5877
J. Phys. Chem. 1991,95, 5871-5881 nature of the measurements, and the simplicity of the model, great significance cannot be attached to this discrepancy. Clearly, however, the effect of larger well depths is manifested in the stronger negative temperature dependence of Ar relative to Ne. It is likely that the attractive interactions also play a role in the 298 K relaxation with Ar, and possibly also with Ne. The conclusion of earlier studiesB that the HF(J-13) relaxation by Ne and Ar is dominantly impulsive at 298 K must thus be reexamined in light of the current lower temperature measurements.
IV. Conclusion We have measured the rate constants for rotational relaxation of highly rotationally excited HF(J= 13) with H F between 225 and 298 K. The temperature dependence of H F rotational self-relaxation matches well the previously observed negative temperature dependence of H F vibrational self-relaxation. This is evidence that rotational energy transfer at high levels of excitation, where the energy gaps to neighboring states are large, begins to show similarity to a vibrationaltnergy-transfer process. The negative temperature dependence can be partially explained
by models which take the depth of the attractive interaction explicitly into account. In addition, we have seen evidence for vibrational deactivation of HF(u=l) by (HF), clusters. The excited (HF), species subsequently dissociates (or isomerizes), which is manifest as a transient decrease in the absorption of the species. By comparing absorption spectra of the clusters with the spectra of this transient decrease in absorption, we estimate that the tetramer species is some 5 times less efficient than the hexamer in relaxing HF(u= 1). Preliminary measurements of rotational relaxation rates for HF(J= 13) He, Ne, and Ar are also reported. Cross sections for relaxation with He decrease to lower temperature, indicating an impulsive relaxation mechanism, but cross sections with Ne and Ar are larger at 225 K than at 298 K, implying that attractive interactions are important in the HF(J =13) Ne, Ar relaxation.
+
+
Acknowledgment. We gratefully acknowledge the National Science Foundation for support of this research. Registry No. HF, 7664-39-3; He, 7440-59-7; Ne, 7440-01-9; Ar, 7440-37-1.
A Molecular Dynamics Study of Cage-to-Cage Migration in Sodium Y Zeolite: Role of Surface-Mediated Diffusion Subramanian Yasbonath Solid State and Structural Chemistry Unitt and Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore 560 012, India (Received: July 5, 1990)
The details of cage-to-cage migration have been obtained from an analysis of the molecular dynamics trajectory of a probe adsorbate. It is observed that particles utilize the region within a radius of 2 A from the window center but with diffusion taking place predominantly at 1.6 A from the window center and a potential energy of nearly -12 kJ/mol. A barrier of about 0.5 kJ/mol is observed for surface-mediated diffusion. Surprisingly, for diffusion without surface mediation for a particle going from one cage center to another, there is an attractive well near the window instead of a barrier. At low adsorbate concentrations and room temperature, the predominant mode for cage-to-cage migration is surface-mediated diffusion. The analysis suggests that particles slide along the surface of the inner walls of the a-cages during migration from one cage to another.
1. Introduction In the past the diffusion of small adsorbed molecules in zeolites has been investigated by means of several experimental methods such as NMR, uptake, and neutron scattering studies, etc.l-s In spite of these many different studies there is not a proper understanding of these systems. For example, the different methods have yielded values of diffusion coefficients varying over several orders of magnitude.'q6 The diffusion coefficients obtained from NMR data are usually much larger than those obtained by uptake mea~urements.~,' Further, it has not been possible to gain much knowledge about other related quantities such as either the site and cage residence times, the barriers to cage-to-cage migration and site-to-site migration, or the path and the mechanism of diffusion or their interrelationships. Stimulation results and theoretical investigations on several small molecules have shown that the region near the inner walls of the su rcage in X-and Y-type zeolites is the region most populatedy3 However, at higher adsorbate concentrations and higher temperatures the molecular dynamics results show that the region near the cage center also becomes populated? This is also observed by Cohen de Lara and Kahn in their study of methane in NaA by infrared and neutron scattering techniques? Zwanzig and @workers have tried to understand the motion in a periodic potential." Bagchi, Zwanzig, and Marchetti have reported results on diffusion in a 'Contribution No. 704.
0022-3654191/2095-5811S02.50/0
two-dimensional periodic p0tentia1.l~ Studies such as these when extended to a three-dimensionalnetwork of connected cages are likely to be relevant to the problem of migration in zeolites. In general, there can be two different modes for the diffusion of the adsorbates in the supercages. The first mode is the surface-mediated diffusion or surface diffusion. In this mode, the adsorbate glides along the surface of the zeolite and may be (1) Barr-, R. M. Zeolites and Clay Minerals as Sorbents and Molecular Sieves; Academic Press: New York, 1978. (2) Karger, J.; Pfiefer, H. Zeolites, 1987, 7 , 90. (3) Gammn, 1.; Wright,P. A.; Rayment, T.; Thomas,J. M.Chem. Phys. Lett. 1986, 123, 145. (4) Cohcn de Lara, E.; Kahn, R. J . Phys. 1981, 42, 1029. (5) Stockmeyer, R. Zeolites, 1984, 4, 81. (6) Ruthven, D. M.ACS Symp. Ser. 1977, No. 40,320. (7) Karger, J.; Caro, J. J . Chem. Soc., Faraday Tram I 1977, 73, 1363. (8) Woods,G. B.; Pananiotowulos, A. Z.; Rowlinson, J. S.Mol. Phvs. - 1988,63,49. (9) Yashonath, S.;Demontis, P.; Klein, M. L. To k published. (10) Yashonath. S.: Thomas. J. M.: Nowak. A. K.: Chcetham. A. K. Nature, 1988, 331,'601. (1 1) Demontis, P.; Yashonath, S.;Klein, M. L. J . Phys. Chem. 1989, 93, 5016. (12) Yashonath, S.; Demontis, P.; Klein, M. L. Chem. Phys. k t t . 1988, 153, 551. (1 3) Fitch, A. N.; Jobic, H.; Renouprcz, A. J. Phys. Chem. 1986,90,1311. (14) Zwanzig, R. J . Stat. Phys. 1983, 30, 255. (15) Bagchi, B.; Zwanzig, R.; Marchetti, M. C. Phys. Rev. A 1985, 31, 892.
0 1991 American Chemical Society
5878 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 TABLE I: Parameters Employed in the Calculation of Adsorbate-Adsorbate and Adsorbate-Zeolite Interactions A. lo3 kJ/mol A6 B. lo6 kJ/mol Xe-Xe 34.913 165.84 Xe-0 8.2793 11.1345 Xe-Na 2.9 143 7.9079
A'*
Yashonath TABLE 11: Details of the Molecular Dynamics Simulation time step temp ( T ) 364 K 40 fs tot. run time (U*d -1 2.1 kJ/mol 2600 ps
considered to be quasi two-dimensional. In the second type of diffusion, the adsorbate is far from the surface and diffuses from one cage to another with no, or little, mediation from the surface and this is likely to be very similar to the process of diffusion found in fluids. At lower concentrations and temperatures when the population of the adsorbate is significantly larger near the inner surface of the cage4v9and small or negligible toward the cage center, the predominant mode of diffusion is likely to be surface-mediated diffusion. Further, the barrier heights and related information such as the diffusion path, etc., regarding each of these modes of diffusion would be of considerable interest. It is also not known which of the two, the site-to-site migration or the cage-to-cage migration, is the slower and hence determines the overall migration rate. Recently, Thirumalai, Mountain, and co-worker~'~J~ have outlined methods for obtaining measures to ensure convergence and suggest that fairly long simulation runs are required. In the present study, we have carried out simulations for 1 ns or longer in order to get an accurate estimation of properties. In order to avoid the complications resulting from having both the translational and the orientational degrees of freedom for the adsorbate, we have performed molecular dynamics calculations on a monatomic adsorbate and tried to answer some of these questions. Results of the simulation are analyzed with particular emphasis on cage-to-cage migration. 2. Computational Details The recently reported structure of Fitch et al.13 is used for zeolite Y in the present study.1° However, there is an error in the position of the O(3) atom in Table I of ref 13. The correct values for the coordinates of atom O(3) are (0.1746,0.1746, -0.0335) and not (0.01 764,0.1764, -0.0335) as reported. The zeolite framework and the cations are treated as rigid or fixed. The ratio of Si/Al = 3.0 is assumed as in a previous study.I0 For this Si/Al ratio the sodiums occupy the SI and SI1 sites completely. The unit cell composition13is Na4(Si + Al)1920384, and the space group is Fd3m with a = 24.85 A. The interaction between the adsorbate, a, and the zeolite is assumed to be of the form
uaz = x4az = E( Z
-$+ $) raz
z = 0, Na
raz
The interactions are confined to the oxygen and the sodiums of the zeolite. This approximation has been used by earlier worked8 and is in accordance with the fact that the silicon atoms are surrounded by the oxygens. The short-range potential parameters are the same as that for xenon interacting with sodium Y zeolite reported by Kiselev.I8 The potentials were, however, shifted to obtain 4az(rc)= 0. A cut-off radius, r,, of 12 A has been employed throughout. We have, however, not included the polarizibility term in the Kiselev potential and retained only the short-range repulsion and dispersion terms. A 6-12 Lennard-Jones form of interaction has been used for adsorbateadsorbate interaction (UJ.The parameters employed here are the same as those used by Rowlinson and co-workers for xenon.* The potential parameters are listed in Table I. The mass of the adsorbate was taken to be 131 amu. It was found that long simulations of 2.6 ns were necessary to obtain accurate estimates of properties of interest to the present study. Equilibration was (16) Thirumalai, D.; Mountain, R. D.; Kirkpatrick, T. R. Phys. Rev. A 1989,39,3563. (1 7) Mountain, R. D.; Thirumalai, D. J . Phys. Chem. 1989, 93, 6975. (1 8) Kiselev, A. V.; Du, P.Q. J. Chem. Soc., Faraday Trans. 2 1981,77, 1.
Figure 1. (a, top) Picture of the a-cage consisting of 48 Si and 72 0 atoms. The diameter of the cage is about 1 1.8 8, and that of the window is 8 A. (b, bottom) Each a-cage connected to four other a-cages in a tetrahedral fashion through the shared 12-membered rings or windows.
carried out for 200 ps and temperature adjusted to the desired value by repeated scaling of velocity. Calculations were carried out for an adsorbate concentration of 1 atom/cage and one unit cell of Nay. At the start of the simulation, the adsorbates were placed at the center of the cages. Simulations were carried out as already pointed out without the inclusion of the zeolite atoms in the molecular dynamics integration. The Verlet algorithm was used for the integration of the position coordinates of the guest species with periodic boundary conditions. All calculationswere carried out in the microcanonical ensemble. Other details of the run are given in Table 11. 3. Results and Discussion Interconnected A104and Si04tetrahedra give rise to an infinite network of connected cages in three dimensions known as zeolite Y. There are two types of cages, the smaller cages known as the sodalite cages and the somewhat bigger cages called the supercages or the a-cages. Most adsorbates cannot penetrate the smaller cage, and it is only the bigger or the a-cage where the adsorption takes place. There are eight such a-cages in a unit cell of Nay. The a-cage has tetrahedral symmetry and is nearly spherical in shape. The radius of the a-cage may be taken to be 5.9 A. Each a-cage
Dynamics of Cage-to-Cage Migration in Sodium Y Zeolite
The Journal of Physical Chemistry, Vol. 95, No. 15, 1991 5879 -in 7
-12.5
h
0
m
m
12 0
240
360
6,degrees Figure 2. Potential energy due to the zeolite as measured by a probe adsorbate particle lying in the plane of the window as a function of 8, the angle between the line joining the particle with the window center and the line joining one of the six in-plane oxygens with the window center. The curves are drawn at different distances from the window center, namely, r = IS, 1.7.2.0, 2.2 A.
-1151 -4
1
I
I
-2
0
2
4
tops
Figure 4. Molecular dynamics average of potential energy of adsorbate in the interval 4to +4 ps of the time of crossing over from one cage to another.
o -2-0'-
e.kJ/mol -12.5
0
2
1
raw, A
Figure 5. Distribution of potential energy of adsorbate at the instant when crossing over from one cage to another, obtained from the average
Figure 3. Potential energy of a probe adsorbate particle due to the
of the molecular dynamics trajectory.
zeolite. The particle is in the plane of the 12-ring window connecting the two supercages with 8 = 0'. r,, is the distance between the adsorbate and the window center.
2.2 A it is always repulsive and large. For still larger values of r the potential is very large and positive and hence not relevant to cage-to-cage migration. The functional dependence of the potential on r is depicted in Figure 3 for 8 = 0 ' . Note that the minimum in the potential occurs at r = 1.5-1.6 A and is about -12 kJ/mol. The potential also depends strongly on 6 for larger values of r. The periodicity exhibited is 60'. The potential is highest at 8 = Oo, 60°, 120°, etc., when the guest lies on the line joining the window center with one of the in-plane oxygen atoms. At 8 = 30°, 90°, 150°, etc., the potential is a minimum, corresponding to the guest being between the in-plane oxygen and the out-of-plane oxygen. Also, up to about 1.7 A from the window center there is little or no dependence of U,,on 8. In Figure 4 we show the molecular dynamics average of the potential energy of the adsorbate within -4 to +4 ps of the crossover time for going from one cage to another. The errors in the reported values of energy are less than 0.1 kJ/mol. It is seen that the particle experiences a barrier of nearly 0.5-0.6 kJ/mol just before crossing the window. At the window itself, there is a small potential minimum of about 0.2 kJ/mol. This is in contrast to the general understanding that the barrier is highest at the window. It is clear that the window itself provides a minimum in the energy of interaction. This is in agreement with the results of infraredI9 and molecular dynamics" studies of benzene adsorption in NaY where it was found that benzene adsorbs at the window. The potential energy distribution for the particle in the plane of the window during cage-to-cage migration is shown in Figure 5. In agreement with Figure 2, the main band is observed near -12 W/mol, which is followed by a tail toward higher energy. Some particles crossing over to a neighboring cage possess a significantly greater potential energy, though their number is small. The variation of the distance between the particle and the window center when the adsorbate is in the plane of the window during diffusion from one cage to another is shown in Figure 6. The error in the reported distance is less than 0.1 A. The minimum distance of approach to the window center is about 1.6 A on the
has four windows (see Figure la). The lines connecting the centers of the windows to the center of the a-cage form a tetrahedron. The window is the common boundary between two neighboring cucages. Thus, each a-cage is connected to four other a-cages tetrahedrally, which in turn are connected to four other cages each, and so on, ad infinitum (see Figure 1b). The diameter of the window is about 4.5 A. The window is made up of 12 Si and 12 0 atoms. Of the 12 0 atoms, six lie in one plane, three above and three below this plane. Below, whenever a reference is made to the plane of the window we mean the plane of the six oxygens. We refer to the a-cage simply as the cage. Over a period of time the adsorbate migrates from one cage to another. We have calculated details of the energy and the position of the adsorbate before, during, and after crossing from one cage to another, using the molecular dynamics trajectory of 2.6-11s length. During this period, we found that there were about 1600 cage-to-cage crossings. An atom was assigned to a given cage if the distance from the center of that cage was less than the distance from any other cage center. The potential energy surface near the window is expected to influence greatly the nature of the motion, the energetics, and other relevant properties during cage-to-cage crossing or migration. It is, therefore, worthwhile to look at the potential energy surface at the window. We have plotted the potential energy for an atom lying in the plane of the window defined by the six oxygen atoms of the 12-member ring. The distance from the center of the window (taken to be the center of the 12 oxygen atom array) is r and the angle between the line joining the atom and the window center and the line joining the cage center with one of the six in-plane oxygens is 8. In Figure 2 the potential energy of the adsorbate due to the field provided by the zeolite is shown as a function of 8 for different values of r. Several interesting observations can be made. The potential felt by an adsorbate particle becomes increasingly positive and large as one moves away from the center of the window; at r = 1.5 A the potential is attractive for all values of 8, whereas r =
(19) de Mallmann, A.; Barthomeuf, D. Zcolircs, 1988, 8, 292.
5880 The Journal of Physical Chemistry, Vol. 95, No. 15, 1991
Yashonath
I
\
I
/ I
1
-4
-2
I
1
I
I
0
2
4
,
oh
trajectory.
I
I
8
r,,A
t. Ps
Figure 6. Variation of the distance r,, between adsorbate and window center in the interval -4 ps to +4 p of the time of crossover from one cage to another cage, obtained by averaging the molecular dynamics
,
I
4
Hgwe 8. Distance between the center of the parent cage and the particle, r ,plotted against distance between the center of the daughter cage and tRe particle, rd, obtained from the molecular dynamics data. Note the predominance of the surface mediated mode of migration. -3.
A
-1
- 9b
,
1
I
I
8
4
I
I
12
rp,A
Figure 7. Distribution of r,, at the instant when a particle is crossing
over from one cage to another cage, obtained from the molecular dynamics calculation. average, in agreement with Figure 3. There is, however, a small fraction of particles that actually pass through the center of the window. This can be seen in Figure 7,where we show the disthe distance between the adsorbate and window tribution of raw, center. It is clear that there is a large distribution of rawthe largest being at a distance slightly larger than 2 A. The distribution is unlikely to show any significant dependence on 8 at small raw.At large raw, the distribution is likely to show pronounced dependence
on e.
It is possible to conceive of two modes of diffusion-one with surface mediation and the other without any surface mediation. The former is largely two dimensional, while the latter is three dimensional in character. It is interesting to see whether cageto-cage migration takes place through surface mediation or, as in bulk, without the surface playing a role. In the latter case, the distance of the particle from the surface is likely to be large throughout, or at least during some part of, the cage-to-cage migration. In surface-mediated migration, the particle essentially skates along the surface and therefore is expected to be at a considerable distance from the centers of the parent cage (the cage from which the particle is exiting) and the daughter cage (the cage into which the particle is entering). We define rp as the distance of the particle from the center of the parent cage and f d the distance from the particle to the center of the daughter cage. In Figure 8 we have plotted averaged values of rpagainst rd for trajectories in the neighborhood (-3.5 to +3.5 pp) of the c r m e r instant. It is seen that both rp and f d do not take values of r less than 4.0 A. This means that the particles remain near the inner walls of the a-cage throughout the process of cage-to-cage migration. This clearly shows that surface-mediated diffusion is the predominent mode of cage-to-cage migration at the low concentration of one adsorbatelcage. This is in agreement with earlier molecular dynamics and Monte Carlo calculations on xenon, methane, and benzene where it was found that at low concentrations and low temperatures only the region near the cage surface is populated at all times.e12 It has, however, been observed that at higher concentrations and temperatures the region near the cage
Figure 9. Potential energy curve as a particle traverses from the center of one cage to the center of a neighboring cage plotted against distance between the particle and the center of the parent cage or the cage in which the particle is originally resident. There is an attractive well instead of a barrier for this path.
center becomes increasingly occupied? This has also been confirmed by the IR and neutron scattering studies of methane in NaA by Cohen de Lara and co-workers.‘ The increase in pop ulation near the cage center of adsorbate at higher concentrations and temperatures raises the possibility of adsorbates migrating from one cage to another without surface mediation. One can conceive of a particle near the cage center diffusing from the center of one cage to the center of another cage without coming near the inner surface of the cage. We ask the question: what is the nature of the potential energy surface for a particle diffusing in this way? In order to see this we show in Figure 9 the potential energy of sorbate as it diffuses straight from one cage to another from the center of the parent cage to the center of the daughter cage through the center of the window. Surprisingly, we find that instead of a barrier there is a potential well with a depth of about 5 kJ/mol. Thus, this mode of migration is a distinct possibility at higher concentrations and temperatures. The barrier for site-to-site migration of xenon is not known. However, earlier calculations on similar small molecules suggest that the barrier for site-to-site migration is likely to be at least a few kilojoules per mole. This is more than the barrier for cage-to-cage migration in the immediate neighborhood of the window (0.5 kJ/mol) obtained above. This means that sitatesite migration is the rate-determining step for the diffusion of xenon in Nay. Cage-to-cage migration should begin at the same temperature as site-to-site migration. However, a particle on the average has to travel a much longer distance before it migrates to another cage, and consequently, the frequency of cage-to-cage migration is likely to be smaller than the frequency of sitatesite migration. There are several other factors that play an important role in cage-to-cage and site-to-site migration. The interaction of two or more adsorbates affects the migration. However, at 1 xenon/cage the interaction energy between adsorbattadsorbate is small compared to the adsorbattzeolite interaction and consequently the effect of the adsorbateadsorbate interaction on the
J. Phys. Chem. 1991, 95, 5881-5889 migraton of xenons is a t best small.20 A second point that is worthwhile to note is the fact that the barriers for cage-to-cage migration and for site-to-site migration depend on the adsorbate size. As the size of the adsorbate increases the barrier for cage-to-cage migration increases rapidly. Consequently for large molecules the barrier for cage-to-cage migration is expected to be greater than that for site-to-site migration. Again this depends on the size and dimensions (shape) of the guest adsorbate. Thus, for example, linear alkanes of n carbon atoms are expected to have a smaller barrier than the corresponding branched alkanes. In summary, the particles essentially pass through within a radius of 2 A from the window center. The distributions of energy and rawfor particles in the plane of the window during cage-to-cage (20) Yashonath, S.Chem. Phys. Lett. 1991, 177, 54.
5881
migration show that the particles with an energy of about -12 kJ/mol and at a distance of 1.6 A from the window center predominate. The potential becomes strongly dependent on 0 at large rawand repeats with a periodicity of 60'. The surface-mediated mode of diffusion is the predominant mode of cage-to-cage migration at least up to room temperature and low adsorbate concentrations. The particles migrate from one cage to another always keeping close to the inner surface of the cage. The barrier for the surfacemediated cageto-cage migration is small (0.5 kJ/mol). In contrast, in diffusion without surface mediation, in particular, a particle diffusing from one cage center to another, passing through the center of the window, encounters a potential well instead of a barrier.
Acknowledgment. I thank the anonymous reviewers for their critical comments and helpful suggestions.
Temperature and Concentration Dependence of Adsorption Properties of Methane in Nay: A Molecular Dynamics Study Subramanian Yashonath,* Solid State and Structural Chemistry Unit, Supercomputer Education and Research Centre, Indian Institute of Science, Bangalore, 560 012 India
Pierfranco Demontis: and Michael L. Klein Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104-6323 (Received: October 30, 1990)
Molecular dynamics calculations on methane sorbed in NaY (&/A1 = 3.0) employing realistic methane-methane and methanezeolite intermolecular potential functions at different temperatures (50, 150,220, and 300 K) and concentrations (2,4,6, and 8 molecules/cage) are reported. The thermodynamic results are in agreement with the available experimental data. Guest-guest and guest-host radial distribution functions (rdfs), energy distribution functions, distribution of cage occupancy, center-of-cage-center-of-mass(coc-com) rdfs, velocity autocorrelation functions for com and angular motion and the Fourier transformed power spectra, and diffusion coefficients are presented as a function of temperatureand concentration. At 50 K,methane is localized near the adsorption site. Sitesite migration and essentially free rotational motion are observed at 150 K. Molecules preferentially occupy the region near the inner surface of the a-cage. The vibrational frequencies for the com of methane shift toward higher values with decreasing temperature and increasing adsorbate concentration. The observed frequencies for com motion are 36,53, and 85 cm-' and for rotational motion at 50 K, 95 and 150 cm-' in agreement with neutron scattering data. The diffusion coefficients show a type I behavior as a function of loading in agreement with N M R measurements. Cage-to-cage diffusion is found to be always mediated by the surface.
1. Introduction The catalytic and separation properties of faujasites-an important class of zeolites- are well-known. The three-dimensional network of linked SO, and AIO, tetrahedra give rise to a three-dimensional structure of interconnected cavities of different sizes. Many organic molecules are adsorbed in one or more of these cavities at specific sites. The sorption properties of faujasites clearly depend on the nature of the guest and on the host-guest interaction. The study of sorption characteristics of faujasites is complicated by the presence of a large number of factors that influence the properties of the sorbatezeolite system. The Si/AI ratio, nature of the extraframework cations, presence of sorbed water molecules, temperature, and the loading or the adsorbate concentration are just some of the factors tfiat determine the properties of the gu&tzeolite system.'-) For example, a decrease in the Si/Al ratio will influence the adsorbatezeolite interaction due to the increased negative charge of the framework. Further, electroneutrality- requires . an increase in the number of cations. To whom correspondenceshould be addressed. 'On leave of absence from: Dipartimento di Chimica, Universita di Sassari, Sassari, Italy.
0022-3654/91/2095-5881$.02.50/0
These cations occupy sites that block the windows and channels, making it more difficult for the guest species to migrate from one cavity to another. In addition to these, the difficulty of characterization of the zeolite and the inherent limitations of the techniques employed complicate matters. Thus, for example, the self-diffusion coefficients for the guest species measured by different methods have yielded values that differ by several orders of magnitude.,J Adsorption of the simplest member of the hydrocarbon family in faujasites, viz. methane, has been investigated by several different techniques. Calorimetric studies on the sorption of methane in NaX and NaY have been reported.&" Measurements of (1) Ruthven, D. M. Principles of Adsorption and of Adsorption Pnmsscs; John Wiley and Sons: New 1984. (2) Barrer, R. M. Zeolites and Clay Minerals as Sorbents and Molecular Sieues; Academic Press: New york, 1978. (3) Fyfe, C. A.; Thomas, J. M.; Klinowgki, J.; Gobbi, G. C. Agnew. Chem., Inr. Ed. End. 1983, 22, 259. (4) Ruthen, D. M.; Loughlin, K. F.; Derrah, R. 1. Adv. Chem. Ser. 1973, No. 121, 330. (5) Karger, J.; Caro, J. J . Colloid Interface Sei. 1975, 52, 623. (6) Barrer, R. M.; Sutherland, J. W. Proc. R. Soc. London, A 1956, 237, 439.
0 1991 American Chemical Society
