Diffusion of Pure CH4 and Its Binary Mixture with CO2 in Faujasite

Feb 26, 2010 - E. Bataillon, 34095 Montpellier Cedex 05, France, Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560...
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J. Phys. Chem. C 2010, 114, 5027–5034

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Diffusion of Pure CH4 and Its Binary Mixture with CO2 in Faujasite NaY: A Combination of Neutron Scattering Experiments and Molecular Dynamics Simulations I. De´roche,† G. Maurin,*,† B. J. Borah,‡ S. Yashonath,‡ and H. Jobic*,§ Institut Charles Gerhardt Montpellier, UMR 5253 CNRS, UM2, UM1, ENSCM, UniVersite´ Montpellier 2, Place E. Bataillon, 34095 Montpellier Cedex 05, France, Solid State and Structural Chemistry Unit, Indian Institute of Science, Bangalore-560012, India, and Institut de Recherches sur la Catalyse et l’EnVironnement de Lyon, UniVersite´ de Lyon, CNRS, 2 AVenue A. Einstein, 69626 Villeurbanne, France ReceiVed: October 31, 2009; ReVised Manuscript ReceiVed: February 11, 2010

The self-diffusion properties of pure CH4 and its binary mixture with CO2 within NaY zeolite have been investigated by combining an experimental quasi-elastic neutron scattering (QENS) technique and classical molecular dynamics simulations. The QENS measurements carried out at 200 K led to an unexpected selfdiffusivity profile for pure CH4 with the presence of a maximum for a loading of 32 CH4/unit cell, which was never observed before for the diffusion of apolar species in a zeolite system with large windows. Molecular dynamics simulations were performed using two distinct microscopic models for representing the CH4/NaY interactions. Depending on the model, we are able to fairly reproduce either the magnitude or the profile of the self-diffusivity. Further analysis allowed us to provide some molecular insight into the diffusion mechanism in play. The QENS measurements report only a slight decrease of the self-diffusivity of CH4 in the presence of CO2 when the CO2 loading increases. Molecular dynamics simulations successfully capture this experimental trend and suggest a plausible microscopic diffusion mechanism in the case of this binary mixture. 1. Introduction The separation of gas mixtures is the key step in many industrial processes1 such as the purification of natural gas2 or the production of extra pure hydrogen required for use in fuel cells.3 Separation based on membranes seems to offer an interesting option, conciliating at the same time the technological simplicity, acceptable energy cost, and remarkable performance.4 The main issue with membrane technologies lies in the selection of an appropriate microporous material, which favors both a high selectivity for the considered gas mixture and a relatively fast diffusivity for the separated component. The dynamics of the considered species in such a microporous system has thus a major influence on its separation ability. NaY, an intensely investigated zeolite material with FAU topology, has been found to be very promising for gas mixture separation5,6 and, in particular, for the CO2/CH4 mixture.7 In order to obtain a deeper understanding of the separation mechanism, in complement to the thermodynamics of the system of interest, the dynamic properties need to be determined. Further, it is not sufficient to study each gas component separately; the binary mixture has to be explored also. Plant et al. have previously investigated the diffusion of CO2 in the NaY and NaX systems at 300 K by combining quasielastic neutron scattering (QENS) and molecular dynamics (MD) simulations.8 While the computation approach explored the dynamics of the individual gas molecules and thus provided the self-diffusion coefficient (Ds), the QENS experiment provided information regarding the collective motion, i.e., the corrected (D0) and the transport diffusivity (Dt) as CO2 is a coherent scatterer. The investigated CO2 loadings ranged from * To whom correspondence should be addressed. E-mail: herve.jobic@ ircelyon.univ-lyon1.fr (H.J.); [email protected] (G.M.). † Universite´ Montpellier 2. ‡ Indian Institute of Science. § Universite´ de Lyon.

50 to 100 molecules per unit cell (u.c.), and an almost linear decreasing profile for Ds was reported when the CO2 concentration increased, while D0 and Dt slightly increased with the loading. Extrapolating these curves to the domain of low CO2 loadings allowed extracting the diffusion coefficients at zero coverage which lie between 2 and 5.3 × 10-9 m2 s-1. Such values are consistent with those reported elsewhere for Dt in the silicalite system where the calculated and experimental values were defined to be in the range (5.5-7.0) × 10-9 m2 s-1.9 A faster diffusivity of CO2 in silicalite compared to the one in NaY might be explained by the absence of specific adsorption sites in the former material. A large number of both experimental10-12 and theoretical efforts13-17 have been devoted to the study of the dynamic properties of CH4 in the faujasite systems. From an experimental point of view, the self-diffusivity has been first obtained via the pulsed field gradient NMR technique.10 In NaX, the selfdiffusivity was measured by Ka¨rger et al. at temperatures of 22310 and 300 K11 for loadings composed of between 14 and 80 CH4 molecules/u.c. The self-diffusion coefficient showed for both temperatures a monotonically decreasing profile when the CH4 concentration increased, and the self-diffusivity values ranged from ∼1 × 10-8 to ∼3 × 10-9 m2 s-1 at 223 K and from 2.8 × 10-8 to 6.0 × 10-9 m2 s-1 at 300 K. Later, a QENS study explored the influence of the temperature on the dynamics of CH4 in NaY and showed the progressive delocalization of the molecule with increasing temperature.12 From a modeling standpoint via molecular dynamics simulations, a monotonic decrease of the self-diffusivity of CH4 was usually predicted in various zeolite systems.13-17 Krishna et al. reported such a trend for both the all-silica (DAY) and the cations containing faujasite (NaX) at 300 K with values ranging from 3.5 × 10-8 to 1 × 10-9 m2 s-1 for CH4 loadings composed of between 6 and 96 molecules/u.c.13,14 In these works, the diffusive molecule was described via a neutral united atom model, and the CH4/zeolite

10.1021/jp910863z  2010 American Chemical Society Published on Web 02/26/2010

5028 J. Phys. Chem. C, Vol. 114, No. 11, 2010 framework interaction was taken into account only through a Lennard-Jones interatomic potential whose parameters were derived by Dubbeldam et al.15 Further, Beerdsen et al. used the same force field and reported a similar CH4 diffusivity profile and values in the NaY zeolite.16 Yashonath et al. also conducted MD simulations to probe the self-diffusivity of CH4 in NaY at 300 K17 using a five-point charged model developed by Meinander and Tabisz18 for describing the CH4 molecule. They found a linear decreasing profile for Ds in the range of 16-64 CH4 molecules/u.c. with absolute values composed of between ∼3.5 × 10-8 and ∼1 × 10-8 m2 s-1. Ghorai et al. selected two distinct force fields (ABCHY, derived from ab initio calculation, and KDMG, combining Kiselev’s potential for NaY and the one from Murad for CH4) for representing the adsorbate/ adsorbent interactions with the CH4 molecule described by an all-atom model in both cases, and they simulated the CH4 dynamical properties in the NaY system at 300 K for a loading of 8 molecules/u.c. The so-obtained Ds values were 1.5 × 10-8 and 3.4 × 10-8 m2 s-1 for the ABCHY and the KDMG force fields, respectively.19 Some other authors have also investigated via molecular simulations the Maxwell-Stefan diffusivity of CH4 in the faujasite materials, thus extracting the corrected diffusivity D0. In that way, Krishna et al. have found at 300 K a decreasing D0 profile as a function of loading with absolute values varying from ∼3 × 10-8 to ∼2 × 10-9 m2 s-1 for CH4 loadings composed of between 8 and 120 molecules/u.c.20,21 In contrast, only a few experimental studies published so far concern the dynamics of the binary gas mixture CO2/CH4 in the faujasite systems. The permselectivity of the equimolar CO2/ CH4 binary mixture in the NaX membrane, measured by Weh et al. at 296 K, ranged from 1.54 to 1.67.5 Hasegawa et al. have reported selectivities for the CO2/CH4 binary mixture of 13 and 28 in the NaX and NaY membranes, respectively.6 However, the determination of either the self- or the transport diffusivities has not been yet addressed for such a gas mixture. A full description of both thermodynamic and dynamic properties of methane in pure gas and in the presence of CO2 is required in order to provide some insight into the separation mechanism. In this context, the present work aims at completing the previous investigation performed by one of us22 which focused on the thermodynamics of the CO2/CH4 binary mixture in the NaY system by combining gravimetry/manometry/ microcalorimetry measurements and grand canonical Monte Carlo simulations. Further, from this previous study which reported an extensive comparison of various force fields for describing the interactions between the gas mixture and the NaY system, it was possible to define the most accurate set of interatomic potential parameters and microscopic model of the adsorbate, for reproducing the thermodynamic properties, which is then transferred to the exploration of the dynamics reported in the present article. Here, the self-diffusivity of CH4 in NaY at 200 K has been first investigated by means of QENS measurements for a wide range of loadings. Molecular dynamics simulations based on different microscopic models for representing the CH4 molecule and force fields for describing the CH4/NaY interactions were then conducted in order to help interpretation of the experimental evolution of Ds as a function of the CH4 loading, and further to gain a molecular insight into the diffusion mechanism. This dual experimental/simulation approach was further applied to investigate the influence of the CO2 concentration on the selfdiffusivity of CH4 in the same faujasite system. It was then possible to bring out clearly the microscopic mechanism in play during the codiffusion of CO2/CH4.

De´roche et al. 2. Quasi-elastic Neutron Scattering Experiment The quasi-elastic neutron scattering experiments were performed at 200 K on the time-of-flight spectrometer IN6 at the Institut Laue-Langevin, in Grenoble, France. The incident neutron energy was set to 3.12 meV, corresponding to a wavelength of 5.1 Å. Once scattered by the sample, the neutrons are analyzed as a function of flight time and angle. Spectra were recorded at various scattering angles, corresponding to wave vector transfers, Q, ranging from 0.24 to 1.5 Å-1. Spectra from different detectors were grouped in order to obtain reasonable counting statistics, and the Bragg peaks of the zeolite have been carefully avoided. The line shape of the elastic energy resolution could be fitted by a Gaussian function, whose full-width at halfmaximum (fwhm) varied from 81 µeV at small Q to 101 µeV at large Q. The NaY sample was activated by heating under flowing oxygen, up to 720 K. The zeolite was cooled and pumped to 10-4 Pa and then heated up to the activation temperature while pumping (final pressure inferior to 10-3 Pa). The zeolite was transferred inside a glovebox into a slab-shaped aluminum container, which was connected to a gas inlet system. After the recording of the scattering of the dehydrated zeolite, different concentrations of CH4 were adsorbed in situ at 200 K. This temperature was selected to adsorb larger amounts of methane compared to 300 K, while keeping the equilibrium pressure e1 atm. The loadings were determined by volumetry during the QENS experiments. The investigated loadings for the pure CH4 diffusion (labeled from θ1 to θ6) correspond to 9.5, 21.8, 30.7, 40.8, 48.8, and 52.0 CH4 molecules/u.c. In a subsequent step, we partially desorbed CH4 in order to obtain an intermediate loading (corresponding to 26 CH4 molecules/ u.c.), and then three different concentrations of CO2, labeled as θ1′, θ2′, and θ3′, have been introduced into the cell, corresponding to 10.0, 30.0, and 45.0 CO2 molecules/u.c. In this way, we could investigate the diffusion of CH4 perturbed by the presence of CO2 molecules. In the case of methane, neutrons are scattered by the hydrogen atoms which have a large incoherent cross section. Consequently, the diffusion properties of the individual CH4 molecules (the self-diffusion coefficient, Ds) can be extracted. For CO2, the scattering cross sections of carbon and oxygen atoms are more than 10 times smaller than the hydrogen one. Thus, in CO2/CH4 mixtures, the scattering will be dominated by the CH4. 3. Molecular Dynamics Simulations 3.1. Model NaY Material. In order to reproduce the Si/Al ratio of 2.4 for the experimental NaY sample, we have considered the material with the following chemical composition: Si136Al56Na56O384. The distribution of the extra-framework cations in NaY was modeled following the conclusions drawn by Fitch et al. using neutron diffraction:23 6 cations in SI sites, located within the hexagonal prism connecting 2 sodalite cages, 18 cations in SI′ sites, present in the sodalite cage in front of the 6-ring window connected to the hexagonal prism, and 32 cations in the SII site, within the 6-ring windows of the supercage. Two microscopic models have been then considered which differ by (i) the partial charges carried by the atoms of the NaY framework and the CH4 molecule and (ii) the interatomic potential parameters for representing the NaY/CH4 and the CH4/ CH4 interactions. Both models (labeled as model 1 and model 2) are described below.

Dynamic Properties of CH4 in NaY Zeolite

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3.2. Microscopic Model for the CH4-CO2 Molecules and Interatomic Potentials. Model 1. In this model, the NaY zeolite is assumed to be semi-ionic with atoms carrying the following partial charges (in electron units): Si(+2, 4); Al(+1, 7); Oz(-1, 2), and Na(+0, 7), according to the studies previously published by Maurin et al.24 The interaction between the extra-framework cations and the oxygen atoms of the framework is expressed as a sum of a Coulombic term and a Buckingham type potential (eq 1)

V(rij) ) -

( )

qiqj -rij C + A exp - 6 4πε0rij F rij

(1)

where qi, qj correspond to the partial charges of interacting species, rij is the distance separating the species, and A, F, and C are fitted constants. The corresponding Buckingham parameters for the Na+-Oz interaction are A ) 8200 eV, F ) 0.218 Å, and C ) 11.8 eV Å6. The CH4 is represented by a point charge model with the following partial charges carried by each atom (in electron units): C (-0, 48) and H (+0, 12). They have been previously extracted from a Mulliken analysis based on ab initio cluster calculations which consisted of probing the interactions between the Na+ ions embedded in an array of point charges representing the six-ring of zeolite and methane. All the details of these calculations can be found elsewhere.25 This set of charges was then successfully used to simulate the thermodynamics and dynamics of CH4 in zeolites25 and hybrid MOF materials.26 Each atom of the adsorbate provides a contribution to the adsorbate/adsorbent interactions which are described via a sum of a repulsion-dispersion 12-6 Lennard-Jones (LJ) potential and a Coulombic term (eq 2)

V(rij) ) -

[( ) ( ) ]

qiqj σ + 4ε 4πε0rij rij

12

-

σ rij

6

(2)

where ε is the depth of the potential well, σ is the distance at which the interparticle potential is zero, and rij is the distance separating the particles. The CH4/CH4 and the CH4/Na+ LJ parameters were taken from a previous investigation.25 Further, considering that the oxygen atoms of the framework, Oz, exhibit a much higher polarizability as compared to the silicon and aluminum atoms, the only adsorbent/adsorbate dispersion-repulsion interactions taken into account are those between the CH4 molecule and the framework oxygen atoms, the corresponding parameters being previously derived by quantum chemical cluster calculations.25 The CO2 molecule is described using the EPM2 atomic point charge model developed by Harris and Yung27 with the following charges (in electron units): C (+0, 6512) and O(-0, 3256). In addition to the electrostatic interactions, the adsorbate/ adsorbent dispersion-repulsion interactions have been included. The latter considers interactions between the CO2 molecule and the oxygen atoms of the framework and is expressed by means of a LJ potential form. The parameters have been derived in one of our earlier studies involving quantum chemical calculations.24 Finally, all the cross-term LJ interaction potential parameters have been calculated via the Lorentz-Berthelot mixing rule. All the applied Lennard-Jones potential parameters are summarized in Tables 1 and 2.

TABLE 1: LJ Pair Potential Parameters for Describing the Adsorbate/NaY Faujasite Interactions Using Model 1a interaction pair

ε/K

σ/Å

Na-C(CO2) Na-O(CO2) Na-C(CH4) Na-H(CH4) Oz-C(CO2) Oz-O(CO2) Oz-C(CH4) Oz-H(CH4)

88.089 31.336 156.097 102.045 42.120 69.750 57.850 40.820

2.984 2.628 2.735 2.343 3.474 3.100 3.198 2.895

a The label Oz corresponds to the oxygen atoms of the NaY framework.

TABLE 2: LJ Potential Parameters for Describing the Adsorbate-Adsorbate Interactions Using Model 1 atom

ε/K

σ/Å

C (CH4) H (CH4) C (CO2) O (CO2)

35.9 7.66 28.129 80.507

3.447 2.816 2.757 3.033

TABLE 3: LJ Pair Potential Parameters for Describing the Adsorbate-Adsorbate and Adsorbate-Adsorbent Interactions Used in Model 2 interacting species

ε/K

σ/Å

C(CH4)-C(CH4) H(CH4)-H(CH4) C(CH4)-H(CH4) Na-C(CH4) Na-H(CH4) Oz-C(CH4) Oz-H(CH4)

48.74 8.22 20.01 151.63 30.27 122.63 185.14

3.35 2.813 3.081 3.36 3.092 3.08 2.06

Model 2. In this model, the NaY system is considered uncharged. The CH4 molecule is represented by an “all-atom” model without partial charges. The interactions between the CH4 molecule and the adsorbent (framework oxygen atoms and the Na+ cations) are thus expressed as only Lennard-Jones pair potentials whose parameters are listed in Table 3. In contrast to model 1, no electrostatic interaction is considered. 3.3. Grand Canonical Monte Carlo Simulations. Single component adsorption isotherms for the CH4/NaY system were computed up to 1 bar using a grand canonical Monte Carlo algorithm, as implemented in the Sorption module of the Cerius2 software suite.28 The calculations were performed using both models for CH4. We ran the simulations at 200 K, with a simulation box corresponding to 1 unit cell with typically 2.5 × 106 Monte Carlo steps. The framework was kept rigid during the whole adsorption process. The Ewald summation was used for calculating the electrostatic interactions in the case of model 1, and the short-range interactions were computed with a cutoff distance of 12.0 Å. The adsorption enthalpy at low coverage was calculated through the fluctuation over the number of particles in the system and from the internal energy.29 3.4. Molecular Dynamics Simulations. Molecular dynamics simulations were performed using the DL_POLY program30 in the NVT ensemble implementing the Berendsen anisotropic thermostat31 with the time constant set to 0.5 ps. For each simulated gas loading, the starting configurations have been obtained by preliminary Monte Carlo simulations performed in the canonical ensemble. The simulations have been carried out at 200 K, for 3.0 × 106 steps (corresponding to 3 ns), and the simulation box consisted of one unit cell. A spherical shortrange cutoff of 12.0 Å was used, while electrostatic interactions

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(for model 1) were evaluated using the Ewald summation method. For model 2, 2 × 2 × 2 unit cells of zeolite NaY were considered, and the simulations were performed in the NVE ensemble with a spherical cutoff of 15.0 Å. A time step of 1 fs was used to solve the Newton’s equations of motions which yield good energy conservation. The system was equilibrated for 500 ps, and then a further 2.5 ns run was made during which the positions and velocities were stored every 0.05 ps. Periodic boundary conditions were applied in all three directions. The mean square displacement (MSD) values of the CH4 molecule for each loading were then plotted as a function of time, and the linear fits were implemented into the Einstein’s relation (eq 3)32 to extract the values of the self-diffusion coefficient (Ds):

1 1 Ds ) lim 〈|ri(t) - ri(0)| 2〉 6 tf∞ t

(3)

One should bear in mind that the MD simulations with model 1 were conducted using a rigid zeolite framework with fixed coordinates in which only the extra-framework cations were allowed to move, while with model 2 both atoms of the framework and the extra-framework cations were maintained fixed in their initial positions. It is generally admitted that a flexible model for the host system is required for tightly fitting sorbate-zeolite systems, where omission of lattice vibrations leads to an overestimation of the energy barriers for the intracrystalline transport.32 In contrast, when the guest molecules show a much smaller kinetic diameter compared to the zeolite pore openings, several authors suggest that the dynamics of the molecule is not affected when the framework is treated as rigid.33 As the kinetic diameter of methane (3.8 Å) is smaller than the size of the 12-ring windows of faujasite (7.4 Å), keeping the zeolite framework rigid is not expected to significantly influence either the magnitude or the trend of the diffusivity as a function of the loading. Besides, it allows important CPU time savings. 4. Results and Discussion 4.1. Diffusion of the Pure CH4 in NaY. Some of the QENS spectra obtained at 200 K for CH4 in NaY (θ3) are shown in Figure 1. To describe the motion of this adsorbate, the most detailed model consists of an isotropic rotation (radius of gyration of 1.1 Å) convoluted by intra- and intercage jumps.34 The intracage motion corresponds to jumps between SII cations, while the intercage motion corresponds to long-range diffusion. All spectra could be fitted simultaneously using this model, convoluted with the instrumental resolution. An error of 20% is estimated for the self-diffusion coefficients, taking into account the experimental error and the data treatment. As a typical illustration, Figure 1 shows a good agreement between the experimental and the calculated spectra. The experimentally extracted self-diffusion coefficients for CH4 are reported in Figure 2 (full black triangles) as a function of the loading. One can notice an unprecedented, nonmonotonic evolution of Ds for CH4. While the previous experimental data collected on NaX10,11 and ZSM-511,35 by PFG NMR reported a continuous decrease of Ds when the CH4 concentration increases, here the self-diffusivity passes through a maximum for an intermediate loading of 32 CH4/u.c. Our experiment on NaY has been conducted at 200 K. Thus, the maximum undetected before for the diffusion of an apolar molecule in a zeolite system might be, at least partially, due to the use of a lower temperature. Nevertheless, we should point out that similar self-diffusion coefficient evolutions as a function of the loading have been

Figure 1. QENS spectra obtained at 200 K for CH4 in NaY (θ3), for different values of the wave vector transfer: (a) 0.3, (b) 0.53, and (c) 1.19 Å-1. The + symbols correspond to the experimental points and the solid lines to the calculated spectra; the shaded area corresponds to the contribution from intracage motions.

Figure 2. Evolution of the self-diffusion coefficients as a function of the CH4 loading obtained at 200 K: QENS for NaY (2), simulations using model 1 (∇) and model 2 (0).

previously observed for polar diffusive species including water36 and methanol.37,38 This unexpected evolution of Ds (labeled as a “Type IV” diffusion behavior by Ka¨rger et al.11) might be most probably ascribed to some preferential interactions between the host material and the diffusive species. At the initial stage of loading, the methane molecules feel the electric field created by the extraframework cations in sites SII and the zeolite atoms of the supercage. When the concentration of the CH4 molecules increases, the electric field felt by each individual molecule is reduced. The self-diffusion coefficient thus tends to reach a maximum for 32 CH4 molecules/u.c., which in turn corresponds to a loading of 1 methane molecule per extra-framework cation located at the accessible SII sites, within the supercage. We might then suppose that the cations constituting the possible preferential adsorption sites for CH4 are mostly occupied and in this way are “screened” for additional adsorbate molecules which can consequently diffuse without being inhibited. Finally, at higher stages of loading, this thermodynamic effect is counterbalanced by a steric factor. The lack of available space

Dynamic Properties of CH4 in NaY Zeolite for the diffusive species rises with increasing loading, and consequently, the diffusion rate of the methane molecules drops down. Previous lattice gas study with model two-dimensional lattice at different temperatures is relevant here. Bhide and Yashonath have shown in their contribution how a decreasing profile (labeled as a “Type I” diffusion behavior by Ka¨rger et al.11) of Ds with loading can gradually change to an increase followed by a decrease in Ds with loading (Type IV) when one changes either the interaction energy or the temperature.39 The behavior is crucially determined by the ratio ε/kBT. When this ratio is small, then a monotonic decrease is seen; otherwise, when the ratio is large or the temperature low, then an initial increasing trend is followed by a decreasing profile. The position of the maximum in Ds is determined by the number of adsorption sites. Thus, our interpretation is consistent with the findings of the lattice gas study. Molecular dynamic simulations, based on the two models described above, have been conducted in order to confirm/deny the assumptions on the plausible microscopic diffusion mechanism in play. The simulated Ds values as a function of the CH4 loading are reported in Figure 2 for both models. One can observe significant differences between the results obtained from the two models in terms of both magnitude and profile for Ds. Although model 1 allows reproducing very well the experimental Ds values for intermediate and high loadings, it slightly overestimates the experimentally measured diffusivity at low CH4 concentration. The resulting evolution of Ds as a function of loading exhibits a monotonic, slightly decreasing profile, quite consistent with reported results for small diffusing apolar species in zeolite materials.10,11,13,40 However, one can argue that the decrease of Ds when the loading increases is less pronounced than those usually reported at low loading from both experimental and theoretical sides. From a visual inspection of our MD trajectories, we have observed that at low loading the thermodynamic effect, based on the interaction between the CH4 molecules and the extraframework cations, is predominant. Consequently, in contrast to all above cited simulation references, we observe a slight increase of the self-diffusivity when increasing the loading from 8 to 16 molecules of CH4/u.c. Increasing the adsorbate concentration up to 24 CH4 molecules/u.c. leads to a drop of the self-diffusivity that can possibly be explained by the steric effect. Beyond 24 CH4 molecules/u.c., an additional increase of the loading induces a progressive decrease of Ds, explained by the steric hindrance, growing up proportionally to the number of adsorbate molecules. Thus, the predictions from model 1 allow us to conclude that the diffusion of methane in NaY is governed by a combination of thermodynamic considerations, i.e., interactions between the CH4 molecules and the extraframework Na+ cations, predominant at the initial stage of loading, and a steric effect, which becomes significant at intermediate and high loadings. Several authors20 previously suggested that the diffusion of methane in large cage zeolites, such as faujasite, solely depends on the topology of the material. Both of our experimental and simulated outcomes are in sharp contradiction with this previous conclusion, emphasizing that the chemical composition of the host material plays a crucial role even for apolar molecules such as CH4, when one probes diffusion in the low concentration domain. In contrast, the simulations performed using model 2 lead to the presence of a tiny maximum shifted to lower CH4 concentration (16 CH4/u.c.) compared to the experimental one (32 CH4/ u.c.). However, the calculated Ds values are almost 1 order of

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Figure 3. Single component adsorption isotherms of CH4 in NaY obtained at 200 K in the low pressure domain (below 1 bar) by volumetry measurements (2) and by means of GCMC simulations based on model 1 (∇) and model 2 (0).

magnitude lower than the experimental ones in the whole range of loading. This observation thus suggests that model 2 overestimates the strength of interactions between the diffusive species and the zeolite surface. In order to verify this assumption, we computed the adsorption isotherms in the low domain of pressure using both models and compared them with the experimental one (Figure 3). From Figure 3, one can observe that model 1 leads to an underestimation of the adsorbed amount at the initial stage of adsorption whereas the simulations using model 2 significantly overestimate the experimental adsorption isotherm. We have also estimated using both microscopic models the adsorption enthalpy at low coverage. Model 1 and model 2 lead to enthalpy values at zero coverage of 11.7 and 23.8 kJ · mol-1, respectively, while the previously reported experimental values range between 15.5 and 18.5 kJ · mol-1.25 These results clearly support the above-mentioned assumption that the strength of the interaction between the CH4 molecule and the NaY surface is underestimated by model 1, while it is significantly overestimated by model 2. Indeed, model 2 based self-diffusivities are much lower than the experimental values, as the overestimated strength of the Na+/CH4 interactions contribute to slow down the diffusion rate. However, the shape of the experimentally obtained selfdiffusion coefficient evolution curve as a function of loading is roughly reproduced, presenting a maximum at the intermediate loading. 4.2. Codiffusion of CH4/CO2 in NaY. Figure 4 shows some of the QENS spectra obtained for CH4 diffusion perturbed by the presence of different amounts of CO2 in NaY at 200 K. A slight narrowing of the quasi-elastic peak can be observed upon increasing CO2 concentrations, indicating a small reduction of the self-diffusivity of CH4. Figure 5 reports the QENS self-diffusivity coefficients of methane for a loading of 26 CH4/u.c. plotted as a function of the CO2 concentration. It appears that Ds decreases slightly when the CO2 concentration increases. When introducing the first 10 molecules of CO2, the resulting CH4 self-diffusivity remains almost unchanged. Tripling the initial CO2 amount in NaY leads to a self-diffusivity decrease of approximately 10%. Finally, at a CO2 loading of 45 molecules/u.c., the resulting self-diffusivity of CH4 is about 20% lower compared to the one observed in the absence of CO2 molecules. Indeed, one can conclude from this experimental observation that the self-diffusivity of CH4 is only slightly affected by the presence of CO2. The evolution of the self-diffusivity of CH4 in the presence of CO2 molecules has been also explored via molecular

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Figure 6. Simulated self-diffusion coefficients of pure CO2 (b) and in the presence of 26 CH4 molecules/u.c. (O) obtained from MD calculations performed at 200 K.

Figure 4. QENS spectra obtained for CH4 perturbed by increasing loadings of CO2 in NaY zeolite: (a) θ1′, (b) θ2′, and (c) θ3′. The + symbols correspond to the experimental points and the solid lines to the calculated spectra (Q ) 0.3 Å-1).

Figure 5. Self-diffusion coefficients of CH4 molecules in the presence of CO2 molecules reported as a function of the CO2 concentration at 200 K. Experimental and simulated values, obtained respectively by QENS (2) and molecular dynamics simulations using model 1 (∇).

dynamics simulations. In light of the results obtained for the dynamics of pure CH4 in NaY, we decided to select for the exploration of the CO2/CH4 codiffusion the microscopic model 1 which leads to a better agreement between the experimental and simulated self-diffusion coefficient values, in particular within the domain of investigated CH4 loading (26 molecules/ u.c.). One can notice from Figure 5 that our MD simulations reproduce well the absolute values of the self-diffusivity of CH4 in the whole range of CO2 loading while the predicted curve exhibits a sharper decrease compared to the experimental one. The simulated decreasing Ds profile of CH4 can be interpreted from a simple inspection of the MD trajectories as follows: the CO2 molecules introduced in the CH4/NaY system adsorb preferentially to the sodium cations present within supercages and in this way “screen” these possible attractive sites for CH4. Such a microscopic behavior should lead to an enhancement of the diffusion of the alkane molecules. However, the CO2 molecules simultaneously occupy and/or crowd the supercage and consequently reduce the effective diffusing space for the

CH4 molecule. At the lowest CO2 loading (10 molecules/u.c.), the combination of both effects leads to a very slight decrease of the CH4 self-diffusivity. At higher CO2 loadings (30 and 45 molecules/u.c.), the steric hindrance effect becomes much more important and the self-diffusion coefficient of CH4 significantly decreases, respectively, by about 50 and 80% compared to the initial value. In parallel, we have also investigated, only by simulations, the dynamic behavior of pure CO2 and its binary mixture with CH4. In Figure 6 are plotted the self-diffusion coefficients of CO2 as a function of the loading. The data extracted for the pure CO2 are compared with those of CO2 in binary mixture with 26 molecules of CH4/u.c. We observe that the Ds for CO2 exhibits an increasing profile as a function of the loading within the investigated domain of loadings (10-45 molecules/u.c.) for both the pure CO2 and the binary mixture, which is opposite to what was seen for methane. However, it can be pointed out that (i) the absolute values of the self-diffusion coefficients are significantly higher for the pure CO2 than its binary mixture and (ii) the CO2 pure gas selfdiffusivity is increasing in a sharper way. At the initial stage of loading, the CO2 molecules in pure gas phase interact strongly with the extra-framework cations as previously mentioned,41 and consequently the intracage displacements are more probable than intercage long-range diffusion. Increasing the number of CO2 molecules decreases the strength of the Na+-CO2 interaction which contributes to increase the self-diffusivity of CO2. Thus, at the highest investigated CO2 loading corresponding to 45 molecules of CO2/ u.c., we observe the higher self-diffusivity value. From a visual inspection of MD trajectories, we could observe that the dynamics of the CO2 molecule can be seen as a combination of short-range intracage and long-range intercage movements. While at low loading the CO2 dynamics is predominated by the intracage movements, at higher loading the intercage displacements prevail. Furthermore, we might suppose that additionally increasing the CO2 loading would lead to a significant drop of the CO2 self-diffusivity, as previously observed by Plant et al.,42 since the effect of the steric hindrance would become predominant. Regarding the CO2/CH4 binary mixture, at the initial stage of loading, the CO2 molecules still interact strongly with the extra-framework cations, similarly to the case in the pure gas. However, at the same time, the present CH4 molecules encumber the available space creating a steric hindrance effect, thus contributing to limit the CO2 diffusivity. Indeed, the selfdiffusion coefficients are lower and increase in a softer way

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Figure 7. Arrhenius plots of the CH4 self-diffusivity calculated by MD simulations for NaY loaded by 26 CH4 molecules/u.c. in the absence of CO2 (a) and in a mixture with 30 CO2 molecules/u.c. (b).

when the loading increases, in comparison to the diffusion of CO2 in pure gas. Similarly to the case of pure CO2, the dynamics correspond to a combination of intra- and intercage motions. At the initial stage of loading the intracage movements prevail, while at higher loadings the intercage displacements predominate. 4.3. Activation Energies. The values of the activation energies for the diffusion of CH4 in the presence and absence of CO2 have been extracted from molecular dynamics simulations using model 1. Figure 7 reports the Arrhenius plots of the CH4 self-diffusion coefficients for the pure CH4 (Figure 7a) as well as for the binary mixture corresponding to 30 CO2 molecules /u.c. (Figure 7b). For the pure CH4 diffusion, we find an activation energy (Ea) of 3.9 kJ · mol-1 which is slightly lower than the one previously obtained from QENS for a similar CH4 loading12 (6.3 kJ · mol-1). As we have demonstrated above, our forcefield (model 1) does not accurately reproduce the strength of interaction between the adsorbate molecule and the NaY surface, which could explain the discrepancy between the experimental and simulated Ea values. Furthermore, the activation energy for CH4 diffusion in the mixture with 30 molecules of CO2 exhibits a lower value than for the pure gas (2.5 kJ · mol-1). This observation is fully consistent with the revealed microscopic codiffusion mechanism: the CO2 molecules present within the supercage screen the sodium cations so that CH4 molecules do not feel entirely the electric field created by these cations and thus the diffusivity is not slowed down. Consequently, a lower activation energy is required to initiate the diffusion of CH4 in the presence of 30 molecules of CO2. 5. Conclusion In the present paper, we have investigated the dynamic properties of CH4 in the NaY zeolite as both pure gas and in binary mixture with CO2, by combining QENS experiments with molecular dynamics simulations based on two different microscopic models for both the adsorbate and the zeolite framework. An unexpected CH4 diffusion profile with the existence of a maximum for a loading of 32 CH4 molecules/u.c. has been observed experimentally, suggesting, in contrast to a number of previous studies, that the presence of the extra-framework Na+ cations within the supercage gives rise to a significant interaction with the CH4 molecules. Such an unsual trend should be also detected when one deals with longer chain alkanes. Molecular simulations performed in parallel clearly showed that describing such an unusual behavior requires an accurate description of the Na+/CH4 interaction. This conclusion clearly states that if one aims at rigorously reproducing the experimental trend, the force fields involved should be improved either by a

specific fitting procedure or by including some additional terms such as a polarization component. Further, the QENS codiffusion study revealed only a tiny influence of the presence of the CO2 molecules on the CH4 diffusivity. This observation was supported by molecular simulations which showed that such a trend can be interpreted by a balance between the preferential adsorption of CO2 around the sodium cations which tend to “screen” the CH4/Na+ interactions and the reduction of the effective diffusing space for the CH4 molecules as CO2 crowds the supercage. Acknowledgment. This work was supported by the French program ANR CO2 “NoMAC” (ANR-06-CO2-008) and European FP6 RTN “INDENS” project. We thank the Institut LaueLangevin, Grenoble, France for the neutron beam time, Dr. M. M. Koza and Dr. L. Gaberova for their help during the QENS measurements, and the CINES for the computational facility. References and Notes (1) Yang, R. T. Gas Separation by Adsorption Processes; Imperial College Press: London, 1997. (2) Datta, A. K.; Sen, P. K. J. Membr. Sci. 2006, 283, 291. (3) Ahluwalia, R. K.; Wang, X. J. Power Sources 2008, 180, 122. (4) Pettersen, T.; Lien, K. M. Gas Sep. Purif. 1995, 9, 151. (5) Weh, K.; Noack, M.; Sieber, I.; Caro, J. Microporous Mesoporous Mater. 2002, 54, 27. (6) Hasegawa, Y.; Tanaka, T.; Watanabe, K. Korean J. Chem. Eng. 2002, 19, 309. (7) Kusakabe, K.; Kuroda, T.; Murata, A.; Morooka, S. Ind. Eng. Chem. Res. 1997, 36, 649. (8) Plant, D. F.; Jobic, H.; Llewellyn, P. L.; Maurin, G. Eur. Phys. J. 2007, 141, 127. (9) Papadopoulos, G. K.; Jobic, H.; Theodorou, D. N. J. Phys. Chem. B 2004, 108, 12748. (10) Ka¨rger, J.; Pfeifer, H.; Rauscher, M.; Walter, A. J. Chem. Soc., Faraday Trans. 1 1980, 76, 717. (11) Ka¨rger, J.; Pfeifer, H. Zeolites 1987, 7, 90. (12) Jobic, H.; Be´e, M.; Kearley, G. J. J. Phys. Chem. 1994, 98, 4660. (13) Krishna, R.; van Baten, J. M. Chem. Eng. Technol. 2006, 29, 1429. (14) Krishna, R.; van Baten, J. M. Chem. Eng. Technol. 2007, 30, 1235. (15) Dubbeldam, D.; Calero, S.; Vlught, T. J. S.; Krishna, R.; Maesen, T. L. M.; Smit, B. J. Phys. Chem. B 2004, 108, 12301. (16) Beerdsen, E.; Dubbeldam, D.; Smit, B. J. Phys. Chem. B 2006, 110, 22754. (17) Yashonath, S.; Demontis, P.; Klein, M. L. J. Phys. Chem. 1991, 95, 5881. (18) Meinender, N.; Tabisz, G. C. J. Chem. Phys. 1983, 79, 416. (19) Ghorai, P. K.; Sluiter, M.; Yashonath, S.; Kawazoe, Y. Solid State Sci. 2006, 8, 248. (20) Krishna, R.; van Baten, J. M.; Garcia-Perez, E.; Calero, S. Ind. Eng. Chem. Res. 2007, 46, 2974. (21) Krishna, R.; van Baten, J. M. Microporous Mesoporous Mater. 2008, 109, 91. (22) Ghoufi, A.; Gaberova, L.; Rouquerol, J.; Vincent, D.; Llewellyn, P. L.; Maurin, G. Microporous Mesoporous Mater. 2009, 119, 117.

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