9824
J. Phys. Chem. 1996, 100, 9824-9833
Comparison of the
129Xe
NMR Chemical Shift with Simulation in Zeolite Y
Vishwas Gupta, H. T. Davis, and Alon V. McCormick* Department of Chemical Engineering and Material Science, UniVersity of Minnesota, 421 Washington AVenue SE, Minneapolis, Minnesota 55455 ReceiVed: NoVember 28, 1995; In Final Form: March 27, 1996X
We report quantitative agreement between Monte Carlo simulation and the experimental NMR chemical shift of 129Xe adsorbed in the supercages of zeolite Y. This agreement supports previous assertions, originating from Ripmeester and Fraissard, that the Xe shift can in principle provide a sensitive measure of the structure imposed on Xe by the three-dimensional potential field provided by the crystal structure of the zeolite. Up to a loading of 7 Xe/cage at 300 K, we verify that the linear rise of shift with loading is due solely to Xe-Xe interaction. We also find excellent agreement at 144 K between simulation and the nonlinear experimental data of Cheung et al. The nonlinear dependence of shift on loading arises both from repulsive Xe-Xe and from repulsive Xe-O interactions. Finally we verify that the effect of temperature on the shift at zero loading can be related to the change of Xe-O pair correlation function at short separations.
1. Introduction A detailed and quantitative understanding of the behavior of simple probe adsorbates (e.g., xenon and methane) in microporous materials is a first step toward general theories of adsorption and diffusion in these materials. Recent advances in molecular simulation6,7 and 129Xe NMR1-4,8,9 lead us to consider as a prototype the behavior of xenon in zeolite Y. We quantitatively interpret the functional behavior of the 129Xe NMR chemical shift with changing loading and temperature. In the last decade many authors have discussed the potential of 129Xe NMR in the characterization of the zeolitic pore space.1-4,8-12 As xenon is monatomic with a large polarizability and a nuclear spin quantum number of 1/2, any distortion of the spherical electronic cloud produces large perturbations in the NMR chemical shift.13 The sensitivity of the 129Xe chemical shift to its environment has been exploited to study Xe in clathrate hydrates,14 polymer solutions15 and zeolite micropores.8-12,16-19 In zeolites the 129Xe chemical shift depends on the structure, chemistry, temperature, and loading. In many cases Xe explores its various possible sites so quickly that only one averaged shift is measured. It has usually been assumed that in the absence of highly polarizable cations the various contributions to the average chemical shift δ can be decomposed into additive terms: 8,9
δ ) δ0 + δs(T,i) + δXe-Xe(T,i)FXe
(1)
where δ0 is the shift of the reference signal, T is the temperature, i denotes the zeolite type, and FXe is the pore density of Xe. The effect of the zeolite structure is codified in the quantity δs, which is usually assumed invariant with loading but is a function of zeolite structure and of temperature. The contribution to the chemical shift by increasing Xe loading is usually assumed (and often found) to be linear at low loadings, so it is expressed by the term δXe-XeFXe (if Henry’s law applies, it can be expressed as linear in pressure). At high loadings, though, the shift typically shows an increasing slope with loading.10,16 Significant progress has been made in characterizing the zeolite in terms of the 129Xe chemical shift, and there is a good qualitative understanding of the effect of loading and X
Abstract published in AdVance ACS Abstracts, May 15, 1996.
S0022-3654(95)03508-8 CCC: $12.00
temperature.3,8-11 For example, Demarquay and Fraissard11 showed a correlation between the zero loading chemical shift (δs) with the dimension of the void space in the zeolite. Johnson and Griffiths12 argued for a correlation between δs and the surface to volume ratio of the pore. Ripmeester and Ratcliffe have suggested3 that the change in shift with inverse temperature could be a measure of the pore space available to the Xe atom. To obtain a quantitative interpretation of the experimental results and to learn to exploit the Xe shift in complex circumstances (e.g., with coadsorption), one would like to relate the shift not only to average density and pore size but also to detailed features of the Xe density distribution function. Recently Jameson et al.20-23 have achieved very good comparison between calculated and experimental shifts for Xe in NaA using grand canonical ensemble simulations with shielding functions for Xe derived from ab initio quantum mechanical calculations of 39Ar in the presence of various atoms. Their model provides the first quantitative interpretation of the 129Xe chemical shift in zeolite A. Although no such difficulties were reported in ref 22 Nivarthi et al.24 have found that excess polarization results when using standard parameters for the Na cation in cases where the XeNa distance is small. Moreover in the presence of cations, the framework oxygens carry partial negative charges and the polarization due to them has to be accounted for. Hence we restrict ourselves to siliceous zeolite Y. The pore network of zeolite Y consists of large cavities or supercages (Figure 1) roughly spherical in shape with a diameter of ∼13 Å.25 Each supercage is connected to four others tetrahedrally with connecting windows of ∼7.5 Å diameter. There have been several reported simulations of Xe in Y. Using molecular dynamics simulations, Vigne-Maeder26 studied the relationship between the number of collisions of Xe with framework oxygen atoms and the zero loading chemical shift in zeolite Y and silicalite. Yashonath and Santikary27 carried out molecular dynamic studies of Xe diffusion in NaY, and Woods and Rowlinson28 carried out grand canonical simulation of Xe in Y to study adsorption isotherms. In this paper we relate the experimental chemical shift dependence on Xe loading and temperature to the results of Monte Carlo simulation of xenon in zeolite Y. We use the canonical ensemble since we are interested in simulating situations with known average loading, but we will take care © 1996 American Chemical Society
129Xe
NMR Chemical Shift in Zeolite Y
J. Phys. Chem., Vol. 100, No. 23, 1996 9825 TABLE 1: Intermolecular Potential Parameters for Guest-Guest and Guest-Zeolite Interactions
Figure 1. A wire frame model of a supercage of zeolite Y.
to use a large enough system to fairly represent fluctuations in cage occupancies. We do not undertake ab initio calculations of the shielding functions since our aim is to mainly understand the complex interplay of various interactions in determining the 129Xe chemical shift. The variations of chemical shift with Xe loading and temperature are rationalized by the interaction between the Xe-Xe pairs and Xe-O pairs. We seek to confirm whether in Y it is rigorous to decompose the shift into contributions from each type of pair and whether at low loading it is reasonable to assume δs(T,i) and δXe-Xe(T,i) as constant. At high pore loading we will show that both δs(T,i) and δXe-Xe(T,i) become dependent on the Xe density. Using a simple Drude model for chemical shift,20,29,30 with the shift behavior in the gas phase, we calculate the expected density dependence of shift in zeolite Y and find that there is good quantitative agreement with the experimental results. 2. Experimental Method Zeolite Y was obtained from Valfor in the proton-exchanged form with a Si/Al ratio of 160. Xenon gas was obtained from Alpha products with a purity of 99.999% and at natural 129Xe isotope abundance (26%). A weighed amount of the loosely packed zeolite sample was heated in a NMR tube for 24 h at 350 °C under a dynamic vacuum of 10-6 atm to remove water and adsorbed species. For low-loading samples, adsorption at 300 K was measured volumetrically by the fall of pressure of the gas in a known volume. High-loading samples were prepared using the following procedure. A known amount of gas was condensed and frozen inside a thick NMR tube, and then the tube was flame sealed. After equilibration at room temperature, the loading was determined by integrating the NMR signal and calibrating with the low-loading samples. The gas signal obtained in the NMR experiments gives the pressure, since the gas shift is known to depend on pressure.31 The 129Xe NMR experiments were performed on a Varian VXR-500 spectrometer operating at 139.267 MHz. The transverse relaxation time of the adsorbed Xe was found to be 2-4 s, and a relaxation delay of 5 times the relaxation time was used. All chemical shifts are referred to a external standard of Xe gas at 0.92 atm. 3. Simulation Method Canonical ensemble Monte Carlo simulations32 are performed on a system of eight supercages (one unit cell), fixing the total number of Xe atoms and the temperature. The occupancy in any given cage can fluctuate. Periodic boundary conditions were used to eliminate boundary effects.32
atom
C (103 kJ/(mol Å6))
B (106 kJ/(mol Å12))
guest-guest (Xe-Xe) guest-zeolite (Xe-O)
34.913 8.05
165.84 10.84
Initial positions of the adsorbates are assigned randomly with a constraint that we avoid initial placement outside the supercages. The potential due to adsorbate-zeolite and adsorbateadsorbate interaction is calculated, and randomly one of the adsorbates is chosen and translated. The distances of the translation in the three directions are chosen randomly from 0 to an upper limit d, and d is modified every 1000 steps to obtain a translation acceptance ratio of one-half. The energy of the system is recalculated, and for a step difference in potential energy of ∆E, the new state is accepted with a probability Π given by:
Π ) min{1, exp(-∆E/kT)}
(2)
The ensemble averages of potential energy, density distribution, and pair correlation functions are calculated over all states thus generated (except the first 10% which were discarded to remove any bias toward the initial condition). The number of translation steps attempted in a run was kept at 50 000 per Xe atom. A unit cell of NaY has the composition NaxAlxSi192-xO384, where x is the number of aluminum atoms per unit cell. In our experiment we use the proton-exchanged form of Y with a Si/ Al ratio of 160, for which there is only 1 proton per unit cell (per 8 supercages). In our simulations we neglect this proton and the associated aluminum, so we consider only purely siliceous zeolite with no charge on the framework. This allows the simplification that only Xe-Xe and Xe-O interactions are considered. The Xe-zeolite potential employed here is the one proposed by Kiselev and Du.33 The interaction is modeled as a sum of pairwise atom-atom potentials. The pair potential has a Lennard-Jones 6-12 form:
ΦXe-O(R) )
BXe-O 12
-
R
CXe-O R6
(3)
The interactions between the silicon and xenon are taken to be zero, as the close approach of xenon atoms to silicon is prevented by the oxygens.34,35 The zeolite framework was assumed to be rigid, and the crystallographic data of Fitch et al.36 for the oxygen positions were used. The Xe-Xe interactions are also taken to be of the Lennard-Jones form
ΦXe-Xe(R) )
BXe-Xe 12
R
-
CXe-Xe R6
(4)
The values of the constants are provided in Table 1. To simulate the variable temperature behavior of Xe at vanishing loading, we carry out the Monte Carlo simulation with a number of sorbate molecules with the sorbate-sorbate interactions turned off. This allows a computationally efficient way of sampling the configuration space and is equal to averaging several single Xe runs. This method has been successfully employed in molecular dynamic simulations of gases in zeolites.26 4. Model for shift 4.1. Gas Phase. The shift behavior of 129Xe in the gas phase has come to be well characterized31,37-39 and is understood to be dominated by paramagnetic deshielding. As a pair of Xe
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Gupta et al.
atoms approach each other the induced dipole-induced dipole (i.e., dispersion) interactions cause electronic transitions that result in the paramagnetic shift. Jameson and de Dios20 have shown that the simplest model for dispersion interactions, the Drude model, provides a reasonable prediction of the paramagnetic shielding for Xe (and other noble gases). From this model the change in the shift δ(R) of a Xe pair at separation R (with reference to the free atom shift, δ0) is given by
δ(R) - δ0 ) -[BC/R(0)]/R6
(5)
where B is the shielding hyperpolarizability, R(0) is the static polarizability, and C is the dispersion constant. (For values of R smaller than [R(0)]1/3 (using cgs units as in ref 20, and as described in ref 40), the diamagnetic contribution to shielding becomes significant20 but such regions of R are not explored in the present study.) To predict the experimentally observed chemical shift in the gas, we must average over all possible separations:
δgas(F,T) ) 〈δ(R) - δ0〉 ) F KXe-Xe ∫0
R
g(R,ρ,T) R
6
Figure 2. Xenon adsorption isotherm at 300 K. H(160) from this study, Na(4.8) and H(4.8) from Pires et al.,42 and Na(52.4) from Ito and Fraissard.2 The inset (with the same units) is the isotherm from this study at pressures above 1 atm.
4πR2 dR (6)
where g(R,F,Τ) is the pair correlation function between Xe atoms in the gas and F is the average gas density. The constant ΚXe-Xe ()BC/R(0)) can be fit using the gas phase shift37-39 using the exact pair correlation function for the low-density gas.41 We also use simulations of Xe in a high-density gas to confirm that the experimental data we fit (up to 100 atm) still confirms to the low-density limit of the pair correlation function. 4.2. Zeolite Phase. In the zeolite phase the chemical shift of 129Xe arises from contributions both from Xe-Xe interactions and from Xe-O interactions. We will examine whether eq 5 can be used assuming pairwise additivity to rationalize experimental data. If it can, the shift contribution from the xenon interaction with framework oxygen atoms can be treated in a similar manner as eq 6. Writing both the contributions to the shift
δZe0(FXe,T) ) FXeKXe-Xe ∫0 gXe-Xe(R,FXe,T) 4πR2 dR/R6 + R
FOKXe-O ∫0 gXe-O(R,FO,T) 4πR2 dR/R6 (7) R
The pair correlation functions gXe-Xe(R,FXe,Τ) and gXe-O(R,FXe,Τ) for Xe in the pores of a zeolite are obtained from the computer simulation. Two limiting cases of the above expression are of particular interest as they allow the two contributions to the shift to be studied independently. The first limiting case is constant temperature and variable loading. If, at constant temperature, the introduction of more Xe atoms does not disturb the Xe-O pair correlation (gXe-O), this will imply a constant contribution of the Xe-O interaction to the shift and will confirm that the δs term of eq 1 is independent of loading. We will see from the simulation results that at low loadings this is true, at high loadings though this is not true. We will also be able to confirm whether the Xe-Xe pair correlation function (gXe-Xe) is constant with loading, and hence whether δXe-Xe in eq 1 is constant. The second limiting case of interest is at vanishing Xe loadings, FXe f 0, for which the first term in eq 7 vanishes. The remaining term ()δs) has been shown3 to be temperature dependent. This is consistent with the expectation that Xe placement inside the zeolite cage should change with temper-
Figure 3. Representative 129Xe spectra at 300 K for loadings of 1, 2.1, 3.1, 3.9, 4.8, and 5.9 Xe/cage. The number of scans is very high at 1 Xe/cage to show gas peak.
ature. We will examine whether gXe-Xe from simulation agrees with the measured dependence. 5. Results and Discussion 5.1. Experiment. 5.1.A. Isotherm. Figure 2 shows the Xe adsorption isotherm at 300 K in the siliceous zeolite Y. It is measured volumetrically at low loading and with NMR at high loading. These isotherm data are needed to correctly calculate the shift vs loading curve. Also shown in Figure 2 are the isotherm measurements of Ito and Fraissard2 and Pires et al.42 on Na and H forms of Y with different Si/Al ratios. Our measured isotherm is consistent with the trends evident from published data with varying Si/Al ratio and with sodium/proton exchange. 5.1.B. 129Xe Shift. Figure 3 shows the NMR spectrum of 129Xe in siliceous Y at 300 K and at loadings ranging from 1 to 6 Xe/cage. The smaller peak is from Xe in the gas in equilibrium with the zeolite sample; the taller peak is from the Xe within the supercages of zeolite Y. The peak broadening at high loading is consistent with previous reports for Xe in HY.2 The chemical shift of 129Xe in the zeolite is usually reported to change linearly with loading,8,9 and we confirm this dependence with Xe loading up to 6 Xe/cage. A straight line fit to the data has a slope of 10.5 ppm per additional Xe. Extrapolation to zero loading gives an intercept of 61.5 ppm, which is in
129Xe
NMR Chemical Shift in Zeolite Y
J. Phys. Chem., Vol. 100, No. 23, 1996 9827
Figure 4. 129Xe spectra at different temperatures for a sample with room temperature loading of 1 Xe/cage. 64 scans with a delay of 20 s were used for each of the spectra. The temperatures are in degree, Celsius.
Figure 6. (a) Spectra from a nonselective inversion recovery experiment. The time is in seconds. (b) Spectra from a selective inversion recovery experiment where the gas peak is selectively inverted initially. The time is in seconds.
Figure 5. Variable temperature shift for room temperature loading sample of 1 Xe/cage. Also shown are the results from Ripmeester3 for dealuminated Y, the shift corrected for loading change, and the predicted shift from simulations. (The latter are discussed in section B under zeolite phase simulation.)
good agreement with Ito and Fraissard’s2 result of 58 ppm and de Menorval et al.’s43 result of 60 ppm. Figure 4 shows variable temperature spectra for a closed sample with a room temperature loading of 1 Xe/cage. As reported for a large number of zeolites,3,9 the chemical shift decreases as the temperature increases. Part of the trend is due to decreasing loading. It is evident in Figure 4 that the intensities decrease with temperature because for this closed system increasing the temperature results in a redistribution of the Xe to the gas phase. It would be ideal to measure δs(T) (i.e., at zero loading) as a function of temperature. At high enough temperatures, we can expect that the loading becomes low enough that further change of the shift with temperature will be exclusively a result of changing Xe-O interactions; that is
dδs ∂δ ≈ 1/Tf0 ∂(1/T) d(1/T) lim
(8)
Figure 5 shows our shift dependence on temperature along with the results of Ripmeester and Ratcliffe3 for dealuminated Y at some (not reported) low loading. The two data sets converge at such high temperatures that the loading becomes very low and so are qualitatively consistent with eq 8. In section 5.2.B we will attempt a comparison with simulation. Ripmeester and Ratcliffe44 pointed out that in an open cage system like Y, Xe exchange with the gas phase can influence the relaxation times and sometimes even the chemical shift. Since we observe both the gas phase and zeolite phase signal,
we estimate the influence of exchange on the chemical shift by measuring exchange rates using selective and nonselective inversion recovery. Figure 6a shows the result of a nonselective inversion recovery experiment on a high-loading sample. The gas phase Xe has an apparent relaxation time of 2.5 s, whereas the known relaxation time is on the order of hundreds of seconds.38 As reported by Ripmeester,44 this fast recovery confirms that exchange is significantly influencing the magnetization recovery measurement. The additional measurement of the selective inversion spectra shown in Figure 6b allows us to estimate the exchange time as ∼5 ms. Even though this exchange rate would clearly interfere with the measurement of relaxation times, it can at worst influence the chemical shift of the intrazeolite peak by 200 Hz (e.g., ∼2 ppm). 5.2. Simulation. 5.2.A. Contribution of Xe-Xe Interaction to the 129Xe Chemical Shift. 5.2.A.i. Gas Phase. To confirm the applicability of the Drude model and to obtain the parameter ΚXe-Xe, we carry out simulations of Xe gas at densities similar to that inside the zeolite. The resulting Xe-Xe pair correlation function for different densities is shown in Figure 7 along with the zero density analytical form for dilute gases.41 The XeXe pair correlation function closely follows the low density analytical result, which stands in agreement (eq 6) with the observation that the gas chemical shift changes linearly with density. The parameter KXe-Xe that fits the gas data (see Figure 8) is 23.08 (ppm Å6)/mol, and we will see that this value also produces reasonable agreement when used to calculate the XeXe contribution to shift in the zeolite. We note, however, that this value of ΚXe-Xe is considerably larger than a theoretical estimate obtained using eq 5 (with B ) 371.8 × 10-21 ppm m2 V-2 (ref 31), R(0) ) 4.462 × 10-43 kJ m2 V-2 (from ref 40, converted to SI units as described therein) and C ) 34.913 × 103 kJ Å6 mol-1 (Table 1)). 5.2.A.ii. Zeolite Phase: Xe Sites and Density Distribution. The density distribution of Xe inside the supercage is shown in three dimensions using surfaces of constant density.45 Figure 9 shows the density distribution for Xe at 298 K at a loading of 3 Xe/cage. The volume enclosed by the surface has a higher adsorbate density than the volume outside.
9828 J. Phys. Chem., Vol. 100, No. 23, 1996
Gupta et al.
Figure 7. Xe-Xe pair correlation function in the gas phase at 300 K. N denotes the number of Xe atoms used in a cubic simulation box of side 24.85 Å.
Figure 8. 129Xe chemical shift vs density in the gas phase. The solid line is the experimental data from refs 31, 37-39, and the circles are the simulation points. The gas density is reported in amagats as in those refs 31, 37-39.
In Figure 9a the density threshold is the same as the average density. The density distribution is tetrahedrally symmetric about the center of the cage. As the density threshold is raised to 5 times the average density, we see localized pockets of adsorbate density which represent the favored adsorption sites at locations suggested by the potential map.46 Figure 9b shows that there are 10 such sites: 6 of these are arranged octahedrally (one in front of each of the central four rings), and the remaining 4 sites are arranged tetrahedrally (one in front of each six ring). The distance between octahedral sites is 6.5 Å; that between tetrahedral sites is also 6.5 Å. However, the distance between a tetrahedral site and a neighboring octahedral site is only 3.9 Å, so a pair of Xe atoms cannot sit at the centers of neighboring tetrahedral and octahedral sites without significant repulsion; they may, though, relax away from the center (and each other) with some energy penalty. The site location, shape, and size vary little up to a loading high enough that repulsion between adsorbates becomes significant; at that point the size (at a given density threshold) shrinks as shown by Van Tassel in NaA.7 5.2.A.iii. Zeolite Phase: Simulations at 300 K. Before examining the contribution to the shift by Xe-Xe interactions, we first examine whether we may assume that the Xe-O pair correlation function is constant with increasing loading. Figure 10a shows the Xe-O pair correlation function at average Xe
Figure 9. Isodensity surface for an average of 3 Xe/cage at 300 K. The volume enclosed inside the surface has a higher adsorbate density than the volume outside. The density reported here in the figures is normalized with respect to the average density. Isodensity surface at (a, top) 1 × average density and (b, bottom) 5 × average density. The front three sites form one face of the octahedron. The zeolite cage structure is shown schematically; its actual structure is shown in Figure 1.
loadings of 1, 3, 5, and 7. There is no appreciable change in the behavior of Xe-O pair correlation over this range. This confirms the assumption that, for this loading range, δs is not a function of loading. Figure 10b shows the Xe-Xe pair correlation function at loadings of 1, 3, 5, and 7. There is a peak at the LennardJones minimum (4.6 Å), implying that the Xe atoms have sufficient mutual attraction that they relax toward each other even though site centers are separated by 6.5 Å. This accounts for the volume of sites seen in Figure 9b. Since neither the
129Xe
NMR Chemical Shift in Zeolite Y
Figure 10. (a) Xe-O pair correlation function at different loadings (Xe/cage) at 300 K. (b) Xe-Xe pair correlation function at different loadings at 300 K.
Figure 11. Xe-Xe contribution to shift. Shown are simulation and experimental results from this study, Ito and Fraissard’s,2 deMenorval,43 and Chen et al.47 Also shown is the gas phase Xe-Xe contribution to shift vs density expressed as (no./cage) where the crystallographic cage radius of 5.4 Å is used in defining the volume. The inset is the simulated Xe-Xe contribution to shift up to high loadings at 300 K.
Xe-O pair correlation nor the Xe-Xe pair correlation change up to 7 Xe/cage, eq 7 predicts that the shift should increase linearly with loading. Subtracting the zero loading limit from the experimentally measured shift, then, shows the experimentally measured contribution of Xe-Xe interaction to shift. Figure 11 shows this contribution obtained from our study and from the data of Ito and Fraissard,2 of de Menorval et al.,43 and of Chen et al.47 for NaY (Si/Al ) 2.5). Our measurement is close to that in NaY at low loadings; at loadings beyond 1.5 Xe/cage, though, our measurement is somewhat lower. This might be expected
J. Phys. Chem., Vol. 100, No. 23, 1996 9829
Figure 12. High-loading pair correlation functions: (a) Xe-Xe pair correlation at higher loading (no./cage) at 300 K and (b) Xe-O pair correlation at high loading (no./cage) at 300 K.
since the isotherms (Figure 2) change with dealumination and cation exchange. However, our shift might also be influenced by defect mesopores which can be formed by dealumination (as has been observed for mordenite48,49). A comparison of the calculated and experimental shift values is also presented in Figure 11. At low loadings, there is good match between the various experimental results and the simulation. At higher loadings, the experimental values diverge from the calculated values, but there is still agreement within 30%. It is worthwhile to recall the simplicity of the shift model which now has no adjustable parameter and the ideality of the simulation (wherein the zeolite is rigid and static). Figure 12a shows the Xe-Xe pair correlation at 300 K at loadings of 8 per cage and higher. Such loadings would require high pressures (>10 atm), but the simulation is instructive in that it shows that the Xe atoms clearly crowd each other. Moreover, these high-loading simulations allow us to discern that the Xe-O correlation (Figure 12b), while remaining constant up to 7 Xe/cage, changes appreciably at high loading. Xe-Xe crowding and Xe-O crowding should lead to a nonlinear change of shift with loading (Figure 11 inset). This type of nonlinear rise has been observed for Xe in zeolite L8 and NaA16 at 300 K, but to achieve sufficient crowding in Y requires low temperatures (see below). Figure 13 shows the average potential energy and the separate contributions of Xe-Xe and Xe-O interactions calculated in the simulation. The calculated energies compare well with the values of Kiselev and Du33 and of Yashonath and Santikary.27 The total potential energy varies linearly up to 10 Xe/cage. At higher loadings, though, the potential energy shows positive curvature, due to both Xe-O and Xe-Xe crowding. Even though Xe-Xe interactions contribute only a fraction of the potential energy, they mirror the expected behavior of the shift
9830 J. Phys. Chem., Vol. 100, No. 23, 1996
Gupta et al.
Figure 13. Potential energy of interaction UT at 300 K and its components, UXe-Xe and UXe-O with varying loading.
at high loading. In fact the shift may be a more sensitive measure of the crowding than the isotherm. 5.2.A.iV. Zeolite Phase: Simulations at 144 K. Cheung et al.5,50 reported variable loading experiments on zeolite Y at 144 K. These Xe shifts changed with loading in nonlinear fashion, and we use simulation to determine whether this is due to crowding. Figure 14 shows the isodensity surfaces obtained for an average loading of 3/cage. In Figure 14a the density threshold is the same as the average density; we see that the density distribution is more localized than that at room temperature (Figure 9a). A higher threshold (Figure 14b) shows that the octahedral and tetrahedral sites are still present. Figure 15 shows the Xe-O and Xe-Xe pair correlation functions at several loadings. Here the Xe-O pair correlation function indicates that the Xe-O contribution to the shift should remain constant up to a loading of 10 Xe/cage. Note that the initial rise and decline at separations of 3.5-4.0 Å suggest much more strict Xe-O order at N ) 12 Xe/cage. The Xe-Xe pair correlation, however, changes with loading even at low values of 7 Xe/cage. The Xe-Xe separation changes a great deal with loading at high values. The decline in gXe-Xe at R ) 6 Å corresponds to sharpening of sites. The Xe-Xe contribution to the chemical shift as evaluated from the pair correlation function is shown in Figure 16 along with the experimental result of Cheung et al.5 for NaY and Cheung and Fu50 for dealuminated Y at 144 K. The agreement is excellent for loadings up to 8 per supercage for NaY and for all loadings for dealuminated Y. From Figure 15b it is clear that the Xe-Xe pair correlation function increases sharply beyond a loading of 7 Xe/cage. However, the experimental shift increases more rapidly in NaY than calculated by the simulations. This implies that the Xe-O contribution to the shift (δs) probably no longer remains constant and so contributes to the nonlinear rise of shift. 5.2.A.V. Effect of Zeolite Potential, Xe Potential, and Zeolite Structure. To further elucidate the effect of the various contributions to the potential field on the shift behavior, we report additional simulations that neglect (1) the zeolite-Xe attractive potential field, (2) the Xe-Xe attractive potential, (3) both the attractive potentials, and (4) the crystal structure altogether by smoothing the wall oxygens to a spherical cavity. We replace the attractive potentials with a hard sphere potential.51 The adsorbate pore potential for a smooth spherical cavity is taken from Keffer et al.52 and is a Lennard-Jones potential integrated over the entire solid volume outside the spherical pore. We have carried out simulation for the above four cases up to a Xe loading of 5 Xe/cage at both 300 and 144 K. Figure 17 shows the Xe-Xe contribution to the chemical shift for the modified simulations at 300 K. Figure 18 shows
Figure 14. Isodensity surface for an average of 3 Xe/cage at 144 K. Isodensity surfaces at (a, top) 1 × average density and (b, bottom) 5 × average density.
the Xe-Xe and Xe-O pair correlation function at 300 K at a loading of 1 Xe/cage. When the attractive potential field of the zeolite is neglected, the Xe atoms are able to come closer to each other. This results in a higher slope of the shift vs loading curve. The Xe-O pair correlation, however, loses the first peak at a separation of 3.6 Å. When the Xe-Xe attractive potential is neglected, the Xe atoms move farther apart. This results in a smaller shift slope. The Xe-O pair correlation, however, shows no difference from the normal simulation. When both the Xe-O and Xe-Xe attractive potentials are turned off, the resulting shift vs loading behavior is midway between the above two results; however the shift becomes nonlinear. When the crystal structure is neglected altogether and Xe is placed inside the smooth spherical cavity, the slope is smaller than in any of the above cases. The shift resulting from the models at 144 K is shown in Figure 19. While the trends are the same as those at 300 K,
129Xe
NMR Chemical Shift in Zeolite Y
J. Phys. Chem., Vol. 100, No. 23, 1996 9831
Figure 17. Xe-Xe contribution to shift from various models as a function of loading at T ) 300 K. LJ denotes Lennard-Jones 6-12 interaction, and HS denotes hard sphere interaction.
Figure 15. Low-temperature pair correlation functions: (a) Xe-O pair correlation function at 144 K for different loadings (no./cage) and (b) Xe-Xe pair correlation function at 144 K for different loadings (no./ cage).
Figure 16. 129Xe chemical shift at 144 K. The simulation points are triangles joined by the best fit line, and the experimental results of Cheung et al.5 on NaY are the squares. Cheung and Fu’s50 experimental results on steam-dealuminated Y are the circles. Here the Xe-Xe contribution to the shift is obtained from Cheung’s data by subtracting their zero density shift limit.
differences between the models become more pronounced since lower temperatures more strongly favor low-energy configurations. This set of modified simulations helps show the role of the various interactions in determining the structure of the adsorbed fluid with respect to the wall atoms (gXe-O) as well as the positional correlations of the adsorbed Xe among themselves (gXe-Xe) and the resulting effect on the shift behavior. 5.2.B. Contribution of Xe-O Interaction to the 129Xe Chemical Shift. In section A we established that the Xe-O interaction contribution to the shift is constant at 300 K at low loadings. We can estimate KXe-O when the concentration of Xe is low enough that Xe-Xe interactions can be neglected.
Figure 18. (a) Xe-Xe pair correlation for different models of interaction at N ) 1/cage at T ) 300 K. (b) Xe-O pair correlation function for different models at N ) 1/cage at T ) 300 K. LJ denotes Lennard-Jones 6-12 interaction, and HS denotes hard sphere interaction.
As the temperature is increased, two opposing factors influence the shift: (a) the distribution function of xenon-oxygen pairs tends to be less localized, resulting in a reduction of shift, and (b) at higher temperatures the Xe atom can probe distances closer to the oxygen by more effectively climbing the repulsive potential, resulting in an increase in shift. While the analogous competition in the bulk fluid produces nonmonotonic behavior,39 in zeolites the shift generally decreases monotonically with increasing temperature.3 The simulations required to study the effect of Xe-O interaction on the zero loading shift are done at infinite dilution.
9832 J. Phys. Chem., Vol. 100, No. 23, 1996
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Figure 21. Change of loading with temperature for a sample with a room temperature loading of 1 Xe/cage. Figure 19. Xe-Xe contribution to shift from various models as a function of loading at T ) 144 K.
Figure 20. Xe-O pair correlation function at vanishing loadings for different temperatures.
Figure 20 shows the Xe-O distribution functions for a single Xe in the unit cell at several different temperatures. As expected the Xe-O pair correlation function changes at close separation with increasing temperature. While up to 3.35 Å (roughly, the van der Waals separation between a Xe-O pair) the number of oxygen neighbors of the Xe atoms remains almost constant, for R ) 3.54 Å (which gives the minimum in the Xe-O potential), the number of oxygen neighbors decreases with increasing temperature. This supports the idea that the increased shielding of Xe with increasing temperature (at low loadings) is primarily due to delocalization. Figure 5 shows the experimentally measured shift with varying temperature. In section 5.1 we found that part of the measured change of shift with temperature was due to changing loading. We can correct for the contribution to the shift of the changing loading as follows. Figure 21 shows the integrated spectral intensity for the variable temperature spectra of Figure 4. The relaxation delay used was long enough (20 s) that changes in relaxation time with temperature should not affect the integration. As a first approximation to estimate the zero loading shift, we assume that the dependence of shift on loading is linear as in Figure 11 and independent of temperature. This assumption has been supported for Xe in NaA22 at low loadings. The corrected shift (at zero loading) with temperature is plotted in Figure 5 along with the measured data. Note that the correction becomes larger at lower temperatures (higher loadings). Figure 5 shows the predicted change of chemical shift at zero loading with temperature using the second term in eq 7. The simulation curve is consistent with the zero loading data of Ripmeester,3 of this study, and (not shown) the 88 ppm value
(extrapolated to zero density) at 144 K from Cheung et al.5 The best agreement with the experimental result was produced by integrating gXe-O up to about 3.9 Å in the integration of the second term in eq 7. Physically this would mean that the shift is mainly affected by oxygen atoms which are very close to the xenon. A similar result has been found by Vigne-Maeder26 in molecular dynamic simulations of Xe in Y and silicalite in relating the zero loading chemical shift to the number of Xe-O collisions. The constant KXe-O obtained using an integration limit of 3.9 Å to match the low-loading shift is 7.3 × 104 ppm Å6. Comparison with KXe-Xe shows that the Xe-O interaction is only one-third as effective as the Xe-Xe interaction in deshielding the Xe nucleus. This is consistent with the fact that a xenon atom can be more easily polarized by the induced dipole of another xenon atom than by interaction with a less polarizable oxygen atom. 6. Conclusions We have presented a quantitative analysis of the 129Xe NMR chemical shift behavior in zeolite Y using Monte Carlo computer simulations. By considering the effect of internuclear separation on known shielding for gaseous Xe, a simple model can relate the Xe pair correlation functions to the chemical shift in the zeolite. At low loadings, we find that the Xe-O pair correlation does not change with loading. This confirms that δs is constant at low loadings, as has typically been assumed in interpreting the experimental results. Also at low loadings the Xe-Xe pair correlation confirms that the shift should increase linearly with loading. Comparison of simulations at 144 K with the experimental 129Xe chemical shift in Y of Cheung et al.5 and Cheung and Fu50 also yielded excellent agreement. At higher loadings (N > 7 Xe/cage), it was found that the shift vs loading behavior should take an upward curvature. One reason is that the XeXe pair correlation does not remain constant at high loadings, and it peaks at smaller separations. Also the Xe-O contribution to the shift (δs) does not remain constant anymore; the Xe-O correlation function becomes more peaked at smaller separations. The variation of shift with temperature at vanishing loadings can be rationalized by the change in the xenon-oxygen pair correlation function. Increasing the temperature causes the delocalization of Xe with respect to the oxygens resulting in a smaller chemical shift. Furthermore, we found that in this open pore zeolite (unlike, e.g., in NaA), the changing loading of Xe with temperature makes the variation of shift with temperature steeper and hence requires it to be accounted for carefully. Simulations in which alternatively the Xe-O and Xe-Xe interactions were made hard spheres indicate that the presence of the attractive potential field of the wall oxygens tends to
129Xe
NMR Chemical Shift in Zeolite Y
lower the shift vs loading slope, meaning that the zeolite potential tends to keep the Xe atoms apart. When the Xe-Xe attractive potential is switched off, the shift vs loading slope falls down. Simulations in a comparably sized smooth sphere also indicate that the shift vs loading slope is sensitive to the nature of the walls and their potential field. While we have treated the case of Xe in Y, the above approach can be readily applied to Xe adsorbed in other zeolites. Acknowledgment. We appreciate the support provided by the Minnesota Supercomputer Institute and the National Science Foundation (through a PYI grant) for this research. One of us (V.G.) was supported by a fellowship from Chevron and the University of Minnesota Graduate School. References and Notes (1) Ito, T.; Fraissard, J. Proceedings of the 5th Conference on Zeolites Heyden, 1981, p 510. (2) Ito, T.; Fraissard, J. J. Chem. Phys. 1982, 76, 289. (3) Ripmeester, J. A.; Ratcliffe, C. I. J. Phys. Chem. 1990, 94, 7652. (4) Ripmeester, J. A.; Ratcliffe, C. I. J. Phys. Chem. 1995, 99, 619622. (5) Cheung, T. T. P.; Fu, C. M.; Wharry, S. J. Phys. Chem. 1988, 92, 5170-5180. (6) Van Tassel, P. R.; Davis, H. T.; McCormick, A. V. Mol. Phys. 1991, 73, 1107. (7) Van Tassel, P. R.; Davis, H. T.; McCormick, A. V. Mol. Phys. 1992, 76, 411-432. (8) Barrie, P. J.; Klinowski, J. Prog. NMR Spectrosc. 1992, 24, 109158. (9) Fraissard, J.; Ito, T. Zeolites 1988, 8, 350. (10) Chen, Q. J.; Fraissard, J. J. Phys. Chem. 1992, 96, 1809. (11) Demarquay, J.; Fraissard, J. Chem. Phys. Lett. 1987, 136, 314. (12) Johnson, D. W.; Griffiths, L. Zeolites 1987, 7, 484. (13) Jameson, C. J.; Jameson, A. K.; Cohen, S. M. J. Chem. Phys. 1973, 59, 4540. (14) Ripmeester, J. A.; Ratcliffe, C. J.; Tse, J. S. J. Chem. Soc., Faraday Trans. 1 1988, 84, 3731. (15) Miller, J. B.; Walton, J. H.; Roland, C. M. Macromolecules 1993, 26, 5602. (16) McCormick, A. V.; Chemlka, B. F. Mol. Phys. 1991, 73, 603. (17) Smith, M. L.; Corbin, D. R.; Abrams, L.; Dybowski, C. J. J. Phys. Chem. 1993, 97, 7793. (18) Chen, Q. J.; Springuel-Huet, M. A.; Fraissard, J. Chem. Phys. Lett. 1989, 159, 117. (19) Jameson, A. K.; Jameson, C. J.; de Dios, A. C.; Oldfield, E.; Gerald, R. E., II. Turner, G. L. Solid State NMR 1995, 4, 1. (20) Jameson, C. J.; de Dios, A. C. J. Chem. Phys. 1992, 97, 417. (21) Jameson, C. J.; Jameson, A. K.; Gerald, R., II. de Dios, A. C. J. Chem. Phys. 1992, 96, 1676-1689. (22) Jameson, C. J.; Jameson, A. K.; Baello, B. I.; Lim, H. J. J. Chem. Phys. 1994, 100, 5965-5976.
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