NMR behavior of the clathrate hydrate of tetrahydrofuran. III. Effect of oxygen

JOURNAL

OF MAGNETIC

RESONANCE

38,537-544

(1980)

NMR Behavior of the Clathrate Hydrate of Tetrahydrofuran. III. Effect of Oxygen* J. A. RIPMEESTER, Division

of Chemistry,

National

S. K. GARG, Research

Council

AND of Canada,

D. W. DAVIDSON Ottawa,

Ontario,

KlA

OR9

Received August 23, 1979 The effect of dissolved oxygen on the proton resonance lineshape and second moment of tetrahydrofuran deuteriohydrate between 4.5 and 260 K is interpreted in terms of the magnetic fields of the electron spins of reorienting oxygen molecules located in nearest-neighbor cages. After sufficient equilibration time, spin-lattice relaxation in the presence of oxygen becomes exponential at temperatures between 50 and 250 K with Ti almost independent of temperature. Examples are cited of clathrate hydrate studies in which lineshapes and relaxation were affected by the presence of oxygen. Because of its large solubility in clathrate hydrates (- 0.7 mol/liter atm in structure II), particular care is required to exclude oxygen.

Previous reports from this laboratory have described proton (I) and deuterium (2) NMR studies of tetrahydrofuran (THF) hydrate and their interpretation in terms of the reorientation of the guest THF molecules and the reorientation and translational diffusion of the host water molecules. We wish to consider here the effect of paramagnetic molecular oxygen on (a) the proton resonance lineshape and (b) the proton spin-lattice relaxation in C4Hg0*17DzO. The solubility of 02 in THF hydrate, as in other simple structure II clathrate hydrates is particularly great since 02 molecules can readily occupy the otherwise empty 12-hedral cages (3). These small cages outnumber by 2 to 1 the 16-hedral cages occupied by THF molecules. Incorporation of air during the formation of THF hydrate is known (4) to raise the congruent melting point. EXPERIMENTAL

METHODS

A number of samples of THF deuteriohydrate were prepared in the presence of air or oxygen. The most extensively studied sample was made under 3 atm of O2 in a sample tube attached to a gas handling line by flexible stainless-steel tubing. The THF+17D20 solution was nucleated by alternate shaking and cooling. The sample was cycled between 0 and 8°C for several days with the pressure readjusted to 3 atm as hydrate formation progressed. The sealed sample was stored for conditioning at - 13°C. * Issued as NRCC No. 17913 537 All

0022~2364/80/060537-08$02.00/O Copyright @ lY80 by Academic Press. Inc. rights of reproduction in any form reserved, Printed m Great Britain

538

RIPMEESTER,

GARG,

AND

DAVIDSON

Samples of the structure II deuteriohydrates of SF6 and acetone were prepared under conditions designed to exclude oxygen. SFs* 17D20 clathrate was made under 3 atm of SF6 with a procedure similar to that described above. The D20 used to prepare sample 1 was thoroughly degassed by several freeze-pump-thaw cycles; for sample 2, both D20 and SF6 were degassed. Acetone DzO hydrate was obtained from a thoroughly degassed solution and frozen and conditioned at -25°C. (The HZ0 hydrate of acetone decomposes at - 20°C (5).) Some He gas was added to all samples to provide good low-temperature thermal contact between the hydrate samples and the sealed containing tubes. Proton NMR lines were recorded between 4 and 270 K at 56 MHz as absorption derivative curves with marginal-oscillator and phase-sensitive detection. Proton and 19F (for SF6*17D20) spin-lattice relaxation times were obtained from 90”-7-90” pulse sequences with a Bruker SXP pulse spectrometer. The cryostat and temperature-control system were as before (1,Z). Temperatures below - 70 K were measured with a calibrated Lakeshore Cryotronics carbon-glass resistance thermometer to avoid the sensitivity to magnetic field shown by the germanium resistor previously employed (2). PROTON

LINESHAPES

The molar magnetic susceptibility of molecular oxygen in the gaseous state follows the Curie law (6) x = 4p*NS(S + 1)/(3kT)

= 1.000/T

emu mol-‘,

[II

where /3 is the Bohr magneton, N Avogadro’s number, and S = 1 the electron spin of the 02 molecule in the 3E ground state. Magnetic susceptibility measurements have shown this classical relationship to apply accurately to O2 encaged in the p-quinol clathrate to below 10 K (7). The O2 molecule, on average, has an effective magnetic dipole moment of l.OOOHO/(NT) = 1.660 x 1O-24 Ho/T in the direction of the field Ho and a magnetic nucleus located at a position r from an O2 molecule experiences a local field whose component parallel to Ho is

H 1oc.r

1.660 x 1o-24 3 cos* 8 - 1 =

T

r3

Ho,

PI

where 0 is the angle between r and Ho. For a polycrystalline sample the resulting paramagnetic contribution to the second moment of the nuclear resonance is

SM,,, = (H:,,,,)

= 2’204 ;;r;-48H

i

since ((3 cos* 8 - l)*) = $. Each large cage occupied by THF has 12 nearest-neighbor small cages capable of containing 02 molecules and located at a center-to-center distance of (11&z/8 = 7.12 A, since a unit cell parameter of a = 17.17 8, has been measured (8) for THF hydrate at 135 K. Ten second-neighbor small cages occur at 33’2a/8 = 11.15 A. The

CLATHRATE

HYDRATE

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539

TETRAHYDROFURAN

contribution to the second moment by O2 molecules located in second-neighbor and more remote cages is less than 10% of the nearest-neighbor contribution and is neglected. With r = 7.12 A, Eq. [3] becomes

[41

Sk&,,, = 1.692 x 10-5n,fH;/T2,

in which ni is the number of nearest-neighbor cages occupied by 02 and f is a factor which depends on the orientational mobility of the THF molecules. At high temperatures the THF molecules effectively undergo isotropic reorientation (2) and the protons may be located at the cage center (f = 1). At very low temperatures where the THF molecules are rigid and assumed to be fixed in random orientations, f = (1+ h2)/(1 - /z’)~, where h2 = s2/r2 and s2 is the mean square distance of the protons from the cage center (9). If the center of mass of THF is near the cage center, the rigid lattice value off is about 1.6. It has already been shown (I) that over much of the temperature range the reorientational processes produce only incomplete averaging of the interproton interactions in THF. We may conveniently, if roughly, estimate the value off at any temperature from the second moment measured for THF*17D20 in the absence of 02. The lower curve of Fig. 1 shows the smoothed results of the earlier study (I), which extend between the rigid lattice second moment of 13.9 G2 and the isotropic value of 0.1 G2. With this diamagnetic contribution labeled SMdia, the total second moment of an Oa-containing sample may be written as SM~1.692~

[51

10-5~iH~T-2[1+0.6(SM~i~-0.1)/13.8]+SA4~~~.

Figure 1 shows the experimental second moments for the sample prepared under 3 atm of O2 gas. Because TI behavior (see below) showed the sample to be initially heterogeneous, the proton lines were recorded after the prolonged conditioning

0.1

0

50

FIG. 1. Experimental and calculated THF.17D20. Inset shows the derivative

100

150

proton second moments lineshape at 4.46 K.

200

250 of an oxygen-containing

sample

of

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which led to simple exponential decay. Low-temperature lineshapes were somewhat different following the conditioning, but the second moments were hardly affected. These are satisfactorily represented over the whole range of temperature by Eq. [5] with nl taken to be 2.1 (upper second-moment curve in Fig. 1). The resonance lineshapes are structureless and not markedly asymmetric above 50 K, where SM,,,, is less than SMdis. Below 30 K, SM,,, > S&i, and the shape becomes increasingly asymmetric. For example, the spectrum at 4.46 K (inset of Fig. 1) shows a shoulder at about 25 G upfield from the line center and absorption which extends far out into the wings, especially on the low-field side. The probability that a THF molecule has IZ nearest-neighbor O2 molecules is p = 12! l9”(1- 19)‘2-” ” (12--n)!n! ’ where 0 is the chance that an individual cage is occupied. For 0 = 2.1112 = 0.175, the relative numbers of THF molecules with 0, 1,2 . . . O2 neighbors are 0.009, 0.253, 0.295, 0.209, 0.100, 0.034, 0.008,. . .) respectively. The resulting spectrum is the sum of generally asymmetric lines similar to those shown for molecules with axially symmetric shielding tensors with negative values of g/l - uI. The most likely number of 02 neighbors is 2, for which an upfield peak at - 121/T G, or - 27 G at 4.46 K, is expected. Although the importance of excluding O2 from samples to be used for Tl measurements has long been realized, it has not been obvious that even relatively small amounts of O2 can distort the lineshapes recorded for clathrate deuteriohydrates at the low temperatures necessary to achieve rigid lattice conditions. In an early study of the structure I hydrate of ethylene oxide a rigid lattice second moment for EOa7D20 of 11.4 f 0.4 G2 was reported (9). Subsequent reexamination of the experimental lineshape for the purpose of comparison with the shape calculated for the four-proton system (10) led to a second moment of 9.7 * 0.3 G2. It is likely that the original spectrum, which contained some absorption extending out to 10 G and more in the wings (9), was affected by the presence of O2 in an amount some three orders of magnitude less than the amount in the example illustrated in Fig. 1. A confirmatory observation is that the fine structure characteristic of the rigid EO four-proton system was better defined at 5 K than at 2 K (see Fig. 4 of Ref. (9)). SPIN-LATTICE

RELAXATION

As expected, oxygen has a profound effect on the spin-lattice relaxation. Figure 2 shows the difference at 130 K between THFa17DzO prepared in the absence (curve A) and presence (curve B) of air. The decay for the latter is much faster and is not exponential. The relaxation of the sample prepared from an initially degassed solution subjected to 3 atm of O2 showed significant changes with sample conditioning. The behavior of the fresh sample could be almost quantitatively described by two relaxation times which differed by a factor of 1000 at 130 K (11 msec and 12 set, respectively). The longer relaxation (curve C of Fig. 2) was essentially identical to

CLATHRATE

HYDRATE

OF

TETRAHYDROFURAN

541

0.6 0.4 MO-M(t) MO

0.2

0.06

FIG. 2. Magnetization prepared in the presence

0

IO

30

TIME 2

decay curves of THF.17D20 of air, (C) fresh sample prepared

at 130 K. (A) Degassed under 3 atm of oxygen.

sample,

(B) sample

that shown by oxygen-free hydrate and appears to have originated in the part (about 35%) of the sample which had incorporated negligible amounts of O2 during crystallization. After several weeks of conditioning at -13°C this component has disappeared and the relaxation could be approximately represented by a single short Tr. Finally, after more than a year of conditioning, the relaxation at temperatures above 50 K became completely exponential. These T1 values are shown in Fig. 3 along with earlier results (1) for a degassed sample. At low temperatures unique values of Tr could not be defined because of the extreme breadth of the resonance

FIG.

3. Spin-lattice

0

50

relaxation

times

100 of THF.17DzO

150 without

200 oxygen

250 and with

-2

mol%

oxygen.

542

RIPMEESTER,

GARG,

AND DAVIDSON

lines already described. Relaxation at the line center was extremely slow compared with that in the wings. Spin diffusion was not sufficiently rapid between protons of THF molecules which have O2 nearest neighbors and those which do not to result in a common T1. The effects of relatively small amounts of O2 impurity may be seen in some earlier studies of clathrate deuteriohydrates at relatively high temperatures where the inherent relaxation is slow (Fig. 4). The first measurements of acetone deuteriohydrate (II) showed nonexponential relaxation and relaxation times were reported as fo, the time for half decay of the magnetization. The value of to was essentially independent of temperature, at 2.5 set between 100 and 200 K (dashed line, Fig. 4A). Our measurements of a degassed sample, on the other hand, give exponential relaxation and T1 values which pass through a maximum of 17 set at about 150 K. In Fig. 4B values of Tl for 19F relaxation in three samples of SF6*17D20 are compared. For a specific sample the results are practically independent of Larmor frequency over the temperature range illustrated. The lower curve is the mean of a large number of measurements at 20 and 52.7 MHz for which “slightly nonexponential” decay was observed over the whole temperature range (12). The middle curve represents the mean of measurements at 9.2, 17, and 36 MHz of our sample 1. The upper curve shows 12.0- and 56.4-MHz data for sample 2 which showed no departure from exponential relaxation. Although precautions were taken to exclude air from all three samples, it appears likely that Dunn and McDowell’s

CH3 COCH3

* 17 D20

l.O-

0.5

SF6*17D20

0.0

-0.5 0

IO

20

30

40

FIG. 4. Relaxation times measured for different samples of acetone and sulfur hexafluoride deuteriohydrates.

CLATHRATE

HYDRATE

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TETRAHYDROFURAN

543

sample and our sample 1 contained enough air to lower the maximum Tl value at 48 K from 2.0 to 0.65 and 1.0 set, respectively. The difference is of considerable importance in defining the spin-rotation contribution to the relaxation which, as Dunn and McDowell indicated, is responsible for the fall in T1 above 50 K. The effect of O2 on spin-lattice relaxation is to introduce an additional relaxation mechanism which is almost independent of temperature over a wide range of relatively high temperatures. This is shown by THFm17D20 for large 02 content (Fig. 3) and by the differences between the curves plotted for the two deuteriohydrates in Fig. 4 for relatively small amounts of Oz. In the case of acetone the difference between the two curves is representable by an O2 contribution to the relaxation rate of AT;’ = 0.31 f 0.04 set-’ between 77 and 180 K. For SF6 the difference between the curves representing Dunn and McDowell’s sample and our sample 2 is AT;’ = 1.00 * 0.06 set-’ between 40 and 140 K. Some estimate may be made of the amounts of O2 actually present. With the assumptions of sample homogeneity, rapid spin diffusion, and a linear dependence of the relaxation rate on O2 concentration, one finds AT;l

= 5000[0*],

r71

where [OJ is the mole fraction of oxygen in a structure II hydrate. The proportionality factor comes from T;’ (OJ = 10 msec between 50 and 230 K (Fig. 3) for the same sample of THF.17D20 whose second moment indicated a cage occupancy factor of 0.175 ([OJ = 0.019). Use of the values of AT;’ given above for the original samples of acetone (11) and SF6 (12) deuteriohydrates gives O2 mole fractions of the order of 6 x 10e5 and 2 x 10-4, respectively. These values may be put into perspective by estimation of the oxygen content expected for a hydrate prepared in equilibrium with 1 atm of air (PO, = 0.2 atm). The Langmuir constant in the equation relating cage occupancy to O2 pressure (fugacity), 8 = KPo,(l

+KP&,

Bl

has a mean value of K = 0.16 atm-’ for the 14- and 12-hedral cages of the structure I oxygen hydrate, whose composition is about 02.6.10H~O and decomposition fugacity 100 atm at 0°C (3). If this value is taken to apply also to the 12-hedral cages of structure II hydrates, PO, = 0.2 atm gives 0 - 0.031 and [OJ - 3.4 x 10P3. Equation [8] also gives 8 - 0.32 for THF hydrate prepared in equilibration with 3 atm of 02, in general agreement with 13= 0.175 found for the experimental sample which was not fully equilibrated with O2 and which, before conditioning, was free of O2 over - 35% of its volume. To ensure the absence of an appreciable effect of O2 on the measured T, of clathrate hydrates at relatively high temperatures its contribution must be 100 set or longer. From Eq. [7] this requires [OJ to be less than 2 x 10m6 or the partial pressure of 02 to be less than 1.1 x 10e4 atm under hydrate formation conditions. CONCLUSIONS

The large solubility of molecular oxygen in clathrate hydrates (about 0.7 mol/literatm of 02) requires particular efforts to ensure the absence of air for

544

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DAVIDSON

definition of the proper NMR lineshapes at low temperatures and of the TI behavior at relatively high temperatures. The effect of O2 on lineshapes of guest-molecule nuclei to below 5 K may be ascribed to the local magnetic fields of the electron spins of “free” O2 molecules in neighboring cages without appreciable correction for restricted rotation of the O2 molecules. The presence of oxygen may lead to nonexponential relaxation, at least in unconditioned samples. For relatively high 02 content, the experience with THF hydrate suggests that exponential behavior (except at very low temperatures) may be achieved by sufficient conditioning to give a uniform distribution of O2 throughout the sample. Such equilibration is very slow, in agreement with other evidence for the slow translational diffusion of hydrate-enclathrated molecules (3). For low O2 content, spin diffusion may not be fast enough to ensure exponential relaxation even if the composition is uniform. Such diffusion-limited relaxation behavior can become quite complex, as illustrated by the studies by Haupt and Miiller-Warmuth (13) and others of nuclear relaxation in the presence of paramagnetic impurities in low concentrations. The mechanism of relaxation must involve coupling of the nulcear spins of the guest molecules to the electron spins of O2 molecules and an electron spin relaxation process which is insensitive to temperature at relatively high temperatures. The latter may be more appropriately studied by EPR T1 measurements of enclathrated Oz. REFERENCES 1. S. K. GARG, D. W. DAVIDSON, AND .I. A. RIPMEESTER, J. Magn. Reson. 15,295 (1974). 2. D. W. DAVIDSON, S. K. GARG, AND J. A. RIPMEESTER, J. Magn. Reson. 31,399 (1978). 3. D. W. DAVIDSON, in “Water: A Comprehensive Treatise” (F. Franks, Ed.), Vol. 2, p. 115, Plenum, New York, 1973. 4. S. R. GOUGH AND D. W. DAVIDSON, Can. J. Chem. 49,269l (1971). 5. G. J. WILSON AND D. W. DAVIDSON, Can. J. Chem. 41,264 (1963); J.-C. Rosso, C. CANALS, AND L. CARBONNEL, C. R. Acad. Sci. Paris Ser. C 281,699 (1975). 6. J. H. VAN VLECK, “The Theory of Electric and Magnetic Susceptibilities,” p. 266, Oxford Univ. Press (Clarendon), London, 1932. 7. A. H. COOKE, H. MEYER, W. P. WOLF, D. F. EVANS, AND R. E. RICHARDS, Proc. Roy. Sot. A 225,112 (1954); H. MEYER, M. C. M. O’BRIEN, AND J. H. VAN VLECK, Proc. Roy. Sot. Ser. A 243,414 (1957). 8. D. F. SARGENT AND L. D. CALVERT, J. Phys. Chem. 70,2689 (1966). 9. S. K. GARG, B. MORRIS, AND D. W. DAVIDSON, J. Chem. Sot. Faraday Trans. II 68,481 (1972). 10. S. K. GARG, J. A. RIPMEESTER, AND D. W. DAVIDSON, J. Magn. Reson. 35, 145 (1979). 11. P. S. ALLEN, A. W. K. KHANZADA, AND C. A. MCDOWELL, J. Mol. Strucr. 14,9 (1972). 12. M. B. DUNN AND C. A. MCDOWELL, Chem. Phys. Len. 15,508 (1972). 13. J. HAUF-T AND W. MUELLER-WARMUTH, Z. Naturforsch. A 22,643 (1967).