J . Phys. Chem. 1990, 94, 157-162
d ) = 0.1332. Again, clearly, the a site can have a much larger population than the others. There are obvious differences in the derived populations for the CD,' and ND2 cases, for which there are several possible sources: ( I ) The assumed value of LDND for the chloride may not be correct. (2) The results apply at different temperatures in the two cases. The ND, case at lower temperature should be expected to have a larger m i t e population. ( 3 ) In the ND2 case the static tensor components may be different at the four sites due to different hydrogen bond strengths. The CD,' tensor should not be affected in this way. (4) The position of the C,, rotation axis will be displaced away from the carbons toward the nitrogen on going from (CD3)2NH2f to (CH3),ND2+, because of the isotopic weights. This must affect the behavior of the two. One final consideration is the question of whether a four inequivalent site model (C,,') without C2flips could produce the same line shapes. For (CD3)2NH2C1the resulting averaged tensor in this case is not diagonal in the reference frame chosen with the Z axis parallel to the C, axis. In addition to the terms given in eq 15-1 7 there are also a13 = y4(u - c ) sin a23
= Y4(b - d)sin
0 cos @(V,,- Vxx)
(20)
0 cos p(V,,
(21)
- Vxx)
When this tensor is diagonalized, all three principal components have dependence on the site populations and hence on temperature. In the (C2 C,,') model the a,, component is independent of the populations. Since the observed line shapes do not show a temperature dependence of V z i ( s a 3 , ) ,once it has emerged, while Vx; and Vyy' vary, this seems to rule out the model with C,,' alone. Furthermore, numerical calculations of the tensor averaged only by Cishow that, to obtain a result with V,; and 7' within -3% of the observed values in the 316 K spectrum, the population of site c must be nearly equal to that of site a, with much lower populations for sites b and d. If such populations were actually present, then a disorder would have been detected in the 0-phase
+
157
X-ray structure. So this also is strong evidence against C,,' motion on its own. It seems, therefore, that if the inequivalent site model for the 0-phase is correct, it distinguishes C,,' from (C2 C,,') motion. With regards to previous modelsS note that the (C, C,,') model does not require any concerted process of the lattice, since one principal site has much higher occupancy than the others and this would be dominant in the X-ray structure.
+
+
Conclusion The new 2H N M R results show conclusively that methyl group reorientation occurs in the low-temperature phase of dimethylammonium chloride and that the bromide and iodide salts show simple activated 2-fold flips of the whole cation above room temperature. A model, based on the 2H N M R results and consistent with all other available data, suggests that two motions are involved in the unusual behavior of the @-phaseof the chloride, approaching the transition to the a-phase: (a) 2-fold flips about the C2 axis of the ion and (b) flips among four inequivalent sites (C,,) about a crystal axis parallel to the C.-C vector. One of the four sites has a greater population than the other three, but as the temperature increases the population difference decreases. One might speculate whether this behavior triggers the transition to the a-phase where the four sites become equivalent. Again it should be emphasized that the equivalent-site model for the aphase cannot distinguish between C,,and (C2 + C,,) motion, though in view of the fact that the ' H T , results definitely show two motions,) (C, C,,) seems most likely. One must conclude, in the final analysis, that all the N M R results to date do not permit one to distinguish among the structural models for the a-phase proposed in the original X-ray diffraction study.4 Note that although the C2 motion would make the two N-D's equivalent on the N M R time scale, they would still be inequivalent on the infrared vibrational time scale right up to the melting point. Registry No. (CHJ2ND2+X- (X = CI), 123675-01-4; (CH,)2ND2+X(X = Br), 123675-02-5; (CH,),ND2+X- (X = I), 108371-98-8; (C-
+
DJ)2NH,CI, 53 170-19-7.
Nuclear Magnetic Resonance Studies of Guest Species in Clathrate Hydrates: Line-Shape Anisotropies, Chemical Shifts, and the Determination of Cage Occupancy Ratios and Hydration Numberst M. J. Collins, C. I. Ratcliffe,* and J. A. Ripmeester Chemistry Division, National Research Council of Canada, Ottawa, Ontario, Canada K l A OR9 (Received: April 7, 1989)
NMR spectra of the guest molecules PH,, H2Se, D2Se, D2S, CD3F, CD3CI, CD3Br, C2D2,and C2D4in their structure I clathrate hydrates have been obtained by use of *H, I9F, ,IP,and "Se nuclei. Components due to guests in the small and large cages have been distinguished by using isotropic chemical shift and static line-shape anisotropy differences. Low-temperature magic angle spinning was used in some cases to resolve the two components. Guests in the small cages are invariably found to have a lower field isotropic shift than those in the large cage. The static line shapes are isotropic for guests in the small spherical cages, whereas in the large oblate cages they have a residual anisotropy. Relative cage occupancy ratios 8S/eL have been obtained from the observed NMR intensities, and together with similar results from previous NMR studies, these have been used to derive hydration numbers. This represents a new and nondestructive method of determining structure I hydrate compositions.
Introduction Clathrate hydrates' consist of an icelike network of host water molecules hydrogen bonded together to form cages that surround individual guest molecules. Most of the known clathrate hydrates form one of three structures known as structures I (cubic Pm3n), 'Published as NRCC No. 30425.
I1 (cubic Fd3m),2 and H (hexagonal P6/mmm),3 and which one forms depends to a large extent on the size ofthe Particular guest. (1) Davidson, D. W. In Water, A Comprehemiue Treatise; Franks, F., Ed.,
New York 1972;
2.
(2) Jeffrey, G. A. In Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Ed.; Academic Press: London, 1984; Vol. 1, Chapter 5 , and references therein.
0022-3654/90/2094-0l57$02.50/0Published 1990 by the American Chemical Society
158 The Journal of Physical Chemistry, Vol. 94, No. 1, 1990
Each of these structures consists of small and large cages. Hydrates also form with mixed guest species, and in fact structure H, which accommodates some of the largest guests, only appears to be stable when small molecules, such as H2S, CH,, or Xe, are also included to occupy the small cages. The empty host lattices appear to be unstable with respect to ice. In general the clathrate hydrates are nonstoichiometric in that the cages are not 100% occupied, particularly for structure I, and the determination of composition requires considerable and careful effort., They can be treated as solid solutions, and the theory of localized surface adsorption, which has been adapted to describe the statistical thermodynamic proper tie^,^ appears to work reasonably well. The thermodynamic description requires a knowledge of such parameters as composition, hydration number, relative cage occupancy ratio, Langmuir constants, and decomposition pressures. Only recently has it been found possible to make a direct experimental determination of the cage occupancy ratio; Iz9Xe N M R of xenon structure I hydrate readily distinguishes Xe in the small and large cages6 and the relative amounts of Xe in each can be obtained from the integrals of the two N M R lines. Combined Xe NMR and calorimetric compositional analysis on a sample, prepared under three-phase (ice/hydrate/gas) equilibrium conditions at 0 0C,7then allowed the determination of absolute cage occupancies and the chemical potential of the water molecules in the hypothetical empty hydrate lattice relative to ice, ApowI. More recently, we reported that it was also possible to distinguish CH, in the small and large cages of structures I and I 1 using 13C CP/MAS N M R S 8 In this paper we present results of N M R studies of numerous guest molecules in clathrate hydrates (mainly of structure I) in which it has been possible to distinguish guests in the different cages using various NMR nuclei and techniques. (Some of these results have been mentioned briefly in earlier conference proc e e d i n g ~ . ~ )This has permitted the determination of cage occupancy ratios to varying degrees of accuracy, and we show how this may be used to give hydration numbers based on the statistical thermodynamic theory of clathrate hydrates. Another feature that has emerged from earlier studies of Xe and CHI hydrates6~*~10 is that the smaller the cage the further downfield the chemical shift (of Iz9Xeor 13C,respectively) of the guest. An exception to this has been found in the case of I3C0 structure I hydrate, which showed no detectable chemical shift difference in the two cages.”J2 It was therefore also of interest to determine whether other N M R nuclei would show this effect.
Experimental Section Most of the samples for which new results are presented here were prepared in the following manner: A known amount of water (or D 2 0 ) was frozen rapidly by squirting onto a surface cooled to 77 K. This ice was then powdered and loaded into a glass sample tube (IO-” 0.d.) which was then attached to a vacuum line and pumped down while cooled to 77 K. An appropriate amount of the gaseous guest material was then condensed into the tube, which was then sealed. Liquid guest materials were added to the ice before the tube was cooled and evacuated. The sealed tube was warmed to dry ice temperature and allowed to (3) Ripmeester, J. A.; Tse,J. S.; Ratcliffe, C. I.; Powell, B. M. Nature 1987, 325, 135.
(4) Cady, G. H. J . Chem. Educ. 1983,60,9i5. ( 5 ) Van der Waals, J. H.; Platteeuw, J. C. Adv. Chem. Phys. 1959, 2, 1 . (6) Ripmeester, J. A.; Davidson, D. W. J . Mol. Struct. 1981, 75, 67. (7) Davidson, D. W.; Handa. Y . P.; Ripmeester, J. A. J . Phys. Chem. 1986, 90,6549. (8) Ripmeester, J . A.; Ratcliffe, C. I. J . Phys. Chem. 1988, 92, 337. (9) Collins, M.J.; Davidson, D. W.; Ratcliffe, C. I.; Ripmeester, J. A. In Dynamics of Molecular Crystals; Lascombe, J., Ed.;Elsevier: Amsterdam, 1987: 497. .. . . o r (IO) Ripmeester, J. A.; Ratcliffe, C. I.; Tse, J. S. J . Chem. SOC.,Faraday Trans. I 1988,84, 3731. (11) Davidson, D. W.; Desando, M. A.; Gough, S. R.; Handa, Y. P.; Ratcliffe, C. 1.; Ripmeester, J. A.; Tse, J. S. Nature 1987, 328, 418. (12) Desando, M. A.; Handa, Y. P.; Hawkins, R. E.; Ratcliffe, C. 1.; Ripmeester, J. A. J . Inclusion Phenom., in press.
Collins et al. 77~e
n
100 ppm
Figure 1. 77Se CP static spectra of H,Se structure I hydrate.
sit for 30-60 min, and then placed in a freezer at -10 or -40 OC for several weeks to condition. Some samples had been stored for considerably longer periods before examination by magic angle spinning (MAS) NMR. Deuterated materials, CD3F, CD3CI, CD3Br, C2DZ,CzD4, D2S, and DzO were obtained from M.S.D. Isotopes. HzSe and DzSe were prepared by the addition of HzO or DzO to A12Se3as described in ref 13. Since the deuterons of D2S and DzSe will exchange with water, their hydrates for ZHN M R studies were prepared with DzO. PH3 was obtained from Matheson. NMR spectra were obtained by use of a Bruker CXP180 pulse spectrometer and 4.24-T cryomagnet at the following frequencies: 2H, 27.63 MHz; 19F, 169.34 MHz; 72.86 MHz; 77Se,34.32 MHz. Static line shapes were measured with a Bruker variable-temperature (VT) gas-flow probe (zH measurements) and a Bruker dual-frequency probe modified for VT work (I9F, 31P,and ”Se). Temperature was controlled by use of a Bruker B-VT 1000 controller. Magic angle spinning (MAS) spectra were obtained by use of a Chemagnetics VT probe with capped Delrin spinners. All the probes were precooled before loading the samples. The phase-alternated quadrupole echo technique’, was used to record the 2H N M R spectra. 77Sespectra of HzSe hydrate, static 31Pspectra of PH3hydrate, and all the I9F spectra of CD3F hydrate were obtained by using a CYCLOPS pulse sequence15 with pulse lengths of -5 ps. MAS 31Pspectra were obtained both with and without ‘H cross-polarization (CP). ‘H decoupling was also used for the experiments involving HzSe and PH3 hydrates. For the MAS experiments the samples were removed from their sealed glass tubes and loaded into the Delrin spinners at low temperature. The low-temperature spinning rates were steady
(! 3) (a) Kruis, A.; Clusius, K. Z . Phys. Chem., Ab?.B 1937.38, 156. (b) Kruis, A.; Clusius, K. Phys. Z . 1937, 38, 510. (14) Davis, J. H.; Jeffrey, K. R.; Bloom, M.; Valic, M. I.; Higgs, T. P. Chem. Phys. Lett. 1976, 42, 390. (15) Stejskal, E. 0.; Schaefer, J. J . Magn. Reson. 1974, 14, 160.
N M R Studies of Guest Species in Clathrate Hydrates
The Journal of Physical Chemistry, Vol. 94, No. I, 1990 159
'H
CD,Br
PL
233K
200
A
220
Figure 5. 2Hspectra of CD,Br (top) and CD,CI (bottom) structure I hydrates. The very sharp central lines are due to excess guest materials. A broader isotropic component is visible for CD,CI in the small cages.
2H
270 K
50 DDm
Figure 2. I'P static spectra of PH,structure 1 hydrate. The sharp low and high field lines are due to liquid and gaseous PH,(excess), respectively.
31P
,
10 PPm
Figure 3. IlP M A S spectrum of
I
PH, structure I hydrate at 200 K.
,
't
10 kHz
,
Figure 6. 2Hspectra of C2D2(top) and C2D, (bottom) structure I hydrates. The very sharp central lines, due to excess guest materials, overlay broader isotropic components due to guests in the small cages.
at values between 2600 and 3100 Hz dependent upon the temperament of the spinner.
2 kHz
Figure 4. I9F M A S spectrum (left) and 2Hstatic spectrum (right) of CD3F structure I deuteriohydrate.
Results and Discussion NMR spectra are shown in Figures 1-8. Before considering these results in detail, however, it will be useful first to discuss some aspects of clathrate hydrates. There is much evidence from earlier workl*16that the host water molecules generally begin t o
160
Collins et al.
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990
1 2
H
,?'\ 260 K
1-12.5k H z i
1
Figure 7. 2HN M R line shapes of host D20 (broad line shape) and guest D2S (narrow line shape) in structure I hydrate. Note the factor of IO scale expansion in the bottom spectrum.
K
230
I/
ii
/I
5 kHz
Figure 8. 2HN M R line shapes of D2Sein its structure I deuteriohydrate at 230 and 270 K, showing the sharpening of features associated with the onset of reorientation of the cage water molecules.
reorientate at rates > I O 3 H z at temperatures above 200 K. At lower temperatures the water molecules freeze into disordered positions so that a large distribution of slightly different cage configurations is produced. This has consequences for the N M R of the guest species. In the regime of static disorder of the host, the potential experienced by each guest molecule will be different from one cage to the next. The guests thus experience different reorientational motions with the result that the observed guest NMR line shape represents a distribution of individual line shapes. As the water molecule reorientations become rapid (> lo4 Hz), the disorder becomes dynamic and on time average all the cages of a particular kind, small or large, become equivalent. The guests then all experience the same potential and thus produce a uniform NMR line shape that is narrower and shows much sharper features ~
(16) Davidson, D. W.; Ripmeester, J. A. In Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D., Eds.;Academic Press: London, 1984; Vol. 3, Chapter 3
than at low temperatures. This effect is visible in Figures 1, 2, and 8. We take advantage of the water motion in the 2H NMR spectra of the D 2 0 hydrates of D2S and D2Se, where the intensity of the D 2 0 echo line shape reduces very dramatically in the region of dynamic averaging, leaving only the line shape of the guest; see Figures 7 and 8. It is the influence of the shape (symmetry) of the individual cages on the guest atoms or molecules that gives rise to distinguishing features in the NMR line shapes of the guest in the small and large cages. The small cage of structure I and the large cage of structure I1 are pseudospherical (have cubic symmetry); the NMR line shapes of guests in these cages are isotropic. On the other hand, the small cage of structure I1 and the large cage of structure I are oblate ellipsoidal (noncubic symmetries) and the line shapes of their guests are anisotropic. This is well exemplified by the 129XeN M R of Xe in the different cages of structures I, 11, and HIo and by the "Se N M R of HzSe structure I hydrate (Figure 1). It should be emphasized, however, that Xe is unique in that it is the only monatomic guest which has been studied by NMR. With no rotational degrees of freedom involved, its line shapes basically arise because its many-electron cloud is readily polarized and this senses the environment through weak interactions, though averaging of the chemical shift anisotropy through translational motions may be involved.I0 All other guests studied by NMR are polyatomic, and their N M R line shapes are strongly dependent on their reorientational motions which cause averaging of the chemical shift or quadrupole coupling tensors. The relative intensity ratio of the lines for guests in the different cages, whose measurement is one of the aims of the current work, is another obvious factor that helps to distinguish the two lines; structure I has 3 large cages for every small one.
Chemical Shift Results ("Se, 31P,I9F NMR) Static 77SeN M R line shapes of H2Se structure I hydrate are shown in Figure 1. At the higher temperatures line shapes of the guests in the two types of cages are completely resolved due to a sizable chemical shift difference of 29.7 ppm and are readily distinguished by their shapes and intensities; the more intense large cage line has an anisotropy bu = 34.7 ppm. Again the small cage line occurs at lower field. This permits quite an accurate determination of OS/OL. Note the much broader unresolved line shape at 77 K, showing the influence of frozen-in disorder of the cage molecules. In the 240 K spectrum there is a weak feature, corresponding to excess liquid H2Se, 63 ppm to low field of the small cage line. The NMR spectra of the static, sealed sample of phosphine (PH,) structure I hydrate, Figure 2, show lines due to excess PH,, present as liquid (the line at lowest field) or gas (the line at highest field). As the temperature increases, the liquid line shifts gradually to higher field, presumably an effect of decreasing density, and gradually intensity transfers from the liquid line to the gas line. The line shape of PH, in the hydrate, which occurs between the gas and liquid lines, shows no significant shift with temperature, though again the line shape narrows and sharpens up a little as the water molecules begin to reorientate rapidly. This line shape consists of two overlapping lines with the small cage component at lower field, based on the intensity argument. Relative to the gas line, the large cage line is 17.3 ppm downfield. The liquid line shows a linear dependence of the chemical shift with temperature. Extrapolation to 250 K indicates that the liquid line must strongly overlap the small cage guest line at 250 K, so it is more realistic to attempt to extract Os/OL from the 140 K spectrum where there is no interference. If one assumes that the two components are broadened isotropic functions, a rough estimate of O s / & = 0.7 (at 140 K) can be obtained. A more accurate determination of OS/8, was made possible by completely resolving the two lines using magic angle spinning (MAS), Figure 3, though the composition may be different for the MAS sample since some decomposition while in the spinner was evident. The static 19F N M R line shape of CD3F/D20 structure I hydrate was broad and featureless. Lines for guests in the two
-
N M R Studies of Guest Species in Clathrate Hydrates
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990 161
TABLE I: Isotropic Chemical Shifts of Spin '/*Nuclei in Guests in Clathrate Hydrate Cages (6 Scale, ppm) guest NMR" struct I S struct I L struct I1 S struct I1 L T, K ( f l K) ref Xe 129Xestatic 242 f 2 152 f 2 225 f 2 80 f 2 200-240 10 H2Se "Se static 29.7 f 1.2 0 240 this work PH3 3'P MAS 8.17 f 0.3b 0 200 this work CDiF I9F MAS 4.65 f 0.2 0 243 this work *CH4 13C CP/MAS -2.84 f 0.15 -5.21 f 0.15 -2.73 f 0.15 -6.27 f 0.15' 193 8 CH3*CH2CH3 13C CPJMAS 18.5 f 0.15d 193 8 co "C CPJMAS 184 184 153 11, 12 "C shifts given relative to TMS = 0. 129Xeshifts given relative to gas at zero density. Where no reference was used for "Se, "P, and I9F, the large cage shift has been set to zero. bExcessPH3 gas in sample tube at undetermined pressure at --17.3 ppm. CGas-phasevalue -7.0 ppm, solution -2.3 ppm. "Solution value 15.9 ppm. cages were partially resolved, however, using MAS (Figure 4), and again the weaker line of the small cage guest is at lower field. From this spectrum one can obtain a good estimate of the chemical shift difference between the two cages of 4.6 ( 5 ) ppm and a reasonable estimate of 0,/0,. The chemical shift results described above all confirm the trend of lower field shifts for the guest in the smaller cage. Table I lists all the known small and large cage chemical shifts for various nuclei of guests in hydrates. As mentioned in the Introduction, I3CO is exceptional in that it shows no chemical shift difference."J* An obvious trend from Table I is that the chemical shift differences between the cages decrease as the atomic number of the nucleus, and hence the number of electrons, decreases.
*HNMR Results In the 2H N M R spectra the quadrupole coupling interaction dominates and the line shapes of the guests in the different cages overlap. However, since all the lines are symmetric about the central Zeeman frequency, they can still be distinguished by their anisotropy and their relative contributions can be obtained analytically. Of the hydrates of the methyl halides CD3X (X = F, CI, Br, I), CDJ hydrate has been studied p r e v i o ~ s l y and , ~ ~ since it is structure I1 with the guest only in the spherical large cage, the ZH N M R line shape is isotropic. Hydrates of the other three (X = F, CI, Br) are structure I, and guests in the nonspherical large cage give axially symmetric anisotropic 2H N M R line shapes, whose width decreases as the size of the molecule decreases (Br F) due to increasing motional averaging. Figure 5 contrasts the spectra for CD,Br and CD,CI: Both spectra show a very sharp line at the center which is due to excess liquid CD3X, but the chloride also shows a second, broader isotropic component which must be due to guests in the small cages. It is quite clear that there is no equivalent signal for the bromide, which would not be expected to fit into the small cages. By subtracting the sharp, excess line and simulating the hydrate line shape, it is then possible to obtain @,/e, for the chloride. In the case of the fluoride, Figure 4, the isotropic signal from the small cage guests is somewhat narrower than in the chloride, which makes its separation from the excess liquid line more difficult. In this case the derived Bs/0, value is a less accurate quantity. For CzD2and CzD4structure I hydrates, Figure 6, again the excess, small and large cage guest contributions are readily separated in the ZHNMR spectra. The 2H NMR line shapes of D2S/D20and D2Se/D20hydrates, Figures 7 and 8, both show the isotropic and anisotropic components for the two cages. There should be negligible excess guest signal in these spectra as the samples were prepared with excess ice and the decomposition pressures at these temperatures are well below 1 atm.' Any 2H exchange between D 2 0 and the D2S or DzSe must be relatively slow as there does not appear to be any averaging of the line shapes from this source. These two figures also illustrate effects of the host lattice dynamics. The 230 K spectrum of DzSe hydrate, Figure 8, shows the broadening and weakening definition of the features of the guest line shape as the waters begin to freeze into disordered positions. Figure 7 shows
-
(17) Davidson, D. W.; Ratcliffe, C. 1.; Ripmeester, J. A. J . Inclusion Phenom. 1984, 2, 239.
the rapid reduction in intensity of the host D 2 0 line shape as the water motion becomes rapid. In the above studies the guest in the structure I large cage always shows a residual axial line shape anisotropy. These anisotropies, when compared with those for the static molecule, provide some information regarding the motion of the guest inside the cage. However, this aspect is not the focus of the present paper and will be discussed elsewhere.
Hydration Numbers from Relative Cage Occupancy Ratios The statistical thermodynamic theory of clathrate hydrates5 gives the chemical potential of the water molecules pcw(h)in a structure I hydrate as RT p d h ) - pw(ho) = -[3 In (1 - 0,) In (1 - e,)] (1) 23 pw(ho) is the chemical potential of water in the hypothetical empty host lattice. There are 23 water molecules associated with 3 large cages and 1 small cage. The two main assumptions underlying the theory are that there are no guest-guest interactions and that the guest does not distort the lattice. When the hydrate is in equilibrium with ice pW(h) = pw(ice), and we can rewrite -Apow = pw(ice) - pw(ho), where now Apow is the chemical potential of the empty lattice relative to ice. Numerous recent experimental and theoretical determinations of &Ow, based on observed or calculated 0, and OL values, all seem to be in reasonably close agreement.7J8-23 From the most recent study, using combined '29XeN M R and compositional determination of a xenon hydrate sample produced under gas/hydrate/ice three-phase equilibrium at 0 "C, Apow = 1297 f 110 J/moL7 By rearranging eq 1, one can then find 0, in terms of 0,
+
and calculate corresponding values of Os, e,, and hence Os/BL and the hydration number n = 23/(30L + Os). The interdependence of these latter two quantities is plotted in Figure 9. Clearly if OS/0, is known from experiment, then one can obtain a good estimate of n. A similar approach can be followed for structure I1 hydrates: -ApowII
@L
RT
= -[2 17
= 1 - exP[
In (1 - 0,)
+ In (1 -eL)]
-17A~~w11 RT ]/(1
- 0,)2
(3)
(4)
+
and n = 17/(20, 0,), since this time there are 17 water molecules associated with 2 small cages and 1 large. For A/AOWII (18) Dharmawardhana, P. B.; Parrish, W. R.; Sloan, E. D. Ind. Eng. Chem. Fundam. 1980, 19, 410. (19) Holder, G. D.; Corbin, G.; Papadopoulos, K. D. Ind. Eng. Chem. Fundam. 1980, 19, 282. (20) Holder, G. D.; Malekar, S. T.; Sloan, E. D. 2nd. Eng. Chem. Fundam.
1984, 23, 123. (21) John, V. T.; Papadopoulos, K. D.; Holder, G. D. AIChE J . 1985,31, 252. (22) Barakhov, S. P.; Savvin, A. Z . ; Tsarev, V. P. Zh. Fir. Khim. 1985, 59, 1039.
(23) Handa, Y. P.; Tse, J. S . J . Phys. Chem. 1986, 90, 5917.
162
Collins et al.
The Journal of Physical Chemistry, Vol. 94, No. 1, 1990
TABLE 11: Summary of NMR Measurements of Guest Molecule Cage Occupancy Ratios and Corresponding Hydration Numbers for Structure I Hydrates struct I" T (K) of hydrate NMR meas hydration guest NMR ( f l K) OS/OL no. ( n ) 243 0.61 f 0.15 6.48 f 0.32 CD3F/ I9F MAS D2O 269 0.53 f 0.15 6.62 f 0.33 CD3F/ *H D2O CD3CI 2H 243 0.27 f 0.06 7.13 f 0.18* D2S/D20 2H 260 0.85 f 0.04 6.11 i O.llE H2Se 77Se 240 0.73 f 0.05 6.29 f 0.13 77Se 275 0.78 f 0.05 6.21 f 0.13 D2Se/D20 2H 230 0.75 f 0.08 6.26 f 0.18 2H 270 0.78 f 0.08 6.21 f 0.18 C2D2 2H 270 0.42 f 0.01 6.83 f 0.07 C2D4 *H 273 0.21 f 0.04 7.26 f 0.13 CH4 I3C CP/MAS 193 0.92 f O.Old 6.03 f 0.08c co "C C P 220 1.11 f 0.06f 6.22 f 0.24 PH3 3'P MAS 201 0.47 f 0.02 6.73 i 0.09 3lP 140 0.70 f 0.05 6.33 f 0.13 Xe 129XeC P 77 0.73 f 0.028 6.29 f 0.09h
Structure I
0.01
6.0
I
6.5
I
7.0
I
7.5
I
8.0
Hydration Number n
Figure 9. Variation of Os/OL versus hydration number n for structure I
hydrates derived as described in the text. The error bars indicate the uncertainty introduced when the errors in the value of Apow are considered.
0.6
6.0
6.5
7.0
7.5
8.0
Hydration Number n
Figure 10. Variation of &IOL versus hydration number n for structure I I hydrates derived as described in the text.
" H 2 0 hydrate except where indicated. *cf. 7.06-7.5624 for CH3CI. Ccf.6.11924 for H2S. dReference 8. ecf. 6.00.2s ZReference 12. EReference 7. hcf. 5.90,266.13-6.39.24
by other technique^^^-^^ (see Table I1 footnotes), and the comparisons are quite favorable. A general trend is that Os/OL increases as the size of the guest decreases, as expected. While the rough estimate for the sealed static sample of PH3 hydrate is reasonable, the &/eL value obtained for PH3 hydrate by using MAS is clearly out of line. Decomposition during the MAS experiment was obvious, but it is of interest that more PH3 has come out of the small cages than the large cages, presumably because of a difference in Langmuir constants. C O appears to be the only molecule to form structure I for which Os/OL > 1; Le., it has a greater affinity for the small cages. This is curious since, on the basis of size arguments, CO, like N2 and 02,would have been expected to form a structure I1 hydrate, which has twice as many small cages as large. We have speculated previouslyI2that perhaps the small dipole moment of CO promotes structure I. Another interesting feature, which emerges from eq 2 when absolute values of Os and 0, are calculated, is that OL ranges from 0.987, for C2D4, to 0.974, for CH4; Le., the large cages are close to full in most cases. C O is again the exception with Or = 0.9.
there is a choice between a recent theoretical value of 1068 J / m ~ l ~ ~Conclusion In the work above we have shown that in very many cases guest (a similar theoretical calculation for structure I gave a value very molecules in the small and large cages of structure I clathrate close to the experimental ones) and a value, determined from hydrates can readily be distinguished in their NMR spectra, either experimental results, of 937 J/mol.Is Figure 10 plots &/eL versus from chemical shift differences or from line shape anisotropy. n for structure I1 using ApowII= 1068 J/mol. This is largely an N M R is so far the only technique that has allowed direct meaacademic exercise for structure I1 hydrates containing a single surement of Os/OL values, though there is some promise for infrared guest species, since most guests occupy only the large cage, and or Raman measurements where distinct vibrational modes for N2, Ar, Kr) that for the few very small molecules or atoms (02, guests in the small and large cages have been Provided occupy both cages no cage occupancy data is currently available. our value of Awew is reasonably accurate, that the theory holds, However, it is of interest to note that the lowest hydration number and that the approximations are not too severe, then the N M R from Figure 10 is -6.09, Le., higher than the 5.67 expected if measurement of Os/OL values gives a new and nondestructive all cages were 100% filled. Compositions for structure I1 Kr method of determining the hydration number (=composition) for hydrate have been found in the range 6.05-6.25,' and the most structure I hydrates. recent value obtained is 6.10.26 Table I1 summarizes the &/eL values for structure I hydrates Registry No. PH3.xH20, 109877-81-8; H2Se.xH20, 123075-24-1; determined by the N M R experiments described above and from D ~ S ~ X H ~123075-25-2; O, D2SaxH20, 123075-26-3; C D ~ F - X H ~ O , a few earlier s t u d i e ~and ~ ~ gives ~ ~ ' the ~ corresponding hydration 123075-27-4; CD3CI.xH20, 123075-28-5; C D ~ B P X H ~ O 123075-29-6; , C~D~~XH 123075-30-9; ~O, C~D,*XH~O 123075-31-0. , number derived from the relationship shown in Figure 9. Hydration numbers for a few of the guests have also been determined (24) Cady, G. H. J . Phys. Chem. 1983,87, 4437. (25) Handa, Y . P. J . Chem. Thermodyn. 1986, 18, 915. (26) Handa, Y . P. J . Chem. Thermodyn. 1986, 18, 891.
(27) Richardson, H. H.; Wooldridge, P. J.; Devlin, J. P. J . Chem. Phys.
1985,83, 4387.
(28) Consani, K.; Pimentel, G. C. J . Phys. Chem. 1987, 91, 289. (29) Fleyfel, F.; Devlin, J. P. J . Phys. Chem. 1988, 92, 631.
