J. Phys. Chem. 1995,99, 619-622
619
The Anisotropic Chemical Shift of 129Xein the Molecular Sieve ALPO-11: A Dynamic Averaging Model? J. A. Ripmeester and C. I. Ratcliffe* Molecular Structures and Dynamics Group, Steacie Institute for Molecular Sciences, National Research Council of Canada, Ottawa, Ontario, Canada KIA OR9 Received: August 9, 1994; In Final Form: October 25, 1994@
The dependence of the anisotropic chemical shift of 129Xetrapped in the one-dimensional pores of the molecular sieve ALPO-11 was measured as a function of xenon loading. The anisotropy is axially symmetric and positive at low loading and then loses its axial symmetry with increased loading. An axial line shape is observed once again with increased loading, this time with the sign reversed from the previous time, with nonaxial line shapes at intermediate and high loadings. Two principal components of the observed shielding tensor vary linearly with Xe loading, and the third is invariant. All this behavior of the line shape is analyzed in terms of a statistical distribution of three types of xenon sites (which have either 0, 1, or 2 neighboring sites occupied by other Xe, Le., OXeO, XeXeO or XeXeXe), each with its characteristic shielding tensor, with fast exchange of the three site types at room temperature.
Introduction The NMR spectroscopy of 129Xe in microporous solids continues to be a popular area of research for both practical and fundamental reasons. A number of recent reviews have documented both the progress and some of the remaining problems which must be Some of the more fundamental problems relate to the extent and rate of motion which the xenon atom undergoes in the porous solid and the interpretation of the resulting average chemical shift? Even empirical correlations which have been measured or proposed?-8 relating the shift to various geometric parameters associated with pore or surface structure, depend on the knowledge of the location of xenon atoms, both in materials used for calibration and the material to be tested. In the highly anisotropic environment of pores and surfaces one expects to observe an anisotropic chemical shift component as well, similar to observations for clathrates and inclusion compounds where the xenon atom is truly In order to impose some limits on the xenon motional trajectory there is then a considerable advantage in studying pore spaces of low dimensionalitywith the pore space of dimensions similar to that of the xenon atom. The observed chemical shift anisotropy of the xenon atom should be an average over the volume sampled by rapid movement of the xenon atom. On the other hand, if the Xe were static at a site on a pore wall, one could expect a relatively large anisotropy. In-either case, the pore -space geometry may give important clues as to the xenon positions and hence an assignment of the shift tensor orientation. The "gas-in-a-bottle" model proposed by Demarquay and Fraissard' to account for loading-dependent shifts in microporous solids cannot be considered to be very satisfactory for most complex pore spaces as it neglects attractive xenon-wall interactions. The number of reported examples of 129Xechemical shift anisotropy observed in zeolites is quite limited (e.g., refs 2, 1013). Springuel-Huet and FraissardlO have previously reported the isotropic chemical shifts of 129Xein the aluminophosphate molecular sieve ALPO-11 as a function of loading. They observed that the line shapes had an anisotropy which changed
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Published as NRCC No. 37297. Abstract published in Advunce ACS Abstracts, December 15, 1994.
0022-3654/95/2099-0619$09.00/0
sign on going from low to high loading. Furthermore, using magic angle spinning to observe the isotropic shifts, they established that in the structurally similar SAPO-11the static line shapes arose from a single anisotropic chemical shift interaction. They attributed the variations in anisotropy to changes in the shape of the electron cloud around the Xe atom as more atoms were packed into the elliptical cylinder. Barrie and Klinowski have also reported observing Xe chemical shift anisotropies in ALPO-11.2q11 They found that the line shapes became more complex on cooling. We have recently studied the changes in chemical shift anisotropy at room temperature in more detail and have developed a dynamic averaging model based on a statistical distribution of xenon site types which can account for the observed loading dependence of the chemical shift anisotropy. A preliminary account of this work has been presented previou~ly.'~ ExDerimental Section 129XeNMR spectra were obtained at 82.98 MHz on a Bruker MSL 300 spectrometer at ambient temperature. Spectra were recorded with a solenoid probe which gave a 90" pulse length of about 5 ps. Samples of &PO-1 1 were obtained from Union Carbide (courtesy of Dr. S. Wilson), calcined to remove the organic template, dehydrated and loaded with calibrated amounts of Xe on a vacuum line, and sealed in 10 mm 0.d. pyrex tubes. Results and Discussion 129XeNMR line shapes are shown in Figure 1. At low loading the line shapes are approximately axially symmetric with positive anisotropy. At higher loading, three tensor components are visible until again two components coincide and an axial line shape with negative anisotropy arises. Finally the line shape becomes nonaxial again and at the highest loadings the anisotropy is again positive. Initial estimates of the chemical shift anisotropy parameters were obtained by measuring the peaks and edges of the spectra. These were then used to simulate spectra and the parameters were adjusted until a reasonable comparison between experiment and simulation was obtained, Figure 1. The agreement is not perfect, since the experimental line shapes are not perfect tensor powder patterns, but is sufficient to give anisotropy parameters to within f 5 ppm
Published 1995 by the American Chemical Society
Ripmeester and Ratcliffe
620 J. Phys. Chem., Vol. 99, No. 2, 1995 A
i B
i
1 4/ E
J I
J
100 ppm
200
200
100 Ppm
Figure 1. Experimental (left) and simulated (right) lZ9XeNMR line shapes for xenon sorbed in ALPO-11. Loading levels: A = 1.58, B = 2.70, C = 3.80, D = 5.16, E = 5.83, F = 8.05, G = 10.30, H = 11.10, I = 13.40, J = 16.40 mol of Xe ( ~ l O - ~ ) of / g dry ALPO-11. A fractional moles Xe/g of dry ALPO-11. The vertical lines at 135 ppm indicate the position populationf= 1 (i.e., fully loaded) corresponds to 16.4 x of the invariant tensor component. 1
J
601 0
I
I
4
I
1
8
I
I
12
I
1
16
x I O - ~mdes Xel g. of dry ALPO-11 Figure 2. lz9XeNMR chemical shift tensor components as a function of loading for xenon sorbed in ALPO-11. The solid lines represent
linear least squares fits to the data, and the dashed line represents the corresponding variation of the isotropic shift. at worst. The behavior of the three principal components of the chemical shift tensor as a function of loading are shown in Figure 2. Within error, one component is constant and the other two show a linear dependence. The isotropic shift value also has a linear dependence in agreement with previous results.10 Structural Considerations. The structure of ALPO-11 consists of distorted comer-sharing A104 and PO4 tetrahedra forming an infinite framework where all the linkages are AlO-P.14 Superficially the pore space of ALPO-1 l can be thought
of as a one-dimensional elliptical cylinder. However, on close inspection of the Van der Waals contacts of a xenon atom with the atoms which form this channel, it becomes apparent that the cylinder is a chain of connected identical cells, with a rotation of 180' about the cylinder axis between adjacent cells (see Figure 3). Size constraints indicate that only one Xe can fit into each cell, a situation equivalent to 4 Xe atoms per crystallographic unit cell or 16.4 x mol of Xe/g of dry ALPO-11, which is consistent with the observed maximum loading level. lo Moving along the long axis of the channel there are slight overlaps with 0 atoms forming the neck between cells, thus indicating that there will be a small barrier to passage between cells. It is also important to recognize that it would be extremely difficult if not impossible for Xe atoms to squeeze past each other inside the channel. When xenon is loaded into the channel one can then distinguish three basic types of sites: (a) xenon with 2 empty adjacent cells (OXeO), (b) xenon with one empty and one filled adjacent cell (OXeXe), and (c) xenon with two xenon neighbors (XeXeXe). Defining the axis along the channel as z and x and y as the short and long axes of the cross section of the channel at the center of the cell, one can describe the freedom of movement (Le., before Van der Waals contacts occur) of a Xe atom with no Xe neighbors as follows: f0.64%, (z), f 0 . 3 6 A (x), +1.49 to -1.38 %, 6).When there is a Xe atom in an adjacent cell Xe-Xe overlaps also come into play, for certain positions of the xenons, and the freedom of movement then depends on the time-dependent location of the second Xe. Model. Our model relies on the very reasonable assumption that Xe has a different chemical shift tensor in each of these three sites. Differences due to next nearest neighbors are considered to be only minor. On the very short time scale each Xe samples only the small cell space that it currently occupies giving an averaged tensor characteristic of that cell type. Xe
Anisotropic Chemical Shift of 129Xein ALPO-11
J. Phys. Chem., Vol. 99, No. 2, 1995 621 TABLE 1: Xenon Site Types and Their Distribution" limiting case N-site binomial distribution type population population
OXeXe Xe&Xe
channel axis Figure 3. The structure of one channel in ALPO-11, indicating the three types of xenon sites. Only A1 and P atoms of the framework are shown, and the atoms bounding one of the cells referred to in the text are shaded. in an adjacent cage restricts the freedom of the Xe considered and modifies the potential surface of the cell, hence the different tensors for the three sites. The model further assumes that movement to empty cells is facile at room temperature, Le., the barrier is quite low. Hence, on the time scale of the reciprocal of the 129Xeshift scale involved, there is rapid exchange among the three basic site types discussed above. The observed tensor at a particular loading is then a dynamic average of the chemical shift tensors for the three types of site weighted by their statistical probabilities. Note also a curious feature of this system; that when a single Xe is considered it does not necessarily have to move for its chemical shift tensor to change, as movement of other Xe atoms into or out of adjacent sites can cause this as well. For the OXeO and XeXeXe cases, symmetry dictates that the three tensor axes will be parallel to the channel axes. For the OXeXe case one tensor axis is parallel to the short axis of the channel, whereas the other two tensor axes are rotated out of the coordinate frame of the channel. However, there is an equal probability of having the rotation in the opposite direction because of the 180" alternation of the cage orientations, so that in the overall averaging when movement between different cells is rapid, the two orientations will give rise to an effective tensor with axes again aligned with all the channel axes. This effective tensor thus represents a 2-site average of the true OXeXe tensor. Unfortunately we do not know a priori which of the channel axes each of the tensor components is aligned with. The xenon occupancy probabilities of the three types of sites as a function of Xe loading must now be considered. First of all, it is assumed that the distribution of xenon site types is purely statistical, i.e., clusters of 2 or 3 xenon atoms are not favored or disfavored in any way. As a precedent, the
"f = M/N = fractional occupancy of ALPO-11 cells. The large brackets on the left-hand side of the equations enclose binomial coefficients. population distribution of isolated xenon clusters observed in NaA zeolite have been treated reasonably successfully assuming strictly statistical methods.15J6 Then we consider all the possible combinations along a chain of cells for a particular number of sites N with a particular number of atoms M,assessing for each Xe whether it has no neighbors (OXeO), one neighbor (OXeXe or XeXeO), or two neighbors (XeXeXe), and counting the number of times each situation occurs. To take account of the ends a wraparound is assumed. The results (Table 1) indicate binomial distributions over the three site types. Since we are dealing with a very large number of atoms we take the limit of N = to give the relative populations. Rapid exchange of the xenons among the three types of sites then brings about dynamic averaging of the components of the three chemical shift tensors weighted by these populations to give the observed effective tensor. Note that the low and high loading limits are special cases; at f = M/N 0 the observed chemical shift tensor corresponds to that for site OXeO and at f 1 to that for site XeXeXe. In the following we use the notation 6x, 6 ~62, to denote the components of the tensors parallel to the channel axes X, Y,Z. We have already pointed out that the principal axes of the tensors for the three types of cell are all aligned with the channel axes. In this special situation the averaged components are given very simply by the population weighted sum over the three sites for each axis orientation:
-
-
-
+ B2J11 -A + Cf = A + ( B -A) 2f-k (A - 2B + C)f 2
(S.JaVe=A(1
-A2
where A = 6~ for (OXeO), B = 6~ for (OXeXe), and C = 6x for (XeXeXe). There are identical expressions for the averaging of the 6 y and 6 ~ .Note that the binomial distribution in fact gives rise to a quadratic dependence on loading, but our results can be treated as linear within error. The condition under which this can occur is ifA - 2 8 C = 0 or B = (A C)/2 and then
+
+
(6x)ave = A + (C - Alf which is linear. Unfortunately we cannot say which sets of tensor components correspond to which channel axis. This problem could be resolved with a single crystal study. However, it is clear from the plots of the observed components versus loading (Figure 2) which components of the OXeO and XeXeXe tensors average together and also that one particular component is invariant. When f = 1/2 the relative population of the OXeXe sites is 1/2 and the populations of the OXeO and XeXeXe sites is 1/4 each. From the observed tensor components at half loading one can then calculate the OXeXe tensor components. The correspond-
622 J. Phys. Chem., Vol. 99, No. 2, 1995
Ripmeester and Ratcliffe
TABLE 2: Xenon Site Types and Corresponding 12%e NMR Chemical Shielding Parameters (ppm)
6P
site type OXeO OXeXe XeXeXe
79.8(6,) 135.1(6,) 190.5(6,)
128.3(6,) 177.3(6,) 225.0(6,)
daw 135.1(6,) 134.6(6,) 134.1(6,)
114.4 149.1 183.5
" J = X,Y,Z The columns correspond to 6 ~6, ~6, ~but , the exact labeling is unknown. In the rows the (6J refer to conventional ordering of the components in the principal axis system of the tensor for each site type. ing tensor components and isotropic shifts of the three sites (using results derived from linear least squares fits to the data points) are given in Table 2. Note that the columns under 6, in Table 2 correspond to the sets of parallel tensor components whose weighted averages for different xenon loadings fall on the linear plots of Figure 2. A lower limit for the xenon exchange rate can be estimated as follows: we must fiist recall that the powder line shapes are actually built up from many overlapping frequency components corresponding to different crystallite orientations. Taking this into account, the largest separation between two such exchanging components within a crystallite is, from Table 2, 190.5 - 79.8 = 110.7 ppm, equivalent to 9.2 kHz. For this frequency difference the fast exchange limit is about 2.3 x 104 jumpds. The line shapes would be expected to change considerably on cooling, as was indeed found experimentally by Barrie," and at some point the exchange should be slow enough that overlapped line shapes due to the individual cell types should appear. Of course the distribution may no longer be statistical when the motion freezes out. Conclusions This work makes it apparent that in order to improve our understanding of 129XeNMR chemical shifts it is very important to work with more fundamental parameters than just the isotropic component and, in particular, to make use of the chemical shift anisotropy. In this work we illustrate how the continuous variation of the isotropic chemical shift with xenon loading in ALPO-11 can be broken down into a problem
involving three chemical shift tensors characteristic of different xenon site types. This new dynamic model, which accommodates all the known facts, contrasts with the simplistic explanation for the chemical shift anisotropy put forward by Springuel-Huet and Fraissard,'" in which they envisaged a Xe whose electron cloud was fiist molded by the shape of the channel and then influenced by encroaching xenons as more atoms pack along the channel. It is also clear from our structural analysis that in the small diameter channels of ALPO-11, the xenon atom dwells most of the time enclosed in small cells, much as in a clathrate cage, but it is occasionally able to jump from one cell to a neighboring vacant one, behavior which is quite different from that of a gas. Acknowledgment. We would like to thank Dr. S. Wilson for kindly supplying the ALPO-11. C.I.R.would like to thank Dr. P. J. Barrie for useful discussions and for supplying relevant sections of his thesis. References and Notes (1) Dybowski, C.; B a n d , N.; Duncan, T. M. Annu. Rev. Phys. Chem. 1991, 42, 433.
(2) Barrie, P. J.; Klinowski, J. Prog. NMR Spectrosc. 1992, 24, 91. (3) Raftery, D.; Chmelka, B. F. NMR Basic Princ. Prog. 1994, 30, 111. (4) Ripmeester, J. A.;Ratcliffe,C. I. h l . Chim. Acta 1993,283, 1103. ( 5 ) Johnson, D. W.; Grifiths, L. Zeolites 1987, 7, 484. (6) Derouane, E. G.; Nagy, J. B. Chem. Phys. Len. 1987, 137, 341. (7) Demarquay, J.; Fraissard, J. Chem. Phys. Lett. 1987, 136, 314. (8) Ripmeester,J. A.;Ratcliffe, C. I.; Tse, J. S.J . Chem. SOC.,Faraday Trans 1 1988, 84, 3731. (9) Ripmeester, J. A.J . Am. Chem. SOC.1982, 104, 209. (10) Springuel-Huet, M. A.;Fraissard, J. Chem. Phys. Lett. 1989, 154, 299. (11) Barrie, P. J. Ph.D. Thesis, Cambridge University, 1990. (12) Pellegrino, C.; Ito, T.; Gabelica, Z.; Nagy, J. B.; Derouane, E. G. Appl. Catal. 1990, 61, L1. (13) Ripmeester, J. A.;Ratcliffe, C. I. Proc. 9th Int'l Zeolite Conf.; Montreal, 1992,; von Ballmoos, R., et al., Eds.; Butterworth-Heinemann, 1993, 571. (14) Bennett, J. M.; Richardson, J. W., Jr.; Pluth, J. J.; Smith,J. V. Zeolites 1987, 7, 160. (15) Chmelka, B. F.; Raftery, D.; McCormick, A. V.; de Menorval, L. C.; Levine, R. D.; Pines, A. Phys. Rev. Len. 1991, 66, 931. (16) Jameson, C. J.; Jameson, A. K.; Gerald, R.; de Dios, A. C. J . Chem. Phys. 1992, 96, 1676. JP942102F
