J. Phys. Chem. B 2000, 104, 8491-8497
8491
Diffusion of Benzene in NaX and NaY Zeolites Studied by Quasi-Elastic Neutron Scattering Herve´ Jobic,*,† Andrew N. Fitch,‡ and Je´ roˆ me Combet§ Institut de Recherches sur la Catalyse, CNRS, 2 AVenue Albert Einstein, 69626 Villeurbanne, France, ESRF, BP 220, 38043 Grenoble, France, and Institut Laue-LangeVin, BP 156, 38042 Grenoble, France ReceiVed: March 15, 2000; In Final Form: June 21, 2000
Quasi-elastic neutron scattering (QENS) has been used to study the diffusion of benzene in NaX and NaY zeolites. The self-diffusion coefficient is found to decrease with increasing loading in both zeolites. In NaX, the diffusivities obtained from QENS are in reasonable agreement with those obtained by pulsed-field gradient NMR or frequency-response methods, but a large discrepancy is observed with results from the tracer zerolength column technique. In NaY, where the experimental results are scarce, the diffusion coefficients derived from QENS compare well with those from different simulation techniques. At low benzene concentrations, extrapolation of the QENS values to 300 K yields diffusivities that are almost 2 orders of magnitude lower in NaY than in NaX. This reflects the strong influence of the cation distribution at this temperature. The activation energy for diffusion in NaY, 33.7 kJ/mol, is about twice that in NaX, 17 kJ/mol, at low loading.
Introduction Zeolites are natural or synthetic crystallized microporous materials. They are widely used for numerous industrial applications, such as catalysis or the separation of gases and hydrocarbons. However, there is no quantitative theory at the present time that is able to predict the transport properties of any adsorbed molecule in a particular zeolite structure. Each system is unique, and the concepts of free diameter for the zeolite channels or kinetic diameter for the molecules are of limited value. The number of computer simulation techniques available for the study of the diffusion process of guest molecules in zeolites has increased tremendously in recent years. Apart from the traditional molecular mechanics or molecular dynamics (MD) studies, new techniques have emerged for slowly diffusing molecules, such as kinetic Monte Carlo1 or “Bluemoon” simulations.2 Most of these methods are hierarchical and use transition-state theory. They have been found to be effective at determining diffusivities of large molecules, e.g., in silicalite.3 Apart from silicalite, which is an ideal system for simulations, as there are no compensating cations, faujasites have been considered in a number of calculations1,4-15 in view of the discrepancies in the diffusivities of aromatics reported in this structure. The problem is that the diffusion measurements have generally been carried out with NaX crystals, whereas most of the simulations were performed in NaY, so that the comparison of simulations with experiment is limited. In particular, the largest Si/Al ratio that was studied with pulsed-field gradient NMR (PFG NMR) spectroscopy is 1.8 because large Y zeolite crystals are not available. The size of the crystals is unimportant in quasi-elastic neutron scattering (QENS), so one can use crystals smaller than 1 µm without problems. Relatively high diffusivities for benzene in NaX were obtained by PFG NMR,16 QENS,17 frequency-response,18 and * Author to whom correspondence should be addressed. E-mail:
[email protected]. † CNRS. ‡ ESRF. § Institut Laue-Langevin.
piezometric experiments.19 On the other hand, zero-length column (ZLC) chromatographic and gravimetric measurements20,21 gave values lower by at least 1 order of magnitude. A more recent study using the tracer ZLC method22 reported a self-diffusion coefficient increasing with increasing loading, whereas an opposite trend had been found previously by microscopic methods. Auerbach and co-workers have addressed the concentration dependence of benzene diffusion in a number of papers. In NaX, they have applied kinetic Monte Carlo (KMC) simulations and various other theories, and they found qualitative agreement with the PFG NMR data.13,14 In NaY, the simulations predict a diffusivity that increases at high loadings.14 Such a prediction can be tested with QENS. The location of benzene in NaY was obtained by powder neutron diffraction.23 The first type of benzene lies in the supercage at ∼2.7 Å from the SII sodium ions, the center of the molecule being on the cube diagonal. A second adsorption site was found in the twelve-ring window between adjacent supercages. In NaX, some benzene was found on SII sites, but none in the windows.24 However, less than half of the adsorbed benzene could be located, suggesting that the other molecules may be disordered. In the present work, QENS has been used to study the diffusion of benzene in both NaX and NaY zeolites, to elucidate the influence of the cation distribution on the mobility of this molecule in the faujasite structure. The self-diffusion coefficients, loading dependence, and activation energies are compared with the results obtained from other experimental techniques and simulation methods. Experimental Section The previous QENS measurements on benzene in NaX were performed with a time-of-flight (TOF) instrument having an elastic energy resolution of ∼19 µeV, full-width at halfmaximum (fwhm).17 To study benzene in both NaX and NaY, a spectrometer with a higher energy resolution was required. The backscattering (BS) spectrometer IN16, at the Institut LaueLangevin, Grenoble, France, was selected. The energy resolution
10.1021/jp000994f CCC: $19.00 © 2000 American Chemical Society Published on Web 08/10/2000
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Jobic et al. Theory The QENS spectra for benzene, which are obtained after subtraction of the contribution from the dehydrated zeolites, can be interpreted in terms of incoherent scattering from the hydrogen atoms only, because of the large incoherent cross section of hydrogen. The energy domain studied in this work, (12 µeV, is so narrow that only translational motions of benzene are observed. It has been found previously17 that the correlation time for the rotational motion is very short, ∼1 ps, so that any quasi-elastic broadening due to this motion will look perfectly flat on our time scale. However, the measured intensity will be affected by the elastic incoherent structure factor (EISF) of the rotational motion. Further, the total intensity of the spectra will be decreased, for increasing momentum transfer values, through a Debye-Waller factor because of fast vibrational modes. Even if faujasite has a cubic structure, the diffusion in this zeolite is not totally isotropic. However, in the Q range considered in this work, the incoherent scattering function can be well-described by a Lorentzian function
S(Q,ω) )
Figure 1. Diffraction patterns for NaX determined from a comparison of the elastic peak intensities of the zeolite, at each angular position, with those obtained for a vanadium standard: (a) on a TOF instrument (IN6, λ ) 5.12 Å) and (b) on a BS spectrometer (IN16, λ ) 6.27 Å).
on this instrument can be fit with a Gaussian curve with a fwhm of about 0.9 µeV. Unpolished Si(111) crystals were used as analyzers, and the energy transfers were analyzed in a window of (12 µeV. Although the energy resolution is much better than on a TOF machine, the momentum transfer resolution is worse. This is illustrated in Figure 1. It appears that the Bragg peaks of the zeolite can be more easily avoided on a TOF instrument. On IN16, the 220, 311, and 331 reflections cannot be resolved, so some Bragg intensity will appear in several detectors. The technique for dealing with this additional contribution is presented in the Results section. The NaX (Si/Al ) 1.23) and NaY (Si/Al ) 2.43) samples were activated by heating them under flowing oxygen (up to 670 K for NaX and 720 K for NaY). After being allowed to cool, the zeolites were pumped to 10-4 Pa while being heated again. Samples containing different benzene quantities were prepared. They were transferred inside a glovebox into cylindrical aluminum containers of annular geometry. The thickness of the containers was selected to give transmissions of about 90%. The cells were placed in a cryofurnace so that measurements could be made in the range 270-550 K. At high loadings and high temperatures, the concentration of molecules in the vapor phase increases, so that the true concentration of benzene in the zeolite crystals is less than the quoted values. Cells containing different amounts of dehydrated zeolites were also prepared. Their signal was subtracted from the spectra recorded with the samples containing benzene for the same zeolite powder thickness. Normalization and absorption corrections were made using standard ILL programs.
∆ω(Q) 1 π ω2 + [∆ω(Q)]2
(1)
where pQ corresponds to the neutron momentum transfer and pω to the energy transfer. When the momentum transfer values are sufficiently small, i.e., when one is looking at the diffusion over large distances in real space, the translational motion follows Fick’s law and the half-width at half-maximum (hwhm) of the Lorentzian is simply given by ∆ω(Q) ) DQ2, where D is the self-diffusion coefficient. Provided that a linear variation of the broadening is obtained as a function of Q2, the diffusivity can be determined without a model. At larger Q values, the hwhm deviates from a straight line, this deviation being characteristic of a jump diffusion.25,26 For benzene in faujasites, the simplified version of the Singwi-Sjo¨lander model27 was found to correctly describe the data. It is based on the assumption that the time taken for the jump is much shorter than the residence time on a given site, τ. The hwhm of this model is given by
∆ω(Q) )
Q2〈r2〉 1 6τ 1 + Q2〈r2〉/6
(2)
This model implies that the jumps can be described by a spatial probability distribution of the form
F(r) )
( )
r r exp 2 r r0 0
(3)
The mean-square jump distance corresponding to this distribution is
〈r2〉 )
∫0∞ r2F(r) dr ) 6r20
(4)
The limit of eq 2, for small Q, is 〈r2〉Q2/6τ, that is, DQ2, using the Einstein expression in three dimensions
D)
〈r2〉 6τ
(5)
At large Q values, the width tends assymptotically toward τ-1, the mean jump rate. The advantage of fitting all of the spectra
Diffusion of Benzene in NaX and NaY Zeolites
J. Phys. Chem. B, Vol. 104, No. 35, 2000 8493
Figure 2. Comparison between experimental (+) and calculated (solid line) QENS spectra obtained at different temperatures for benzene in NaY zeolite, at a loading of 2 benzene molecules per supercage, on average (Q ) 0.29 Å-1). The dotted line represents the resolution function.
Figure 3. Comparison between experimental (+) and calculated (solid line) QENS spectra obtained at different temperatures for benzene in NaY zeolite, at a loading of 4.5 benzene molecules per supercage, on average (Q ) 0.29 Å-1). The dotted line represents the resolution function.
simultaneously with such a model is that the broadening can be simulated over the entire Q range.
because the broadenings due to the translation are large compared with the instrumental resolution. All spectra obtained at the different loadings and temperatures could thus be fit individually. The broadenings obtained in NaX as a function of Q2 are plotted in Figure 6 for two benzene loadings at 350 K. Because of the Bragg contribution in several spectra, the scattering of the data is worse than that recorded by a TOF instrument. This is mainly observed at high Q values, where the intensity of the Lorentzian due to diffusion decreases. Some of the broadenings derived in NaY at two temperatures are reported in Figure 7 for a concentration of 2 molecules per supercage. All of the spectra obtained at the different Q values could be fit simultaneously with the Singwi-Sjo¨lander jump model (the same model was also used for the preliminary measurements, ref 17). The error bars for the first two detectors are about 30%, so that the estimated error on the diffusion coefficient is 50% (taking into account the data corrections). When there is a Bragg contribution in the spectra, or when Q values are high, the error bars may reach 60%, so that the likely errors on 〈r2〉 and τ are at least on the order of this value. The widths calculated with the model are plotted in Figures 6 and 7 as solid lines. This means that the broadenings of all individual spectra could follow the Q2 variation predicted by the model, after a small adjustment of the Bragg intensities and of the background. This implied only a small rise for the weighted profile R factor, Rwp, typically from 25% to 26%.
Results Some of the spectra obtained in NaY for a loading of 2 benzene molecules per supercage, on average, are shown in Figure 2. At this momentum transfer value, 0.29 Å-1, the broadenings that are measured can only be due to long-range translation. The length scale probed at this Q value is 21.6 Å, which is larger than the cage-to-cage distance. The first detector at 0.165 Å-1 corresponds to a space scale of 38 Å. The spectra could be fit with a Lorentzian function, due to the diffusion, convoluted with the instrumental resolution. It is clear from Figure 2 that the broadening, hence the diffusivity, increases with increasing temperature. When the loading increases, Figure 3, the broadenings observed at the same temperatures decrease, which means that the diffusivity decreases. A similar trend was found in NaX, but lower sample temperatures could be used, in comparison with those used for NaY, to obtain reasonable broadenings. The first two detectors were fit without any additional intensity due to the Bragg scattering. An elastic intensity due to unresolved Bragg peaks was considered in all of the other spectra.28 For detectors 5-13, this contribution was positive, e.g., Figure 4. For spectra 3 and 4, the Bragg contribution was negative; see Figure 5. This fitting procedure could be applied
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Figure 4. Comparison between experimental (+) and calculated (solid line) QENS spectra obtained for benzene in NaX zeolite at 350 K, for a loading of 1.5 benzene molecules per supercage, on average. The spectra obtained at the different Q values were fit individually, and the separation between the quasi-elastic (dashed curve) and positive Bragg contributions is indicated for Q g 0.65 Å-1.
Discussion At low Q values, the broadenings measured at various loadings and temperatures in NaX and NaY zeolites reach the Fickian regime: the hwhm is proportional to Q2. This means that the diffusion coefficients can be determined without a model. At larger Q values, deviations from the linear behavior are observed, which indicates jump diffusion. The jump diffusion model that applies to both NaX and NaY does not correspond to jumps of a fixed length, as could have been expected if the molecules were jumping between the centers of two adjacent supercages. Such a model, with a jump distance of about 11 Å, would give a maximum in the broadening curves for Q ≈ 0.43 Å-1 (Q2 ) 0.185 Å-2). We do not find any maximum at this Q value for any of the loadings or temperatures (e.g., Figures 6 and 7). The Singwi-Sjo¨lander model was found to fit the spectra correctly. Two jump length distributions corresponding to this
model are plotted in Figure 8. They correspond to the two curves represented in Figure 7 for 2 molecules in NaY at two different temperatures. The rms jump lengths derived for the two distributions, 2.9 and 6 Å, are shorter than the distance between the centers of two adjacent supercages. The fact that this distribution applies signifies that jumps within a supercage (r < 6 Å) are much more probable than jumps between supercages. Only at high temperature does the probability for jumps larger than 10 Å become sizable. This means that the mean residence time derived at 450 K corresponds virtually to the residence time on a given site, whereas at 550 K, this time is closer to the residence time in a cage. Ideally, the jump model should differentiate both residence times. A model including jumps within a supercage convoluted by jumps between cages can be derived. However, it involves additional parameters that are difficult to determine because of the limited time window of the spectrometer and because of the Bragg contribution in the
Diffusion of Benzene in NaX and NaY Zeolites
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Figure 7. Broadenings obtained for benzene in NaY zeolite, for a concentration of 2 molecules per supercage, on average: (+) at 450 K, 〈r2〉1/2 ) 2.9 Å and τ ) 0.3 ns; (O) at 550 K, 〈r2〉1/2 ) 6 Å and τ ) 0.26 ns. The different points correspond to individual fits of the spectra, and the solid line to a simultaneous fit with all spectra.
Figure 5. Comparison between experimental (+) and calculated (solid line) QENS spectra obtained for benzene in NaX zeolite at 350 K, for a loading of 1.5 benzene molecules per supercage, on average: (a) Q ) 0.43 Å-1 and (b) Q ) 0.54 Å-1. The quasi-elastic contribution is shown by the dashed curve, and the Bragg scattering is negative.
Figure 8. Jump length distributions corresponding to the SingwiSjo¨lander model, for benzene in NaY: (a) at 450 K and (b) at 550 K (loading of 2 molecules per supercage). The rms jump lengths are indicated for the two curves.
Figure 6. Broadenings obtained for benzene in NaX zeolite, at 350 K, for 2 different benzene loadings: (0) 1.5 molecules per supercage, on average, 〈r2〉1/2 ) 2.77 Å and τ ) 0.21 ns; (+) 4 molecules per supercage, 〈r2〉1/2 ) 2.07 Å and τ ) 0.33 ns. The different points correspond to individual fits of the spectra, and the solid line to a simultaneous fit with all spectra.
spectra. The two parameters of the model that we used, 〈r2〉 and τ, should rather be viewed as effective parameters. One finds, in both zeolites, that 〈r2〉 and 1/τ decrease when the loading increases or when the temperature decreases. In the small Q range, the time scale probed is at least 1 order of
magnitude larger than the τ values, so that intercage motion can be followed. The diffusivities obtained in NaX from the present QENS study and from the previous measurements17 extrapolated to 468 K are shown in Figure 9 on a linear scale. It is nice to discover that the two sets of data overlap perfectly, although they were obtained with different spectrometers. The diffusion coefficients measured by frequency response are very close to the QENS values. Those obtained by PFG NMR spectroscopy are larger, by a factor 3 to 4, but both methods appear to converge, at low loading, toward the same value of 10-5 cm2 s-1. The TZLC diffusivities are about 2 orders of magnitude lower at low loading, coming closer to the microscopic values at high loading. It is interesting to notice that macroscopic methods, such as ZLC, are best performed on very small quantities of adsorbent
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TABLE 1: Self-Diffusion Coefficients Determined by QENS for Benzene in NaX and NaY Zeolitesa NaX NaY a
1.5 molecules/supercage 4 molecules/supercage 2 molecules/supercage 4.5 molecules/supercage
270 K
310 K
350 K
400 K
1.2 × 10-7
3.1 × 10-7
6.0 ×10-7 2.1 × 10-7
1.4 ×10-6 3.97 × 10-7
450 K
500 K
550 K
7.25 × 10-7 4.3 × 10-7 1.1 × 10-7
9.5 × 10-7 2.2 × 10-7
2.2 ×10-6 4.5 × 10-7
Values are in cm2 s-1.
Figure 9. Loading dependence of the diffusivities derived by different methods for benzene in NaX at 468 K: (2) QENS, asterisked symbols are taken from ref 17; (O) PFG NMR (ref 16); (]) frequency-response (ref 18); and (0) TZLC (ref 22). The curve predicted by simulations (ref 13), dashed line, is scaled down by a factor of 5.
(∼1 mg), whereas a microscopic method such as QENS necessitates sample quantities ranging between 2 and 4 g. The loading dependence reported from the TZLC measurements is at variance from those of all other methods. The curve predicted by the simulations13 has been scaled down by a factor of 5 to avoid flattening out the other results. It appears that the simulations are closer to the PFG NMR values than to the QENS ones, but slightly different rate coefficients would probably give a different behavior. Furthermore, the second adsorption site considered in the simulations, with benzene facing Na(III′) cations in the windows, should be verified by diffraction measurements. The self-diffusion coefficients obtained at two different loadings in NaX are given in Table 1, and the values are plotted in Figure 10 versus inverse temperature. The activation energies are 17 kJ/mol at low loading and 16 kJ/mol at high loading. This is smaller than the values reported by PFG NMR experiments, which are about 25 kJ/mol at low benzene concentrations and 20 kJ/mol at medium pore-filling factors.16 The activation energy obtained from ZLC measurements is 25 kJ/mol,21 whereas a value of 24 kJ/mol has been estimated from a small temperature range by the FR technique.18 Lower activation energies for diffusion were also found by QENS for n-pentane in NaX, compared with the PFG NMR or ZLC methods.29 A similar situation was encountered for short linear alkanes in ZSM-5, where small and constant activation energies were derived by QENS, in agreement with various simulation results.30 Our activation energy value for benzene in NaX is in keeping with NMR spin-lattice relaxation measurements and molecular mechanics simulations in NaX, which gave values of 14 and 15 kJ/mol, respectively.8 In NaY, the diffusion of benzene has been studied more by theoretical than by experimental methods. The diffusivities
Figure 10. Arrhenius plot of the self-diffusion coefficients of benzene in NaX obtained by QENS at two different loadings: (]) 1.5 molecule per supercage, on average; (O) 4 molecules per supercage.
Figure 11. Arrhenius plot of the self-diffusion coefficients of benzene in NaY obtained by different methods: (1) QENS at a loading of 2 molecules per supercage; (2) QENS for 4.5 molecules per supercage, on average; (O) kinetic Monte Carlo simulations (ref 10); (0) constrained reaction coordinate dynamics (ref 15); and (+) MD simulations (ref 6).
obtained by QENS are given in Table 1, and they are compared with the results of various theoretical methods in Figure 11. It is satisfactory to notice that experiment and simulations (performed at infinite dilution) agree within 1 order of magnitude. The value extrapolated from the QENS measurements at room temperature, 4.6 × 10-9 cm2 s-1 at low loading, is in good agreement with the results of a kinetic Monte Carlo simulation, which gave 3.5 × 10-9 cm2 s-1 for the same Si/Al
Diffusion of Benzene in NaX and NaY Zeolites ratio.10 At low benzene concentrations, the self-diffusion coefficient obtained by QENS at 300 K in NaX is almost 2 orders of magnitude higher, which reflects the strong influence of the cation distribution. This is in qualitative agreement with PFG NMR experiments, which yielded lower diffusivities for a Si/ Al ratio of 1.8 compared with 1.2,16 whereas no difference was found by uptake-rate and ZLC measurements between NaX and natural faujasite.21 The activation energies determined by QENS are 33.7 kJ/mol at low loading and 29 kJ/mol at high loading. These values are in reasonable agreement with those derived experimentally by 2H NMR spectroscopy, 40 kJ/mol,31 or from simulations performed at low loadings, namely, 41 kJ/mol,7 44.8 kJ/mol,11 and 49.5 kJ/mol.15 However, the KMC simulations predict a diffusion coefficient that increases with the loading at 300 or 400 K.12 For example, at 400 K, the diffusion coefficient for 5 molecules per supercage is 2 orders of magnitude larger than that for 1 molecule.12 This behavior is in contradiction with the QENS measurements, which indicate a decrease in the diffusivity with increasing loading, in both NaX and NaY zeolites. Conclusions Quasi-elastic neutron scattering spectra of benzene adsorbed in NaX and NaY zeolites have been measured at various loadings and temperatures. At small momentum transfer values, the length scale probed by the technique is larger than the cageto-cage distance, so that intercage migration is effectively followed. The broadenings measured in this Q range vary linearly with Q2, which corresponds to Fickian diffusion. At larger Q values, motions within a supercage come into play, and a jump diffusion model with a distribution of jump lengths was fit to the spectra. Jumps within a cage were found to be more probable than jumps between supercages, but the residence times on a given site and in a cage could not be extracted from the data. In NaX zeolite, the diffusivities obtained from QENS are in good agreement with the PFG NMR or frequency-response values. In all of these techniques, and in a kinetic Monte Carlo simulation, the diffusivities decrease with increasing loading, whereas the reverse trend is observed in TLZC experiments. In NaY, the diffusion coefficients determined by QENS are in reasonable agreement with those obtained by various theoretical methods. It has been realized for a long time that, in NaY, the reduced number of sodium cations, compared with the number in NaX, should enhance the potential energy barriers. This is found experimentally for the first time by QENS: the activation energies for diffusion are about twice as large in NaY as they are in NaX.
J. Phys. Chem. B, Vol. 104, No. 35, 2000 8497 Acknowledgment. The neutron experiments were performed at the Institut Laue-Langevin, Grenoble, France. We thank Prof. S. M. Auerbach and Prof. M. Be´e for discussions. References and Notes (1) Auerbach, S. M.; Metiu, H. I. J. Chem. Phys. 1996, 105, 3753. (2) Forester, T. R.; Smith, W. J. Chem. Soc., Faraday Trans. 1997, 93, 3249. (3) Maginn, E. J.; Bell, A. T.; Theodorou, D. N. J. Phys. Chem. 1996, 100, 7155. (4) Demontis, P.; Yashonath, S.; Klein, M. L. J. Phys. Chem. 1989, 93, 5016. (5) Klein, H.; Kirschhock, C.; Fuess, H. J. Phys. Chem. 1994, 98, 12345. (6) Klein, H.; Fuess, H.; Schrimpf, G. J. Phys. Chem. 1996, 100, 11101. (7) Auerbach, S. M.; Henson, N. J.; Cheetham, A. K.; Metiu, H. I. J. Phys. Chem. 1995, 99, 10600. (8) Auerbach, S. M.; Bull, L. M.; Henson, N. J.; Metiu, H. I.; Cheetham, A. K. J. Phys. Chem. 1996, 100, 5923. (9) Auerbach, S. M. J. Chem. Phys. 1997, 106, 7810. (10) Auerbach, S. M.; Metiu, H. I. J. Chem. Phys. 1997, 106, 2893. (11) Jousse, F.; Auerbach, S. M. J. Chem. Phys. 1997, 107, 9629. (12) Saravanan, C.; Jousse, F.; Auerbach, S. M. J. Chem. Phys. 1998, 108, 2162. (13) Saravanan, C.; Jousse, F.; Auerbach, S. M. Phys. ReV. Lett. 1998, 80, 5754. (14) Saravanan, C.; Auerbach, S. M. J. Chem. Phys. 1999, 110, 11000. (15) Mosell, T.; Schrimpf, G.; Brickmann, J. J. Phys. Chem. 1997, 101, 9476; 1997, 101, 9485. (16) Germanus, A.; Ka¨rger, J.; Pfeifer, H.; Samulevic, N. N.; Zdanov, S. P. Zeolites 1985, 5, 91. (17) Jobic, H.; Be´e, M.; Ka¨rger, J.; Pfeifer, H.; Caro, J. J. Chem. Soc., Chem. Commun. 1990, 341. (18) Shen, D.; Rees, L. V. C. Zeolites 1991, 11, 666. (19) Bu¨low, M.; Meitk, W.; Struve, P.; Lorenz, P. J. Chem. Soc., Faraday Trans. 1 1983, 79, 2457. (20) Goddard, M.; Ruthven, D. M. Zeolites 1986, 6, 283. (21) Eic, M.; Goddard, M.; Ruthven, D. M. Zeolites 1988, 8, 327. (22) Brandani, S.; Xu, Z.; Ruthven, D. Microporous Mater. 1996, 7, 323. (23) Fitch, A. N.; Jobic, H.; Renouprez, A. J. Phys. Chem. 1986, 90, 1311. (24) Vitale, G.; Mellot, C.; Bull, L. M.; Cheetham, A. K. J. Phys. Chem. 1997, 101, 4559. (25) Jobic, H. In Recent AdVances in Gas Separation by Microporous Membranes; Kanellopoulos, N., Ed.; Elsevier, in press. (26) Gergidis, L. N.; Theodorou, D. N.; Jobic, H. J. Phys. Chem. B 2000, 104, 5541. (27) Singwi, K. S.; Sjo¨lander, A. Phys. ReV. 1960, 119, 863. (28) This could be checked during some of the most recent measurements, at which time a new detector diffraction bank was installed on IN16 below the scattering plane. Diffraction patterns were recorded simultaneously with the inelastic spectra, within the same Q range. The intensities of the Bragg peaks could then be monitored with a reasonable resolution so that their variation upon adsorption and with temperature could be followed. (29) Jobic, H. Phys. Chem. Chem. Phys. 1999, 1, 525. (30) Jobic, H. J. Mol. Catal. A 2000, 158, 135. (31) Isfort, O.; Boddenberg, B.; Fujara, F.; Grosse, R. Chem. Phys. Lett. 1998, 288, 71.
