9417
J. Phys. Chem. 1992,96,9417-9421
Self-Diffusion of Rare Gases in SlllcalRe Studied by Molecular Dynamics S.El Amrani, F. Vigo&Maeder,* and B. Bigot Institut de Recherches sur la Catalyse, 2 av. Albert Einstein, F-69626 Villeurbanne Cedex, France, and Ecole Normale Sup8rieure de Lyon, 46 all8e d'ltalie, 69361 Lyon C8dex 07,France (Received: May 1, 1992)
The motion of rare gases adsorbed in silicalite has been simulated by using simple Lennard-Jones atom-atom potentials. The silicalite framework has been assumed to be rigid and was represented by the oxygen atoms. The MD simulations have been carried out in the microcanonical (NVE) ensemble. Four loadings have been considered: infinite dilution and 2,5, and 9 atoms per unit d (u.c.). The dimtsion coefficientshave been computed from the Einstein relation at Merent temperaturea in the range 200-500K. At 300 K and for 2 atoms/u.c., values of 24,12,and 2 X lo+' m 2 d have been obtained for neon, argon, and xenon, respectively. Values of 2 and 3 kJ.mo1-l for the activation energies have been derived for neon and argon; they are nearly independent of the loading. For xenon, the activation energy varies from 6 kJ.moI-' at 0 atoms/u.c. to 3 kJ.mo1-' at 9 atoms/u.c. The distribution of the adsorbed atoms along the channels has been investigated in relation with the potential energy values inside the void space. The concept of supermobility has been revisited.
Introduction Molecular transport plays an important role in the catalytic and sorption properties of zeolites. The sensitivity to the shape and volume of the adsorbed moleculesand consequently to the geometric feature of the zeolitic void s p a c e i s probably one of the origins of the so-called shape selectivity of zeolites. Three stages can be differentiated in the transport of molecules: (i) the transport through the intercrystalline space that does not depend on the inner structure of the zeolite crystals; (ii) the transport through the crystal surface that is difficult to simulate because the surface is not well-known in the case of zeolites; (iii) the transport inside the cavities or channels whose structure can be derived from crystallographic data. This last step can be related to the intracrystallineselfdiffusion, i.e. to the moving of adsorbed molecules in the system at equilibrium, in which there is no transport of the adsorbed compound at a macroscopic level. The molecular dynamics technique (MD), which solves the classical equations of motion, is well suited for simulating the individual motion of the molecules under equilibrium conditions. In recent years it has been largely used for studying the diffusion of molecules in ~eolites.~-'~ The rare gases from neon to xenon form a set of spherical atoms of increasing sizes and so appear appropriate to explore some simple size effects. Such effects have been long recognized in the adsorption properties of microporous media,ls characterized by very large adsorption energies. The systems rare gases-polymer carbons have been analyzed in terms of potential energy profiles of the adsorbed atoms, calculated by using potentials of atom-site type; the comparison with experimental data led to an evaluation of the pore size.I6 More recently, Derouane" used a continuum model for the solid to define the concepts of curvature and nesting effect. These considerations have been illustrated in recent molecular simulations, for example those of methane in zeolites of various pore sizes. At low coverage and low temperatures, the methane molecule occupies preferentially small cavities, if any, i.e., the tight channels ampared to the broad channel intersections in the case of silicalite' and the side pockets compared to the channels for m~rdenite.~In the absence of small cavities the adsorbed molecule resides mostly in the vicinity of the supercage walls.%' At higher coverages and temperatures, the molecules can get out of the regions of low potential. As conccms the influence of the size of the adsorbed species on diffusion, Derouane introduced the concept of floating molecule and supermobfity when the van der Waals radius of the adsorbed molecule is close to the pore radius." No evidence of this behavior has been yet demonstrated. In the present work, we examine systematically the size effect on the diffusivity by varying the size of the adsorbed atoms. The main features of the considered rare Author to whom correspondenceshould be addresscd at Institut de Recherches sur la Catalyse.
0022-3654/92/2096-9417$03.00/0
TABLE I: Main Faturea of Neolq Argon, rad Xenoa Comprnd to MethwO
Neb Ap
Xeb CHP
1.60 1.88 2.16 1.94
20.2 40.0 131.3 16.0
-0.529 -1.028 -1.737 -0.811
-0.280 -1.183 -3.437 -1.802
" ( ~and 4 denote the depth of the potential energy minimum corresponding to the interaction of atom R with an oxygen atom of the zeolitic framework or with another R atom. The equilibrium R-O distance is obtained by adding to the R radius the value taken for the oxygen atom radius (1.52 A). bReference20. CReference8 (%w is given for 3.885 A as equilibrium distance).
gas atoms, neon, argon, and xenon, are collected in Table I, together with those of methane, regarded as a spherical molecule, for comparison. It is worthy to note that, in the rare gas series, the increase in size is accompanied by an increase in mass and in interaction energies, so that pure size effects are difficult to isolate. The considered zeolite, silicalite, presents the advantage for this study in that it is aluminum free, i.e. it does not contain any strong adsorption site of a chemical nature and it has channels of molecular size. Another reason for choosing silicalite was its structural analogy with ZSM-5, a very important molecular sieve and catalyst. The nearly two-dimensional channel network can be seen on the potential maps of Figure 1: the straight channels are parallel to the 0,axis, while the swalled sinusoidal channels are constituted by segments whose axes, parallel to Ox,are slightly shifted one from the other in the 0, direction. The diameter of the channel void space, derived from the potential maps by adding the rare gas atom diameter to the distance between the curves of zero energy, is on the order of 6 A. The size of the intemections ranges from 7 to 9 A. In our calculations, the silicalite structure has been assumed rigid and has been taken from the crystallographic data of the orthorhombic isostructural ZSM-5.'* The unit cell contains 96 silicon and 192 oxygen atoms; the m e t e r s are a = 20.07 A, b = 19.92 A, and c = 13.42 A. The simulations have been performed at four loadings (2,5, and 9 atoms per unit cell (u.c.) and infinite dilution, 0 atom/u.c.) that are small in comparison with the theoretical maximum loading, since the full packing by xenon, the biggest of the considered atoms, can be estimated at about 20 atoms per unit cell. In fact, however, the saturation capacity deduced from the adsorption isotherms corresponds to loadings markedly lower than this maximum value, that is, at 300 K, 12 X e / ~ . c . ' ~ Computatiod Procedure The potential energy has been calculated by using the Lennard-Jones atom-atom model potentials proposed by Kiselev et 0 1992 American Chemical Society
El Amrani et al.
9418 The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 0
-5
-
-10
'5.1 5 E
-35
El ( - 1 6 .
-121
0( - 1 2 .
-81
m
( -8.
-41
ea
(
12
1 4 Z (A)
13
( I ) Straight channel
0, . - I
7
8
9 Z (A)
( b Sinusoidal channel
Figwe 1. Potential map of argon in silicalite: (a) in the mirror plane of a sinusoidal channel 0, = 4.98 A); (b) in the median plane of a straight channel (x = 10 A). The rectangles indicate what has been defined as channel intersection, straight channel and sinusoidal channel, in the analysis of the distribution of the atoms in the channel network (Figures 4-6). Energies are in kl-mol-'.
alea in which the silicalite framework is represented by the oxygen atoms only; as generally done, the silicon atoms are considered screened by oxygen and their contributions to the potential are not taken into account. The energy of a specific adsorbed atom is obtained by summing the contributions of all the atoms, oxygen or other rare gas atoms, belonging to a cube of edge length 28 A and centered on the atom under considerations; this value of the cutoff distance ensures a precision of 1% for the potential energy. By use of a cuttoff cube, rather than a cutoff sphere, the neighbors of a rare gas atom could be identified by comparing the components of the distance vector to half the edge length, which saves from calculating all atom-atom distances. On the other hand the oxygen atoms have been classified in order of increasing x values, and as the distribution along the x axis of the oxygen atoms contained in the unit cell is nearly uniform in silicalite, the oxygen atoms whose x values are contained in a certain range could be quickly identified. With this procedure the calculation of the force acting on a particle is 50% faster, but this advantage is in fact partly lost because the number of particles taken into account is higher in the cube than in the sphere. The distribution of the interaction energy with the framework is visualized on the potential maps of Figure 1 for argon. For neon and xenon very similar maps are obtained, but with different potential ranges: [-6, -21 kl*mol-l for Ne, [-14, -61 for Ar, and [-30, -181 for Xe. As expected, the channels are regions of low potential and the higher potential values are located in the middle of the intersections. By following the minimum energy path on the potential maps, energy barriers of 1.7 and 3.8 kJ*mol-' are found for neon and argon. For xenon two values are obtained following the direction: 11.6 M-mol-' in the sinusoidal channels and 5.1 in the straight channels. These barriers are located at the channel intersections. Details on the variation of the potential as a function of the distance to the wall of the channels are given in Figure 2. We observe that for xenon, the largest atom, the potential hole is uniform, whereas for neon the curve presents two minimia, one near each wall; the energy barrier in the middle of the channel is nevertheless small with respect to the kinetic energy for the considered temperatures and it is not expected that neon sticks to the channel wall. Potential profile without minima, like that for xenon, have been used to define "floating" molecules17and the question is whether xenon achieves supermobility. The MD simulations have been performed in the microcanonical ensemble. Periodic boundary conditions have been used with a box consisting of a certain number of crystallographic unit cells dependins on the loading: one for 0,s. and 9 atoms/u.c. and three for 2 atoms/u.c. The equations of motion have been integrated by using the Verlet algorithm2' with time steps of 5 X lo4 ps. The trajectories were typically of a 125-ps duration with storage of data every 100 steps. The temperatures were calculated at the end of the simulations from the mean kinetic energy. Results corresponding to very close temperatures were simply averaged.
1 -Ne _ - _A r
-30 -35
xe 8
9
10
11
12
13
14
1 5 Z (A)
( c ) Channel interrecbon
Figure 2. Variation of the potential energy of neon, argon, and xenon along a direction rpendicular to the cavity walk (a) in the sinusoidal channel (x = 15 y = 4.98 A); (b) in the straight channel (x = 10 A, y = 10 A); (c) in the channel intersection ( x = 10 A, y = 4.98 A).
$
TABLE II:
lad htwpi~ (in w.mrl) of ~ e ,
-OS
Ar, md Xe in Silidte at 306 Ka
0Ju.c. neon
argon xenon
-3.8 -11.8 -27.8
aEd4 2Ju.c. -3.8 -11.9 -28.1
AH*@)
9Ju.c.
-3.8 -12.1 -29.1
-3.8 -11.9 -27.7
-6.3 -14.4 -30.2
Exponent (B)denotes that the corresponding values have been calculated by assuming a Boltzmann distribution for one adsorbed atom (loading tending toward zero). The adsorption enthalpies are given by AH,b - RT. The results given in Tables I1 and I11 for rounded temperatures have been obtained by interpolation between the temperatures of the simulations. The coeffkients of selfdiffusion D have been evaluated by using the Einstein relationship. In practice D is given by a fit of the mean square displacement ( (Ar)2) to the equation2' ((Ar)2) = A ( t ) + B + 6Dt with lim,-= A ( t ) = 0 (1) For N particles ((Ar)2) is calculated as function of time t by the expression N
((Ad2)= (1/N)
n
c c Ir& + t ) - rr(t,)12/n
/ = I 1-1
(2)
where t, defines different time origins taken on the trajectories. For trajectories of 125 ps, t, was chosen to extend from 0 to 115 ps with n = 2300, so that the diffusion coefficients have been determined on a time scale of 10 ps. Decreasing the number of time origins introduced large fluctuations in the variation of ( (Ar)2) with t, due to pax statistics. Actually the motion becomes strictly diffusive after longer time scale, evaluated at 30 ps for argon in silicalite at infinite dilution and 229 K.22 Nevertheless we have verified that relation (l), used in the range 1-10 p, gives a quite reasonable D value (5 X lo4 m 2 d to compare with 4.8 X lo+' m2&, obtained with the very long trajectory). Activation energies for self-diffusion have been obtained by assuming that the diffusion obeys the equation D = A exp(-E*/RT).
The Journal of Physical Chemistry, Vol. 96, No. 23, 1992 9419
Self-Diffusion of Rare Gases in Silicalite TABLE Ilk Self-Diffusion Coefficients (hId dd')8t Different Temperaturea md Actir8th Ewrgies E* for the Diffusion (in
w.mt')'
200K 37.0 (20.5) 14.6 13.6 10.7
300K 54.5 (28.4) 24.4 20.1 15.6
400K
E*
71.1 (33.5) 31.5 24.5 18.8
1.37 0.89 0.67
2JU.C. 5Ju.c. 9Ju.c.
10.2 (4.9) 7.1 5.0 3.7
1.25 1.06 0.84
2.3
2Ju.c. 5Ju.c. 9JU.C.
29.4 (19.5) 14.9 11.5 8.8 11.9 (3.0) 4.6 3.3 2.4
(5) 3 3 3
O/U.C.~
19.9 (12.3) 11.6 8.7 6.6 7.1 (0.8) 2.4 2.0 1.8
2 (2) 3 2 2 4
4 3 1.9
6.5 4.5 2.6
~
neon
O/u.c.6
argon
2JU.C. 5Ju.c. 9Ju.c. OJu.c.6
xenon
(-1
xenonC
0Ju.c. 4Ju.c. 8Ju.c.
0.6 0.7 1.o 1 1.7 1.3
methand
2Ju.c. 4Ju.c. 8JU.C.
2.8 2.5 (3.7) 2.9 (2.8)
6 (13) 7 5 3
Am 2.67
-25
2.56
8.30 4.31 2.06 0.74
6.6 2.8
"In the product Am, m and A represent the atomic weight of the rare gas atom and D exp(E*/RT), respectively. A m is expressed in lo6 m2 *s-1 .g.mol-'. Results obtained with a Maxwell-Boltzmann distribution of velocities; the values in parentheses correspond to simple single atom trajectories with very narrow velocities distribution. CMD simulation (ref 9). Infinite dilution 0Ju.c. has been simulated by turning off sorbatesorbate interactions entirely. The activation energy at 16 Xe/u.c. has been found equal to 2.8 Id-mol-'. dExperimental valuca obtained by NMR (in parentheses) and neutron scattering (ref 25). Activation energy amounts to 4.7 & 0.7 Id-mol-', a value independent of the loading.
The simulations at infiite dilution (0 atom/u.c.), corresponding to systems with only one diffusing atom, have been handled in a specificway. As no energy exchange with the zeolitic framework or other diffusing atoms is taken into account in such calculations, the velocity distribution reflects only the potential energy fluctuations and is very narrow. In order to have a correct Maxwell-Boltzmann distribution, about 30 trajectories of one isolated atom, with temperatures ranging from 10 to 1500 K,have been combined together, with weighting factors selected to give the expected distribution. For the simulations at f d t e occupancies we verified that the velocity distribution is sufficiently broad owing to the collisions between diffusing atoms, though the MaxwellBoltzmann distribution is not perfectly reproduced.
Adsorption Energy and Distribution of the Diifirsig Atoms in the CbinneLS The values of the adsorption energy A& at 300 K,calculated as an average of the potential energy of the atoms along the trajectories, are reported in Table 11. The adsorption enthalpies can be evaluated by using the relation AH* - RT. In the fourth calculated by assuming column are reported values of that the distribution of the adsorbed atoms in the channel network is purely statistical and depends only on the energetic factor by following the Boltzmann law
where i represents 4 X lo5 different positions in a quarter of unit cell. The temperature dependence of Ma& and is given as well as hE,b for 1 atom/u.c., does not in Figure 3. include any adsorbateadsorbate interaction, so that the corresponding enthalpies of adsorption should be compared to the experimental initial isosteric heat of adsorption. The increase in -AEd as a function of loading can be attributed to the interaction between the adsorbed atoms. Very small for neon and argon, it becomes significant for xenon because the interactions of X e X e
-35
-Ne-theo -Ar-theo -Xe-theo 0 Ne-S/uc x Ar-Oluc %{ A Ar-S/uc
-
1 0
-=-
200
400
600
T (K)
Figure 3. Adsorption energy, AE,, of neon, argon, and xenon vs temperature. The markers correspond to values derived from the simulations. The curves refer to AEh(B), calculated by assuming an ideal Boltzmann distribution of the adsorbed atoms in the channels.
'4 *
7 7 0.
Figure 4. Distribution of neon in silicalite at 300 K and for 9 atoms per unit cell. The three parts, channel intersections, straight channels, and sinusoidal channels, are defined in Figure 2. The smooth curves correspond to the 'ideal" Boltzmann distribution and the jagged ones to the simulations.
are stronger and act at larger distances (Table I). The isosteric heat has experimentally been evaluated to be respectively -15 W.mo1-l for argon adsorption23at 77 K and -26.6 Id-mol-' for xenon adsorption24at temperatures ranging from 121 to 296 K. They have been found to be constant for loadings below 20 ato m s / ~ . ~for. argon and below 11 atoms/u.c. for xenon. These values may be compared with ours, calculated for 9 atoms/u.c.: -15.3 kJ.mol-' for argon, obtained by extrapolation to 77 K,and -32 Id.mol-' for xenon at 300 K. In view of the experimental error on the isosteric heat of adsorption, estimated to f5 Idemol-l, the agreement between these results is quite satisfactory, which supports the fact that the model potential parameters used in our simulations are relevant. The distribution of the adsorbed atoms in the channel network is represented in Figures 4-6,for two temperatures and loadings. It is compared to the "ideal" distribution derived from the Boltzmann rule, that is given by the function (4) where xi, yi, are %k are the coordinates of the nodes of a threedimensional grid of approximately 0.1 A stepsize (the exact value is a submultiple of the unit cell parameters). The distribution corresponding to a simulation has been evaluated by using the symmetry operations of the silicalite space group to translate all the points of the trajectory in the same channel parts or intersection, represented in Figure 1. The distribution function is then obtained by dividing the void space into slices about 0.1 A thick, perpendicular to the channel axis, and by counting the number of points located in each one. The distribution is normalized in the same way as the ideal one. The main featum of the ideal curvea of Figum 4 4 are maxima that correspond to the potential holes (Figure 1) and that increase from neon to xenon. The occupancy of the intersection is smaller than that of the channels and i n c " with the temperature. The ideal curves and the ones deduced from the simulations are quite similar. The differences come from the fact that the "ideal" curva do not take into account the existence of energy barriers or the loading. So, at low temperature, the adsorbed atoms can be blocked in potential holes because of energy bamers too large in
9420 The Journal of Physical Chemistry, Vol. 96. No. 23, 1992
I .o
I
0.5-
0
El Amrani et al.
450
i
-at
@)
L
K
-r5
2 Ar/u c.
E
0
0 - 7
-
(C)
I&
-7.5
- *\
-
200 K
05
*
od,
-8
9 Ar/u.c.
io
' Y
-
I
m
2l i
-7.5
I .o
0.50.
e
io
' Y
1
Ilntersection IStralght Channel]
-8.5
1
Sinusoidal Channel
Figure 5. Distribution of argon in silicalite at different temperatures and loadings. For explanations, see Figure 4. 1
7
I.
ol
450 K
c
9
(b) 450 K
0.l a w
Ed,
6
*
io
2 xe/u c
1
' Y
T-----l
-
1
2 3 1000/T
4
5
6
7
--cm -*-e ..+.
7. Cormtcd diffusion cosffcients referred to neon, D-/mN, = Dmlmrr. for three loadings: 0 atom (a). 2 atoms (b), and 9 atoms (c)
there is a larger number of adsorbed atoms than the channels can contain (Figures 5c and 6c). This effect is more pronounced in the case of xenon, the largest rare gas atom. On the contrary, for neon the energy bamers and the occupied volume are small and the distribution is identical to the ideal curve for all temperatures and loadings considered in this work (Figure 4). At higher temperature the distributions approach the theoretical onea for both loadings of argon (Figure 5a,b). For xenon (Figure 6a,b) the intersection is more occupied than in the "ideal" distribution, even at low occupancy; this is not observed at low temperature and 2 atoms/u.c. because the atoms do not often leave the potential wells of the channels.
(C)
250 K
9 Xeluc
(d) 250 K
1
Sinusoidal Channel
t
FIplrc 6. Distribution of xenon in silicalite at d i f f m t temperaturea and loadings. For explanations, see. Figure 4.
comparison with the kinetic energy; this OCCUTS essentially in the sinusoidal channel (Figures 5d and 6c). Nevertheless the w u panty of all channel potential wells would be probably similar if more sorbate atoms were introduced in the simulation. At high loading, the channel intersections are more occupied than is indicated by the single-molecule Boltzmann distribution, because
Self-Diffdon cafficicab, The variation of the diffusion coefficients with temperature and loading is given in Table III; as expected, they increase with temperature and decrease with loading (the minimum for xenon at 2 atom/u.c. is too small to be significant). The activation energiw are given in the next to last column. At M i t e dilution it is seen that the fit of the velocity distribution to MaxwellBoltzmann incram nearly 2-fold the diffusion coefficient values. Thec4nmtim spochlly important for xenon that can be "trapped" in potential wells at low temperatures, results in a sizable lower of the activation energy. The diffusivity in the rare gases series decreases from neon to xenon. From the comparison with experimental values,2s we observe that the diffusion of argon is of the same order as that of methane; the larger mass of aGon is compensated by its smaller size. Good agreement is obtained for xenon with the MD simulationsof June et al.? but with m e w h a t different values at Mite dilution. In actual fact, considering that the velocity is inversely proportional to the square root of the mass for a given temperature, the diffusion coefficients scale as the reciprocal of the mass of the dilhing In order toremove the influence of the maas, we have calculated corrected diffusion coefficients Ow, = Dm. The values of D,, versus temperature are reported in Figure 7
+.
Self-Diffusionof Rare Gases in Silicalite for three loadings. The slope gf the lines corresponds to the activation energies. Whereas the order of magnitude of the D coefficients is well separated for thedhree atoms, the Dm coefficients range in the same domain. Nevertheless if the mass were the dominating factor for the diffusion, the three curves = f(l/‘r? would be identical. Other factors besides the mass act on the diffusion: (i) the values of the energy barriers (related to the activation energies) that are different at small loading (Figure 7a,b); (ii) the steric hindrance inside the cavities that can explain that the D,, values for the three atoms are not equal at high loadings despite similar activation energies (Figure 7c). The differences between the D,, values for argon and neon can be exclusively attributed to factor i. For xenon, factor ii plays already a part at infinite dilution since the straight line corresponding to xenon on Figure 7a does not cross the ordinate axis at the same point as for argon and neon. The activation energies for 0 atom/u.c. are similar to the height of the energy barriers appearing along the path of minimal energy established from the potential maps (see above). For xenon, the comparison concerns the barrier along the skaight channel, which is consistent with the contribution of this direction to the total diffusion coefficient: D,/D = 2156, DJD = 73%, D,/D = 6% (these contributions are about the same for argon and neon, 3596, 55%, and 5% in the three directions respectively). The decrease of the activation energies with the loading is due to the additional energy resulting from the interaction between the diffusing atoms. This variation is particularly marked for xenon and leads to a singular behavior for this atom. At small loading and low temperatures (under 400 K), the diffusion of xenon is slowed down because of the large energy barriers. But at high temperatures these barriers are easily overcome and D,, is higher than for neon or argon. In this case (small loading and high temperature) the xenon atom can be said to achieve supermobility. On the contrary, at high loading the motions of xenon atoms are hindered by the high occupancy of the void space and D,, is slightly lower than for neon or argon though the activation energies are similar. The limiting values of D,, for T,, are reported in the Am column of Table 111. By examination of the rare gas series, it appears clearly that xenon, a “floating molecule” with respect to the size, demonstrates the supermobility concept, but only in very restrictive conditions: high temperatures, low occupancies, and similar mass in the series. These requirements are not fulfilled in reality and the diffusivity decreases from neon to xenon.
Conclusion The systematic study of the diffusion of rare gas atoms of increasing size, mass, and interaction energy displays that all these factors influence the diffusivity. For the considered set the most important factor is the mass. This will not necessarily be the case if we compare systems, like argon and methane, for which the mass and size do not vary in the same direction. The diffusion coefficient obtained for neon, the lightest of the considered series, at low loading, can be considered as the largest value that can be reached in silicalite, i.e. 4 X lo-*m 2 d at r c ” temperature.
The Journal of Physical Chemistry, Vol. 96, No. 23, I992 9421 The large interaction energy and size of xenon lead to a peculiar behavior of this atom that permits clarification of the concept of floating molecule and supermobility. When the size of the molecules increases, approaching that of the microporous cavities, this is generally accompanied by an increase of the mass and of the interaction with the framework. This larger interaction does not just result in the decrease of the potential energy but is also accompanied by an increase of the energy barriers related to the corrugation of the inner surface of the cavities. Consequently the molecule can float only at sufficiently high temperatures to overcome these barriers. Furthermore, as for xenon, the floating motion is not necessarily translated into faster diffusion (supermobility) because of the mass increase.
Refem~ceaa d Notes (1) Ruthven, D. M. Principles of Adsorption and Adsorption Processes; Wiley: New York, 1984. (2) Yashonath, S.;Demmtk, P.; Klein, M. L. Chem. Phys. Lett. 1988,153, 551. (3) Leherte, L.; Lie, G. C.; Swamy, K. N.; Clementi, E.; Derouane, E. G.; Andre, J. M.Chem. Phys. Lett. 1988, 145,237. (4) Cohen De Lara, E.; Kahn, R.; Goulay, A. M. J. Chem. Phys. 1989, 90,7482. ( 5 ) den Ouden, C. J. J.; Smit, B.; Wielers, A. F. H.; Jackson, R. A.; Nowak, A. K. Mol. Simulation 1989, 4, 121. (6) Pickett, S.D.; Nowak, A. K.; Thomas, J. M.; Peterson, B. K.; Swift, J. F. P.; Chettham, A. K.; de Ouden, C. J. J.; Smit, B.;Post, M. F. M. J. Phys. Chem. 1990,94, 1233. (7) June, R. L.; Bell, A. T.; Theadorou, D. N. J. Phys. Chem. 1990,94, 1508. (8) Demontis, P.; Fob,E. S.;Suffriti, G. B.; Quartieri, S.J. Phys. Chem. 1990,94, 4331. (9) June, R. L.; Bell, A. T.; Tbeodorou, D. N. J. Phys. Chem. 1990,94, 8232. (10) Nowak, A. K.; den Oudens, C. J. J.; Pickett, S. D.; Smit, B.; Cheetham, A. K.; Post, M. F. M.; Thomas, J. M. J. Phys. Chem. 1991,95, 848. (11) Titiloye, J. 0.;Parker, S.C.; Stone, F. S.;Catlow, C. R. A. J. Phys. Chem. 1991, 95,4038. (12) Catlow, C. R. A.; Freeman, C. M.; Vessal, B.; Tomlinson, S. M.; Leslie, M. J. Chem. Soc., Faraday Trans, 1991,87, 1947. (13) Goodbody, S.J.; Watanabe, K.;MacGowan, D.; Walton, J. P. R. B.; Quirke, N. J. Chem. Soc., Faraday Trans, 1991, 87, 1951. (14) Leherte, L.; Andre, J. M.; Derouane, E. G.; Vercauteren, D. P. J. Chem. Soc., Faraday Trans. 1991,87, 1959. (15) de Boer, J. H. The Dynamical Character of Adsorption, 2nd ed.; Oxford University Press: Oxford, 1968. (16) Everett, D. G.; Powl, J. C. J. Chem. SOC.,Faraday Trans. I 1976, 702, 619. (17) Derouane, E. G. Chem. Phys. Lett. 1987,142,200. Derouane, E. G.; Andrg, J. M.; Lucas, A. A. J. Catal. 1988, 110, 58. (18) Olson, D. H.; Kokotailo, G. T.; Lawton, S.L. J. Phys. Chem. 1981, 85, 2238. (19) Springuel-Huet, M. A. ThCe, P. et M. Curie (Paris VI), 1988. (20) Kiselev, A. V.; Lopatkin, A. A.; Sbulga, A. A. Zeolites 1985,5,261. (21) Fincham, D.; Heyes, D. M.Adv. Chem. Phys. 1985, 493. (22) El Amrani, S.;Kolb, M.J. Chem. Phys. 1992, 96, 4857. (23) Muller, U.; Reichert, H.; Robens, E.;Unger, K. K.; Grillet, Y.; Roquerol, F.; Rouquerol, J.; Pan, Dongfeng; Mersmann, A. Fresenius Z . AMI. Chem. 1989.333.433. (24) BUlow, M.’; Hirtel, U.; Miller, U.; Unger, K. K. Ber. Bunsenges. Phys. Chem. 1990,94,74. (25) Jobic, H.; BSe, M.; Caro, J.; Biilow, M.; KPrger, J. J. Chem. Soc., Faraday Trans. I 1989,85,4201.
