J. Phys. Chem. 1994,98, 4666-4672
4666
Analysis of 129Xe Chemical Shifts in Zeolites from Molecular Dynamics Calculations F. Vign6-Maeder Institut de Recherches sur la Catalyse, 2 av. Albert Einstein, 69626 Villeurbanne CCdex, France, and Ecole Normale SupCrieure de Lyon, 46 allCe d7talie, 69361 Lyon CCdex 07, France Received: December 6. 1993" The qualitative dependence on cavity size of 129XeNMR chemical shifts for xenon sorbed in zeolites is usually interpreted in terms of collisions between xenon and cavity walls. Molecular dynamics simulation at infinite dilution is a powerful tool to give insight into the collision effect. Contact time and the number of collisions with oxygen atoms of the framework are derived from MD calculations in pure siliceous zeolites of various cavity size (Y zeolite, silicalite, and mordenite) a t different temperatures. Correlation between chemical shifts and the number of binary collisions is found. The occurrence of two signals in mordenite spectra cannot be interpreted by the model of pure siliceous framework. It is assumed a certain number of side pockets are blocked, possibly by cations. The ratio of accessible pockets, derived from N M R spectra, increases with temperature from 0.015% to 12% in N a mordenite. The diffusion coefficient with the blockage of the pockets taken into account m 2 d a t 300 K. has been determined to be 4.3
Introduction The chemical shift of Iz9Xehas been shown to bevery sensitive to its physical or chemical environment. In pure gas phase or gaseous mixtures, strong dependence on density has been observed and has been essentially related to binary co1lisions.l For xenon atoms sorbed in microporous solids such as clathrates? zeolites,Ss and polymers,6 IZ9XeN M R spectra have been analyzed in terms of pore size, structural defects, adsorption sites, and concentration of other species, cations, or metallic clusters. In the last few years Iz9Xe N M R has been extensively employed as a useful technique to characterize porous materials. Its applications and limitations have been recently r e ~ i e w e d . ~ The relation of the chemical shift 6 to zeolites structures has been clarified by Fraissard et al. by expanding 6 as the sum of terms each of which corresponds to a definite perturbation affecting the xenon atom8
6 = 6,
+ 6, +, ,a + 6, + ,6
where 60 is the reference. 6~ and 6~ are related to the presence of exchangeable cations and paramagnetic species, respectively. For zeolites exchanged with small univalent cations like H+, Li+, and Na+, 6~ is zero and BE is very small (a few parts per million in Y zeolite,g about 10 ppm in H-ZSM-5I0). Dealumination could be a way to diminish the cation content, Le. the 6~ contribution, but care should be taken because the pore structure can be considerably affected during the 6xe represents the Xe-Xe interactions and is proportional to the xenon density inside the zeolite when only two body collisions are significant. 6s arises from collisions between xenon and the inner surface of the cavities and is obtained by extrapolation of the 6-60 values to vanishing xenon loading (6xCtends toward zero and b~ is neglected). 6s is the term that contains the dependence of the chemical shift of sorbed xenon on the structure of the void space. It is in fact very sensitive to the zeolite structure: it generally increases as the pore size decreases, ranging from 60 ppm for faujasite to 100 ppm for ZSM-5 and 220 ppm for mordenite side pockets, at room temperature. But a simple correlation between 6s and pore dimensions seems difficult to obtains7 The linear dependence on the void space available for the xenon atom, suggested by experimental data for small pores, cannot be applied to zeolites with larger pores.4 Analysis of 6, based on model calculations of 0
Abstract published in Aduance ACS Abstrucrs, April 1, 1994.
xenon-zeolite interaction energy distinguishes two different behaviors: xenon is solidlike in small trapping sites and gaslike in larger adsorption sites.4 Correlations have also been proposed with the mean free path of a single Xe atom within modeled zeolite structures,I2 with the surface area to volume ratio13 or with the surface curvature of the cavities.14 The influence of temperature has also been analyzed" by averaging chemical shifts of xenon adsorbed on the surface or moving in the free space. But these models do not seem suitable for the full range of pore dimensions and shapes studied in the literature. A more fundamental approach has been considered by using ab initio calculations of 39Arshielding as a model for xenon trapped in zeolite cages.15 In the present work, an attempt is made to relate xenon-zeolite collisions to some features of 6, by using molecular dynamics simulations a t infinite dilution. Y zeolite and silicalite are considered as porous solids with large and small cavities, respectively. Mordenite is studied as an example of zeolite containing very small cavities, the so-called side pockets, and also as a case of solid providing two possible adsorption zones, i.e. the side pockets and the larger main channel. Simulations of adsorption of xenon in zeolites have been recently performed in silicalite16-18 and NaY-zeolite,Igbut relations with 129XeNMR spectra have not been considered.
Model Representation and Molecular Dynamics Calculations The interaction energy between the sorbate xenon and the oxygen atoms of the zeolite lattice has been calculated by using the Lennard-Jones atom-atom potential proposed by Kiselev et a1.20 As generally done, the silicon atoms are considered screened by oxygen and their contributions to the potential energy are not explicitly taken into account. We consider only zeolites without aluminum. So no cationic interactions are introduced. The M D calculations have been carried out with rigid frameworks whose geometrical characteristics are reported in Table 1. The void space available for xenon is the usual void space to which a part of the van der Waals volume of the xenon atom has been substracted. It has been evaluated as the space where xenon has negative potential energy when it is put at the nodes of a grid of approximately 0.02 A side length. The cavity shape for the three zeolites is visualized in the potential maps of Figure 1, where all the contour lines correspond to negative potential energy. Modeling the infinite-dilution state with the assumption of a rigid zeolite lattice necessitates numerous single-molecule runs
0022-3654/94/2098-4666%04.50/0 0 1994 American Chemical Society
Iz9XeChemical Shifts in Zeolites
The Journal of Physical Chemistry, Vol. 98, No. 17, 1994 4661
TABLE 1: Geometrical Features of Zeolite Frameworks faujasite
silicaliteb
(U.C.)
si1920384 a=b=c = 24.85 A
volume (AS) void spaced volume (A3)
cage: 345.43
si960192
a = 20.07 A b = 19.92 A c = 13.42 A ' / ~ U . C .1918.2 : I/~u.c.:1341.3
unit cell
( 1 1 8 U.C.1
surface (A2)
cage: 271.7
pore dimensions (A) 6 13.0
2
mordenitee SGOW
a = 18.13 A
b = 20.49 A c = 7.52 A '/z ~ c . 1396.8 : ('/4 U.C.) (I/z u . 4 channels: 74.47 channel: 88.68 intersection: 42.7 pocket: 26.12 channels: 125.0 channel: 74.19 intersection: 25.7 pocket: 129.9 channel: 6 8. channels: $J 7.0 pocket: $J 5.5
Reference 21. Reference 22. e Reference 23. The void space is here defined as the space accessible to the center of mass of the xenon atom. a
20
15
-
63:
10
-
5-
TABLE 2 Diffusion Coefficients (in mZ.s-l) at Different Temperatures and Activation Energies for the Diffusion (in kJmol-1) ~~
faujasite
T (K) . . 100 150 200 250 300 350 400 450
E*
silicalite U
0.79 2.9 5.1 7.6 9.4 10.9 12.5 12.7 3.0
b
c
0.5 3.5 8.2 12.5 14.4 4.1
1.2 2.4 3.6 4.9 6.3 7.1 5.4
1.0 4.0 6.5 6.6
mordenite
d
e
1.7 2.9 4.8 7.3 9.1 10.8 12.3 3.9
0.7 1.1 2.2 4.3 4.9 6.1 7.5 5
f
2o z
0.2 0.5 1.1 2.0 18.0
Reference 19 (loading lXe/cage). D values calculated by interpolation between the values given in this reference. The values yet given in ref 18 (200,300, and 400 K) ought to be divided by 2. Reference 16 (infinite dilution). Exclusively in the main channel. Including the pocket trajectories in a proportion derived from the Xe NMR spectra of Na mordenite @paket &,*,,el of Table 4).fIncluding the pocket trajectories in the proportion given by the Boltzmann distribution (POof Table 4).
+
in order to ensure sufficient sampling of phase space. A computationally more efficient way is to consider a great number of sorbate molecules without interaction between them.16 To reduce the number of calculations, we have combined 30-50 trajectories of one isolated xenon atom, with weighting factors selected to give the correct Maxwell-Boltzmann velocity distribution at the considered temperature. This procedure has previously been used to study the diffusion of rate gases in silicalite.18 It gives diffusion coefficientsand activation energies that compare very well with the results of full simulations at infinite dilution in silicaliteI6 or at low loading in NaY zeolite19 (Table 2). The trajectory calculations have been carried out in the microcanonical ensemble with a time step of 0.005 ps. The trajectory duration was of 2000 ps. Mean temperatures ranged from 2 to2000K. Startingpoints wereinregions ofdeeppotential energy. The diffusion coefficients have been derived by using the Einstein relationship. The trajectories have been averaged so as to obtain eight mean temperatures between 100 and 450 K. In the case of mordenite, the parts of the trajectories inside the main channels and the side pockets have been treated separately, so that the xenon-zeolite interactions can be independently analyzed in both cavities. Analysis of the Interaction of Sorbed Xenon with the Cavity Wall Radial distribution functions g(r) for pairs of adsorbate and zeolite oxygen atoms are calculated as
10
15
Y
20
Figure 1. Potential maps of xenon in (a) Y zeolite (plane containing the center of two supercages: x = 3a/8), (b) silicalite (median plane of straight channel: x = a/2), (c) mordenite (mirror plane: x = a/2); (d) mordenite with three sodium cations (sites I: a / 2 , 0 , 0 and a/2, b, c/2. Site IV: 0.4727a, 0.6831b, 0.8663~). Dimensions of the maps: 6 X c. Distances in A. Energies in ldmol-I; 2 kJmol-l between two next contour lines.
where n(r) is the number of oxygen atoms in a spherical shell around xenon, of inner radius r - Sr f 2 and outer radius r + Srf 2, averaged over the whole trajectory. V(r) is the volume of this spherical shell of thickness Sr, and N is the number of oxygen atoms contained in the crystallographic unit cell of volume V. The graphs of g(r) as function of r are shown in Figure 2 at temperatures of 150and 450 K. At low temperatures they present well-marked peaks. The first onecorresponds to X e - 0 distances, denoted RlSomsx, of 3.6 A for Y zeolite, 3.7 A for the mordenite channel, 3.8 A for silicalite, and 4.1 A for the mordenite side pocket. These values are close to the sum of the van der Waals
4668
VignkMaeder
The Journal of Physical Chemistry. Vol. 98, No. 17, 1994 0 Y zeolite mordenite channel 1;1 silicalite 0 mordenite pocket
g(r), 3
1
;:
mordenite pocket
4
6
8
10
12 r
yo]
(A)
silicalite
1
2
3
4
5
6 7
8
9 1011
flax
Figure3. Timespent by xenon inproximitytosimultanwuslyno.oxygen atoms, as function of no,, at 150 K. Proximity is defined by distances lower than &150, corresponding to the first peak in the distribution functions of Figure 2. Time in percent of the trajectory duration.
3-
4
6
8
10
12 r
(A)
mordenite channel 2-
TABLE 3 Comparison of Experimental Values of Xenon Chemical Shifts (in ppm) with Results Obtained from (1) the Contact Time T (in percent of the Trajectory Duration), 4 = 1.057; ( 2 ) the Mean Number of Binary Interactions, Ne 4 = ZON,; ( 3 ) Dependence with r" and Integration from 0 to m; (4) Dependence with +and Integration from 0 to a Cutoff Radius calculated ~~
,wlite
I50
86(144K)'C R7 - (173- K V 61,'59,b5SC 95(160K)' 85 (173 K)' 118.n100d 107(144K)' 103 (I73 K)b 10Zb 209 (I60 KQ 220 (173 K)' 216,'26Sd \-
mordenite (channel) 4
6
8
IO
1 2 r (A)
Y zeolite
silicate mordenite (pocket)
300 I50 300 150 300 150 300
101
83
40, 16.5
84
91 103
63 94
34, 16.0 48,22.5
64 99
~~I
96 73 IO4 105
44,23.4 80 57.30.0 105
103 97 56,29.7 103 I05 144 (21or) . . 72.35.1 210 105
148(21@) 74.34.4 217
Reference4. Reference 11. Reference 24. Reference 26. e Reference 5. lCalculated with & = 29 No.I Second values correspond to integration from r = 4 A to -.
2
4
6
8
IO
12r(A)
Figure 2. Distribution function of the X 4 distances: (-) at I50 K (-1 at 450 K. radii of xenon and oxygen (3.68 A), but it is somewhat surprising that they increase as the cavity size decreases. This can be understood in relation to the potential energy distribution inside thecavities (Figure 1). In the narrow mordenite side pocket the potential energy is minimal in the middle of the cavity, where an adsorbed atom interacts to the same extent with all oxygen atoms building the cavity wall. On the contrary, in the large Y zeolite cavity, a sorbate atom optimizes its position with respect to only a few atoms of the wall, the other ones being t w far away. This is exemplified by the number of oxygen atoms the sorbed xenon comes simultaneously near, at low temperature. In Figure 3 is reported the time during which xenon is at distances lower than Rtso,., from one or more oxygen atoms, as a function of the number ofoxygenatomsbeing simultaneouslywithinthisdistance range. It isohservedtbatatlowtemperaturesorhatexenonspends a large time in the vicinity of two oxygen atoms in Y zeolite, two to three in the mordenite channel, five in silicalite, and nine to ten in the mordenite side pocket. At high temperature (Figure 2), peaks in the radial distribution functions are only observed
for mordenite side pockets and, to a lesser extent, for silicalite. Thisimplies that thexenonatomisnotany morelocalized,except in the smallest cavities. The radial distribution functions as well asthepotentialmapsunderscorethe fact thatsorbedxenonmoves in a strongly varying potential at small distances from the walls and clearly differs from a gaslike molecule constrained in a box. Correlation with the 6, Term of the Chemical Shift Several parameters related to the interaction of the sorbed xenonwith thecavitywall bavebeenderivedfrom thesimulations and will be compared with experimental 6, values (Table 3). As reference for our model of purely siliceous Y zeolite, we take 6, values obtained for Na-Y zeolite,'J1 as it has been shown that the interaction with Na+ cations must be weak at rmm temperature9 as well as at 144 K.24 For silicalite, experimental data have been reported only at 144 K .' At r r " temperature, it has been demonstrated"." that the xenon chemical shift in H-ZSMS presents greater sensitivity to aluminum content than in Y zeolite, probably due to the smaller size of the pores. The 6, values given at 295 K in H-ZSM5 have been extrapolated to zero A1 content in order to obtain the value in silicalite. The 6, values at other temperatures have been obtained for H-ZSMS with sufficiently high Si/AI ratios to be accepted as values for pure silicalite." The spectra for mordenite depend markedly on
l29Xe Chemical Shifts in Zeolites
’I
The Journal of Physical Chemistry, Vol. 98, No. 17, 1994 4669
6s (PPm) -100
- t r
A
- - &L - - -
(d’)
200
-90
- - - mordenite channel - - silicalite -mordenite pocket
-80
100 200 300 400 T(K) Figure 4. Contact time versus temperature. Contact is defined by at least one distance Xe-0 lower than 4.0 A. Right scale in ppm: 6s = k~ with k fitted tosilicalite experimentalvalues ( k = 1.05). Time in percent
of the trajectory duration. the nature of the cations. There can be one or two signals, depending on the cations and the temperature range.2~~.26,~~ Two signals are observed for Na-Z whatever the temperature range. They coalesce above different temperatures for H-Z or the dealuminated sample. The higher chemical shifts of Na-Z spectra do not vary with the xenon loading and so seem to be characteristic of xenon sorbed in side pockets. On the contrary, the lower chemical shift signals in the H-Z or Na-Z spectra are interpreted as average values corresponding to the rapid exchange between the main channel and the side pockets. Therefore, the values related to the pure main channel are only available at low temperature, a t which exchange between both adsorption sites is negligible. Thechemical shift ofsorbatexenon is attributed to thedistortion of the electron cloud when in contact with the wall of the cavity. Correlation with the 6, term of the chemical shift of sorbed xenon is treated in this work by looking for some relation with two parameters derived from the trajectories: the contact time of xenon atom on the inner surface of the cavities and the number of binary interactions with the oxygen atoms of the cavity walls. ContactTime. The assertion that the value of 6, should depend on 7, the amount of time the xenon atom spends in contact with the surface, is first examined. We consider the xenon atom being “in contact with the surface” as long as it is at a specific Xe-0 distance, R,, from at least one oxygen atom. The value of R, should be selected in such a way that 7 , like a,, increases as the cavity size decreases, especially at low temperature, for which 7 is very sensitive to the R, value. The number of suitable values for R, is in fact very limited. Due to the behavior of xenon explained above, 7 in the mordenite side pocket a t low temperature becomes smaller than in the other cavities when R, is lower than 3.9 A. On the other hand, for R, higher than 4.1 A, the 7 values are leveled at 100% at low temperature, whatever the cavity size. The value of 4.0A for R, appears to be a compromise. It yields the contact times reported in Figure 4versus temperature. Though the experimental variation of 6, with temperature is roughly reproduced by 7, the contact times for the various cavity sizes do not sufficiently differ to be correlated with 6, through a simple relationship. In Table 3, values of 6 , are calculated by assuming a linear dependence between 7 and 6,, fitted with silicalite results. The values of 6, obtained in this way for mordenite side pockets are too small, and those obtained for Y zeolite are too large. This leads to the conclusion that 6, is not simply dependent on the time of contact with the cavity wall, as defined above. Number of Binary Interactions. In order to take into account the atomic structure of the wall, we assume 6s can be expressed
=
01 0 0
200
300
400
T
(K)
Figure 5. Chemical shifts calculated from the mean number of binary interactions; 6s = 20 Nc (lines: (a) Y zeolites, (b) mordenite channel, (c) silicalite, (d) mordenite pockets), compared to experimental values: ( 0 )Y zeolithe: (e) silicalite,ll (A) and (A) mordenite.‘ Curve (d’) corresponds to 6s = 29 NEfor mordenite pockets.
as a sum of xenon-oxygen pair contributions, depending only on the interatomic distance.
(3) where ii and ii, denote the position of xenon and oxygen atoms, respectively. Thus 6s can be e v a l ~ a t e d as 2 ~the ensemble average by using the above pair distribution function g(r) (2) with lii ai(= r
We first assume the pair contribution 6so is independent of r below a certain distance R, and is zero above. It takes the very simple form 6,’(r)
= 6,’
62(r) = 0
when R, L r when R,
(5)
