Diffusion of CH4, CO2, and Their Mixtures in

Article pubs.acs.org/JPCC

Diffusion of CH4, CO2, and Their Mixtures in AlPO4‑5 Investigated by QENS Experiments and MD Simulations Sébastien Rives,†,‡ Hervé Jobic,*,‡ Andrew M. Beale,§,∥,⊥ and Guillaume Maurin*,† †

Institut Charles Gerhardt Montpellier, UMR 5253 CNRS, UM2, UM1, ENSCM, Université Montpellier 2, Pl. E. Bataillon, 34095 Montpellier Cedex 05, France ‡ Institut de Recherches sur la Catalyse et l’Environnement de Lyon, Université de Lyon 1, CNRS, 2. Av. A. Einstein, 69626 Villeurbanne, France § Inorganic Chemistry and Catalysis, Debye Institute for Nanomaterials Science, Utrecht University, Universiteitsweg 99, 3584 CG Utrecht, The Netherlands ∥ Department of Chemistry, University College London, 20 Gordon Street, WC1H 0AJ London, United Kingdom ⊥ Research Complex at Harwell, Rutherford Appleton Laboratory, Harwell Oxford, Didcot, Oxon OX11 0FA, United Kingdom S Supporting Information *

ABSTRACT: Quasi-elastic neutron scattering (QENS) measurements in combination with molecular dynamics (MD) simulations have been performed to characterize the dynamics of CH4, CO2, and binary mixtures of different compositions in the zeolite-type AlPO4-5 material. The experimental and simulated self-diffusion coefficients (Ds) for CH4 in the presence of CO2 are in very good agreement in a whole range of CO2 concentrations, showing a decreasing profile when the CO2 loading increases. Similar to the diffusion of light gases in other nanoporous materials, the experimental and simulation approaches both evidence a fast mobility for CH4 at low loading in this zeolite. Complementary to this, the MD simulations predict a slightly faster diffusivity for CH4 in binary mixtures with CO2 when compared to its behavior as a single component, which is concomitant with a speeding up of the CO2 molecules. QENS further reveals a nonmonotonous evolution of the transport diffusivity for CO2 as a function of the loading. This peculiar behavior is reproduced by MD simulations, with the minimum being shifted to a higher concentration. A deep analysis of the MD spatial densities indicates that both CO2 and CH4 experience a 1D-type normal diffusion along the AlPO4-5 channels in a hollow cylinder with a hexagonal base. Finally, QENS and MD allow the exploration of the rotational dynamics of CH4 as a pure component and in a binary mixture.

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INTRODUCTION The recovery of CO2 from its gas mixtures with CH4 is a key step in the treatment of natural gas fields that presently contain increasing concentrations of CO2.1,2 There is a growing demand to substitute the current purification technologies based on absorption/desorption with amine solvents. Thus, there is a search for new processes to deal with CO2 bulk removal with the aim of reducing the equipment size and energy cost; in addition, their installation on floating platforms is envisaged. Physisorption-based processes, such as pressure swing adsorption, appear to be an attractive economic alternative. These processes involve the use of porous solids that have been mainly selected because of their ability to be highly selective for CO2 over CH4, to adsorb a relatively large amount of CO2, and to allow easy regeneration without requiring a costly heating step. Porous zeolites and activated carbons have been mainly envisaged for such applications. In this context, the separation performances of a large library of zeolites have been screened using experimental and computational high-throughput approaches.3−6 Most of these investigations mainly probed the thermodynamic aspect of the © 2013 American Chemical Society

coadsorption process and evidenced that the selective capture of CO2 is driven either by interactions with specific adsorption sites or by steric hindrance. However, aside from the thermodynamic consideration, the kinetic behavior of the gas mixtures, which is also expected to impact these separation processes, has been scarcely addressed. In contrast to the diffusion of single-component gases that have been intensively investigated from experimental and computational strategies in porous solids including zeolites7−19 and MOFs,20−26 only a few attempts have been reported so far that use these adsorbents to probe the dynamics of the binary mixtures. Most of the work on this topic has been tackled computationally by several groups that successively explored the CO2/CH4 codiffusion in various zeolites and MOFs using molecular dynamics simulations.15,26−32 This modeling effort was completed by a very limited number of experimental investigations30−32 that were based on the use of quasi-elastic Received: April 30, 2013 Revised: June 14, 2013 Published: June 17, 2013 13530

dx.doi.org/10.1021/jp4042827 | J. Phys. Chem. C 2013, 117, 13530−13539

The Journal of Physical Chemistry C

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resultant white powder contained only the reflections present for the AlPO4-5 (AFI) structure (P6/mcc). Quasi-Elastic Neutron Scattering Measurements. The AlPO4-5 sample was activated by pumping at 600 K. It was transferred in a glovebox into a slab-shaped aluminum container that was connected to a gas-inlet system, allowing in situ adsorption. After recording the scattering of the empty material, three loadings of CO2 (2.2, 3.9, and 4.5 molecules/ u.c.) were investigated at 200 K, and the amounts adsorbed were determined by volumetry. For the intermediate loading that corresponds to 3.9 CO2/u.c., measurements were performed at two other temperatures to derive the activation energy of the diffusion. After these runs, CO2 was evacuated by pumping the cell at 373 K. Even if the scattering from CO2 was weak, it was verified after desorption that the signal from the degassed AlPO4-5 was identical to that of the starting material. A concentration of 0.7 CH4/u.c. was thus introduced, the spectra were measured at 200 K at this low-methane loading, and three concentrations of CO2 were successively added that corresponded to 0.6, 1.2, and 2.1 molecules/u.c. The activation energy for the diffusion of CH 4 was estimated from measurements at two temperatures in FeAlPO4-5 at a concentration of 0.6 CH4/u.c.. The QENS experiments were carried out at the Institut Laue−Langevin, Grenoble, France, using the time-of-flight (TOF) spectrometer IN6. The incident neutron energy was set to 3.12 meV, corresponding to a wavelength of 5.12 Å. After scattering by the sample, the neutrons were analyzed as a function of the flight time and angle. The TOF of the scattered neutrons is related to the energy transfer (ℏω), and the scattering angle, the momentum transfer (ℏQ). Spectra from different detectors were grouped to obtain reasonable counting statistics and to avoid the Bragg peaks from AlPO4-5. The wave-vector transfer range, Q, of the detector groupings varied from 0.34 to 1.4 Å−1. The TOF spectra were transformed to an energy scale after subtracting the scattering from the bare AlPO4-5. The elastic energy resolution could be fitted by a Gaussian function whose half-width at half-maximum (HWHM) varied from 40 μeV at small Q to 45 μeV at large Q. Molecular Dynamics Simulations. The crystal structure of the AlPO4-5 (Pcc2 symmetry, unit cell parameters: 13.794, 23.9, and 8.417 Å) was built using the atomic coordinates previously reported by Demontis et al.44 The partial charges carried by each atom of the framework were taken as 1.5, 2.5, and −1 e for Al, P, and O, respectively. In addition to the Coulombic interactions between all atoms of the framework and the guest molecules, the oxygen atom was also considered as an interacting Lennard-Jones (LJ) site with the corresponding LJ potential parameters issued from the UFF force field.45 AlPO4-5 was treated as flexible using the force field developed by Demontis et al.44 Regarding the guest molecules, although CO 2 was represented by the EPM2 three-point-charged rigid model reported by Harris and Yung,46 we envisaged two different models for CH4: (i) a rigid charged five-sites model47 with a C−H distance of 1.09 Å and charges of −0.66 and 0.165 e on the C and H atoms, respectively (model 1), and (ii) a flexible charged five-sites model48 with harmonic bonds and charges of −0.48 and 0.12 e on the C and H atoms, respectively (model 2). An additional united atom model has also been considered, which led to results similar to the ones obtained using model 1 (data not shown). The LJ crossing parameters for the CO2/ CH4 and guest/oxygen atom of the AlPO4-5 interactions were

neutron scattering (QENS) measurements to characterize the diffusivity of CH4 in the presence of CO2 in the 3D-type NaY faujasite30 and in both the windows and cages of the 3D and 1D tunnel-like MOFs.31,32 Some other authors investigated the dynamics of the same mixture in carbon molecular-sieve membranes using a pulsed-field NMR technique.33 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 such porous solids. This holds particularly true for the zeolite-type AlPO4-5 solid, where even though the thermodynamic CO2/CH4 coadsorption behavior has been characterized,34 its dynamics counterpart is still unexplored; the only study on its codiffusion emanating from Sholl et al.,35 which explored the Ne/CF4 binary mixture. The reasons for the interest in exploring AlPO4-5 include its simple 1D model with a cylindrical pore diameter of ca. 7.3 Å and its relatively smooth inner surface due to the absence of specific adsorption sites such as the extra-framework cations present in many other zeolites. Furthermore, the dimensionality and diameter of its channel and the absence of specific interacting sites at its pore surface are both analogous to the features of the MIL-47(V) MOF-type solid (lozenge pore channel with a diameter of 8 Å), for which we have extensively investigated the diffusion of a series of confined molecules over the past few years. By analogy to this latter MOF, where, for instance, n-butane experienced a blowgun effect occurring after a particular exchange of momentum with the relatively flexible host framework,36 AlPO4-5 is suspected to present a certain complexity of its lattice dynamics that can affect the diffusive behavior of certain adsorbed molecules including ethane as quoted by Demontis et al.37 In this context, we propose to explore the dynamics of CO2 and CH4 as single components and as binary mixtures of various compositions in this zeolite-type material by combining molecular dynamics (MD) simulations and quasi-elastic neutron scattering (QENS) experiments that have already proven to be successful for capturing the dynamics of various single components and binary mixtures in zeolites and MOFs.21,23,24,26,30−32,36,38−43 We aim to (i) determine the loading dependence of the selfdiffusivity for CH4 in the presence of CO2, (ii) compare both the profile and absolute diffusion-coefficient values with those obtained for the single components, (iii) explore the evolution of the transport diffusivity for CO2 as a function of the gas concentration, and (iv) further address the microscopic codiffusion mechanism for both diffusive species through a detailed analysis of both the QENS spectra and MD trajectories with particular attention being paid to the rotational dynamics of CH4.

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MATERIALS AND METHODS Synthesis and Activation of the Material. AlPO4-5 (AFI) was synthesized as follows. Orthophosphoric acid (H3PO4, Acros Organics, 85 wt % in water) was initially mixed with pseudoboehmite alumina (Catapal B, 73.6 wt % Al2O3, Sasol North America, Inc.) and the structure-directing agent triethylamine (TEA) (Acros Organics 99%). The subsequent gel was homogenized by mixing before transfer into an autoclave for a hydrothermal treatment at 175 °C for 4 h. The resultant material was vacuum filtered and oven dried (120 °C) before calcination in flowing air (50 mL/min) using a heating profile of 5 °C/min from room temperature to 550 °C and a dwell time of 3 h. An X-ray diffraction pattern of the 13531



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obtained using Lorentz−Berthelot mixing rules. The whole set of interatomic-potential parameters are summarized in the Supporting Information (Table S1). The MD simulations were further performed using the DL_POLY simulation package49 to explore the diffusion of the single guest molecules and their binary mixtures. The calculations were performed in the canonical (NVT) ensemble at 200, 250, and 300 K. A Nosé−Hoover thermostat was used with a relaxation time for the thermostat of 0.5 ps. The simulation box consisted of 16 unit cells (2 × 1 × 8) loaded as follows to mimic the experimental conditions: (i) CH4 (CO2) as single gas from 4(4) to 72(168) molecules, and (ii) in binary mixture with 4 CH4 molecules successively associated with 8, 20, and 32 CO2 molecules. All of the initial configurations were generated by preliminary canonical Monte Carlo simulations using the Complex Adsorption and Diffusion Simulation Suite (CADSS) software.50 Each MD simulation was typically conducted for 2 × 107 MD steps (i.e., 20 ns) with a time step of 1 fs following 1 ns of equilibration. The long-range Coulombic interactions were handled using the Ewald summation method, whereas all of the LJ interactions were calculated with a cutoff radius of 11.5 Å. The velocity Verlet algorithm was used to integrate the Newton equations of motion, and the quaternion algorithm was applied for the rotational motion of rigid molecules. The self- (Ds) and corrected (Do) diffusion coefficients were calculated from a linear fitting of the mean-square displacement (MSD) of the center of mass of a single target diffusive molecule and of all of the diffusive molecules, respectively, using Einstein’s expression. In the latter case, longer MD runs of 80 ns were considered to improve the statistics, and the diffusion coefficients were extracted from 5 different trajectories; hence, the uncertainties range from around 5% for the lowest loading to less than 1% for the higher loadings. The transport diffusion coefficients (Dt) were further computed from Do and from the knowledge of the thermodynamic correction factor (Γ) derived from the GCMC simulated adsorption isotherms. The rotational diffusion coefficients (Dr) for methane at each considered loading were then extracted from the angular-velocity autocorrelation functions (AVCF) evaluated every 100 MD steps (i.e., 0.1 ps) from 10 MD trajectories of 500 ps.

Figure 1. Comparison of the experimental (crosses) and fitted (solid lines) QENS spectra obtained for AlPO4-5 after adsorbing 0.7 CH4/ u.c. (a) followed by a coadsorption of 0.6 (b), 1.2 (c), and 2.1 (d) CO2/u.c. (T = 200 K, Q = 0.39 Å−1). The dotted lines correspond to the instrumental resolution.

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1, a very good agreement is obtained between the experimental and calculated spectra. The HWHM values of the translational component from methane are reported in Figure 2. All of the spectra measured at the different Q values could be fitted simultaneously with the simplified version of the Singwi−Sjölander53 jump-diffusion model. This simplified model is based on the assumption that the time taken for the jump can be neglected. The root-meansquare jump lengths vary from 7.7 Å for pure CH4 to 6 Å at the highest concentration of CO2. The experimental Ds values for pure CH4 at 0.7 CH4/u.c. and for CH4 perturbed by CO2 are shown in Figure 3 at T = 200 K. It appears that Ds(CH4) in a mixture monotonously decreases from 1.35 × 10−8 to 5.7 × 10−9 m2 s−1 for loadings varying from 0.62 to 2.1 CO2/u.c. This decreasing trend, which is similar to one that we previously observed for the same mixture in the NaY zeolite30 and different MOFs,31,32 is very well reproduced by our simulations using both CH4 microscopic models. The calculated Ds(CH4) values are also in excellent agreement with the QENS data in the whole range of CO2 loading experimentally explored, with model 2 allowing an even better qualitative accordance with the experimental Ds(CH4) trend,

RESULTS AND DISCUSSION To follow the influence of CO2 on the self-diffusivity of CH4, the QENS spectra corresponding to a low methane loading (i.e., 0.7 CH4/u.c.) were first measured. As shown in Figure 1a, the broadening relative to the instrumental resolution is large, even at a small Q value. When CO2 is further adsorbed, the broadening and therefore the diffusivity decrease with increasing CO2 loading (Figure 1). The scattering from CH4 is governed by the large incoherent cross section of hydrogen so that in this case it is the selfdiffusivity that is obtained.51 In CH4/CO2 mixtures, the much larger cross section of hydrogen ensures that the scattering is dominated by CH4. The spectra were fitted with a Lorentzian function, corresponding to the translational motion, and convoluted with the instrumental resolution. The anisotropy of the diffusion in this 1D system was taken into account using a powder average.52 The refinements for CH4 additionally have to include the rotational motion, which could be described by the isotropic rotational-diffusion model, where Dr is the isotropic rotational diffusion coefficient. As shown in Figure 13532



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Table 1. Comparison of the Self-Diffusion Coefficients for CH4 and CO2 in Various Nanoporous Materials

Figure 2. Half-width at half-maxima (HWHM) of the QENS spectra measured for AlPO4-5 after adsorbing 0.7 CH4/u.c. (●) followed by a coadsorption of 0.6 (△), 1.2 (◊), and 2.1 (□) CO2/u.c. (T = 200 K). The symbols are obtained from individual fits of the spectra, and the curves with simultaneous fits using a jump-diffusion model.

material (type)

T (K)

nads (CH4/ u.c.)

Ds(CH4) (m2s‑1)

method

ref

NaX (3D)

223

14−80

3.0−10.0 × 10−9

7

NaX(3D)

300

14−80

6.0−28 × 10−9

NaX(3D) NaY(3D) MIL-47(V) (1D) MIL-53(Cr) (1D) UiO-66(Zr) (3D) LTA(3D)

300 200 230

6−96 9.5−52 0.75−4.5

1.0−35 × 10−9 5.3−7.9 × 10−9 1.2−7 × 10−8

PFGNMR PFGNMR MD QENS QENS

250

0.4−2.8

1.1−4.5 × 10−8

QENS

21

230

4.4−16.5

2.0−2.8 × 10−9

QENS

26

301

101.3 kPaa

1.4 × 10−10

57

CHA(3D)

301

101.3 kPaa

1.1 × 10−11

DDR(3D)

301

101.3 kPaa

1.6 × 10−12

DDR(3D)

298

0−8

2−3 × 10−12

NaY (3D) ZSM-5 (3D) AlPO4-5(1D)

200 200 155

24 2 0.7

PFGNMR PFGNMR PFGNMR TSTKMC QENS QENS QENS

material (type)

T (K)

4.9 × 10−9 2.8 × 10−9 1.6 × 10−9 Ds(CO2) nads (CO2/ u.c.) (m2s‑1)

NaX(3D) NaY(3D) MIL-47(V) (1D) ZIF-68(1D) ZIF-70(1D) MFI(3D) DDR(3D) UiO-66(Zr) (3D)

300 300 230 298 298 300 298 230

21−78 25−71 1−8 0−60 0−60 2 0−8 7−45

0.7−4.0 × 10−10 0.1−1.3 × 10−9 1.5−2.0 × 10−9 1.5−8.0 × 10−10 1.8−5.5 × 10−9 7 × 10−9 1−2 × 10−10 2.4−6.7 × 10−10

8

15 30 21

57

57

27

11 58 52

method

ref

MD MD MD MD MD MD MD MD

18 18 24 22 22 17 27 26

a

Figure 3. Self-diffusion coefficients for CH4 as a function of the total loading (CO2 + CH4) at 200 K. Black, QENS; red, MD model 1; and blue, MD model 2. The full symbols (solid lines) are the single component, and the empty symbols (dashed lines) are the CH4/CO2 mixture with 0.75 CH4/u.c..

In the absence of the experimental adsorption isotherm, these values correspond to the pressure.

the single gas for the whole part of the investigated loadings. This is consistent with a slightly lower mean activation energy (Ea) associated with the CH4 diffusion in the mixture (2.1 vs 2.4 kJ/mol for the single component). Although these Ea values are much smaller than those in other zeolites and MOFs with 1D channels, such as ZSM-5 (4.7 kJ/mol11) and silicalite (5.7 kJ/mol55), or with cages, such as UiO-66(Zr) (6 kJ/mol26) and NaY (6.3 kJ/mol11), they are very close to the experimental ones obtained for pure methane in an Fe-substituted AlPO4-5 framework (3.1 kJ/mol) and in MIL-47(V) (3.0 kJ/mol).21 Furthermore, the slight increase in the diffusivity for CH4 in the presence of CO2 is similar to that previously observed in several MOFs, including UiO-66(Zr),26 MIL-47(V),32 and MIL53(Cr).32 The self-diffusivities for CO2 were also simulated for both the single components and binary mixture cases and show a monotonic decrease when the loading increases (Figure 4). In contrast to CH4, the CO2 species do not experience a rapidmobility phenomenon at low loading. This emphasizes that such quadrupolar CO2 molecules are expected to lead to less smooth host−guest interactions than those for apolar molecules such as CH4. Furthermore, the Ds(CO2) values are only slightly lower than those for CH4 in this material, and this trend differs with what is usually observed in other porous solids (Table 1). This result is consistent with the very similar

whereas the absolute values from model 1 are closer to the QENS data. It is also noticeable that there is a steep increase in Ds(CH4) at low loading that is reminiscent of the unusually fast mobility evidenced for a series of light gases confined at low concentrations in a 1D straight-channel-type MIL-47(V) MOF21,38 and carbon nanotube.54 As shown in Table 1, CH4 diffuses as rapidly as in MIL-47(V), and the corresponding diffusivity is at least 1 order of magnitude faster than the values reported for other 3D-type zeolites and MOFs. This is confirmed by the MD simulations that reproduced more significantly the steep change of Ds(CH4) using model 2. It suggests that such a fast mobility phenomenon can be generalized to light molecules diffusing in porous 1D solids that show relatively flat host−guest-interaction energy surfaces, which indicates the absence of specific adsorption sites. It can be noticed that the lower diffusivity previously obtained for AlPO4-5 by QENS (Table 1) is probably due to defects.52 Figure 3 further compares the simulated Ds(CH4) values in both the single and mixture components. It reveals that CO2 weakly affects the diffusivity of CH4, leading for a given total number of molecules to Ds values slightly higher than those in 13533



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Figure 4. Simulated self-diffusion coefficients for CO2 as a function of the loading at 200 K. Black line, single component; blue line, mixture with 0.75 CH4/u.c (model 1); red line, mixture with 0.75 CH4/u.c (model 2).

simulated mean activation energies obtained for the diffusion of the single CH4 (2.5 ± 0.4 kJ/mol) and CO2 (2.4 ± 0.4 kJ/mol) molecules. One can notice that the simulated Ea for Ds(CO2) is much smaller than the values previously reported in other zeolites and MOFs such as in silicalite (5.8 kJ/mol17), MIL-47 (6.4 kJ/mol24), NaY (8.4 kJ/mol18), and UiO-66 (10.9 kJ/ mol26). This observation emphasizes that the mobility of the faster CH4 is enhanced by the slower CO2 molecules in the binary mixture, for which the diffusivity is slightly sped up, as shown in Figure 4, regardless of the CH4 model employed. This mutual speeding-up is consistent with that which we recently reported for the MIL-47(V) solid32 and can be explained by some correlation effect in the 1D channel as quoted by Krishna et al.56 Some of the experimental QENS spectra measured for CO2 are further shown in Figure 5. A comparison between Figure 5a and b shows that the broadening with respect to the instrument resolution decreases for the second loading, indicating that diffusivity decreases. For the third loading, the broadening is so large that a small modification upon the adsorption of the residual intensity between the Bragg peaks creates a negative elastic peak. The contribution from CO2 can nevertheless be determined by adding to the fits a negative elastic component. Because the scattering from CO2 is totally coherent, one can derive from the QENS spectra the transport diffusivity.51 Similar to that for CH4, the spectra were best fitted to a 1D diffusion. There is no rotational contribution from this coherent scatter in the selected Q range.51 The transport diffusivities were extracted at small Q values in the Fickian regime. The experimental values of Dt are reported in Figure 6 for T = 200 K and exhibit a nonmonotonous evolution with a minimum at 3.9 CO2/u.c. with Dt = 1.5 × 10−9 m2 s−1. The thermodynamic correction factor Γ has been extracted from the QENS spectra, giving Γ values continuously increasing with the CO2 concentration, within experimental accuracy. This increase in Γ with the loading has already been observed for CO2 in other materials as well as the convergence toward 1 at low loading.26 Subsequently, the corrected diffusivity Do can be calculated from the relation Do = Dt Γ−1. As for Dt, the experimental Do also exhibits a minimum, but it is a bit less pronounced. The Do values extracted from the MD simulations slightly decrease in the range of CO2 concentrations experimentally explored (Figure 6). However, complementary calculations from above 6 CO2/u.c. evidence a nonmonotonous trend for Do, which is consistent with the presence of a minimum that is

Figure 5. Comparison between the experimental (crosses) and fitted (solid lines) QENS spectra obtained for AlPO4-5 at different concentrations of CO2: (a) 2.2, (b) 3.9, (c) 4.5 molecules/u.c. (T = 200 K, Q = 0.34 Å−1). The dotted lines in panels a and b correspond to the instrument resolution.

Figure 6. Evolution with CO2 loading of the Ds (black squares), Dt (red circles), and Do (blue triangles) extracted from the MD simulations (solid lines and full symbols) and QENS experiments (dashed lines and empty symbols) at T = 200 K.

shifted compared to the experimental findings. Although the range of experimental values (5.3 × 10−9, 1.1 × 10−9, and 2.4 × 10−9 m2 s−1 for 2.2, 3.9, and 4.5 CO2/u.c, respectively) is well reproduced by our computations (6.4, 3.9, and 4.1 × 10−9 m2 s−1 for 6, 8, and 9 CO2/u.c, respectively), the deviation in the position of the minimum might call for a more accurate description of the CO2−AlPO4-5 interactions. This is also reflected in the lower simulated activation energy for Do (2.6 kJ/mol for 4 CO2/u.c.) in comparison to the experimental value for Dt (6 kJ/mol for 3.9 CO2/u.c.). To further derive the simulated transport diffusion coefficients, the thermodynamic correction factor has been extracted from the GCMC-calculated adsorption isotherms (Figure S1). It has been shown that Γ remains below 1 up to a concentration of 4.5 CO2/u.c., which is much lower than the experimental values in the same range of concentrations, 13534



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supporting the concept that the strength of the CO2−AlPO4-5 interactions is overestimated by the force field employed. Above this loading, the simulated Γ significantly increases (1.6, 4.5, and 8 for 6, 8, and 9 CO2/u.c, respectively). The resulting Dt remains only slightly changed up to 5 molecules/u.c. and increases globally in the ranges of 5−9 molecules/u.c. Here again, this evolution is reminiscent to the experimental profile, whereas the position of the step change is shifted to a higher concentration. Complementary calculations have been performed for 9.5 and 10.5 CO2/u.c. to explore the behavior of Do at very high loading. One observes in Figure 6 that above 9 CO2/u.c. the simulated corrected diffusivity again decreases continuously. The presence of a local minimum or an inflection point on the Do profile has been already evidenced theoretically and experimentally for CF459,60 and n-hexane/n-heptane61 in MFI zeolite and to a lesser extent for CH4 in faujasite.62 By analogy to what has been previously reported, we suggest that this peculiar behavior could be due to the formation of shorttime CO2 clusters. To shed some light on the diffusion mechanisms for CH4 and CO2 in AlPO4-5, the spatial density probabilities have been extracted from the MD trajectories. The most probable positions for CH4 and CO2 are comprised in a hollow cylinder of hexagonal shape (Figure 7a and d). One observes that the corners of the hexagon are shifted by an angle of π/6, which supports the concept that the two molecules preferentially interact with the pore wall in a different manner. This is illustrated in Figure S2, which clearly indicates that CH4 and CO2 are located in the vicinity of distinct interacting sites (i.e., the oxygens of a four- and six-membered rings, respectively), whereas the characteristic host/diffusive species distances are shorter for CO2. Furthermore, the radial-distribution functions plotted for the mean distance between the center of mass of the two diffusive species and the center of the AlPO4-5 channels are reported in Figure 8a and show that CO2 is slightly closer to the pore wall than CH4, which is concomitant with a relatively stronger host−guest interaction (Figure S3). A noticeable observation is the difference in the densities along the channel for CH4, whereas there is almost none for CO2 (Figures 7b and 8b). Hence, the stronger interaction between CO2 and the pore wall would be counterbalanced by a lower energy barrier in the longitudinal direction of the AlPO4-5 channels. This could also explain the lower activation energy for the CO2 diffusion at high loading where the collisions with the other CO2 molecules can favor the longitudinal diffusion, whereas at low loading the higher activation energy is governed by the CO2−pore wall interaction. In addition, although the effect of the mixture only slightly affects the radial distribution for CH4 (Figure 8) with an associated shift of the densities along the channel (Figures 7c and 8b), there is almost no change in the spatial distribution for CO2. Similarly, when the loading for the pure component increases there is a modification of the radial distribution, with the molecules tending to be closer to the pore wall and the longitudinal partition is slightly shifted (Figures S4−S7). However, the spatial partition of methane in AlPO4-5 manifests a significant difference between the low- and highloading regimes. At low loading, there is an important fraction of CH4 molecules close to the channel center concomitant with a more homogeneous longitudinal partition. This observation can explain the fast mobility for CH4 where an increasing

Figure 7. Cumulated densities in the xy plane for the single components (a). Cumulated densities in the yz plane for the single components (b). Cumulated densities in the yz plane for the binary mixture (c). Left, CH4; right, CO2. Free-energy isosurfaces at 2 kJ/mol (d). Left, single CH4 (2.75/u.c.); middle, single CO2 (2.75/u.c.); and right, binary mixture (0.75 CH4 and 2CO2/u.c.).

proportion of the CH4 molecules are diffusing in the center of the channel with fewer constraints. From the radial and longitudinal density maps, it is possible to draw the diffusion pathways for CH4 and CO2 within the porosity of AlPO4-5. One observes that the displacements in the plane of the pore are equivalent for both molecules. (i) A move from one site to another in the first environment present in the hexagonal ring is represented by the arrow between positions a0 and a1 in Figure 7a. The associated activation energy is rather low for both species (Ea < 0.5 kJ/mol), with a jump length of 1.7 Å for CH4 and 1.9 Å for CO2. (ii) A move from one site to another in the second neighbors in the hexagonal ring (a0 → a2) with an equivalent activation energy that is slightly higher for both CH4 and CO2 (Ea ≈ 1.5 kJ/mol) and a jump length of 3 Å for CH4 and 3.4 Å for CO2. (iii) A move passing through the center of the pore from one adsorption site to an opposite site in the hexagonal ring (a0 → a3) with activation energies of about 2.5 and 3.5 kJ/mol for CH4 and CO2, respectively, and with jump lengths of 3.5 and 4 Å, respectively. To confirm further the existence of a normal 1D diffusiontype behavior evidenced by the use of such a model to fit the experimental quasi-elastic peaks, the passing frequencies (η) have been computed from the MD trajectories using the 13535



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for methane and argon in the same porous solid, but they use a smaller simulation box (2 × 2 × 2) that is expected to generate an unphysical boundary effect. In contrast, Tepper et al.,64 who used a larger simulation box (2 × 2 × 60) for representing AlPO4-5, evidenced that the trajectories issued from MD runs at 300 K can be accurately described using a hop-and-cross model with a passing frequency of 0.6%, which is more consistent with our findings. Finally, the isotropic rotational diffusion coefficient, Dr, extracted from the QENS experiment was shown to decrease from 1.5 × 1011 s−1 for pure CH4 to 8.5 × 1010 s−1 for the highest concentration of CO2. These values are higher than those obtained by QENS in ZSM-5 for pure CH4 (2.5 × 1010 to 4.2 × 1010 s−1 at 200 K58), although they remain lower than those for methane adsorbed on graphite (6 × 1011 s−1 at 55 K65) or for bulk solid methane (1012 s−1 at 21 K66).

Figure 8. Radial distribution of the mean distance between the center of mass of the diffusive species and the center of the AlPO4-5 channels at 200 K (a). Longitudinal distribution of the center of mass of the diffusive species (b). Black, pure CO2 (2.75/u.c.); blue, pure CH4 (2.75/u.c.); red, CH4 in a binary mixture (0.75 CH4 and 2 CO2 /u.c.).

method defined by Thomson et al.63 The passing frequency is calculated by the ratio number of successful passing events to the number of passing attempts. To avoid any confusion on the interpretation of η, the choice of the passing tolerance parameter has been set to the LJ diameter of the molecules of interest when two similar molecules attempt to pass by and to the average LJ geometric parameter when one considers the case of two distinct molecules. Following this procedure, we obtained η between 1 and 5% at 200 K. The evolution of η with the loading is plotted in Figure 9. In the single component, η(CH4) is twice that of η(CO2), and these passing frequencies slightly decrease when the loading increases. Moreover, in a mixture η decreases continuously from η(CH4) to η(CO2) when the number of adsorbed CO2 molecules increases. The values of the passing frequencies computed here are lower than those reported by Thomson et al.63 (30% at 295 K)

Figure 10. Evolution of the rotational diffusion coefficient for CH4 as a function of the total loading at 200 K. Black squares, QENS; blue line, MD model 1; red line, MD model 2. The full symbols (straight lines) are the single component, and the empty symbols (dashed lines) are the CH4/CO2 mixture with 0.75 CH4/u.c..

The simulated Dr extracted from the angular-velocity autocorrelation functions shows the same evolution with CO2 concentration, and the simulated rotational diffusion coefficient only slightly overestimated the experimental Dr by a factor of 2.5. One can notice that the calculated Dr for CH4 as a pure component is within the same order of magnitude as those previously simulated by Bhide and Yashonath67 on the same guest−zeolite system also using MD simulations. One can notice that CH4 rotates a bit faster when one uses model 1 for representing the diffusive species. This most probably is due to some energy dissipation through the C−H vibrational modes taken into account in the flexible model 2. Furthermore, as was already noticed for the translational diffusion, the simulated Dr for CH4 as a pure component is very similar to those calculated in the mixture in the whole range of investigated loadings.

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CONCLUSIONS This joint experimental−modeling approach first revealed a fast diffusivity for CH4 at low loadings in the AlPO4-5 material that is similar to what has been previously observed for light gases in 1D-type porous solids. The resulting Ds values are at least 1 order of magnitude faster than those in other zeolites and MOFs. It was further evidenced that both CO2 and CH4 are slightly sped up in binary mixtures in comparison to that of the single components. The loading dependence of the transport diffusivity for CO2 was shown to present a minimum by the QENS measurement, which was further reproduced by the MD

Figure 9. Evolution of the passing frequencies as a function of the loading at 200 K in the single component for CH4 (red circles), CO2 (black squares), and CH4/CO2 mixture with 0.75 CH4/u.c. (blue triangles). 13536



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(11) Jobic, H.; Bée, M.; Kearley, G. J. Mobility of Methane in Zeolite NaY between 100 and 250 K: A Quasi-Elastic Neutron-Scattering Study. J. Phys. Chem. 1994, 98, 4660−4665. (12) Skoulidas, A. I.; Sholl, D. S. Molecular Dynamics Simulations of Self-Diffusivities, Corrected Diffusivities, and Transport Diffusivities of Light Gases in Four Silica Zeolites to Assess Influences of Pore Shape and Connectivity. J. Phys. Chem. A 2003, 107, 10132−10141. (13) Beerdsen, E.; Dubbeldam, D.; Smit, B. Loading Dependence of the Diffusion Coefficient of Methane in Nanoporous Materials. J. Phys. Chem. B 2006, 110, 22754−22772. (14) Krishna, R.; van Baten, J. M. A Molecular Dynamic Investigation of the Diffusion of Methane-Ethane and Methane-Propane Mixtures in Zeolites. Chem. Eng. Technol. 2006, 29, 1429−1437. (15) Krishna, R.; van Baten, J. M. Loading Dependence of SelfDiffusivities of Gases in Zeolites. Chem. Eng. Technol. 2007, 30, 1235− 1241. (16) Makrodimitris, K.; Papadopoulos, G. K.; Theodorou, D. N. Prediction of Permeation Properties of CO2 and N2 through Silicalite via Molecular Simulations. J. Phys. Chem. B 2001, 105, 777−788. (17) Papadopoulos, G. K.; Jobic, H.; Theodorou, D. N. Transport Diffusivity of N2 and CO2 in Silicalite: Coherent Quasielastic Neutron Scattering Measurements and Molecular Dynamics Simulations. J. Phys. Chem. B 2004, 108, 12748−12756. (18) Plant, D. F.; Jobic, H.; Llewellyn, P. L.; Maurin, G. Diffusion of CO2 in NaY and NaX Faujasite Systems: Quasi-Elastic Neutron Scattering Experiments and Molecular Dynamics Simulations. Eur. Phys. J. 2007, 141, 127−132. (19) Sirjoosingh, A.; Alavi, S.; Woo, T. K. Grand-Canonical Monte Carlo and Molecular-Dynamics Simulations of Carbon-Dioxide and Carbon-Monoxide Adsorption in Zeolitic Imidazolate Framework Materials. J. Phys. Chem. C 2010, 114, 2171−2178. (20) Skoulidas, A. I.; Sholl, D. S. Self-Diffusion and Transport Diffusion of Light Gases in Metal-Organic Framework Materials Assessed Using Molecular Dynamics Simulations. J. Phys. Chem. B 2005, 109, 15760−15768. (21) Rosenbach, N.; Jobic, H.; Ghoufi, A.; Salles, F.; Maurin, G.; Bourelly, S.; Llewellyn, P. L.; Devic, T.; Serre, C.; Ferey, G. QuasiElastic Neutron Scattering and Molecular Dynamics Study of Methane Diffusion in Metal Organic Frameworks MIL-47(V) and MIL-53(Cr). Angew. Chem., Int. Ed. 2008, 47, 6611−6615. (22) Liu, D.; Zheng, C.; Yang, Q.; Zhong, C. Understanding the Adsorption and Diffusion of Carbon Dioxide in Zeolitic Imidazolate Frameworks: A Molecular Simulation Study. J. Phys. Chem. C 2009, 113, 5004−5009. (23) Salles, F.; Jobic, H.; Ghoufi, A.; Llewellyn, P. L.; Serre, C.; Bourelly, S.; Férey, G.; Maurin, G. Transport Diffusivity of CO2 in the Highly Flexible Metal-Organic Framework MIL-53(Cr). Angew. Chem., Int. Ed. 2009, 48, 8335−8339. (24) Salles, F.; Jobic, H.; Devic, T.; Llewellyn, P. L.; Serre, C.; Férey, G.; Maurin, G. Self and Transport Diffusivity of CO2 in the MetalOrganic Framework MIL-47(V) Explored by Quasi-Elastic Neutron Scattering Experiments and Molecular Dynamics Simulations. ACS Nano 2010, 4, 143−152. (25) Krishna, R.; van Baten, J. M. Highlighting a Variety of Unusual Characteristics of Adsorption and Diffusion in Microporous Materials Induced by Clustering of Guest Molecules. Langmuir 2010, 26, 8450− 8463. (26) Yang, Q.; Jobic, H.; Salles, F.; Kolokolov, D.; Guillerm, V.; Serre, C.; Maurin, G. Probing the Dynamics of CO2 and CH4 within the Porous Zirconium Terephthalate UiO-66(Zr): A Synergic Combination of Neutron Scattering Measurements and Molecular Simulations. Chem.Eur. J. 2011, 17, 8882−8889. (27) Jee, S. E.; Sholl, D. S. Carbon Dioxide and Methane Transport in DDR Zeolite: Insights from Molecular Simulations into Carbon Dioxide Separations in Small Pore Zeolites. J. Am. Chem. Soc. 2009, 131, 7896−7904. (28) Babarao, R.; Jiang, J. Diffusion and Separation of CO2 and CH4 in Silicalite, C168 Schwarzite, and IRMOF-1: A Comparative Study from Molecular Dynamic Simulation. Langmuir 2008, 24, 5474−5484.

simulations when it was shifted in position. Detailed studies of the MD spatial densities and trajectories revealed that both CO2 and CH4 experience a 1D normal-type diffusion mechanism along the AlPO4-5 channels in a hollow cylinder with a hexagonal base, with CO2 interacting more strongly with the pore wall than the CH4 molecule. Finally, the experimental rotational diffusion coefficients for CH4, which were very well reproduced by the MD simulations, are shown to be only slightly modified in the presence of CO2, consistent with the behavior of the translational diffusion.

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ASSOCIATED CONTENT

* Supporting Information S

Force field parameters, simulated adsorption isotherm, and guest−guest and guest−host interaction energy. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected] (H.J.), guillaume. [email protected] (G.M.). 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 IN6 and Dr. M. M. Koza for his help during the experiments. We are grateful to Dr. A. Gabrieli, Dr. M. Sant, and Prof. G. B. Suffritti for fruitful discussions on the microscopic description of the AlPO4-5 flexibility.

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Diffusion of CH4, CO2, and Their Mixtures in

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