J. Phys. Chem. 1994,98, 4660-4665
4660
Mobility of Methane in Zeolite NaY between 100 and 250 K: A Quasi-elastic Neutron-Scattering Study Hew6 Jobic' Institut de Recherches sur la Catalyse, CNRS, 2 Ave. Albert Einstein, 69626 Villeurbanne, France
Marc B& Laboratoire de Spectrombtrie Physique, Universitb Joseph Fourier, 38402 Saint-Martin d'Hbres, France
Gordon J. Kearley Institut Laue- Langevin, BP 156, 38042 Grenoble Cedex 9, France Received: November 18, 1993; In Final Form: February 14, 1994@
The translational and rotational dynamics of methane in N a Y zeolite have been studied by quasi-elastic neutron scattering (QENS) a t different temperatures and loadings. The QENS results reveal a marked temperature sensitivity. A t 100 K, there is no migration of the methane from cage to cage on the 35-ps time scale of the experiment so that the time spent by a molecule in a supercage is longer than this. At 100 K, 88% of the methane molecules are found to be localized, performing rotational diffusion, and 12% of molecules diffuse in a volume limited by the walls of the supercages. At 150 K, there are no trapped molecules, 44% of methane molecules diffuse between the supercages and 56% diffuse locally within the supercages. A t 200 and 250 K, the proportion of mobile molecules and their diffusion coefficients increase. The QENS results are in good agreement with theoretical methods which predict a progressive delocalization of the molecules with increasing temperature. The self-diffusion coefficients determined by QENS are in excellent agreement with the N M R results and, to a lesser extent, with molecular dynamics simulations. The activation energy for self-diffusion is of 6.3 kJ mol-'.
Introduction The dynamics of methane in zeolites of various structures have been investigated by several experimental and theoretical methods.'-18 In thecaseof methane adsorbed at different loadings and temperatures in ZSM-5, excellent agreement has been observed for the self-diffusion coefficients, for the mean jump lengths, and for the activation energy determined by NMR, quasielastic neutron scattering (QENS) and molecular dynamics (MD) simulations techniques.*Jl-15 Only one QENS measurement has been reported so far on the dynamics of methane adsorbed in the faujasite structure.5 In that study, a fluid-phase model for methane was derived from the QENS results at 295 K, but only one temperature was studied and no diffusion coefficient could be determined because of the limited energy resolution. The siting, energetics, and mobility of methane in NaY have been studied by Monte Carlo methods.6 At 100 K, the molecule was found to be mainly confined to a small region corresponding to the minimum energy in the supercage. At 170 K, methane molecules hop from one energy site to another, the molecule being more mobile and spending 16% of the time in higher-energy sites. At 220 K, the molecule spends 35% of its time in such positions. The distribution of the positions calculated a t 298 K shows the molecule to be highly mobile at this temperature. A detailed MD study of methane in N a y , as a function of temperature and sorbate loading, has recently been published by Yashonath et a1.16 At 50 K, the molecule is essentially localized near an adsorption site, with some residual rotational motion. Site-to-site migration and free rotation are observed a t 150 K. Self-diffusion coefficients have been calculated at 50, 150, 220, and 300 K, but accurate values were obtained only near room temperature, the error being larger at low temperatures because of the relatively short run lengths. Neutron diffraction has not been used sofar to localize methane in NaY at low temperature. However, favored sites, Le., the
* Author for correspondence.
e Abstract
published in Aduance ACS Abstracts, April 1, 1994.
0022-3654/94/2098-4660$04.50/0
minimum-energy adsorption sites, have been found in the supercages by theoretical There are six equivalent sites in a given supercage, near the center of the middle fourmembered oxygen rings. In the present paper, we report QENS results on the dynamics of methane in NaY zeolite, a t different temperatures and loadings. The progressive delocalization of the molecules with increasing temperature, as predicted by theoretical methods, is nicely followed. The self-diffusion coefficients which are determined are compared with those obtained by pulsed-field gradient NMR (PFG NMR) and MD techniques. From the temperature dependence of the self-diffusion coefficient, an activation energy for diffusion is obtained. Experimental Section
Neutron experiments were carried out a t the Institut LaueLangevin, Grenoble, on the time-of-flight (TOF) spectrometer IN5, using an incident energy of 1 meV (A = 9 A). After scattering by the sample, neutrons are analyzed as a function of flight-time and angle. The elastic energy resolution (18 peV) was measured with a vanadium plate. Spectra were recorded in transmission geometry by orienting the sample cell at 130° to the incident beam. The TOF of the scattered neutrons is related to the energy transfer ( h w )and the scattering angle to the momentum transfer ( h Q ) . A wide range of scattering angles (-10' < 28 < 120') is covered by a large number of detectors which are normalized by using the scattering froma vanadium plate which gives isotropic scattering. During the experiment, a total of 110 spectra were recorded simultaneously. Spectra from different detectors were grouped to obtain adequate counting statistics and to avoid the Bragg peaks of the zeolite. The TOF spectra were corrected for detector efficiency, absorption and self-shielding. Background scattering from the bare zeolite was recorded at each temperature and was subtracted from the spectra. The TOF spectra were transformed to the energy scale using standard algorithms. 0 1994 American Chemical Society
Mobility of Methane in Zeolite NaY TheNaY zeolite (LZY-52) was heated at 720 Kunder flowing oxygen and outgassed at a final pressure of 10-3 Pa, a t this temperature. The zeolite was then transferred into a slab-shaped aluminum container of circular geometry (diameter 5 cm), using a glovebox. The cell was fitted with an indium seal, vacuum leak tests having shown that the leak rate was < l e 9 mbar L s-1. The mass oftheactivated zeolite (4.1 g) wascalculated togivesufficient signal at low sorbate concentrations (loadings close to the saturation would require a smaller amount of zeolite to avoid multiplescattering). The neutron transmissionof the bare zeolite, for a wavelength of 9 A, was of 94%. Measurements were achieved at different temperatures, ranging from 100 to 250 K, using a liquid nitrogen cooling loop.
The Journal of Physical Chemistry, Vol. 98, No. 17, 1994 4661 1
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Theory For the system under study, only incoherent scattering need to be considered due to the large incoherent cross section, UH, of hydrogen. The measured quantity is the double differential cross section corresponding to
where the incident and final wave vectors, and k, define the neutron momentum transfer Q as Q = k-b. The intensity scattered by the sample is proportional to the incoherent scattering function, Sinc(Q,w),which is the space and time Fourier transform of the self-correlation function Gs(r,t).If the molecular motions of vibration, rotation, and translation are uncoupled, the total incoherent scattering function is the convolution of the individual scattering functions corresponding to the different motions.19 The spectrometer used in this work enables both the translational and rotational motions of methane to be observed. Higher-energy transfers are required to study the internal modes. Therefore, the contribution of the vibrational motions appears only as a flat background (to take into account the small fraction of the intensity, due to the external modes, which comes into the quasi-elastic region). It is also responsible for the attenuation of the spectra a t increasing Q values, through of a Debye-Waller factor. The incoherent scattering functions for the rotational and translational motions will be examined separately. Rotational Motion. The incoherent scattering function for a rotational motion can be separated into a purely elastic peak and a quasi-elastic component:
An elastic peak exists because the motion is restricted to a finite volume. The elastic-peak intensity is governed by Ao(Q), which is called the elastic incoherent structure factor, EISF. This is the space Fourier transform of the probability distribution of an individual scattering nucleus. The experimental determination of the EISF is however, critically related to the instrumental resolution. For a resolution width Aw, the time scale over which the average of G,(r,t) is performed is of the order of l/Aw (in our case it is of 35 ps). The quasi-elastic term in eq 2 reflects the dynamical behavior of the molecules. It is expressed as a sum of Lorentzian functions whose number and energy width depend on the model. For methane adsorbed in NaY zeolite, the interpretation of the data requires two rotational models. First, an isotropic rotational diffusion model (model 1) which is appropriate for molecules trapped on favored sites at low temperature (100 K) or performing translational diffusion at higher temperatures. Second, a model of diffusion in a sphere (model 2) for molecules residing in the supercages (within the time scale of the experiment). In the isotropic rotational diffusion model, molecular reorientation is assumed to take place through small rotational
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0.7 there is no elastic intensity. Translational Motion. Different jump diffusion models have been used to describe the translational mobility of molecules adsorbed in zeolites.22-2s The present system, methane in N a y , is heterogeneous in that there are trapped and diffusing molecules. For the molecules performing translational diffusion, the model of Fickian diffusion is appropriate:
(9) The profile is again Lorentzian, the hwhm is DQ2 where D, the center of mass diffusion coefficient, is the only adjustable parameter. Results The energy spectra obtained at four sample temperatures: 100, 150, 200, and 250 K, are shown in Figure 3 a 4 , at different momentum transfers Q (in A-l). The average loading was 3 molecules/supercage, for the three lowest temperatures, and 2 molecules/supercage at 250 K. The spectra can be conveniently divided into two parts: (i) a central peak which is either purely elastic or broadened by long-range diffusion and (ii) a broader contribution which is related to rotational motions. At 100 K, Figure 3a, the intensity is mainly elastic, the quasielastic contribution being small, even at large Q values. Furthermore, the absence of broadening of the central part of the spectra, i.e., the existence of a purely elastic scattering, indicates an absence of migration from cage to cage. At 150 K, Figure 3b, the situation is somewhat different. The overall elastic intensity drops rapidly with increasing Q values and there is a broadening of the central peak, indicating longrange diffusion. As the temperature is increased further, Figure 3 0 d , there is a progressive broadening of the translational component, which indicates a further delocalization of the molecules (NB energy scales are different in Figure 3b,c). Spectra for another experiment at 200 K with a loading of 5 molecules/supercage are shown in Figure 3e. Comparison with the results obtained at lower concentration, Figure 3c, reveals only small differences. Discussion The large intensity of the central peak, which is measured over the entire Q range at 100 K, suggests that the molecules are mainly localized (the EISF varies as in Figure 1). Two different types of methane molecules can be observed on the time scale of the experiment. First, there are molecules trapped on minimumenergy adsorption sites697 which perform rotational diffusion with a radius of gyration of 1.1 A (model 1). Second, there is a small proportion of mobile molecules within a supercage (model 2). MD calculations show that the center of mass of the molecules is found mostly in the vicinity of the supercage walls, at low temperature (between 3 and 6 A with respect to the supercage center at 150 K [7]). However, the spatial distribution of the hydrogen atoms is larger (by the C H bond length), and it becomes
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o(A- 1 Figure 2. (a) Elastic incoherent structure factor (EISF) of methane diffusing in a supercage (a = 6 A); (b) mean EISF for 88% of the molecules fixed but performing rotational diffusion and 12% of the molecules diffusing within the volume of the supercages.
difficult to differentiate experimentally between the diffusion of an hydrogen atom within a sphere of radius 6 A or the diffusion within a hollow sphere. Therefore the spectra obtained at different Qvalues have been fitted witha weightedaverageofthescattering function of molecules performing rotational diffusion ( r = 1.1 A) and of the scattering function of molecules diffusing in a sphere (a = 6 A), both convoluted with the measured instrumental resolution. This reveals that 88% of the molecules are rotating on favored sites and that 12% are diffusing in the supercage. The resulting EISF is shown in Figure 2b. A single parameter was used to refine the widths of the Lorentzians for the twospecies. Thevalue obtained for the hwhm of the quasi-elastic broadening, 60 peV, is therefore an average value giving a rotational diffusion coefficient, h, of 4.5 X 10-lo s-I and a diffusion coefficient in the supercage D, of 9 X 10-10 m2s-1. Experimental (+) and calculated (-) spectra arecompared in Figure 3a. The two inserts in that figure show that the contribution from the molecules diffusing within the supercages (D) is mainly elastic at low Q values, whereas it is only quasielastic at large Q values since the EISF of these molecules drops more rapidly with Q (Figures 1 and 2). No elastic broadening resulted from the fits of the data at this temperature because the long-range translation is too slow on the time scale of the experiment. In other words, the broadening due to the translation is negligible compared to the instrument resolution, which corresponds to molecules spending more than 35 ps in a supercage. This value is a factor of 2 larger than the cage residence time calculated from MD simulations.7 At 150 K, the EISF drops more rapidly with increasing Q values (as in Figure 2a), and the elastic peak broadening indicates a diffusion from cage to cage. The spectra have been fitted with the scattering functionscorresponding to two species: (i) methane molecules diffusing in the volume limited by thesupercages (model 2) and (ii) molecules following a Fickian diffusion while performing rotational diffusion. Agreement between experimental and calculated spectra is excellent, as shown in Figure 3b, where the purely elastic and quasi-elastic contributions have been separated. The presence of two distinct methane species (on the time scale of the experiment) is justified by the residual purely elastic intensity which is a clear indication of a local motion, i.e., the molecules in the supercages. The molecules performing longrange diffusion (mean diffusion path 4 nm) do not contribute to any elastic intensity since the EISF of model 1 is convoluted with the translational scattering function, eq 9. At 150 K, 56% of the molecules are found to diffuse in the supercages and 44% diffuse
Mobility of Methane in Zeolite NaY
The Journal of Physical Chemistry, Vol. 98,No. 17, 1994 4663
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Figure 3. Comparison of experimental (+) and calculated (-) QENS spectra obtained at different values of the momentum transfer Q for methane in N a y : (a) at 100 K (3 molecules/supercage), the two inserts show the elastic and quasi-elastic contributions from the rotating (R) and diffusing (D)molecules; (b) at 150 K (3 molecules/supercage), the purely elastic and quasi-elastic contributions have been separated; (c) at 200 K (3 molecules/ supercage); (d) at 250 K (2 molecuIes/supercage); (e) at 200 K ( 5 molecuIes/supercage).
4664
Jobic et al.
The Journal of Physical Chemistry, Vol. 98, No. 17, IF'94 1 E-07
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1o ~ / T ( K ) Figure 4. Self-diffusion coefficients of methane in NaY versus 1 / T obtained by: (m) QENS, (+) PFG NMR, and (X) M D simulations.The solid line has been fitted to the experimental values only.
between the supercages. For the latter, the self-diffusion coefficient, D,defined in eq 9, is 3.2 X l e 9 m2 s-l. The models used at 150 K were also found to be equally valid a t 200 and 250 K, Figure 3c,d, the proportion of mobile molecules increasing with temperature. At 200 K, 70% of the molecules diffuse between the supercages with a self-diffusion coefficient D equal to 7 X 10-9 m2 s-1. At 250 K, 82% of the methane molecules perform long-range diffusion, the self-diffusion coefficient being 1.1 X 10-8 mz s-1, Extrapolation of the proportion of mobile molecules to room temperature indicates that all methane molecules would then be diffusing between the supercages. The experiment performed a t 200 K with a higher loading, Figure 3e, shows that the proportion of mobile molecules increases to 77% and the self-diffusion coefficient to 7.6 X 10-9 m2 s-l. The dynamics of the rotational motions are also modified, the hwhm of the quasi-elastic broadening changing from 57 to 106 peV. This can be understood from the results of MD simulations which show that for higher loadings, the fraction of highly mobile molecules increases.16 Therefore, the average diffusion coefficient in the supercage is expected to increase. The present QENS results indicate that, below room temperature, not all methane molecules perform simple Fickian diffusion in NaY zeolite. The spectra cannot be interpreted by thejump diffusion model of Chudley and Elliott.26 In this model, a molecule vibrates on a given site, building up a thermal cloud and then diffuses rapidly to another site (within the time scale of the experiment). In the present case, the residual elastic intensity shows that a molecule can be trapped in a supercage, during its migration from cage to cage. The time for which it is trapped increases with decreasing temperature. This interpretation is in accord with the M D ~imulations.~J6On a longer time scale, e.g., the N M R time scale, a linear variation of the mean-square displacement with observation time will be found, corresponding to Fickian diffusion, but with a reduced diffusion coefficient. Considering that, at 150 K, a moleculediffusesduring 44% of the time, the true self-diffusion coefficient to be compared with that obtained from N M R is not 3.2 X 10-9 mz s-1 but 1.4 X 10-9 m2 s-1. This is because the neutron measurement corresponds to a "snapshot". The calculation of theself-diffusion coefficient considers only the time where the molecule is diffusing. Time spent trapped in the supercages does not contribute to Fickian diffusion. This effective diffusion coefficient, as well as those obtained at 200 K (4.9 X 10-9 m2 s-1) and 250 K (9 X mz s-1) are shown in Figure 4 vs 1 / T . The PFG N M R results of Karger et al. obtained with the same loading in NaXZ and the
M D values of Yashonath et al. in NaYI6 are also included in the figure for comparison. It appears that the QENS and PFG N M R results are in excellent agreement, which indicates that the longrange diffusion of methane is similar in NaX and NaY zeolites. There is also agreement with the MD simulations at 300 K, but the MD runs at lower temperatures are probably too short. From the experimental QENS and PFG N M R results, an activation energy for the self-diffusion of methane of 6.3 kJ mol-' is derived, which is larger than the value obtained in ZSM-5,4.7 kJ mol-Ie8 This reflects the different geometry of the pore volume in the two zeolites, and it explains why restricted diffusion was not observed by QENS for methane in ZSM-5at 200 K, on a time scale of 25 ps.22 The translational and librational motions of molecules adsorbed in zeolitic systems can also be studied by inelastic neutron scattering (INS) using higher energy neutrons.27 The density of states measured by INS is, however, weighted by the scattering cross sections and by the atomic displacements. For methane, the spectral intensity comes from the hydrogen atoms and the scattering from rotation is a factor 6 greater than from translation because of a smaller effective mass. For methane adsorbed a t 200 K in ZSM-5, the maximum of the frequency distribution is at 72 cm-l.28 When adsorbed a t 30 K in Na-mordenite, the translational and rotational contributions of methane could be separated, giving peak maxima at 25 and 54 cm-1, r e s p e c t i ~ e l y . ~ ~ These results can directly be compared with power spectra obtained by Fourier transform of the velocity self-correlation function. This calculation has been made by Yashonath et al. for methane in NaY at 50 KI6 and shows a band at 50 cm-1 due to translations, a band at 150 cm-l due to librations, and a band at 100 cm-I of mixed character. It appears that the calculated values occur a t much higher frequencies than the experimental ones. Conclusions
Quasi-elastic neutron-scattering reveals the local and longrange mobility of methane adsorbed in NaY zeolite, at different temperatures and loadings. The temperature dependence of the QENS results is much more pronounced than the concentration dependence. At 100 K, methane molecules cannot diffuse from cage to cage and spend more than 35 ps in supercages. On the time scale of the experiment, 88% of the molecules have a fixed center-of-mass and are freely rotating; 12%of the molecules are diffusing locally within a supercage. At 150 K, there are no fixed molecules, 44% of methane molecules are diffusing between the cages, while performing rotational diffusion. The remaining 56% are diffusing locally in the supercages. We conclude that the transition between local and long-range mobility occurs between 100 and 150 K. As the temperature increases, the proportion of mobile molecules increases. At 200 K, 70% of the molecules migrate between the supercages, rising to 82% at 250 K. At room temperature, all the molecules are expected to be highly mobile, in agreement with theoretical methods. The self-diffusion coefficients determined by QENS for methane in NaY are in excellent agreement with the values obtained for methane in NaX by the PFG N M R technique. The activation energy for the selfdiffusion of methane is larger in the faujasite structure, 6.3 kJ mol-', than in the silicalite structure, 4.7 kJ mol-', which accounts for the different dynamics measured for methane in the two zeolites. Acknowledgment. We thank G. Clugnet for his assistance in the preparation of the samples.
References and Notes f l ) Ruthven. D. M. ACS Svmo. Ser. 1977. No. 40. 320. (2j KHrger, J.; Heifer, H . ; k a k h e r , M.; Walter,.A. J . Chem. SOC., Faraday Trans. I 1980, 76, 117. (3) Cohen de Lara, E.; Kahn, R. J. Phys. 1981.42, 1029.
Mobility of Methane in Zeolite NaY (4) Cohen de Lara, E.; Kahn, R.; Mezei, F. J. Chem. Soc., Faraday Trans. 1 1983, 79, 1911. ( 5 ) Stockmeyer, R. Zeolites 1984, 4, 81. (6) Yashonath,S.;Thomas, J.M.;Nowak,A.K.;Cheetham,A.K.Nature
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(16) Yashonath, S.;Demontis, P.; Klein, M. L. J. Phys. Chem. 1991,95, 5881. (17) Heink, W.;Kirger, J.;Pfeifer, H.;Salverda,P.;Datema,K. P.;Nowak, A. J. Chem. SOC.,Faraday Trans. 1992,88, 515. 1988, 331,601, (18) Demontis, P.; Suffriti, G. B.; Fois, E. S.;Quartieri, S.J. Phys. Chem. (7) Yashonath, S.;Demontis, P.; Klein, M. L. Chem. Phys. Lett. 1988, 1992, 96, 1482. 153, 551. (19) B b , M. Quasielastic Neutron Scattering; Adam Hilger: Bristol, (8) Jobic, H.; B b , M.; Caro, J.; Biilow, M.; Urger, J. J. Chem. Soc., 1988. Faraday Trans. 1 1989,85, 4201. (20) Sears, V. F. Can. J. Phys. 1966, 44, 1299; 1967, 45, 234. (9) Woods, G. B.; Rowlinson, J. S.J. Chem. Soc., Faraday Trans. 2 (21) Volino, F.; Dianoux, A. J. Mol. Phys. 1980, 41, 271. 1989, 85, 765. (22) Jobic, H.; B b , M.; Kearley, G. J. Zeolites 1989, 9, 312. (10) Cohen de Lara, E.; Kahn, R.; Goulay, A. M. J. Chem. Phys. 1989, (23) Jobic, H.; Renouprez, A.; B&, M.; Poinsignon, C. J. Phys. Chem. 90, 7482. 1986, 90, 1059. (11) June, R. L.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1990,94, (24) Jobic, H.; B b , M.; Urger, J.; Pfeifer, H.; Caro, J. J. Chem. Soc., 8232. Chem. Commun. 1990, 341. (12) Nowak,A.K.;denOuden,C. J. J.;Pickett,S.D.;Smit,B.;Cheetham, (25) Jobic, H.; B b , M.; Caro, J.; Biilow, M., Kirger, J.; Pfeifer, H. In A. K.; Post, M. F. M.; Thomas, J. M. J. Phys. Chem. 1991, 95, 848. Studies in Surface Science and Catalysis; Ohlmann, G., Pfeifer. H., Fricke, (13) Catlow, C. R. A.; Freeman, C. M.; Vessal, B.; Tomlinson, S. M.; Elsevier: Amsterdam, 1991; Vol. 65, p 445. R., Us.; Leslie, M. J. Chem. SOC.,Faraday Trans. 1991, 87, 1947. (26) Chudley, C. T.; Elliott, R. J. Proc. Phys. Soc. (London) 1961, 77, (14) Titiloye, J. 0.;Parker, S.C.; Stone, F. S.;Catlow, C. R. A. J. Phys. 353. Chem. 1991, 95,4038. (27) Jobic, H. Spectrochim. Acta 1992, 48A, 293. (15) Goodbody, S.J.; Watanabe, K.; MacGowan, D.; Walton, P. R. B.; (28) Jobic, H. Chem. Phys. Lett. 1990, 170, 217. Quirke, N. J. Chem. Soc., Faraday Trans. 1991,87, 1951. (29) Jobic. H., manuscript in preparation.
