5170
J . Phys. Chem. 1988, 92, 5170-5180
‘*‘Xe NMR of Xenon Adsorbed in Y Zeolites at 144 K T. T. P. Cheung,* C. M. Fu, and S. Wharry Phillips Research Center, Phillips Petroleum Company, Bartlesuille, Oklahoma 74004 (Received: September 21 1987; I n Final Form: March 22, 1988) ~
’29XeNMR spectra of xenon adsorbed in Na-Y, K-Y, Mg-Y, Ca-Y, and B-Y zeolites have been measured as a function of the xenon loading at 144 and 293 K. At low xenon loadings, the Iz9Xechemical shift shows two types of dependence on the xenon density in the supercage: linearly increasing and paraboliclike with a minimum. At 144 K, all the zeolites except Ca-Y have a linear dependence, whereas at 293 K, both Ca-Y and Mg-Y show a paraboliclike curvature. These dependences can be explained in terms of rapid exchange between xenon atoms adsorbed at special sites in the supercage and those remaining in the gas phase in the cages. Strong xenon adsorption at the special sites leads to the paraboliclike behavior, whereas weak adsorption yields the linear dependence. Formation of a partial bond between the xenon atom and 2+ cation by donation of one of the xenon 5p electrons to the empty s-orbital of the cation is proposed to explain the strong xenon adsorption in zeolites with 2+ cations. The bond formation introduces low-lying electronic excited states which lead to a large paramagnetic contribution to the chemical shift. By variation of the rate by which a sample is cooled to 144 K, it is shown that there is only one special adsorption site per supercage in the Y zeolites. In Na-Y, Mg-Y, and K-Y, the site can accommodate one xenon atom while in Ca-Y and Ba-Y, two xenon atoms can share the same site. At 144 K, a gas-liquid phase transition is observed when the xenon loading is between 7 and 9 xenon atoms/cage. The transition is characterized by rapid increase in the chemical shift and collapse of the line width. Before the transition, there are large increases in the line width that may be interpreted as the inhomogeneous broadening due to large fluctuations in the xenon number density in the cages. Measurements at 144 K with high loadings of xenon indicate that the supercage in Y zeolite can hold between 10 and 11 xenon atoms. The resulting chemical shift is between 250 and 270 ppm downfield from the resonance of 2 atm of xenon gas (at 293 K). At even higher xenon loading, the excess xenon condenses on the exterior surface of the zeolite microcrystallites to form solid xenon, which has a chemical shift of 304 ppm downfield.
Introduction In this paper, we report results of Iz9Xe nuclear magnetic resonance (NMR) of xenon adsorbed in Y zeolites at 144 and 293 K. Recent investigations’-8 have demonstrated that IZ9XeN M R is a very sensitive probe of the electronic environment inside zeolite cages. The large polarizability of monoatomic xenon leads to large N M R chemical shifts that depend on the type of cationsZas well as metal clusters3 in the cages. The chemical shift, u, of xenon adsorbed in zeolites, when measured with respect to that of an isolated xenon atom, can be decomposed into two terms: (1) a contribution due to xenon collisions with the cage wall; (2) a contribution due to collisions between xenon atoms. For a given type of zeolite and a given Si/Al ratio, the first term varies only with the kind and number of cations in the cage. There are several reasons for doing lZ9XeN M R measurements at 144 K. First, at the limit of zero xenon density, u is determined by the xenon collisions with the cage wall. The differences in u between 144 K and room temperature provide information about the interaction between a xenon atom and the cage wall and its variation with different cations. Second, at 144 K, which is below the normal freezing temperature of bulk xenon gas, there is a high probability for the formation of diatomic xenon moleculesg inside the zeolite cages. As will be shown below, the pairing of xenon atoms can occur readily in zeolite cages with 2+ cations. This may shed some light on the nature of the “electric field” effect observed by others for zeolites with 2+ cations.2,s (1) Ito, T.; Fraissard, J. P. Proc. 5th Int. Conf. Zeolites, Naples 1980, 510-515. (2) Ito, T.; Fraissard, J. P. J . Chem. Phys. 1982, 76, 5225; J. Chem. SOC., Faraday Trans. 1 1987, 83, 451. (3) de Menorval, L. C.; Fraissard, J. P.; Ito, T.J . Chem. SOC., Faraday Trans. 1 1982, 78, 403. (4) Ito, T.; de Menorval, L. C.; Guerrier, E.; Fraissard, J. P. Chem. Phys. Left. 1984, 111, 271. ( 5 ) Springuel-Huet, M. A.; Ito, T.; Fraissard, J. P. Proceedings of the Congress on Structure and Reactivity of Modified Zeolites, Prague; Elsevier: Amsterdam, 1984. (6) Ripmeester, J. A.; Davison, D. W. J . Mol. Strucf. 1981, 75, 67. (7) Ripmeester, J. A. J . Am. Chem. SOC.1982, 104, 209; J. Magn. Reson. 1984, 56, 247. ( 8 ) Scharpf, E. W.; Crecely, R. W.; Gates, B. C.; Dybowski, C. R. J . Phys. Chem. 1986, 90, 9. (9) Bernardes, N.; Primakoff, H. J . Chem. Phys. 1959, 30, 691.
0022-3654/88/2092-5 170$01.50/0
Third, in contrast to bulk xenon gas, xenon trapped inside zeolite cages may not go through a phase transition when cooled below the normal freezing temperature, because the phase transition is a cooperative phenomenon requiring the participation of many atoms, but there can only be a finite number of xenon atoms trapped inside a zeolite cage. Monte Carlo calculations1° have shown that in free space, a cluster of 13 xenon atoms or less does not go through gas-liquid and liquidsolid transitions until temperatures below 86 and 66 K respectively, in contrast to 166 and 161 K for bulk xenon. On the other hand, xenon atoms inside a zeolite experience an additional potential due to the cage wall. This constitutes an external pressure on the xenon atoms, thus affecting the transition temperatures. Low-temperature lZ9Xe N M R of xenon adsorbed in zeolites provides an excellent testing ground for statistical mechanical calculations of critical phenomena of atom clusters in a confined volume. While the size of the zeolite cage (usually given in terms of the free diameter) can be determined by conventional methods like X-ray diffraction, there remains uncertainty about the actual free volume available in the cage because of uncertainty involving the cations. A potentially better method for determinating the free volume is to measure the number of particular atoms or molecules of known sizes that will fill up the cage. In this respect, low-temperature Iz9XeN M R of the adsorbed xenon is an ideal tool because xenon condensed inside the zeolite cage has a resonance signal significantly different from that condensed on the exterior surface of the zeolite microcrystallite, and the spherical symmetry of the xenon atom provides uniform packing of xenon atoms in the cage. In this article, we present results of Iz9Xe N M R of five Y zeolites: Na-Y, K-Y, Mg-Y, Ca-Y, and Ba-Y, measured at 144 and 293 K. Y zeolites are chosen because of their importance as cracking catalysts in petroleum refining and their large cages, in which several xenon atoms can be adsorbed. There are several type of cages in Y zeolite. Xenon, with a diameter of 4.4 A, can go only into the supercage, which has a free diameter of 13 A and a pore opening of 8-9 A. Other cages, such as the &cage have entrances sizes too small for xenon. Ito and Fraissard* have also examined these five zeolites at room temperature. Their results (10) Etters, R. D.; Kaelberer, J. Phys. Reu. A 1975, 1 1 , 1068; J . Chem. Phys. 1977, 66, 3233; J . Chem. Phys. 1977, 66, 5112.
0 1988 American Chemical Society
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5171
Xenon Adsorbed in Y Zeolites TABLE I
sample Na-Y
formula per unit cell’ NaJ2.6H2.2X
K-Y
K42.4Na10.4H2.0X
Mg-Y Ca-Y
Mg26.3Na2.2X
Ba-Y
Ba20.6Na13,6X
Ca22.3Na10.2X
a(293K,O): PPm 58 74 77 120 124
a( 144K,0),b
PPm 86 88 89 143 151
cage
do( 1 4 4 K , ~ ) / d p l o , ~
PPm cage 16.1
capacityd
8.8 17.6
10.0 9.8 10.2
6.4
10.9 9.9
‘X = (A102)54.8(Si02)137.2. buncertainty is f2 ppm. CUncertaintyis f0.5 ppm cage. dCage capacity is defined as the number of xenon atoms required to fill a supercage. Uncertainty is f0.3 xenon atoms/cage. will be compared with ours and discussed. Experimental Section Sample Preparation. Zeolite catalysts with different cations were prepared by ion exchange with LZ-Y52 Na-Y zeolite (from Linde). The compositions of the exchanged zeolites as well as the starting Na-Y zeolite were determined by X-ray fluoresence of the digested samples. The framework %/A1 ratios obtained from solid-state 29SiN M R were in excellent agreement with the bulk ratios from X-ray fluorescence, indicating the high integrity of the zeolite framework and the absence of amorphous materials. This is confirmed by X-ray diffraction patterns. From results of elemental analysis, the formula weights of the zeolites per unit cell can be derived and are given in Table I. For convenience, we refer to each sample according to its exchanged cation. All zeolites were calcined in air at 7 7 3 K for 2 h after ion exchange and drying. A known amount of zeolite was loaded into a special 10-mm N M R tube with an attached vacuum valve. The total weight (sample + N M R tube) was measured. Then the sample was outgassed to about 1 X 10” Torr, heated gradually to 773 K, and maintained at this temperature for 8-12 h. A known amount of xenon (99.995% pure from Matheson) was introduced into the sample by chilling the sample region of the N M R tube to about 7 7 K with liquid nitrogen. At this temperature, the vapor pressure of xenon gas in equilibrium with solid xenon is negligible. Therefore all the xenon was either adsorbed into the zeolite or condensed on the exterior surface of the zeolite microcrystallites. Finally the N M R tube was sealed by the vacuum valve. At 144 K, the zeolite acts like a cryogenic pump. Therefore the amount of gaseous xenon above the zeolite is very small, typically less than 0.2% of the total amount. The percentage of the gaseous xenon is largest at the moment when solid xenon begins to appear, because there has to be sufficient xenon partial pressure before the solid can form. The amount of xenon remaining in the gas phase depends on the amount of zeolite in the N M R tube. We estimate the amount of gaseous xenon to be less than 3% of the total amount of xenon present. Therefore for practical purposes, the amount of adsorbed xenon is given by the amount of xenon we introduced into the sample. After completion of N M R measurements, the sample was warmed to room temperature, and xenon was pumped off. Immediately after air was allowed into the N M R tube, it was sealed again to prevent further absorption of moisture by the zeolite and weighed. The weight loss, compared to the total weight with air present before heat treatment, was taken to be the moisture content of the zeolite and subtracted from the weight of the sample to obtain the true dry weight. From the formula weight per unit cell and the dry weight of the zeolite, we calculated the total number of supercages in the sample, using the fact there are eight supercages per unit cell. Then the amount of xenon adsorbed by the zeolite at 144 K can be determined in terms of the number of xenon atoms per supercage, pcff. One should bear in mind that pen represents the true xenon density, p, inside the supercage when the xenon loading is not beyond the capacity of the supercages, Le., all xenon atoms are trapped inside the zeolite. When the loading exceeds that which can be held by the supercages, condensation of excess xenon on the exterior surface of the zeolite microcrystallites begins to occur, and peff is not the true xenon density in .the supercage. N M R Measurement. N M R spectra were obtained with a conventional single-pulse Fourier transform technique using a
JEOL J N M GX-270 spectrometer with a Iz9Xefrequency of 74.60 MHz. For each loading of xenon, spectra were measured at both 293 and 144 K. The temperature in the N M R coil a t the lowtemperature regime was calibrated with respect to the normal freezing point of xenon (161 K). Typically, spectra were obtained under nonspinning conditions with a 1 0 - k ~radio frequency pulse and a pulse delay of 2 s. Pulse delays of 4 and 10 s were used for some samples with high xenon loading in the 144 K experiments. The Iz9XeNMR chemical shifts are referenced to external xenon at 2 atm of pressure and room temperature. Under these conditions, xenon has a chemical shift that differs by less than 1 ppm from that of xenon extrapolated to zero All resonance signals of xenon adsorbed in zeolites were shifted to higher frequencies (Le., downfield) from the reference. We adopt the convention of a downfield resonance from the reference having a positive chemical shift. As will be shown below, spectra at 144 K depend on the rate at which a sample is cooled to that temperature. We employed three different cooling rates, which for convenience are labeled as equilibrium cooling, rapid cooling, and intermediate cooling. In these cooling methods, a sample is first cooled to 164 K at a rate of approximately 5 K/min and held there for 5 min. In equilibrium cooling, a sample is then cooled from 164 to 144 K in 2 K steps. At each step, the sample is allowed to equilibrate for 2 min. Data acquisition begins after the samples has been at 144 K for 2 min. In rapid cooling, a sample is cooled from 164 to 144 K as fast as possible. Data acquisition commences immediately after 144 K has been reached. The cooling rate for intermediate cooling is similar to that for the rapid cooling. A sample is rapidly cooled to 154 K where it is equilibrated for 5 min. Then it is cooled rapidly to 144 K. Data acquisition begins after the sample has been held at 144 K for 2 min. Results 129XeN M R spectra for xenon trapped in Na-Y and Ca-Y zeolites at 144 K produced by equilibrium cooling are shown respectively in Figures 1 and 2 for various loadings of xenon. The spectra of xenon in Mg-Y (not shown here) are similar to those of xenon in Na-Y. There is a general trend in these spectra that when peffis between 3 and 7 xenon atoms/cage, a shoulder appears at the high-field side of the resonance, leading to a large increase in the line width. The line shape resembles that of a powder pattern due to an axially symmetric chemical shielding tensor (see Figure 1). As peff increases, the shoulder decrease in intensity and moves toward the main resonance. When peff > 7 xenon atoms/cage, the resonance collapses back to a very narrow line. The spectra of xenon in K-Y (not shown) are very similar to those of xenon in Ba-Y shown in Figure 3. In contrast to Na-Y or Ca-Y, the resonance remains narrow, and the high-field shoulder is barely detectable when pen is between 3 and 6 xenon atoms/cage. At higher loading of xenon with peff > 10 xenon atoms/cage, spectra of xenon in these five zeolites all show two well-resolved resonances, with the smaller one located at 304 ppm downfield and the major one at 250-270 ppm. Since solid xenon resonates at 304 ppm at 144 K, we identify the 304-ppm peak as excess ~~
~~~~~~~
(11) Jameson, A. K.; Jameson, C. J.; Gutowsky, H. S. J . Chem. Phys. 1970, 53, 2310. (12) Jameson, C. J.; Jameson, A. K.; Cohen, S. M . J . Chem. Phys. 1973, 59, 4540.
5172 The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 1
Cheung et al. BaY
NaY 12 X E N O N K A G E
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CHEMICAL SHIFT I PPM I NaY-ZBOLSPE:l2O-Xa NKR CBXYICAL SBIR
Figure 1. IZ9XeNMR spectra of xenon adsorbed in Na-Y at 144 K by equilibrium cooling. The xenon loading is given in terms of the effective number of xenon atoms/cage, perf.
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Figure 4. lz9XeNMR chemical shift of xenon adsorbed in Na-Y as a function of xenon loading, pelf. and X represent respectively data obtained at 144 K with equilibrium cooling and at 293 K. The arrows indicate the presence of the exterior solid xenon peak at 304 ppm. Note the change in the scale of the abscissa between 144 and 293 K. See text for details.
+
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Figure 2. Iz9Xe NMR spectra of xenon adsorbed in Ca-Y at 144 K by equilibrium cooling. The xenon loading is given in terms of the effective number of xenon atoms/cage, perf.
xenon frozen on the exterior surface of the zeolite microcrystallites. A further increase in the xenon loading only increases the intensity of the 304-ppm peak in comparison to the peak between 250 and
270 ppm but does not change peak positions. The chemical shifts of the resonance of xenon trapped inside these five zeolites are shown as a function of pefrin Figures 4-8. If several resonances are present, as in the case of Na-Y, the chemical shifts of the major resonance are plotted. The arrows indicate the presence of the second resonance at 304 ppm. In Figure 9, we summarize the full width at half-maximum (fwhm) of the resonance of xenon trapped inside the zeolites as a function of perf. One should note that in spectra with single peak, the fwhm represents the spin relaxation rate, but in multiline spectra, it serves as an indicator of the dispersion in the distribution of the resonances. In Figures 4-8, the chemical shifts of the same samples measured at 293 K are also shown. In principle, one should plot the data as a function of p , the actual number of xenon atoms per supercage trapped in the zeolite. p is different from pew because, at 293 K, there is a considerable amount of xenon remaining in the gas phase above the sample. However, p is proportional to
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5173
Xenon Adsorbed in Y Zeolites KY-zEoLIR:I29-xe MLR ClaYICAL
s m tR
+
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Figure 5. Iz9Xe N M R chemical shift of xenon adsorbed in K-Y as a function of xenon loading, perf. + and X represent respectively data obtained at 144 K with equilibrium cooling and at 293 K. The open square represents data obtained at 144 K with intermediate cooling. The arrows indicate the presence of the exterior solid xenon peak at 304 ppm. Note the change in the scale of the abscissa between 144 and 293 K. See text for details. uY-~oml29-x.
144K
X
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+
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Figure 6. Iz9Xe N M R chemical shift of xenon adsorbed in Mg-Y as a function of xenon loading, perf. + and X represent respectively data obtained at 144 K with equilibrium cooling and at 293 K. The arrows indicate the presence of the exterior solid xenon peak at 304 ppm. Note the change in the scale of the abscissa between 144 and 293 K. See text for details. zoo
MIR CBBMICAL S
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2
4
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10
14
10
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I4
16
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Figure 7. Iz9Xe N M R chemical shift of xenon adsorbed in Ca-Y as a function of xenon loading, pen. + and X represent respectively data obtained at 144 K with equilibrium cooling and at 293 K. The arrows indicate the presence of the exterior solid xenon peak at 304 ppm. Note the change in the scale of the abscissa between 144 and 293 K. See text for details.
Figure 10. fwhm of lz9Xe N M R of xenon adsorbed in Na-Y, K-Y, Mg-Y, Ca-Y, and Ba-Y at 293 K as a function of xenon loading, pelf. See text for discussion about the scale of the abscissa. peffw h e n the amount of xenon adsorbed i n a zeolite is linear with t h e xenon partial pressure above t h e sample (see Appendix); this condition should hold for most zeolites a t m o d e r a t e loadings of xenon.2 Therefore, u has the s a m e functional dependence on perf a s it has on p. T h e 293 K spectra always consist of a single sharp
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
5174
Cheung et al. BaY
1
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2 xenon atoms/cage. The line width and dispersion of the resonance in Ba-Y are much smaller than those
Figure 13. 129Xe NMR spectra of xenon adsorbed in Ba-Y at 144 K by
rapid cooling. in Na-Y and Ca-Y. The resonance in Ba-Y shows a weak shoulder on the high-field side when perf < 2 xenon atoms/cage, but the shoulder moves to the low-field side when perf> 2 xenon atoms/cage. The dispersion becomes obvious when peff > 3 xenon atoms/cage. While the spectra of xenon in Mg-Y and K-Y are not shown here, their changes as a function of perfare similar to those of Na-Y in the sense that when peff is larger than unity, the resonance of xenon in both zeolites begins to show structure. In Mg-Y, the resonance is broad and disperses in a manner similar to that of Na-Y. On the other hand, the spectra of xenon in K-Y remain narrow with a width similar to those of Ba-Y, but the resonances now have a shoulder on the low-field side. The poor signal-to-noise ratios in the rapid cooling experiments, in particular those with low loadings of xenon, are due to two factors: (1) the resonance is generally broader, thus spreading the spectral intensities over a wider region of the spectrum; (2) the total data acquisition time is only about 100 s, which means that there are only 50 scans in the signal averaging compared to 200 scans in a typical equilibrium cooling experiment. It should be emphasized that the cooling rate affects the position of the 129Xeresonance in Na-Y, K-Y, and Mg-Y only when the xenon loading is larger than the threshold of 1 xenon atom/cage. At this point, the dispersion of the resonance begins to occur in the rapid cooling experiments. For Ca-Y and Ba-Y, the threshold loading is 2 xenon atoms/cage. When the loading is less than the threshold, the chemical shift is independent of the cooling rate. This is illustrated by the results shown in Figure 5 for K-Y, where we have compared the equilibrium cooling data at low xenon loading with those obtained after intermediate cooling. The differences in the spectra between equilibrium and rapid cooling experiments suggest that when peff is larger than the threshold (which depends on the type of cations), xenon is adsorbed by the zeolite in a nonequilibrium condition in the rapid cooling experiments. Therefore, if the sample is held at 144 K for an extended period of time, the spectrum will evolve to that obtained with equilibrium cooling. In Figure 14, we show such an evolution as a function of the delay time from the moment that rapid cooling to 144 K has been achieved. Here the total data acquisition time for each spectrum is reduced to only 1 min to minimize spectral changes during data acquisition. From Figure 14, we can estimate that it takes about lo3 s for the nonequilibrium spectrum to return to the equilibrium one.
The Journal of Physical Chemistry, Vol. 92, No. 18. 1988 5175
Xenon Adsorbed in Y Zeolites I
CaY 2.1XENON~AGE
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the differences. It is possible that in our sample, some of the Mg2+ cations may exist as Mg(OH)+ due to the hydrolysis reaction Mg2+ + H 2 0
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Figure 14. Evolution of 129XeNMR spectrum of xenon adsorbed in Ca-Y at 144 K with rapid cooling as a function of the delay time at which the sample is allowed to equilibrate. pcff is about 2.1 xenon at-
oms/cage.
Discussion We first consider data measured at 293 K. For zeolites with 1+ cations, we observe a linear increase of u with peff, which is in agreement with the results of Ito and Fraisard.2 The linear relation between u and the xenon density in the cage is due to diatomic xenon-xenon collisions, having been derived theoreti~ ~pure ~ ~ 'xenon ~ ~ ~ ~gas. The callyI3and verified e ~ p e r i m e n t a l l y ~for extrapolation of u to zero peff, which is the same as the extrapolation to zero p, gives the contribution of the xenon-cage wall interaction. The results are given in Table I. They are in good agreement with those determined by Ito and Fraissard.2 We have also extrapolated the results for Li-Y, which yield 60 f 2 ppm. The fact that Y zeolites with H+, Li', and Na+ cations2 all have a similar u ( T = 293 K, p = 0), while that of K-Y is significantly larger, suggests that in zeolites with 1 + cations, u ( T = 293 K, p = 0) is affected by the size of the cation only when the radius of the cation is larger than that of Na+, which has a radius of 0.97 A. One explanation is that 1 + cations usually locate near the A104- groups (which form part of the zeolite cage wall) to minimize the electrostatic energy. The electron cloud associated with the A104- groups is highly extended spatially and may completely shield the cations from the xenon if they are small enough. Once the cation is buried within the electron cloud of the A104- groups, it does not matter what sizes the cations are as far as their electrostatic effect on the xenon concerned. It is likely that K+, with a radius of 1.33 A, protrudes beyond the electron cloud and alters the electronic environment of the cage wall seen by the xenon atom, thus affecting its chemical shift. With the exception of B a y , zeolites with 2+ cations show a chemical shift with a paraboliclike dependence on pep It decreases at first as pcffincreases and then increases after passing through a minimum. Similar behavior has also been observed by However, chemical shifts of xenon in the Mg-Y are smaller, and the extent of the upward turn at low pen is less drastic than reported by Ito and Fraissard, even though our sample has a higher degree of ion exchange. At this moment, we do not know the origin of (13) Adrian, F. J. Phys. Reu. A 1964, 136, 980. (14) Streever, R. L.;Carr, H. Y . Phys. Reu. 1960, 121, 20. (15) Hunt, E. R.; Carr, H . Y. Phys. Reu. 1963, 130, 2302.
-
Mg(OH)+ + H+
The maximum heat treatment of our sample is 773 K, which is lower than the 873 K employed by Ito and Fraissard. Ito and Fraissard have proposed an explanation for the upward turn of u at small p in zeolites with 2+ cations. It is based on the adsorption of xenon at special sites in the zeolite cage. In the following, we extend this idea to incorporate the rapid exchange between the adsorbed xenon at the special sites and those remaining in the gas phase. This theory will form the basis for our interpretation of the 144 and 293 K data. The theory describes the collision between a xenon atom and the cage wall as an adsorption process. It assumes that there are N , special adsorption sites in each zeolite supercage and that adsorption a t one site is independent of adsorption at the other sites. Furthermore, adsorbed xenon atoms do not interact with each other or with those remaining in the gas phase within the cage. For the time being, we shall restrict ourselves to each site adsorbing only one xenon atom. Let us (us> 0) be the chemical shift of a xenon atom adsorbed at a special site. The chemical shift of a xenon atom remaining in the gas phase in the cage is {,( T)p,, which is the same as that of the pure xenon gas. pg is the xenon gas density within the supercage. We have explicitly indicated that cg (s, > 0) is a function of temperature. The observed chemical shift of a xenon nucleus is given by the average over all types of collisions experienced by the xenon atom. The average over collisions is essentially a time average, which according to statistical mechanics is equivalent to an ensemble average. We limit ourselves to two types of collisions: those between xenon atoms and the adsorption sites and those between xenon atoms themselves. Assuming that the exchange rate between the adsorbed xenon with those in the gas phase is much faster than the Iz9XeN M R relaxation rate and the chemical shift difference in hertz, we can write 47-d)) = ( N , / N ) 0 % + [ ( N - N,0)/Nl{,P,
(1)
where 0 is the fraction of the N, sites being occupied on the average, and N is the total number of xenon atoms in each supercage. One can express 0 in terms of p, by a kinetic argument similar to that used in the derivation of the Langmuir isotherm.I6 Let k, and kd be, respectively, the rate constants for adsorption and desorption of a xenon atom on a site. At a given time, the adsorption rate is k,( 1 - 0 ) p , and the desorption rate is kd8. At equilibrium, they must be equal. That is
k,(l - O)pg = kd6
(2)
6 = bPg/(l + bP,)
(3)
which yields where b = k,/kd (note that b has a dimension of length3). Using the fact that N = Vp and pg = ( N - N,B)/V, V being the free volume of the supercage, we obtain the following by substituting eq 3 into eq 1:
dT@) = [bnsu, + {,Pg('
+ bP,)I/(l + bpg + bn,) (4) where n, = N , / V . At small pg such that bp, 1. Then eq 4 reduces to d T @ ) = (ns%
+ C g n , Z ) / p - 2nslg + lgP
(7)
with pB expressed in terms of p . It is evident that there is an initially rapid decrease of u( T,p) as 1/ p . It is more complicated to extend the above treatment to the adsorption of two or more xenon atoms at each site because of the kinetics &tween various degrees of occupany of the sites. Here we consider the simplified version of the problem with the adsorption of two xenon atoms per site by postulating that the two xenons adsorbed on the site are tightly bound. This involves the following assumptions: (1) adsorption rate constants for the first and second xenons to be adsorbed on a site are identical, i.e., k,(O) = k,( 1) = k,; ( 2 ) desorption from singly occupied sites is slow compared to adsorption, i.e., [ka/kd(l)]pg >> 1; (3) desorption from singly occupied sites proceeds much more readily than from doubly occupied sites, Le., k d ( l ) >> kd(2). Here, k d ( m )and k,(m) are respectively the desorption and adsorption rate constants for a xenon atom from a site with m adsorbed xenon atoms. Then the fraction of the sites with double occupany is much larger than that with single occupany, and the chemical shift of the adsorbed xenon is mainly determined by those at doubly occupied sites. Equations 1 and 2 can be rewritten as
dT#) = (2Ns/N)60s-+ [ ( N - 2 N s ~ ) / ~ l g P g (8) k,(l
- 6)pg = 2k,(2)6
(9)
where 6 now represents the fraction of the sites with two adsorbed atoms. us is the chemical shift of a atom at the adsorption sites with the presence of another adsorbed xenon atom and is not the Same as that in eq 1. It follows that all the derived for one xenon per site can be translated to those of two atoms per site by replacing b (=k,/kd) with k,/2kd(2)and N , with 2Ns. to extend eq 1-7 to the where there It is are both strong and weak adsorption sites present in each supercage, so long as the adsorption at each site is independent of the others. principle, ranking of the strength of the adsorption sites among zeolites may be deduced from b, the ratio of adsorption and desorption rate constants. For zeolites with a linear u(T,p), b can be estimated from eq 6. w h e n the dependence is paraboliclike, as in Ca-Y and Mg-Y, one needs to fit eq 4 to the data. Unfortunately, our data at 293 K provide only the dependence of in terms of pcff, discussed in the Appendix, the slope of the chemical shift at 293 K as a function of peff may vary with the amount of the sample as well as the adsorption isotherm of that zeolite. Therefore, the slope of u versus peff curve is insufficient for the determination of b. However, zeolites with a paraboliclike u( T,p) have stronger adsorption sites than those with a linear ,,(T,~) since the condition ofbpg is valid for the former and bpg Ba-Y > K-Y > Na-Y 2 Mg-Y. For double sites with single occupancy in Ca-Y and Ba-Y, the Ordering among K-Y* Na-Y3 and Mg-Y remains the same, but the position of the Ba-Y is uncertain without knowing the value of {, ( T = 144 K). The differences between the intercepts at 144 and 293 K reveal the variation of us and b with temperature. The principal temperature dependence in is due to the desorption process, which usually has an activation energy (that is, b 0: exp(E/kT), where E is the activation energy). Thus a zeolite with a strong xenon adsorption would have a strong temperature dependence in b. However, the ratios (r(144K,O)/u(293K,O) determined from Table I do not follow the same trend as the adsorption strength discussed earlier. In fact, Na-Y, which has weak adsorption sites, turns Out to have the largest ratio Of whereas Ca-Y with the strongest sites has a ratio of only 1.24. This suggests that there is significant temperature dependence in os as well. As pointed O u t by Ramsey," if there are lowlying electronic excited states associated with the adsorption and they are of the order of kT above the ground state, the Boltzmann distribution among these states would lead to a osdepending on temperature. Changes in the location of the cations within the cage may also affect usby altering the accessibility to the xenon atoms. Within experimental uncertainty, the intercepts u(144K.0) for Na-Y. Mg-Y, and K-Y are about the same. The similarity in o( 144K,O) between MgY and zeolites with 1+ cations supports the earlier interpretation that the positions of the Mg2+ions (at least those responsible for the adsorption) at 144 are different from those at 293 K, such that at low temperatures the Mg2+ions are more shielded from the xenon atoms by the electron cloud of the A104- gfoups, in a manner Similar to that of the cations. Changes In the unit cell size, thus the cage size, in zeolites with temperature may also lead to a temperature-dependent us. However, these and the changes in cation locations are In Figures 4-8, zeolites with smaller cations such as Na-Y, Ca-Y, and Mg-Y show a plateau in the u(144K,P) curve at Pcff between and xenon atoms/cage. This is not Observed in K-Y and Ba-Y, which have large cations of similar size. At this level
-
1.53
(17) Ramsey, N. F. Phys. Reo. 1952, 86. 243.
Xenon Adsorbed in Y Zeolites of xenon density, changes in the chemical shift are largely determined by xenon-xenon interactions. At this moment, it is unclear how the size of the cations would affect this interaction. The rapid increase in the chemical shift and drastic reduction in the line width for the five zeolites in the range of peff between 7 and 9 xenon atoms/cage strongly suggests the presence of a gas-liquid transition. The phase transition may be considered as the condensation of the xenon gas into a xenon liquid droplet inside the cage. The critical density for the bulk xenon gas is 1.1 g/cm3 which is about 6 xenon atoms/cage, a value slightly smaller than the transition densities observed for the xenon in the supercage a t 144 K. A liquid phase can be characterized by the presence of a sharp peak in the xenon radial density function at the location corresponding to the xenon-xenon bond distance. The mean xenon-xenon distance decreases, and the number of nearest neighbors increases. This sudden increase in the xenon density within the liquid droplet leads to the rapid increase in the chemical shift. The large decrease in the line width is due to the fact that after the phase transition, the fluctuation of the number density of xenon in the cage is highly suppressed. Also, there is a sudden drop in the mean-square fluctuation of the xenon-xenon distance and the number of bonding neighbors. Together with atomic motions remaining in the liquid droplet, each xenon atom sees a rather uniform electronic environment. (Note that the xenon chemical shift depends on the xenon-xenon distanceT3and the number of bonding neighbors. A drop in their mean-square fluctuations translates into a decrease in the line width.) The leveling off of the chemical shift of the adsorbed xenon to some constant value between 250 and 270 ppm (depending on the type of cations) at high peff indicates the complete filling of the supercage by xenon atoms. Further increases in the xenon loading have no effect on this resonance; instead, a second peak a t about 304 ppm begins to appear, indicating the condensation of the excess xenon at the exterior surface of the zeolite microcrystallites as solid xenon. One can determine the size of the supercage of various zeolites by noting the number of xenon atoms per cage required for the first appearance of the 304-ppm peak. Xenon condensed at the exterior surface has a TI 1 lo2 s, which is much longer than that of the xenon inside the cages. Unless one chooses a very long delay time between pulses, the signals from the 304-ppm peak will be weak in comparison to those of the trapped xenon and difficult to detect. One way to minimize the uncertainty is to fill the supercage with excess xenon in successive increments and plot the intensity of the 304-ppm peak as a function of pefp For a fixed pulse delay, the intensity of the 304-ppm peak is proportional to the amount of exterior xenon. By extrapolating the plot to zero intensity, one obtains the number of xenon atoms just sufficient to fill the supercage. The results for the five zeolites are given in Table I. With the exception of Ca-Y, all the zeolites, regardless of the charge of the cations, have similar cage volumes, which can hold about 10 xenon atoms. This is smaller than the value of 15 xenon atoms/cage expected from the packing of a 13-A diameter cavity with 4.4-A diameter hard spheres. The larger cage volume for Ca-Y may be understood from the fact that, in the ion exchange, it takes half the number of 2+ cations to replace the 1+ cations in the supercage. However, it is surprising to note that Mg-Y has a slightly smaller cage volume than Ca-Y since Mg2+ion is smaller than Ca2+. It is possible that some of the MgZf ions may be present as Mg2+(0H)-, as suggested earlier to account for the chemical shift of Mg-Y at 293 K. The larger size of the Mg2+(OH)- ion would reduce the cage volume available for the xenon. At the limit of complete cage filling, the xenon chemical shifts of 250 and 270 ppm correspond closely to that of the bulk liquid xenon (about 254 ppm). The coexistence of solid xenon at the exterior surface and liquid xenon inside the cage confirms the statistical mechanical predictionlo that the liquid-solid phase transition temperature of a cluster of 10 atoms or less is much lower than that of the bulk. Unfortunately, we cannot determine the liquid-solid phase-transition temperature in the supercage because it is beyond the temperature range available for our instrument.
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5177 At 293 K, the line width of the xenon resonance in zeolites with a linear a( T,p) is about 224 H z and remains more or less independent of peff But for Ca-Y and Mg-Y, which show a paraboliclike a( T,p), the resonance is very broad at low peff and becomes narrower as perf increases. The different behavior of the line width in Ca-Y and Mg-Y can be understood in terms of the rapid exchange mechanism. A xenon nucleus experiences a large fluctuation in the local magnetic field during the adsorptiondesorption process. The magnitude of the fluctuation field, h, is of the order of the product of as,the chemical shift at the adsorption site, and the applied field. The transverse spin relaxation rate 1/T2(s) of an adsorbed xenon atom is approximately 1/T2(s)
-
h2/kd
where we have used l/kd as an estimate for the time a xenon atom spends at the adsorption site. Let 1/T2(g) be the spin relaxation rate in the gas phase. Using the rapid exchange approximation as in eq 1, one obtains fwhm
-
[1/T2(s)
- 1/T2(dIW(1 + b
g
+w+ 1/T2(g) (10)
For zeolites with strong adsorption sites, kd is small, and thus 1/T2(s) >> l/Tz(g). With bp, >> 1, the condition for strong adsorption, eq 10 reduces to fwhm
-
.
-
ns(l/T2(S))/P + 1/Tz(g)
The strong dependence on p explains the rapid decrease in the line width in Ca-Y and Mg-Y as peff increases. There is a general trend in the 144 K line widths shown in Figure 9. The five zeolites all show a maximum in the fwhm at pen between 2 and 5 xenon atoms/cage. The line width decreases rapidly just before the onset of the gas-liquid phase transition indicated by the rapid increase in the chemical shift. We suspect that the increase in the broadening is due to the large fluctuation in the actual number of xenon atoms in the cages. This number fluctuates as xenon atoms move in and out of each cage; the xenon density, p or peff, is simply a time average of this number. Since the chemical shift of the xenon atoms in a given cage depends on the number of xenon atoms in that cage, one would observe a large inhomogeneous broadening due to the number fluctuation if there were no rapid exchange of xenon atoms between cages. For an ideal gas, the magnitude of the fluctuation is the same as p. At 293 K, the fluctuation in each cage is independent of any other cages, and the time scale of the fluctuation is of the order of lo-" s (the linear dimension of the supercage divided by the linear velocity of the xenon atom). Thus on the N M R time scale, the experiment samples only the time average of the fluctuation and the inhomogeneous broadening is motionally narrowed. However, at 144 K, which is below the freezing temperature of bulk xenon, xenon atoms no longer behave like an ideal gas. Just before the gas-liquid phase transition, the number fluctuation is enormous since it is governed by the isothermal compressibility.'* In bulk xenon gas, the isothermal compressibility diverges when approaching the critical temperature. Although it may not diverge in a cluster of few atoms, we expect that it will be large just before the phase transition. The time scale of the fluctuation also becomes very long since xenon atoms with lower thermal energy spend more time in a given cage due to their mutual attractive interactions. In the regime of large number fluctuation and slowing down of the fluctuation, motional narrowing is no longer effective. The large inhomogeneous broadening is quite obvious in Figure 1. The distinct shoulder at the higher field suggests the presence of cages containing fewer xenon atoms than the cages associated with the major peak. The drastic reduction in the line width after the phase transition is due to the large drop in the number fluctuation in the liquid droplets. As indicated by the arrow in the insert in Figure 9 for Mg-Y, there is a small dip in a line width right at the point of (18) Stanley, H. E. Introduction to Phase Transitions and Critical Phenomena; Oxford University Press: New York, 1971.
5178
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
Cheung et al.
the gas-liquid transition. Even though the dip is very small, it can be observed in all five zeolites we have studied. The effect of inhomogeneous broadening due to the distribution in the xenon number density in the supercages can be examined more closely by adsorbing xenon into zeolites in a nonequilibrium condition. In the rapid cooling experiment, a sample is cooled very rapidly from 164 K, a temperature above the freezing point of xenon, to 144 K. This creates a temperature gradient, which leads to a nonuniform xenon number density across the sample. If the time it takes for the system to relax to the equilibrium condition is long in comparison to the N M R time scale, we would observe a broad line and possibly several resonances. For perf > 2 xenon atoms/cage, Ca-Y shows one resonance in the equilibrium cooling experiment, whereas with rapid cooling, two resonances are observed. As shown in Figure 14, it takes about lo3 s for the nonequilibrium spectrum to return to the equilibrium one. Relaxation times of this order of magnitude are expected from the following considerations. The movement of xenon atoms from one cage to another is described by diffusion with a diffusion coefficient being roughly the square of the cage dimension (- 13 %.)divided by the time it takes a xenon atom to transverse the cage. At a xenon density below the critical density, the transverse time is -lo-" s. The time for diffusion to smooth out a macroscopic inhomogeneity of the order of l cm (assuming that interparticle diffusion between zeolite microcrystallites is infinitely lo3 s. fast) is about (1 cm)2/[diffusion coefficient] The rapid cooling experiments also provide information about the adsorption sites. In Na-Y, K-Y, and Mg-Y, two resonances are observed when the xenon loading is larger than 1 xenon atom/cage. But at lower loadings, only one resonance is observed; its position is the same as that observed with equilibrium cooling. This suggests that at low temperatures in these zeolites, there is only one adsorption site per supercage, Le., N,/ I/ = 1, and the site can adsorb only one xenon atom. At 144 K, the majority of the xenon is first condensed at the adsorption site in each cage, regardless of the cooling rate. This accounts for the same chemical shift in the rapid and equilibrium cooling experiments. When the loading is larger than 1 xenon atom/cage, the excess xenon (after all the adsorption sites have been filled) is then weakly bound to the adsorbed xenon via van der Waals interaction to form xenon dimers. The formation of the van der Waals xenon dimers occurs first at the outer region of the sample, which is at a lower temperature due to the temperature gradient. These xenon dimers have a resonance about 25-30 ppm downfield from that of the singly adsorbed xenon atoms at the adsorption sites. Since the xenon-xenon bond in the van der Waals dimer is very weak, the dimer dissociates easily. One of the xenon atoms may diffuse to another cage where it may temporarily form a dimer. Although the diffusion time from one cage to the neighboring cages is much faster than the N M R time scale, it is not fast enough to remove the macroscopic xenon density gradient (probably with 2 xenon atoms/cage at the outer region of the sample and 1 xenon atom/cage at the interior) created by the rapid cooling. Therefore two resonances can be observed. The rapid diffusion time between neighboring cages explains why in equilibrium cooling, only the average resonance between the singly adsorbed xenon atoms and the dimers is observed. The results of N J V = 1 in Y zeolites is in agreement with the heat of adsorption m e a s ~ r e m e n t . ' ~ We have suggested that a van der Waals xenon dimer at the adsorption site has a chemical shift 25-30 ppm downfield from that of a singly adsorbed xenon atom. This interpretation is based on the observation that solid xenon has a face-centered cubic crystal structure and a chemical shift of 304 ppm. Since each of the xenon atoms in the solid has 12 nearest neighbors, the contribution of each nearest-neighbor xenon-xenon bond to the chemical shift is -304 ppm/l2 or -25 ppm. Ca-Y and Ba-Y are different from other zeolites. With rapid cooling, two resonances are observed in Ca-Y when the xenon loading is larger than 2 xenon atoms/cage. At lower loadings,
only a single resonance at the same location as that in the equilibrium cooling is observed. Ba-Y is more complicated. There is a weak shoulder at the high-field side of the main peak when the xenon loading is less than 2 xenon atoms/cage. The shoulder moves to the downfield side when peff > 2 xenon atoms/cage. At perf= 2 xenon atoms/cage, only a single peak is observed. These results suggest that in the Ca-Y and Ba-Y, there are either two adsorption sites per supercage (Le., N J V = 2) with each site capable of adsorbing only one xenon atom or only one adsorption site per cage (Le., N,/V = l), but each site is capable of adsorbing two xenon atoms. In the former, the two resonances observed when perf > 2 xenon atoms/cage are due to the singly adsorbed xenon atoms and the van der Waals dimers formed after all the adsorption sites are filled. In the latter, the two resonances are associated with the adsorbed xenon pairs and the weakly bound trimers, with the trimers located at the downfield side. Data for Ba-Y seem to indicate that the latter interpretation is more appropriate. The weak shoulder observed when perf< 2 xenon atoms/cage can be interpreted as the resonance associating with adsorption sites occupied by only one xenon atom while the main peak is due to those with double occupancy. At perf = 2 xenon atoms/cage, only sites with double occupancy are present, thus producing a single resonance. The observations that only a single resonance is observed in Ca-Y at loadings less than 2 xenon atoms/cage, and that the chemical shift of the high-field component remains unchanged when peff is larger than 2 xenon atoms/cage (see Figure 12) suggest that the two xenon atoms are attached to the adsorption site with equal strength, and the doubly occupied sites are much more stable than singly occupied ones. The adsorption pairs form at the lowest loading of xenon and remain even when perfis much larger than 2 xenon atoms/cage. The paraboliclike u(293K,p) in Ca-Y and Mg-Y indicates the presence of strong adsorption sites at 293 K. Such a dependence persists in Ca-Y at 144 K. Ito and FraissardZ have suggested that the large u(293K,O) observed in Mg-Y and Ca-Y is associated with the "strong electric field" effect. They reason that the contribution of the electric field to the chemical shift goes as the square of the field strength and the electric field of a cation scales with its formal charge. Therefore the electric field contribution to the chemical shift from a 2+ cation is 4 times larger than that of the 1+ cation. A small 2+ cation should have a stronger field effect than a large 2+ cation because of the shorter distance between the xenon atom and the origin of the field. This is, however, opposite to what we observe for Mg-Y, Ca-Y, and Ba-Y at both 293 and 144 K. We suspect that other factors may also influence the chemical shift. In the following, we suggest an alternate interpretation that may explain the strong adsorption as well as the large chemical shift observed in zeolites with 2+ cations. Let us consider the situation of a xenon atom and a 2+ cation, M2+,in empty space. The ionization potential of Xe Xe+ is 12.1 eV, which is about the same as that for M+ M2+. More specifically, for Mg, Ca, and Ba, they are respectively 15.0, 11.9, and 10.0 eV.20 If we neglect for the time being the Madelung repulsion between the M+ and Xe+ ions, which is important only when the two ions are very close together, there is a high probability that the system can exist as (M+,Xe+)in addition to the (Mz+,Xe) configuration. That is, an electron can be transferred from the xenon atom to the Mz+ ion with little or no energy change. The wave function of the system can be described as a linear combination of the wave functions of the (M+,Xe+)and (MZ+,Xe)configurations with approximately equal contributions from each. Taking the Madelung repulsion into account, the (MZ+,Xe)configuration is lower in energy than (M+,Xe+). Their energy separation is, however, sufficiently small that the (M+,Xe+) configuration still contributes significantly to the total wave function. Noting that when the distance between the xenon atom and the cation is sufficiently small, the electrostatic effects due to the A104- groups in the zeolite cage enter only in second order,
(19) Anderson, M. W.; Klinowski, J.; Thomas, J . M. J . Chem. Soc., Faraday Trans. 1 1986, 82, 2851.
(20) See for example: Handbook of Chemistry and Physics; Weast, R. C., Ed.; The Chemical Rubber Co.: Cleveland, 1986.
-
--
The Journal of Physical Chemistry, Vol. 92, No. 18, 1988 5179
Xenon Adsorbed in Y Zeolites we can write, in the first approximation, the ground-state wave function +o as
where
xa and ya are respectively the Sp, and 5py orbitals of the xenon atom, &, is the s atomic orbital of the cation, a and P are the spin functions, and the vertical bars represent the Slater determinant. For simplicity, we consider only the 5p, and 5py atomic orbitals of the xenon atom. aj represents the formation of a valence bond between the xenon atom and cation by donation of one of the xenon 5px electrons to the s orbital of the cation, thus defining the x axis as the bonding axis. The coefficients C, and Cj are positive numbers determined by the variation method. Let H be the Hamiltonian of the system, Ei = ( %i(H19i),Ej = ( aj1qaj),and W = (@ilHl@j). Then the mixing of aj with aistabilizes the energy of the ground state, $o, by t/2[(Ei - E,)’
+ 4W]’/’ + (Ej - Ej)/2
below Ei. We have, for simplicity, neglected the overlap integral between ai and aj. The strong adsorption of xenon to the 2+ cation sites may be the result of this stabilization energy since aj is an adsorption state. The strength of adsorption is governed by two factors: ( 1 ) (Ei - E,), which is approximately given by
Ei - Ej
-
-
-
-[(Xe Xe’) ionization energy - (M+ M2+) ionization energy + Madelung repulsion xenon polarization energy due to the field of the cation]
where the Madelung repulsion is about 2-3 eV; (2) W, which is determined by the overlap between the xenon Sp, and the cation s b orbitals. (E;- Ej) is probably largest for the magnesium ion Mg2+ and smallest for barium because of the larger Mg’ ionization potential. The magnitude of Wshows an opposite trend, being largest for barium due to the large overlap between the xenon 5p and the Ba 6s orbitals and smallest for magnesium. In contrast, the ionization potential of M M+ for a 1+ cation is rather small. The (M,Xe+) configuration does not contribute to the ground state, which is essentially given by the (Mf,Xe) configuration. The xenon adsorption is therefore weaker in comparison. The connection between the large chemical shifts observed in zeolites with 2+ cations and the strong xenon adsorption can be understood by following the argument given by Saika and Slichter” for the interpretation of the large chemical shift observed in fluorine molecules. Theoretical work of AdrianI3 has shown that the chemical shift of xenon gas is dominated by the paramagnetic term. The diamagnetic contribution is several orders of magnitude smaller. In the Appendix, we show that the same situation holds for xenon adsorbed in the zeolite cages. According to Ramsey,22the paramagnetic shielding is given by
-
-
upara
= 2(eh/2mc)’C[1/(En - EO)][(OICLzkb)x k
n
(fllxLzk/rk310) + ( o I x L z k / r : l n ) (n1ZLzklo)l (14) k
k
k
electron from a fixed origin. The universal constants e, m, c, and h are respectively the electron charge, the electron mass, the speed of light, and the Planck constant divided by 25r (note that eq 14 follows the convention of downfield resonances having positive chemical shifts). The paramagnetic contribution is large whenever there are low-lying excited states whose Lzkmatrix element with the ground state is nonzero. For xenon gas and xenon in zeolites with 1 + cations, the contribution mainly comes from the atomic excited states that are more than 8 eV above the atomic ground state. For xenon atoms adsorbed at the 2+ cation sites, low-lying excited states like
(obtained by promoting one of the nonbonding electrons in the doubly occupied ya orbital to the singly occupied xa orbital) have nonzero matrix elements with 1c/o Explicitly, neglecting the overlap of xa and ya with Sb, we have
where ( l / r 3 ) 5 pis the average of l/r3 over the 5p orbital of the xenon, with the xenon nucleus as the origin. When over all the angles between the external magnetic field and the bonding axis between the xenon atom and 2+ cation are averaged, the contribution of $, to the paramagnetic shielding is simply upara
= 2 / ~ ( e h / m c ) ’ C , z ( l / r 3 ) 5 ~ /-( EEO) ,
(17)
Since $, is about (E, - EJ/2 + ]/’[(El - E,)’ + 4w2]’/’ above W when E, E,. Although the the ground state, ( E , - E,) exact value for W is not known, we expect that it is much less than the typical u covalent bonds in diatomic molecules, which are about 4 eV or less. This suggests that (E,,- E,) is much less than the xenon atomic excitation energy. Therefore, whenever there is a considerable mixing of the (M+,Xe+) configuration in the ground-state Le., whenever C, is significant, a large paramagnetic chemical shift is expected. For instance, with C, = 0.1, (E, - Eo) = 2 eV and ( l/r3)5p= 22/a03 (ao being the bohr r a d i ~ s ) , ’we ~ obtain upara= 106 ppm. An alternate way of looking at this is by the molecular orbital (MO) approach.24 The similarity in the M+ M2+ and Xe Xe’ ionization potentials suggests the formation of molecular orbitals by linear combination of the xa of the xenon atom and sb of the cation. Namely, we have
-
-
-
taxa + cbsb
4g
=
~
=I cbxa - cas,
I
-
(18) (19)
as the bonding and antibonding MO, respectively. At the ground state, 4gis populated by two electrons originating from the xenon 5p, orbital while q5u is empty. Again, we take the x axis as the bond direction. The large contribution to eq 14 comes from the excitation of an electron from the nonbonding ya orbital to the antibonding 4”. With use of the fact that (yalL,(C$, - cash) icb and (E,, - E,) AE, where AE is the difference in energy between 4” and ya orbitals, eq 14 can be reduced. After averaging over the angles between the external magnetic field and bond direction and summing over the up and down spin, one obtains
-
upara
= 2/33(eh/mc)’(2Cb2)(1/r3)5,/AE
-
(20)
In) is the nth electronic eigenstate of the system in the absence of the external magnetic field (IO) being the ground state), and E,, is its energy. The subscript k represents each electron in the system. LPkis the orbital angular momentum of the kth electron in the direction of the external field. rk is the distance of the kth
Equation 20 has the same form as eq 17 except with (8, - Eo) replaced by AE and C, by 2”’Cb. This analysis associates the strong xenon adsorption in zeolites containing 2+ cations with the formation of the bonding state @* between the xenon atom and the 2+ cation. The bond may be a weak one depending on
(21) Saika, A,; Slichter, C. P. J . Chem. Phys. 1953, 22, 26. (22) Ramsey, N. F. Phys. Reo. 1950, 78, 699; Phys. Reo. 1951, 83, 540; Phys. Reo. 1952, 86, 243.
(23) Sternheimer, R. Phys. Rev. 1951, 84, 244. (24) Carrington, A.; McLachlan, A. D. Introduction to Magnetic Resonance; Harper and Row: New York, 1967.
5180 The Journal of Physical Chemistry, Vol. 92, No. 18, 1988
the magnitude of C,. The bond formation provides the low-lying excited-state 4,,, which leads to a large paramagnetic chemical shift. The M O picture also suggests the possibility of formation of three-center bonds involving two xenon atoms at a 2+ cation site. This leads to an adsorption of two xenon atoms per site, one interpretation suggested earlier for the rapid cooling experiments in Ca-Y and Ba-Y. Let us consider the simple case of having two xenon atoms interacting with the 2+ cation along the x axis. Then the three-center MOs can be written as bonding MO:
$g
= Cl(x,
& = (x, - xc)/2ll2
nonbonding MO: antibonding MO:
+ ~ , ) / 2 ' +/ ~C2sb
+
$,, = C2(xa ~ , ) / 2 l-/ ~ Cpb
For open three-center bonds where the two xenon atoms do not interact with each other, two pairs of the 5p, electrons, one pair from each xenon atom, fill the bonding 4g and the nonbonding &. The stabilization energy (below the energy of a single xenon atom) is ( [ ( E ,- E J 2 8A2I1/*+ (E, - E,)) in comparison to ( [ ( E , - E,)' + 4A2]'/' + ( E , - Es))for the two-center bond described E,, it is 8li2 A versus 2A. Here E, = ( ( x , earlier. For E, X , ) / ~ ~ / ~ I ~ +( X x~, ) / 2 ' / * ) ,E , = (sblHIsb),and A = ( X # @ b ) . Therefore it will be highly preferable for two xenon atoms to attach to a 2+ cation site if the local geometry around the cation site allows, Le., if there are not steric effects. Effects of the three-center bonds on the chemical shift can be calculated in the same manner as those of the two-center bonds. The main contribution comes from the excitation of electrons from the y , or y, orbital to the antibonding $,. The resulting expression for uparais the same as eq 17 but with C, replaced by C2 and ( E , - Eo) by the energy difference between the y , and antibonding $,, orbitals. Including the interaction between the two xenon atoms will lower the energies of the 4gand & orbitals. This further stabilizes the three-center bond system. The lowering of the energy of the antibonding 4,, reduces its energy separation from they, or y , orbital, resulting in further increase in upara. We have mentioned earlier that small 1+ cations like Naf usually locate near the A104- groups and are shielded from the xenon atoms by the electron cloud associated with the A104groups. However, this would not happen to a small 2+ cation such as Mg2+ or Ca2+because now the 2+ cation has to balance the charges of two AlOC groups. It probably locates somewhere between the two sites, leading to larger exposure to the xenon atoms.
-
+
+
Conclusions We have shown that lz9XeNMR at 144 K can provide valuable information about the electronic environment inside zeolite cages and the cage volume. It also sheds light on the area of critical phenomena of finite systems with only few atoms. The major conclusions are summarized in the following: When the xenon loading is less than 6 xenon atoms/cage, xenon does not go through a gas-liquid phase transition at 144 K, a temperature well below the normal freezing temperature of xenon gas. Similar to results a t 293 K, the lz9XeN M R chemical shift at 144 K retains an initially linear dependence on the xenon density in the cages when the xenon adsorption sites in the cages are weak. It becomes paraboliclike when the adsorption is strong. The initial chemical shift as a function of the xenon loading can be explained in terms of rapid exchange between adsorbed xenon and xenon atoms remaining in the gas phase in the cages. A gas-liquid phase transition is observed when the xenon loading is about 7 xenon atoms/cage. The trcnsition is charac-
Cheung et al. terized by a rapid increase in the chemical shift and a collapse of the line width. Prior to the transition, there is a large increase in the line width due to the large fluctuation in the number density of xenon atoms in the cages. The supercage in Y zeolite can hold between 10 and 11 xenon atoms. The resulting chemical shift is between 250 and 270 ppm downfield from the external reference of xenon gas (at 2 atm and 293 K). At a higher xenon loading, condensation of excess xenon at the exterior surface of the zeolite microcrystallites as solid xenon can be observed. It is identified by the chemical shift of 304 ppm downfield. The rapid cooling experiments indicate that there is one xenon adsorption site per supercage. In Na-Y, Mg-Y, and K-Y each site can accommodate only one xenon atom while in Ca-Y and Ba-Y, two xenon atoms can share the same site. The strong adsorption of xenon in zeolites with 2+ cations may be explained in terms of a partial bond between the xenon atom and the 2+ cation formed by donation of a xenon 5p electron to the empty s-orbital of the cation. The bond formation introduces low-lying electronic excited states which lead to a large paramagnetic contribution in the chemical shift. Acknowledgment. We acknowledge Dr. G. D. Parks for his comments on the manuscript and discussions throughout the course of this work. We also thank L. R. Potts for his technical assistance. Appendix A I . As shown by Ito and Fraissard,2 the 129Xechemical shift depends on p , the average number of xenon atoms per supercage actually trapped inside the zeolite. At room temperature, p is different from peff and is a function of the pressure p of the gaseous xenon above the sample. For g grams of sample in a sealed NMR tube of volume L' at temperature T , p is given by P
= Pen - @L'/RT)Cf/8g)
(A11
where we have used the ideal gas law to relate p to the number of gaseous xenon atoms above the sample. f i s the formula weight per unit cell, and R is the gas constant. p is related t o p by the adsorption isotherm. For moderate loading of xenon, one can write P
-
c'p
(A21
where c'is the proportionality constant. Then eq A1 becomes P
=
(A31
UPeff
+
where u = [ 1 (c'u/RT)(f/8g)]-'. For a fixed amount of sample in a given NMR tube at a given temperature, u is a constant. Thus p is simply proportional to perf. A2. Using eq 11 and neglecting the overlap integral between the xenon 5p and the cation s orbitals, we can show the diamagnetic contribution to the chemical shift to be (A41
+
where the operator 0 is defined as ( x 2 y2)/r3 with the origin of the coordinate centering at the xenon nucleus. The ratio of the diamagnetic and paramagnetic contribution is therefore udia/'para
=
% [ ( E ,- Eo) / ( e 2 / 2 a o ) l[ao-2((
-
-
(0)d/ ( 1 l r 3) 5 p l
-
-
is the Bohr radius. Noting that (( 0)5p - (O),) is smaller than ( 0 ) 5and p using ( l / r 3 ) 5 p 22/ao3 and (0)5p 2/3(l/r)5p 4.4/ao, one finds a.
a0-2((0)5p -
For E , - Eo
-
(0)s)/(1/r3)5p
1-2 eV, udla/upara5 Registry No. '29Xe,13965-99-6.
-
0.2
