−1). Indeed, such a conclusion emphasizes that the kinetics will not be a drawback for the use of such a MOF type material in physisorption-based processes.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]; herve.jobic@ ircelyon.univ-lyon1.fr. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank the Institut Laue-Langevin for allocating neutron beam time on the IN6 spectrometer. This work was supported by the ANR CO2 Program “NoMAC”.

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REFERENCES

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Our joint experimental/modeling approach first evidenced that in both MIL-47(V) and MIL-53(Cr) CH 4 , which is characterized by a fast diffusivity at a low loading below 1 molecule/u.c. in a single component, diffuses significantly slower in the presence of CO2 molecules, and the self-diffusion coefficient continuously decreases when the CO2 concentration increases. We further observed that compared to the single component situation, CO2 tends to slightly enhance the diffusivity for CH4 in both MOFs, the simulations allowing us to mention that concomitantly the slowest CO2 species are either sped up or slowed down in MIL-47(V) and MIL-53(Cr), respectively. A careful analysis of the MD trajectories led to the conclusions that in mixture both gases follow individually a 1Dtype diffusion mechanism, CO2 diffusing mainly close to the pore wall, while the motions of CH4 primarily occur in the central zone of the tunnel. Finally it was established that the magnitude of the self-diffusion coefficients for both species is within the same order of magnitude as those observed for the conventional NaY Faujasite adsorbent, which clearly emphasizes that the separation process in such MOFs will not be limited by kinetics.

S Supporting Information *

Figures S1−S4. This material is available free of charge via the Internet at http://pubs.acs.org. G



Article

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CH4 Mixtures in the MIL-47(V) and MIL-53

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