J . Phys. Chem. 1988, 92, 5006-501 1
5006
Origin of Glassy Crystalline Behavior in the Thermal Properties of Clathrate Hydrates: A Thermal Conductivity Study of Tetrahydrofuran Hydratet John S. Tse* Division of Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada K1 A OR9
and Mary Anne White* Department of Chemistry, Dalhousie University, Halifax, Nova Scotia, Canada B3H 4J3 (Received: August 25, 1987; In Final Form: November 28, 1987)
The thermal conductivity of tetrahydrofuran hydrate was measured from 15 to 100 K. The present data complement earlier measurements at higher temperatures and confirm the speculationon the glassy behavior in the thermal conductivity of clathrate hydrates. The experimental results can be interpreted by using a resonant scattering mechanism. The interactions between localized low-frequency vibrations of the guest molecules with the acoustic phonons of the host lattice are responsible for the thermal glassy behavior of the clathrate hydrates, despite their well-defined crystalline structures.
Introduction Clathrate hydrates are materials composed of nonstoichiometric proportions of guest molecules enclathrated in a lattice formed by water molecules.' The structures of clathrate hydrates fall into at least four distinct categories, in which there are different proportions and sizes of cages.2-5 The structure observed depends on the guest Although the guest molecules in these materials may exhibit positional and orientational disorder, clathrate hydrates have well-defined crystalline structures. In contrast with most crystalline solids, in which the hightemperature (> 100 K) thermal conductivity fulls with increasing temperature as T', the thermal conductivity of clathrate hydrates has been found to increase slightly with increasing temperature.' In addition, the thermal conductivity of clathrate hydrates is unusually low, about a factor of 5 lower than that of ice I,, at temperatures near the melting point, and considerably less (by a factor >20) at lower temperatures.' It appears from measurements at relatively high temperatures that the unusual thermal conductivity is insensitive to the crystal structure and the nature of the guest present.'-12 Three qualitative models have been proposed to rationalize the unusual thermal conductivity of clathrate hydrates. In one,l3 it was argued, on the basis of the large unit cell of both type I and I1 hydrates, that the phonon mean free path is limited by the size of the unit cell. The limiting mean free path was assumed to be inde endent of temperature and chosen arbitrarily to be about 12 The second approachlo suggests that the librational motions of the guest molecules may influence the host lattice modes and reduce the thermal conduction. Until recently, there has been no strong evidence to substantiate either conjecture. Very recently, the thermal conductivity of a structure I1 clathrate hydrate of 1,3-dioxolane in the temperature range 2.5-100 K has been r e ~ 0 r t e d . l ~The experimental results were interpreted on the premise that phonon scattering due to point defects, and tunnelling states arising from proton disorder are the major processes for the dissipation of thermal energy. Although this model fits the data at the very low temperature, it fails to account for the rapid rise in thermal conductivity above 10 K.14 Moreover, proton disorder is not substantially different for ice and clathrate hydrates.' In a preliminary communication of the present results,15 the possibility of the disorder in the guest molecules in limiting the thermal conduction has been suggested. In this paper we perform a more thorough theoretical analysis of the experimental data. We shall show, through the examination of the low-temperature thermal conductivity of tetrahydrofuran clathrate hydrate, that despite their well-defined crystalline structures, clathrate hydrates show glassy behavior that we attribute to low-frequency rattling of the guest in the cage, resulting in strong scattering of 'Published as NRCC 28261.
0022-3654/88/2092-5006$01.50/0
the thermal phonons and unusually low thermal conductivity. The clathrate hydrate chosen was structure I1 tetrahydrofuran (THF) hydrate, THFq17H20, melting point 278.15 f 0.1 K.' The structure has a cubic unit cell3 and consists of 16 dodecahedral cages of water molecules ( d 5 A) and 8 16-sided cages of water molecules ( d 6 A), and the THF guest molecules occupy the larger cages in this structure. Although there is considerable information concerning many clathrate hydrates, the greatest amount of information is known about T H F clathrate hydrate, primarily because it is easily prepared by freezing an aqueous solution of the appropriate mixture; in contrast, the clathrate hydrates that contain lighter molecules must be prepared and handled with an overpressure of the guest gas.l,6 Early measurements of the thermal conductivity of T H F clathrate hydrate had been carried out down to 100 K,'-" and although a recent experiment extended this range to 45 K,'* the magnitude of the heat leak in the latter (ca. 50% at the lowest temperaturesI2) left considerable uncertainty about those results. Reliable results of low-temperature measurements are the sine qua non for delineation of the origin of unusual thermal properties, and, therefore, one of the objectives of the present work was to measure the thermal conductivity of a clathrate hydrate down to low temperatures.
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Experimental Section The method of measurement of the thermal conductivity is particularly important in very poor thermal conductors like clathrate hydrates. We chose to perform the measurements on a single crystal to minimize the possible effects of ice impurity. We carried out measurements on a free-standing crystal to preclude the thermal short-circuit corrections that would be associated with a cell apparatus. ( I ) Davidson, D. W.In Water--A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 2, pp 115-234. (2) McMullan, R. K.; Jeffrey, G. A. J. Chem. Phys. 1965, 42, 2725. (3) Mak, T. C. W.;McMullan, R. K. J . Chem. Phys. 1965, 42, 2732. (4) Allen, K. W.; Jeffrey, G. A. J . Chem. Phys. 1963, 38, 2304. (5) Ripmeester, J. A.; Tse, J. S.; Ratcliffe, C. I.; Powell, B. M. Nature (London) 1987, 325, 135. (6) Davidson, D. W.; Handa, Y. P.; Ratcliffe, C. I.; Tse, J. S.; Powell, B. M. Nature (London) 1983, 311, 142. (7) Ross, R. G.; Andersson, P.; Backstrom, G. Nature 1981, 290, 322. (8) Cook, J. G.; Leaist, D. J. Geophys. Res. Lett. 1983, 10, 397. (9) Ross, R. G . ; Andersson, P. Can. J . Chem. 1982, 60,881. ( I O ) Andersson, P.; Ross, R. G . J . Phys. C.: Solid State Phys. 1983, 16, 1423. (11) Cook, J. G . ; Laubitz, M. J. In Thermal Conducriviry; Hurst, J. G., Ed.; Plenum: New York, 1984; Vol. 17, pp 745-751. (12) Ashworth, T.; Johnson, L. R.; Lai, L.-P. High Temp.-High Pressures 1985, 17, 413. (13) Dharma-wardana, M. C. W . J . Phys. Chem. 1983, 87, 4185. (14) Ahmad, N . ; Phillips, W.A . Solid Stat. Commun. 1987, 63, 167. ( 1 5 ) White, M. A. J . Phys. (Les Ulis, Fr.) 1987, CI,565.
Published 1988 by the American Chemical Society
Thermal Properties of Clathrate Hydrates
The Journal of Physical Chemistry, Vol. 92, No. 17, 1988 5007
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Sample Preparation. A large single crystal of tetrahydrofuran clathrate hydrate was grown by gradual solidification of the appropriate proportion of tetrahydrofuran (BDH analytical grade, >99.5%) and doubly distilled water, overall composition THF16.9H20, in a sealed Pyrex ampule. The ampule was placed in an ice/water/salt bath (to maintain the temperature gradient around the ampule). The cold bath sat on a StirKool (Thermoelectronics) cooling plate, and the entire stage was capped with an unsilvered Dewar flask to insulate the system from room air currents. The temperature gradient along the sample was about 2 K cm-I, and the crystal growth was carried out by increasing the cooling power such that the temperature of the bottom of the sample decreased by about 2 K/day. (Because of the large thermal mass of the cold bath surrounding the ampule, we were able to maintain gradual temperature decreases by stepwise increments of the cooling power.) This method allowed controlled growth of the crystal from the drawn tip at the bottom of the ampule. Although THF clathrate hydrate at its melting point is slightly less dense than water,' we had no problem with floating of the crystal as it grew, presumably because of slight adherence of the crystal in the drawn tip. Large single crystals of T H F clathrate hydrate were grown; for the thermal conductivity measurements reported here, a 35-mm-long (diameter = 25.6 f 0.6 mm) single crystal of exceptional optical clarity was grown during the course of 5 days. Thermal Conductivity Measurements. The steady-state potentiometric methodI6 was used to determine the thermal conductivity. A schematic diagram of the apparatus is given in Figure 1. For the passage of power q through a single crystal of cross-sectional area A , the thermal conductivity, K , is given by
K = -9- d A AT where thermocouples placed a distance d apart are used to measure the temperature difference, AT. The thermocouple used was 0.08-mm diameter AuFe (0.03 at. % Fe)/Chromel (Johnson Matthey; supplied and calibrated by Cryogenic Calibrations Ltd., England; accuracy f0.05 K in the temperature range used). This thermocouple wire was chosen for its high sensitivity and low thermal conductivity, to minimize the thermal short circuit along the thermocouple. The length of the AuFe wire between the contacts along the crystal was 106 mm, again chosen to reduce the flow of heat along the thermocouple wires. The thermocouple junctions were made by spark welding" to reduce the thermal noise associated with using a different joining material. The thermocouples and sample heater (Karma Wire) were frozen into the large single crystal of T H F clathrate hydrate, and the crystal was mounted on the copper heat sink with a little silicone grease (Dow Corning) to aid thermal contact. The bottom of the crystal had been shaved flat with a room-temperature razor blade prior to mounting. All manipulations, including the installation of the crystal in the cryostat, were carried out under a stream of cold dry nitrogen gas. Following installation of the crystal, the sample space of the cryostat was not pumped upon until the temperature was below 250 K to prevent loss of the volatile THF; postexperiment measurement of the refractive index indicated that the sample measured had maintained the initial composition. During the course of the experiment, all cooling and warming of the sample was performed at rates of less than 0.5 K min-I. These temperature manipulations were carried out by the introduction of
