J . Chem. SOC., Furuduy Trans. 1, 1988, 84(11), 3731-3745 The Nuclear Magnetic Resonance of 129Xe trapped in Clathrates and some other Solids J. A. Ripmeester,* C. I. Ratcliffe and J. S. Tse Division of Chemistry, National Research Council of Canada, Ottawa, Ontario KIA OR6, Canada lZ9Xe NMR spectra were obtained for xenon trapped in the cages of clathrate hydrates and a clathrasil sample. The data, together with shift data for solid xenon, have yielded a linear correlation between the radius of the free space available to the xenon atom and the chemical shift. This observation cannot be rationalized by using simple binary collision theory. In order to account for the observation of anisotropic chemical shifts for xenon trapped in non-spherical environments a simple multiple-site model was developed.Several applications of 129Xe NMR spectroscopy are also presented. These include the identification of new clathrate hydrates, the use of '*'Xe NMR to follow changes in site symmetry in a clathrasil and a cyclodextrin inclusion compound, and the observation of trapping sites in crystalline and amorphous solids. Atomic 12'Xe, owing to its large polarizable electron cloud, has chemical shifts which are extremely sensitive to the physical surroundings of the xenon nucleus.1v2 The low- temperature solid has its resonance ca. 300 ppm downfield from the dilute gas. "'Xe NMR chemical shifts have been measured in binary mixtures of gases,3 and in dilute systems these can be understood in terms of a pairwise interaction model. More empirical approaches have been used in attempts to understand the chemical shifts of xenon dissolved in condensed phase^.^-^ For liquids, an approach based on a continuum model for the condensed phase has been used with some S U C C ~ S S .~ Several approaches have been formulated to account for the chemical shifts of xenon trapped in ze01ites.~'~ One of these correlates the chemical shift with the mean free path of the xenon atom,5 the other with the degree of curvature of the interacting surface.' However, detailed correlations of chemical shifts with structure are not well understood. Zeolites are not ideal materials to follow such correlation~,~-~~ as they are made up out of interconnected channels and cages, often with the locations of the exchange cations unknown.Also, the presence of diffusion is a complicating factor. Materials which appear to be ideally suited to test shift-structure relationships are the clathrates, where a xenon guest atom is located in a crystalline host lattice and localized in a well defined ~age.~O-'~ The clathrate hydrates15* l6 and the structurally related cIathrasilsl7 are particularly convenient host systems, as their structures have several types of cage which are not too far from being spherical. Past on the NMR of xenon trapped in the two types of cages of its structure I hydrate showed a downfield shift for xenon in the smaller cage. Also, there was a correlation of the cage shape with the observation of an anisotropic chemical shift. In this contribution, we further explore the relationship between cage size and shape and the chemical shift of the trapped xenon.Then the state of theory available for 12%e chemical-shift calculations will be reviewed, and finally several applications of 12'Xe NMR will be presented. 373 13732 NMR Study of 12’Xe in Solids Experimental In this section we will briefly mention some of the factors which influence the ease with which 12’Xe NMR signals can be obtained. The 12’Xe isotope, with 26.44% natural abundance and gyromagnetic ratio close to that of 13C, should be an excellent nucleus for NMR observation. One factor which rules against this is the absence of efficient spin-lattice relaxation mechanisms, so that for trapped xenon atoms relaxation times of 5-20 min can easily result. In polycrystalline solids where there is an anisotropic chemical shift, and therefore, considerable line broadening, this can lead to intolerably long acquisition times in order to attain a sufficient signal-to-noise ratio.However, in solids the possibility of using polarization transfer techniqueslg becomes an attractive possibility if an abundant nucleus such as the proton is present. The cross- polarization technique, as almost universally practiced today uses matching of the rare- spin and abundant-spin energy levels in the rotating reference frame (Hartmann-Hahn matching). This requires the presence of nuclear dipolar coupling between the abundant and rare spins. For quantitative work the relationship between spectral line intensities and the cross-polarization time must also be explored.In the case of rigidly held directly bonded nuclei, cross-polarization can be complete in times the order of 1 ms or less.2o However, in the case of 12’Xe, where abundant nuclei (protons) are always at least ca. 0.3 nm away, the cross-polarization process takes some tens of ms.lS One interesting advantage of the cross-polarization techniques is that it provides a way of discriminating against the signal from bulk xenon, since the signal can only arise from Xe atoms near to the protons. 12’Xe NMR spectra were obtained on a Bruker CXP-180 NMR spectrometer at a frequency of 49.8 MHz. In cross-polarization experiments, single contacts were used with r.f. field amplitudes of 3&60 kHz. Experiments at 77 K were performed by immersion of the sample directly in liquid nitrogen.Other temperatures were achieved with a conventional gas-flow system and a Bruker BVT- 1000 temperature controller. Magic-angle spinning experiments at room temperature were carried out with a probe utilizing Andrew-Beams spinners. Spinning experiments at low temperatures were performed by using a Chemagnetics probe and temperature controller. The preparation of hydrate,2’ clathrasil17 and cyclodextrin22 samples has been described previously. Results and Discussion Chemical-shift Correlations Isotropic Shifts For the sake of completeness, fig. 1 shows the previously reported 12’Xe NMR spectrum of the type I xenon hydrate,l3? la in addition to spectra of other xenon containing hydrate structures. The low-field, isotropic line of the type I spectrum can be assigned to xenon in the small cage, whereas the high-field line characteristic of an axially symmetric shielding tensor can be assigned to xenon in the more abundant type I large cages.Since the stability of clathrate hydrates depends on non-specific interactions between guest and host, the larger species in a mixture of guests usually determines the structure type due to efficient space-filling of the larger cages. Distribution of guests over the available sites then is determined by the appropriate Langmuir constants and the activities of the guests. The NMR spectrum of 12’Xe in type I1 hydrate was obtained for a mixed xenon-propane hydrate with most of the large cages filled with propane. The signal at high field can be assigned to large cage xenon, whereas the low-field signal, with a pronounced anisotropic chemical shift, can be assigned to xenon in the small type I1J. A .Ripmeester, C. I. Ratelife and J . S. Tse 12 - hedr al 14-hedral 12-hedral 16- hedral 12-hedral A 12-hedral I 100 ppm I 3733 Fig. 1. lz9Xe NMR spectra obtained at 77 K with cross-polarization of (a) Xe type I hydrate. (b) Xe-propane type I1 hydrate and ( c ) Xe-methylcyclohexane type H hydrate. cage. As a general rule, the lineshapes are isotropic for Xe in cages of cubic symmetry, otherwise they show various degrees of anisotropy and asymmetry. If the cage has a unique symmetry axis, an axially symmetric lineshape can be expected. The clathrasil dodecasil-3C in its high-temperature cubic phase is isostructural with type I1 hydrate,23 and as such provides two cages of similar shape and size as type I1 hydrate, but with a SiO, host lattice.The I2’Xe NMR spectrum of a dodecasil-3C sample with tetrahydrofuran and xenon as the main guests is shown later in fig. 6(a), and is reasonably similar to that of type I1 hydrate. The low-field line, due to xenon in the small cages, has the same sign of chemical-shift anisotropy with Aa of 44.9 ppm. The high-field line due to xenon in the spherical large cages has no noticeable anisotropy. Table 1 lists the clathrate types, the cages which occur, their symmetries and free van der Waals’ radii. The latter parameters were derived from the known structures by locating the cage atoms (0 for the hydrates, Si for the clathrasil), calculating th: mean radius .Of the cage, then subtracting the cage atom van der Waals’ radius (1.40 A for 0, 1.96 A for Si).The correlation between chemical shift and van der Waals’ radius of the trapping site is shown in fig. 2. Some additional data at the low-field end of the scale can be obtained by considering solid xenon itself. From the known xenon lattice parameters2* 9nd a xenon van der Waals’ radius derived from the structure determined at 4 K (2.167 A) the radius of the free space available to a xenon atom can be calculated. The overall correlation of the mean free radius of the space available to a xenon atom with the isotrqpic chemical shift is remarkably close to linear, with a slope of - 5.147 x A (ppm)-’. This observation is perhaps surprising in view of the very different interactions that the Xe atom experiences in the different structures.3734 NMR Study of IzgXe in Solids -300 -250 -200 - 150 - 100 - 50 0 (7 (PPm) Fig.2. Correlation of 129Xe isotropic NMR chemical shifts with the free-space radius available to the xenon atom: (1) solid Xe, 21 K; (2) solid Xe, 160 K; (3) dodecasil-3C, small; (4) structure I, small; ( 5 ) structure I, large; (6) structure 11, large; (7) dodecasil-3C, large. Table 1. Summary of cage characteristics and chemical-shift data 0xe(iSO) A o X e structure cage type" symmetry r,/Ab (pprnlc (ppm) hydrate type I hydrate type I hydrate type I1 hydrate type I1 hydrate type H hydrate type H hydrate type H clathrasil dodecasil-3C clathrasil dodecasil-3C m3 42m 3m 43m mrnm 62m 6/mm m3 43m - - 2.50 - 242 2.93 - 152 2.50 - 225 3.28 - 80 2.50 - 232 - -215 2.46 - 253 3.35 -81 - - 0 32 18 0 ca.-= 5 ca. 40 45 0 - " 51262 means that there are 12 pentagonal and 2 hexagonal faces. Mean free radius. Measurements for hydrates made in 200-240 K range for clathrasils at room temperature. Anisotropic Sh ijts All experiments to date indicate that the smaller the cavity in which the Xe atom sits the further downfield is the isotropic chemical shift. The Xe chemical-shift anisotropy tensors for cages which have a unique symmetry axis are found to be axial (see table 1). This requires the oZz component of the tensor to be aligned parallel to the unique symmetry axis. Naively one might expect that if the symmetry axis were also the shortest axis of the cage then B,, would be the low-field component (i.e.anisotropy negative) and vice versa if the symmetry axis were the longest. The results show the exact opposite: Xe in oblate cavities (e.g. structure I hydrate, large cage, and structure I1 hydrate, small cage) shows axial tensors with positive anisotropy, and in prolate cavities (e.g. phenol and P-quinol clathrates)". l4 shows axial tensors with negative anisotropy. [We initiallyJ . A . Ripmeester, C . I . Ratclifle and J . S. Tse 3735 had doubts about whether Xe-P-quinol fit into this pattern, since the cage in P-quinol clathrates has often been described as spherical. However, based on the X-ray diffraction structure of H,S-P-quinol (since the cell for Xe-P-quinol is not known) some simple calculations based on van der Waals’ contacts clearly indicated that the Xe would have more freedom along the three-fold axis of the cage, i.e.the cavity is prolate for Xe.] We are thus faced with the problem of explaining this apparent paradox between the cavity shape/anisotropy sign and the size/shift correlations. One simple model is as follows. Instead of regarding the tensor as that of a static Xe atom at the cage centre, assume that it is an average tensor arising from motion of the Xe atom over the surface of the cavity. This is inherently more plausible than a static Xe atom, since calculations using van der Waals’ hard-sphere contacts indicate that there is room for motion. We have also carried out Lennard-Jones potential calculations for Xe in hydrate cages and find that for large cages the minimum potential is not at the cage centre, and for smaller cages, where the minimum is at the centre, the potential remains quite low for modest excursions from the centre.It is assumed that at any particular site on the inner surface the chemical-shift tensor is axial and has a fixed anisotropy (which we will refer to as the static anisotropy). Further it is assumed that this tensor is oriented such that its o,, component is normal to the surface of the cavity. We know that the observed tensor must be oriented with its o;, along the unique axis of the cage (the prime notation is used to refer to the averaged tensor component). Consequently if we set up the description of the static tensor for any site in terms of this particular cage-fixed coordinate system and then average over all sites the resultant tensor will be diagonal.Furthermore, since the symmetry about this axis is greater than two-fold the averaged tensor must also be axial. We can also apply the axial symmetry to simplify the calculations, since for any particular site which has o,, oriented at an angle a with respect to the cage fixed z axis we can apply axial averaging among that and all other sites at an angle P around the cage axis. The result for such axial averaging at a particular angle is well known for three-fold reorientation of such groups as -CH, or -NHl, although this all follows from standard procedures as outlined by others:25 A 0 2 AoaV = -(3 COS~P- 1) where Aoav is the anisotropy of the averaged tensor at angle p and Ao is the static anisotropy.We must then calculate the population-weighted average over all values of B to obtain the averaged tensor anisotropy for the whole cavity: where PI( is the population at Pi. A simple approximation for is to equate it to the surface area for the element at pi. It is trivial to apply this model to a few simple cavity shapes which have only one or two types of angle populations. A cube, a regular octahedron or a cylinder with height equal to its diameter all give averaged anisotropies of zero. However, if stretched along their axes they all give negative anisotropies, and if compressed they give positive anisotropies. One finds a similar picture for ellipsoidal cavities, although the calculation is not so trivial. A sphere gives zero anisotropy (as it should) and a compression (oblate ellipsoid) produces a positive anisotropy .So the general pattern emerging from this3736 NMR Study of 12’Xe in Solids model is that prolate cavities give negative anisotropy and oblate ones give positive anisotropy. Provided we recognise and accept the implicit assumption that the static tensor has positive anisotropy, this can therefore explain the observed relationship between anisotropy and cavity shape. However, having derived this, one should reflect on the assumptions which have been made. The most serious of these are probably the ones concerning the static tensor, i.e. it is not likely that the static tensor will be strictly axial nor is it likely that it will be identical at every site. However, small divergences may not have a large effect on the calculated average.Theoretical Considerations According to Ramsey’s theory,26 the magnetic shielding of a nucleus can be divided into two components : the diamagnetic term and the paramagnetic term. The diamagnetic term is largely dominated by the contribution from the core electrons. Since the interactions between a free xenon and other molecules are dispersive, there is apparently no need to invoke covalancy in order to rationalize the variation of magnetic shielding in Xe.27 In addition, it is unlikely that the diamagnetic term will be sensitive to the environment. In contrast, the paramagnetic term is related to the induced excitations of the valence electrons into empty and continuum levels by the magnetic field, and it is the dominant contribution to the nuclear shielding for heavy elements. Therefore, the change in the paramagnetic term is mostly responsible for the variation of the 12’Xe nuclear shielding in different physical environments. The variation of the 12’Xe chemical shift in gaseous Xe under pressure has been studied in A virial expansion was used to analyse the experimental results. It was shown28 that at low pressure the chemical shift varies linearly with the pressure.This result suggests that binary collisions (or more exactly, two- body interactions) are the dominant processes at low pressure. At high pressure, higher-order terms (such as three- body interactions etc.) have to be taken into account. In mathematical terms the 12’Xe chemical shielding as a function of the density of the gas can be expressed as a(T,p) = a0+pa,(T,p)+p2a,(T,p)+ * .. * (3) The coefficients of the virial expansion an may be obtained by fitting the experimental data to eqn (3). According to statistical mechanics8 the first virial coefficient a1 can be written as the thermodynamic average of the two-body interactions : q(T, P ) = apW exp [ - W / k T I dr (4) s where a,(r) is the 12’Xe chemical shift when Xe interacts with another molecule at separation r and U(r) is the interaction potential. In principle, if both functions are known eqn (4) can be solved by Monte Carlo simulation and a comparison with experiment can be made. Unfortunately, in reality, an accurate interaction potential is very difficult to construct and knowledge of ap(r) is even scarce^.^' So far, there is no satisfactory theory which describes the nature of the two-body chemical-shift function although several approximate forms have been ~uggested.~’ Some models only consider the contribution from the diamagnetic term and evidently these will not be applicable to Recently, through the studies of “’Xe chemical shifts in different cages in the it was advocated that if the binary collision model is correct, the 12’Xe chemical shielding should be proportional to the number of collisions between the xenon and the atoms forming the cages.5 This conjecture was later tested in a series of calculations and it was found empirically that the chemical shift is inversely proportional to the ‘mean free path’ of Xe in the cage.This simple relationship, however, is not easily comprehended in view of the discussion presented above. Note that the binary collision 129Xe.30J. A . Ripmeester, C. I . Ratclifle and J . S. Tse 3737 model is only strictly valid for dilute gas interactions. Furthermore, the pairwise interaction chemical-shift function is weighted by the Boltzmann distribution which in turn is governed by the interaction potential. Also, this inverse relationship cannot account for the experimental observations presented here. It is informative, however, to analyse the two-body term of the virial expansion in detail. For xenon enclosed in a cage at moderate temperature (> 300 K), it can be assumed that the atom is situated at some equilibrium position from the cage wall. If we make the ansatz that the pairwise chemical shift can be replaced by an average value (op(0)), then eqn (4) can be written as ( 5 ) 01 = (o,(O)) I,.exp [- W l k T I dr- The volume integral in eqn ( 5 ) can be solved using the Lennard-Jones and Devonshire cell If the free volume in the encaged cavity is denoted by 6, then The chemical shift relative to the infinitely dilute Xe gas is where Kp,, is the volume of the cavity. Treating Xe as a hard sphere with radius a and where (R-a) can be identified as the ‘mean free path’ (0 of Xe in the cage. Note here that both (a,(O)) and (U(0)) are also dependent on the nature of the cavity. In the dilute Xe gas when the atoms are far apart (i.e. R $ a), (o,(O)) is very small and the shift from the free-atom value will also be small. Unfortunately, the cubic dependence predicted by eqn (8) does not agree with the correlation shown in fig. 2, where there is a linear correlation of with R.Evidently this empirical correlation requires more than a binary collision model, and we will not carry the analysis further. Another conclusion drawn from this theoretical analysis is that consideration of the binary collision term (two-body interactions) in the virial expansion alone should give the 12’Xe chemical shift approximately proportional to the third power of the ‘mean free path’ with a negative slope. This observation is at variance with the conjecture proposed ear lie^.^ In passing, we would like to point out that eqn (8) is an over-simplified solution to eqn (4). The limited experimental data prohibits a generalization of this relationship.However, any future serious calculations on chemical shielding should start with the full expression [eqn (4)]. To this end, ab initio quantum-mechanical calculations will be very useful in predicting the binary interaction chemical-shift function.12 So far only a few first-principle calculations have been performed. A more thorough theoretical investigation on a specific example will be desirable. Applications of Solid-state 12’Xe NMR Identijication of Hydrates Fig. 1 shows 12’Xe spectra obtained for the type 1,16 IF6 and H33 clathrate hydrates at 77 K. In this instance, our main interest is in the line positions rather than in line intensities. The main point is that each hydrate gives a unique pattern which is easily identified.When powdered ice and xenon are sealed together in a Pyrex tube, type I xenon hydrate forms readily on conditioning at 0 “C. In the presence of other potential guest molecules, type I hydrate reacts to form either type I1 or type H hydrates. This is3738 NMR Study of 129Xe in Solids \ ‘U A 1-100 ppm-i I \ Fig. 3. lz9Xe NMR spectra at 77 K of the reaction product of type I hydrate with tetramethylsilane to give a type H hydrate after storage in an ice-water bath for (a) 0, (b) 4, ( c ) 16, ( d ) 24 and (e) 40 h. illustrated in fig. 3 for a sample to which tetramethylsilane (TMS) has been added as potential guest material. The sample was stored in an ice-water bath, then, it was cooled to 77 K after various !engths of storage time, and the 12’Xe spectrum was obtained.It is quite clear that type I Xe hydrate reacts slowly with TMS to give type H hydrate, as witnessed by the pattern obtained after 40 h of reaction. The reaction rate depends largely on the vapour pressure of the reacting guest material in the sealed tube. For slow reaction rates it is not necessary to wait for the reaction to go to completion. In the case of adamantane guest material it was found that little or no reaction had taken place even after several days. However, it is possible to discriminate experimentally against observing the 12’Xe signal from type I hydrate by adjustment of the delay time while collecting data. The ‘H relaxation time of type I hydrate at 77 K is relatively long, at least several tens of seconds, as there are no efficient relaxation paths.On the other hand, hydrates with proton-containing guest molecules have intrinsic ‘H dipole-dipole relaxation processes because of relatively efficient molecular reorientation. Fig. 4(a) and (b) show 12’Xe spectra obtained for the reaction product of adamantane with type I xenon hydrate obtained with delay times of 60 and 2 s. When the type I Xe pattern is scaled and subtracted from the spectrum in fig. 4(b),J. A . Ripmeester, C. I. Ratclife and J . S. Tse 3739 Fig. 4. '29Xe NMR spectra of mixed type I Xe hydrate and type H Xe-adamantane hydrate : (a) taken with 60 s delay time, (b) taken with 2 s delay time and (c) difference spectrum obtained by subtraction of (b), scaled so as to reduce the Xe type I hydrate contribution to zero, from (a), leaving only the contribution from type H hydrate.I 100 ppm 1 L Fig. 5. '*'Xe NMR spectrum of type I Xe hydrate reacted incompletely with benzene to form a type I1 Xe-benzene hydrate. the remaining spectrum clearly shows the presence of an adamantane/Xe type H hydrate. In case the potential hydrate formers promote a type I1 hydrate, this can be seen right away by the appearance of the high-field line due to xenon in the type I1 large cage (fig. 5). FAR 84 I 2 33740 NMR Study of 12'Xe in Solids Fig. 6. 129Xe NMR spectra of clathrasil dodecasil-3C with Xe and THF as guests (a) 376, (b) 295, (c) 251 and ( d ) 220 K. Iz9Xe NMR and Site Symmetry The clathrasil dodecasil-3C is the structural analogue of type I1 clathrate hydrate.23 Recently it was shown that this clathrasil undergoes a number of phase transition^.^^ The highest temperature phase is cubic, space group Fd3, with 136 SiO, groups per unit cell.23 The large cage has point-group symmetry 43m, with the small-cage symmetry being m3.23 The 12'Xe NMR spectrum of a clathrasil sample with THF as the principal guest in the large cage is shown in fig. 6(a). In agreement with the spherical nature of the large cage, the 129Xe line for xenon in this cage shows no discernible anisotropic chemical shift. On the other hand, the signal for xenon in the small cage is characteristic of an axially symmetric shielding tensor with Ao = 44.9 ppm, in agreement with the cage having a threefold axis. The room-temperature phase of dodecasil-3C is known to be t e t r a g ~ n a l , ~ ~ although the detailed structure is not known.The xenon NMR spectrum, however, does give some indication as to the way the cage symmetries change on going from the cubic to the tetragonal phase. The line associated with xenon in the large cage changes little if at all, indicating the lack of a major change in large-cage symmetry. On the other hand, the line for xenon in the small cage, now has an additional shoulder characteristic of a non-axial shielding tensor (oZz = - 5 . I , oyy = - 29.1, o,, = 34.3 ppm), showing that the cage has been distorted from axial symmetry. Slightly below room temperature, at ca. 270 K, a phase transition to a third phase takes place which so far remains uncharacterized. In this phase the non-axial character of the powder pattern is greater than at room temperature, indicating further distortion of the cage.J .A . Ripmeester, C. I. Ratelife and J. S. Tse 3741 0 CH&H A Fig. 7. 13C and 12’Xe CP/MAS NMR spectra of a Xe a-cyclodextrin inclusion compound, obtained as a function of drying time. Finally, below ca. 240 K there is a third phase transition to a phase which is probably mon~clinic.~~ The 12’Xe powder pattern is now quite complicated, and no longer can it be analysed in terms of a single set of shielding parameters. Apparently this phase has more than one kind of small cage with different shielding parameters for the trapped xenon atoms. A second example of a change in I2’Xe NMR spectrum concomitant with a change in the sample condition is provided by the Xe-a-cydodextrin (aCd) inclusion compound.With small guest molecules an a-cyclodextrin macrocycle, consisting of six anhydro- glucose units bonded head to tail, forms well ordered orthorhombic crystals.22 Usually these materials are higher hydrates, the water molecules forming part of a hydrogen- bonded network which imposes both long-range and short-range order in the crystal. Fig. 7 ( a ) shows 13C as well as 12’Xe CP/MAS NMR spectra of a fully hydrated Xe- aCd inclusion compound. The 13C NMR spectrum is relatively well resolved, and is in agreement with there being one a-Cd molecule per symmetric unit in the crystal. The 12’Xe NMR spectrum consists of a single line ca. 192 ppm downfield from the infinitely dilute gas. For a static sample the 12’Xe NMR spectrum [fig. S(a)] consists of a powder pattern characteristic of an axially symmetric shielding tensor (ACT = 22.4 ppm).These 123-23742 NMR Study of "'Xe in Solids Fig. 8. lZ9Xe NMR powder patterns corresponding to the lZ9Xe CP/MAS NMR spectra shown in fig. 7(a) and (d). Fig. 9. lZ9Xe NMR spectra at 77 K of (a) solid xenon, (b) xenon trapped in solid H,S, (c) xenon trapped in solid tetramethylsilane and (d) xenon trapped in polystyrene. Spectra (b)-(d) were obtained with cross-polarization.J . A . Ripmeester, C . I. Ratclifle and J . S. Tse 3743 chemical-shift parameters are not too different from those for xenon in the small type I hydrate cage. When water is lost on drying of the sample, the 13C NMR spectrum changes markedly, individual lines becoming much less distinct [fig. 7(b)-(d)].This is consistent with a loss of short-range order in the sample. Initially the lz9Xe NMR line shifts to high field as water is lost, perhaps consistent with greater free space available to the xenon atom. Additional loss of water causes increased loss of resolution in the 13C NMR spectrum, although it is difficult to define the changes exactly. Interestingly enough, a second xenon line appears 7.0 ppm to low field of the initial Xe line, and eventually this becomes the only observable Xe line. These observations suggest that when the water content of the crystal is reduced below a certain critical level, the cyclodextrin macrocycle collapses around the xenon atom. The static sample 12’Xe NMR spectrum for the driest sample is shown in fig.8 (b), and is characteristic of a general shielding tensor with oSs = - 6.8, oYy = - 23.3 and ozz = 30.1 ppm. The free space available for the xenon atom, therefore, is smaller and of rather lower symmetry for the dry sample as compared to the hydrated sample. When the sample is rehydrated, the original spectra are again obtained. Xe trapped in Non-clathrate Solids Some exploratory studies were carried out on xenon trapped in solids which do not have distinct cages in order to see if the 12’Xe NMR spectrum could give some information on the trapping sites. Fig. 9 shows 12’Xe NMR spectra obtained for Xe trapped in solid H,S (ca. 5 mol %), tetramethylsilane and polystyrene at 77 K. For comparison purposes a spectrum of solid Xe is also shown. The xenon containing samples were quenched in dry ice-acetone, then cooled to 77 K before a spectrum was recorded.Since ‘H-12’Xe cross-polarization was used, [spectra (b)-(d)] the signal cannot originate from a bulk xenon phase. The 12’Xe signal of xenon trapped in solid H,S consists of a single line some 100 ppm to low field of the solid xenon signal. The correlation shown in fig. 2 then suggests that xenon trapped in H,S has rather less free space than xenon in the pure solid. This is understandable if xenon replaces H,S substitutionally in the lattice, as H,S is a slightly smaller species than xenon (both have f.c.c. structures, with lattice parameters 6.3472 A (Xe at 159 K)24 and 5.805 A (H,S at 142 K35 in its plastic phase)]. For the case of xenon in polystyrene [fig. 9(d)], a very wide line (ca.150 ppm width at half height) is obtained with a peak maximum some 80 ppm to high field of the solid xenon line. Evidently there is a large distribution in the type of site available for xenon in the non-crystalline polymer. Of course, it is not possible to say if part of the linewidth must be attributed to chemical shift anisotropy. On the whole, xenon is not nearly so tightly packed in the polystyrene as in solid xenon. The 12’Xe NMR signal obtained for xenon trapped in TMS shows that there are three different types of xenon site in the TMS lattice at 77 K. We have studied a closely related system, that of xenon in neopentane (ca. 5 mol%) in greater detail. Similar to the case of TMS, xenon trapped in quenched neopentane also shows the presence of three types of site [fig.lO(a)]. If, however, the neopentane-Xe solution is cooled slowly into the range of the neopentane plastic phase (163 K), a single line characteristic of axially symmetric shielding is obtained. This can occur only if the trapped xenon occupies an asymmetric site in an otherwise cubic crystal. For instance, it could replace a vacant methyl group site where a neopentane molecule is missing from the lattice. Further cooling into the region of the neopentane brittle phase (the phase transition in pure neopentane occurs at 140 K) produces a signal shifted slightly to higher field, with no sign of anisotropic shielding. In this phase xenon appears to take up a more central position perhaps at the centre of a vacant neopentane lattice site.The spectrum obtained by quenching the sample of neopentane-Xe to 77 K [fig. lO(a)]3744 NMR Study of lzgXe in Solids Fig. 10. lZ9Xe NMR spectra of xenon trapped in neopentane. (a) Sample quenched in liquid nitrogen, (b) sample slowly cooled to 163 K and ( c ) spectra for a slowly cooled sample in the region of the solid-solid phase transition. (i) 77, (ii) 163, (iii) 127, (iv) 129, (v) 131, (vi) 132 and (vii) 134 K. evidently consists of components attributable to both the plastic and brittle phases, as well as a third component. Conclusions We have shown that the chemical shift of xenon trapped in clathrate cages correlates linearly with the mean free radius of the cage: the smaller the cage, the larger the shift from the dilute gas value becomes, Simple theoretical considerations based on a binary collision model cannot account for this trend, predicting instead a cubic dependence on the cage radius.We have also accounted for the correlation of the anisotropic chemical shift with a deviation of the cage shape from spherical symmetry in terms of a simple model. A number of applications of 129Xe NMR spectroscopy have also been presented. For instance, it was shown that the NMR spectrum of Xe trapped in clathrate hydrates can be used to identify the structure of the hydrate. It was also illustrated that xenon can be used to probe structural changes in crystal lattices, e.g. in a clathrasils and a cyclodextrin inclusion compound. 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