J . Phys. Chem. 1991, 95, 4496-4500
4496
Solid-State Cesium433 NMR Studies of Cations in Cs/Li/Na Zeolite A An Example of Cation Dynamics Involving Three Sites Myong K. A h * Department of Chemistry, Indiana State University, Terre Haute, Indiana 47809
and ~
E.Iton*
M O X
Materials Science Division, Argonne National Laboratory, Argonne, Illinois 60439 (Received: October 1 , 1990;
In Final Form: January 22, 1991)
l13Cs NMR spectra show marked changes in the line shape as a function of temperature for a fully hydrated zeolite A sample containing a mixture of Li+, Na+, and Cs+ ions. A single Lorentzian peak is observed at temperature above 285 K, and three resolvable peaks are observed at temepratures below 268 K. These three peaks arise from the Cs+ ion at the sites of the single eight-membered ring (S8R), the single six-membered ring (S6R), and the a-cage sites near the four-membered rings. The experimental line shapes are satisfactorily simulated by the modified Bloch equations that include the chemical exchange kinetics between these three sites. The analysis yields a lifetime, T , of 0.12 ms for the Cs+ at S8R site at 297 K. The Arrhenius plot yields an activation energy of 44 kJ/mol for the site-exchange process of the charge-balancing Cs+ ions. The exchange between the S6R and S8R sites is considered to be the elementay step of the Cs+ diffusion process.
Introduction
Zeolites are crystalline aluminosilicates that have ion exchange The crystallographic structure of zeolite A may be described in terms of a sodalite cage with a cubooctahedral shape also known as a @-cage. This cage consists of four-membered rings (4R) separated by contiguous single six-membered rings (S6R). The type A structure is obtained by arranging these cages at the corners of a cube by joining the adjacent 4Rs in double four-ring arrangements. This arrangement creates large a-cages separated by a single eight-mebered ring (S8R) between them.3+' Previously we have reported the use of 1 3 % 3 nuclear magnetic resonance spectroscopy (NMR) of solid samples in elucidating the information concerning the cation sites from the two resolved Il3Cs peaks at low temperature.I0 The analyses of the static NMR line shapes as a function of temperature provided details of the cation motion in the zeolite in the absence of any bulk fluid. The fact that the line broadening and experimental line position are not due to the Il3Cs quadrupolar interaction has been demonstrated from the magic-angle spinning (MAS) Il3Cs NMR experiments reported recently in another paper." In that paper we have shown also the '13Cs MAS N M R spectrum of Cs/Li/Na-A zeolite, which suggests the presence of a third resolved Cs site at low temperatures. In this paper we present a detailed analysis of the Cs/Li/Na-A Il3Cs static NMR line shapes in order to elucidate the nature of the three Cs sites and to study the motional characteristics of the cations at these sites. These site-exchange motions are steps in the long-range diffusion of the cations. The room-temperature motions of hydrated charge-balancing cations have been proposed to explain 23NaNMR line shapes1* and interparticle diffusion phenomena.l3-I5 Melchior et a1.l 16 interpreted 29Siand 7Li NMR spectra of Li/Na-A in terms of preferential occupation of cation sites. More recently Weiss and Kirkpatrick observed 131CsN M R spectra of hectorite and other Cs-exchanged clays.17 Similarly resolved 133CsNMR peaks corresponding to different sites were noted in dehydrated mordenite.I8 Experimental Section
The experimental procedures and specifics have been described previously.10J1J9 The N M R spectra were obtained by using a static high-power probe of a Bruker CXP 200 multinuclear spectrometer with a nominal l13Cs frequency of 26.235 MHz at 4.7 T. A standard Bruker variable-temperature control unit was To whom correspondence should be addressed.
0022-3654/9 1 /2095-4496$02.50/0
used without further temperature calibration. All the samples for this work were equilibrated a t 100% relative humidity prior to taking the NMR measurements. A typical run collected 5000 free-induction decay curves (FID)after a 4-rs pulse and an acquisition delay of 19 p s with a 0.5srelaxation delay and with a sweep width setting of 1000 ppm. A 4k fast Fourier transform (FFT) was carried out without arbitrary line broadening. The chemical shifts are referenced with respect to an external 0.1 M aqueous CsCl solution.I0 Due to the large line widths of the spectra at the lowest temperatures, the chemical shift values are limited within f 3 ppm. The formula for the pseudo-unit-cell of zeolite A is M12A112Si12048, where M is a charge-balancing univalent cation. Lithium-substituted type A zeolite was prepared from the sodium-A zeolite by a standard aqueous-ion-exchange techniq~e.'~ It was subsequently ion exchanged in a 0.1 M aqueous CsCl solution. When two or more charge balancing univalent cationic (1) Breck, D. W. Zeolite Molecular Sieves; Krieger: Malabar, 1984. (2) Newsam, J. M. Science 1986, 231, 1093. (3) Broussard, L.; Shoemaker, D. P. J. Am. Chem. Soc. 1960.82, 1041. (4) Gramlich, V.; Meier, W. M. Z . Kristallogr. 1971, 133, 134. (5) Reed, T. B.; Breck, D. W. J. Am. Chem. Soc. 1956, 78, 5972. (6) Seff, K. Acc. Chem. Res. 1976, 9, 121. (7) Dempsey, E. J . Card. 1977, 49, 115. (8) Mikovsky, R. J.; Marshall, J. F.; Burgess, W. P. J . Cafal. 1979, 58, 489. (9) Newsam, J. M.; Jarman, R. H.; Jacobson, A. J. J . Solid Stare Chem. 1985, 58, 325. 1101 Ahn. M. K.: Iton. L. E. J . Phvs. Chem. 1989. 93. 4924. (1 1) Tokuhiro, Ti;Mattingly, M.; Iion, L. E.; Ahn, M. K.J . Phys. Chem. 1989, 93, 5584. (12) Kundla. E.; Samoson, A.; Lippmaa, E. Chem. Phys. Lerr. 1981.83, 229.
(1 3) Kokotailo, G. T.; Lawton, S.L.; Sawruk, S.In Molecular Sieves II; Katzer, J. R., Ed.; ACS Symposium Series, No. 40; American Chemical Society: Washington, DC, 1977; p 37. (14) Fyfe, C. A. Kokotailo, G . T.; Graham, J. D.; Browning, C.; Gobbi, G. C.; Hyland, M.; Kennedy, G. J.; DeSchutter, C. T. J . Am. Chem. Soc.
1986, 108, 522. (15) Borbely, G.; Beyer, H. K.: Radics, L.; Sandor, P.; Karge, H. G. Zeolites 1989, 9, 428. (16) Melchior, M. T.; Vaughan, D. E. W.; Jacobson, A. J.; Pictroski, C. F. In Proceedings, 6rh International Zeolite Conference, Reno, 1983; Olson, D., Bicio, A., Eds.; Butterworths: London, 1984; p 684. (17) Weiss, C. A., Jr.; Kirkpatrick, R. J.; Altaner, S.P. Geochim. Cosmochim. Acta 1990, 54, 1655; in press. (18) Chu, P. J.; Gerstein, B. C.; Nunan, J.; Klier, K. J . Phys. Chem. 1987, 91, 3588. (19) Tokuhiro, T.; Iton, L. E.; Peterson, E. M. J . Chem. Phys. 1983, 78, 7473.
0 1991 American Chemical Society
The Journal of Physical Chemistry, Vol. 95, No. 11. 1991 4491
Cations in Cs/Li/Na Zeolite A
0
-200 ppm
A
200
0
6
-200 ppm
-200
Figure 1. Full spectra of I"Cs FT NMR at 4.7 T of Cs' in Cs/Li/Na-A zeolite. The singlet at room temperature and three resolvable peaks at the lower temperature are shown.
species are present, we designate it by M,M'?M'',, where the numbers denoted by the subscript for each ionic species add up to the number of framework A1 in the pseudo-unit-cell. Elemental analyses of Al, Si, Cs, and Li of the final sample indicated the composition All 1,7Si12,3C~2.~LiS.3Na3.9r where the N a values was deduced from the charge-balance requirement. Note that this sample was prepared from a Li/Na-A sample obtained by a single exchange of Na-A zeolite with aqueous lithium salt solution; hence the high residual sodium content. (The designation of this sample as Li/Cs-A zeolite in the previous publication" was made before the sample was chemically analyzed and reflects a misidentification of the parent Li-A zeolite as one of the highly exchanged samples which contained 11-67 Li+ ions/unit cell prior to the Cs+ ion exchange. None of the content of ref 11 is affected by this correction. As described in an earlier p~blication,'~ the procedure for near-complete (97%) exchange of the Na+ by Li+ requires a sequence of five successive exchanges of the Na-A with fresh batches of the Li+ solution.) Figure 1 shows two of the experimental spectra in the entire sweep range of IO00 ppm. The low-temperature spectrum of 253 K demonstrates three partially resolved peaks located at 72, 29, and 2 ppm. The room-temperature spectrum is a singlet with a chemical shift of 35 ppm and half-height width of 21 ppm. At 308 K, although the spectrum is not shown, the peak narrows to the half-height width of 12 ppm. Because the resonances do not extend beyond the f200 ppm range, the simulations are restricted to this range. The limited range spectra, shown in Figure 2a and the simulated spectra in Figure 2b, are discussed next.
Results The experimental spectra in Figure 2a show the temperature dependence of the line shapes. At temperatures above 285 K the observed line shape is that of a single Lorentzian. The line width becomes narrower at higher temperatures. Below 285 K the line continues to broaden and becomes nonsymmetric. At temperatures below 268 K resolution of three separate peaks can be observed, although the signal-to-noise ratio degrades due to the large line widths. The three peak positions do not vary within experimental error as the temperature continues to decrease. As demonstrated in the two-site case of Cs/Na-A, the shape changes are consistent with 133Csspin relaxation due to a chemical site-exchange mechanism.I0 In this case, however, the presence of three sites is apparent from the low-temperature spectra. We label the Cs ions a t the highest field site to be I, the lowest field site 11, and the middle site 111. Although the peak due to site 111 is small and looks as if it might be due to an impurity, there is no trace of this peak in the high-temperature collapsed spectra, implying that all three sites are involved in the exchange process. To extract the chemical site-exchange parameters, we simulate the experimental data using the modified Bloch equations at steady state.20 The NMR absorption intensities are proportional to the
iv\" J L I
-200
273K
2oo
6
260
I
2oo
h
I
I
I
.200
O
i
200ppm
'
1
0
I
.zoo
I
- 2 0 0 ppm
a b Figure 2. (a) Portion of the experimental '33CsNMR spectra at the specified temperatures. (b) Spectra simulated by using the three-site exchange with the parameters specified in Table I. The three position markers on the axis signify the position of the three separate peaks in the absence of the exchange process.
imaginary part of the transverse magnetization in the rotating frame. For this approach to be valid, we must verify that the isotropic chemical shift modulation due to the site exchange determines the line shapes. Since 133Csis a quadruopolar nucleus with 7/2 spin. the quadrupolar contribution to the spin relaxation must be assumed (20) Johnson, C. S.,Jr. In Aduonces in Magnetic Resononce; Waugh, J. S.,Ed.; Academic Press: N e w York, 1965; Vol. I , p 33.
4498 The Journal of Physical Chemistry, Vol. 95, No. 11, 1991
Ahn and Iton
TABLE I: CS/U/Na-A 'Ws N M R Line-Fit Panmeters'
263 273 278 285 297
0.20 0.15 0.15 0.050 0.00
0.33 0.25
0.25 0.083 0.00
0.083 0.062 0.062 0.021 0.00
0.084 0.22 0.33 0.46 0.73*
# P I = 0.49, PII= 0.47, Pill = 0.04. *With ul,ll = 1.16 X 104/s the lifetime of a Cs ion in S8R is
to be unimportant and contribute to the constant line widths of 1/T2only.*'Z Comparison of the resolved static spectra obtained at 4.7 T with the previously published MAS spectra" obtained at the higher field of 7.0 T shows that the quadrupolar interaction does not contribute to the peak positions and that the major features of the line shapes are not determined by this interaction. We discuss this point in more detail later. Simulation of the experimental line shapes requires solution of the three simultaneous linear Bloch equations.m This is done by considering the Cs+ ions undergoing a threesite hopping process involving sites 1-111, as 111 ==r I = I1 = 111 There are three steady-state modified Bloch equations given by (1)
where M+]is the transverse magnetization in the reference frame rotating at the frequency o f j the subscripts j and 1 stand for two different sites to be chosen from I, 11, or 111; and a is a constant. Solving these equations involves specifying the following parameters: the three site lifetimes, T ~three ; limiting relaxation times, Ta; three population factors, Pj; and six pu, which are the jump probabilities of a Cs+ ion leaving site 1 and reaching the destination site o f j with the condition that pjj = 0. An absorption spectrum, 1 0 , is the imaginary part of the rotating frame transverse magnetization: 10 = Im (M+I + M+II + M+III)
(2) The simulations were carried out until the experimental shapes were reproduced with the set that required the least number of arbitrary parameters. The parameters used to generate the set of simulated spectra shown in Figure 2b are listed in Table I. The values of the inverse time constants, 1 / T u and 1 / 3 , are listed in units of the chemical shift difference of the sites I and I1 in rad/s. The chemical shift difference, q l 1is, given by u1.11 =
2*(foI
-fad
where the site frequencies, foj, were introduced earlier. Although the simulations were carried out with the least number of constraints, the best-fit parameters are consistent with the following:
(3)
= p11/711 = 1/7111 and when I, j , and k stands for three different sites: 4/71
TPU = 1
(4) (5)
The three peak positions and population factors can be estimated from the low-temperature resolved peaks. With them only one of the three lifetimes, T], need be arbitrarily assigned. Including the three constant relaxation times, Tu,four arbitrary constants need to be specified for each simulation. Note that the contribution to the line widths from 1/TZjbecomes smaller, as expected, (21) Vasavada. K. V.; Kaplan, J. I. J. Magn. Reson. 1985, 61,32. (22) Westlund, P. 0.;Wennerstrom, H. J . Magn. Reson. 1982, 50, 451.
0.084 0.22 0.34 0.48 0.76 r1=
0.040 0.10 0.16 0.23 0.36
0.12 ms at 297 K.
at higher temperatures. In spite of the many constraints imposed, the comparison of spectra in Figure 2a with those in Figure 2b shows that the experimental line shapes are reproduced well by the simulations. To provide a critical assessment of the plausibility of the model and the resulting line fits, we demonstrate in the Appendix, using a concrete example of a set of altered spectra, that a satisfactory fit cannot always be obtained even when some of the above constraints are relaxed. This serves to convince us that the analyses presented here are realistic and that the simulated spectra are not arbitrarily fit with a fortunate combination of parameters.
Discussion Type A zeolite contains several possible sites for monovalent cations.24 Cs+ ions are introduced by ion exchange in aqueous solutions. Since the diameter of a Cs+ ion is larger than the largest opening provided by S6R for the sodalite cages, the Cs+ ions at this level of exchange are present only on the a-cage side of the zeolite structure as we have demonstrated previo~sly.'~.~' For a unit cell containing 12 monovalent cations there are three S8R sites and eight S6R sites available for the Cs+ ions. The twelfth site is located in the a-cage near a 4R.2S The site assignments for the Cs/Li/Na-A have been discussed earlier." The low-field peak, 11, with a chemical shift value of 72 ppm corresponds to the Cs+ ions located at the S6R sites. The high-field peak, I, at 2 ppm is assigned to S8R sites. The central peak, 111, at 29 ppm is left to be assigned to the sites near the 4R. Because of the overlapping peaks with the large line widths of the low-temperature resolved spectra, the chemical shift values may differ from the previously reported MAS values by as much as 3 ppm, which is well within the experimental uncertainties. The chemical shift values for the sites I and I1 in Cs/Li/Na-A are smaller in absolute magnitude than those of the corresponding sites in Cs/Na-A.I6 This is not surprising, since lithium contracts the crystallographic cubic unit cell dimensions of the type A zeolite to 120.4 pm, whereas all other known type A zeolites have the corresponding values within 132 f 6 pm.'J6 This contraction results in smaller coordination distances between the framework oxygen and the Cs+ ion, and the "'Cs chemical shift values are expected to be different. Another noticeable difference between the spectra of Cs/Na-A and Cs/Li/Na-A is the Cs+ ion distribution among sites I at S8R and I1 at S6R. A larger population of Cs+ ion is located in site I for Cs/Na-A than in site I1 with PI = 0.70 and PI1= 0.30. For the Cs/Li/Na-A the populations at the two sites are nearly equal with the population distribution of PI = 0.49, PII= 0.47. The remainder is in the site 111 near 4R with PIII= 0.04. This shift in Cs+ population is due to the fact that Cs+ ions must compete for favorable sites against the other types of cations, Na+ or Li+, present in the unit cell. The distribution of Cs+ in the Cs/Na-A shows that the smaller sodium ion occupies the choice site of the S6R, whereas the bulkier Cs+ ions prefer the larger S8R sites. In contrast to this the Cs/Li/Na-A distribution at this low Cs+ loading shows that Cs+ ions are nearly equally distributed in both S6R and S8R sites, indicating that the hydrated Li+ ions are capable of competing effectively for the S8R against the larger Cs+ ions. The high hydration energy of Li+ compared to that of Na+ makes it more (23) Vance, T.B.; Scff, K. J . Phys. Chem. 1975. 79,2183. (24) Hw,N. H.; Dejsupa, C.; Scff, K. J. Phys. Chem. 1987, 91, 3943. (25) Subramanian, V.; Seff, K. J . Phys. Chem. 1980,81, 2928.
The Journal of Physical Chemistry, Vol. 95, No. I I , I991 4499
Cations in Cs/Li/Na Zeolite A
sites
Nat
I. S8R 11, S6R 111, 4R
0
cs+
Lit 1.75
3.9
2.95
0
0.60
1.25
1
1.15 0.10
1
200
#The values are arranged to add up to 11.6 monovalent cations with the assumption that Na ions preferentially occupy S6R sites.
0
-2do
XK 0-2
2'
-
9'
0
t
/
-260
-
/
I
b
200
/O
..
I
I
3.8x 1 0 - 3
3.5 ~ 1 0 ' ~
K-1
1/ T
Figure 3. Arrhenius plot of In (l/z) versus I / T . The least-squares fit gives an Arrhenius activation energy of 44 kJ/mol for the three-site-exchange process of the Cs+ in the type A zeolite.
difficult to remove H20from its coordination sphere. The diameter of hydrated Li+ ion is larger than that of the dehydrated Na ion, and it is better accommodated at the S8R site than at the S6R site. Additionally, the possibility that the contraction of the framework dimensions due to the introduction of Li+ ions affects the Cs+distribution cannot be rules out.% Since the Na+ ions preferentially occupy the S6R sites, a complete site distribution of the three cations can be obtained. This distribution is presented in Table 11. The Arrhenius plot of the logarithm of the rate constants ( l / q ) is a stright line within the experimental error as shown in Figure 3. The slope of the line gives an activation energy of E' = 44 kJ/mol for the Cs+ ion site-exchange process. This value is somewhat higher than that for the Cs/Na-A, 38 kJ/mol. The static sample NMR spectrum at 297 K in Figure 1, top, (obtained at 4.7 T) is noticeably different from the MAS spectrum at a comparable temperature of 293 K reported previously (at 7.0 T)." The former is a Lorentzian-shaped singlet, whereas the latter shows shoulders that suggest incomplete collapse of the three site peaks at the comparable temperature of 293 K. This difference is expected, in part, from the difference in the Larmor frequencies of the spectrometer at 4.7 and 7.0 T, for the static and MAS spectrometers, respectively. The simulated line shape is determined by the reduced lifetime factor, 2rf&11~j where 61,11 is the chemical shift difference of the sites I and I1 in units of ppm. To obtain the same line shape, the higherfo of the MAS requires the shorter values that are reached at the higher temperatures. Also note that the site-exchange rate depends on the availability of the hydration water. Although all the samples are exposed to 10096 relative humidity prior to taking the spectra, the large volume of dry gas needed to operate the MAS probe over a sample tube, which is not air-tight, lowers the relative humidity of the sample. The dryer sample for the MAS results in a slower exchange rate affecting the line shape. (26) Barrer, R. 62. 1956.
M.;Klinowski, J. J. Chem. Soc., Furuduy Truns. I
1972,
I
I
200
0
-2b0
XK 200
,
0
-200
kK
Figure 4. Experimental spectra obtained by Fourier transforming the altered FID after dropping the first six points by lefi shvfing. The enhanced resolution aids assignment of chemical shift values while the line shapes are altered. (b) Simulated spectra corresponding to the beat fit of the altered spectra.
We now discuss the effect of MAS on the line shapes. MAS averages out the anisotropic part of the static Hamiltonian primarily narrowing the static line widths, l/Tv When the anisotropic contribution is due to the interactions between the spin dipoles, the line narrowing by MAS is limited only by the MAS sample spinning frequency. On the other hand the MAS line narrowing for a quadrupolar interaction is at best limited to the factor of 3.6,27whereas the peak position is determined by the magnitude of the interaction, MAS frequency, and the Larmor frequency of the spectrometers. Since there is no difference in the peak positions on the ppm scale between the static and MAS spectra, we conclude that the quadrupolar shift is negligible within experimental error. The contribution to the peak position and line widths due to the anisotropic chemical shift tensor should be small, since MAS narrows the line widths and could shift the peak positions to the isotropic chemical shift values. We see no such change in the peak positions or expected line narrowing in the MAS spectra. In Cs/Li/Na-A the three values of l / T v corresponding to the three sites are different. This difference may arise from the difference in the number of water molecules associated with the coordination sphere of the Cs+ ions at each site. If we assume that the primary dipolar interaction is between the spin dipoles of the 1 3 % 3 and the protons in the hydration water, then l/Tu is affected not only (27) Freude, D.; Haase, J.; Klinowski, J.; Carpenter, T. A. Chem. Phys. Lett. 1985. 119, 365.
Ahn and Iton
4500 The Journal of Physical Chemistry, Vol. 95, No. 11, 1991
by the number of water molecules coordinating the Cs+ ion but also by the time-dependent reorientational and exchange motions of the water molecules. It has been pointed out that the site lifetimes met the constraint imposed by eq 4. The site lifetimes are proportional to the site populations for sites I and 11, as was the case for the corresponding S6R and S8R sites of the Cs/Na-A. This implies that the site-exchange rate involving the two sites, I at S6R and II at S8R, is gooerned by first-order kinetics. In contrast, the lifetime for Cs+ions at the site III near 4R is independent of its steady-state population, Pie, indicating a zeroth order in Cs+ion population. The lifetime at site 111 is determined by factors other than those involving the Cs+ ions directly. One such factor is the presence of the large number of water molecules at the center of the a-cage.6 Undoubtedly for the site near 4R, Cs+ ions are away from the cage walls. Both the chemical shift value and the relatively narrow line width (long T2111) suggest that the Cs+ ions at this site are highly solvated by water molecules. It is reasonable to assume that Cs+ ions at the I11 sites near 4R are coordinated with four or more water molecules. The transfer of a Cs+ ion from site I11 into I or I1 site requires taking away more than one water molecule from the coordination sphere in order to provide the needed coordination with the framework oxygen atoms in the S6R or S8R. The coordinating water is expected to be highly labile, and the site exchange should be dominated by the motion of the water molecules, resulting in the zero-order exchange with respect to the concentration of Cs+ ions at site 111. An alternative explanation for the zero-order kinetics is that the lifetime of the Cs+ ion in the site 111 is governed directly by the Li+ ion lifetime. It should be noted that the occupancy of this site by Li+ is 0.6 ion/unit cell, compared to only 0.1 ion/unit cell for Cs+. The Cs+ ion site-exchange dynamics discussed in this paper provides a detailed local view of the Cs+ ion diffusion process. We first assume that the Cs+ ion is capable of moving from one unit cell to another at room temperature by going through the S8R openings only. The S6R and 4R openings are too small for the ions to pass through without rupturing the zeolitic framework. The combination of the lifetime, T ~ and ~ small ~ , population, P!lI, a t site 111 makes it unlikely for the loosely held ions at the site near 4R to contribute much, if at all, to the overall motion diffusion process of the Cs+ ions. This leaves the site-exchange motion between the S6R and S8R to be effectively contributing to the diffusion process.
We envision the Cs+ ion diffusion process to involve these ions hugging the interior wall of the a-cage and hopping from one S6R to an adjacent S8R. The next step is to move onto the original S6R or another contiguous one away from the first S6R. The latter motion can occur in either the original a-cage or in the adjacent cy-cage which shares the S6R. Only when the ion is located at the center of the S8R is it capable of moving into the next unit cell. Such two-dimensional conditional random-walk processes should result in the overall diffusion of the Cs+ ions across the entire c r y ~ t a l . ~ * * * ~ Acknowledgment. This work is supported by the U S . Department of Energy, BES-Materials Sciences, under Contract W-31-109-ENG-38 (L.E.I.), NASA Lewis Research Center Grant NAG3-952, and Indiana State University Research Committee (M.K.A.). We thank Dr. Mathew Hulbert and his associates of PitmawMoore for the elemental analyses of the zeolite samples. Appendix
When a simulation of a line shape involves setting a number of parameters, there is always a possibility that any shape can be reproduced falsely by adjusting the parameters arbitrarily. To show that this is not the case in simulating the '"Cs NMR spectra by using the modified Bloch equations, we show in Figure 4 one example of failure to obtain a set of satisfactorily simulated spectra of altered experimental spectra. The spectra in Figure 4a are obtained by six times left shifting the 1k digitized fid data. This procedure corresponds to deleting the first six FID points or setting the acquisition delay to 114 ps. It was done to enhance the resolution of the broad, overlapping low-temperature spectra. The fast Fourier transform of the altered spectra aided the assignment of peak positions. The calculated spectra in Figure 4b represent the best line-shape simulation of the altered spectra in Figure 4a at the specified temperatures. It is clear that the fits are much worse than those shown in Figure 2. The parameters used in calculating Figure 4b are also different from those listed in Table I and are purposely not listed in order to avoid confusion. Registry No. Cs, 7440-46-2; Li, 7439-93-2; N a , 7440-23-5. (28) Ahn, M. K.; Jensen, S.J. K.; Kivelson, D. J. Chem. Phys. 1972,57, 2940. -. - .
(29) Chandrasekhar,S.Reu. Mod. Phys. 1943, I S , 1.
