The Journal of
Physical Chemistry
0 Copyright, 1987, by the American Chemical Society
VOLUME 91, NUMBER 25 DECEMBER 3,1987
LETTERS Thermal Conductivity of Xenon Hydratet Y. Paul Handa** and John G. Cooks Divisions of Chemistry and Physics, National Research Council of Canada, Ottawa, Ontario, Canada K l A OR6 (Received: September 10, 1987)
The thermal conductivity of xenon hydrate has been measured from 235 to 255 K. The results show no temperature dependence, and the average value is 0.36 A 0.01 W m-l K-I. The latter result indicates that the rotational motion alone of the guest molecule is not responsible for the unusually small thermal conductivitiesof clathrate hydrates, as has previously been suggested in the literature.
Introduction Clathrate hydrates are nonstoichiometric inclusion compounds in which water molecules form the host lattice. Most hydrates exist as one of two cubic structures termed structure I and structure 11. These compounds can encage a wide variety of guest molecules differing in size and shape. The interaction between the host and the guest is quite weak, so that most properties of the hydrates can be taken as a sum of the contributions from the host and the guest. Since the concentration of the guest is quite small, the properties of the hydrate are determined largely by the host lattice. Furthermore, because of the similarity of the three-dimensional hydrogen-bonded network of water molecules in hydrates and in ice Ih, a number of properties of the hydrates, especially those of the host lattices, are almost the same or similar to those of ice' provided due allowance is made for the differences between the densities of the hydrates and ice. Thus, the heat capacities,* sound vel~cities,~ enrichment of heavy isotopes of hydrogen and oxygen in the l a t t i ~ e and , ~ some spectroscopic, electrical, and mechanical properties' of hydrates are similar to those of ice. Issued as NRCC No. 28260. *Division of Chemistry. *Division of Physics.
0022-3654/87/2091-6327$01.50/0
TABLE I: Thermal Conductivities, A, of Ice Ih and Clathrate Hydrates compound T j K X/W m-' K-' ref ice Ih 260 2.35 17 structure I hydrates
xenon methane ethylene oxide structure I1 hydrates cyclobutanone tetrahydrofuran 1,3-dioxolane
245 213 263
0.36 0.45 0.49
this work 11 18
260 260 260
0.47 0.51
8
0.51
8
7
However, the thermal conductivity of hydrates is unusual in the sense that it is the only property known so far which differs drastically from that of ice. As recorded in Table I, at 273 K the thermal conductivity of hydrates is only about 20% of that (1) Davidson, D. W. In Natural Gas Hydrates: Properties, Occurrence and Recouery; Cox, J. L., Ed.; Butterworth: Boston, 1983; Chapter 1. ( 2 ) Handa, Y . P.; Tse, J. S. J . Phys. Chem. 1986, 90, 5917. (3) Kiefte, H.; Clouter, M. J.; Gagnon, R. E. J . Phys. Chem. 1985, 89,
3103.
(4) Handa, Y . P. Can. J . Chem. 1984, 62, 1659
Published 1987 by the American Chemical Society
6328 The Journal of Physical Chemistry, Vol. 91, No. 25, 1987 of ice. Another unusual feature is that whereas the thermal conductivity of ice increases with decreasing temperature, that of hydrates decreases slightly so that at about 40 K the thermal conductivity of hydrates is only about 2% of that of i ~ e . ~ . ~ In a careful and detailed study of the thermal conductivity of tetrahydrofuran hydrate, Ross and Andersson' concluded that the coupling of the rotational vibrations of the guest with the lattice vibrations was mainly responsible for the phonon scattering mechanism. In another study, Andersson and Ross* found that thermal conductivity of the hydrates decreased slightly as the size of the guest molecule was increased and concluded that the hindered rotation of the guest makes the guest-host coupling even more effective and thus results in enhanced phonon scattering. However, a polyatomic guest molecule undergoes both translational and (hindered) rotational motions and the thermal conductivity measurements reported in the literature are for hydrates containing polyatomic guests only. Thus, the role played by any possible coupling between the translational motion of the guest and the lattice vibrations cannot be assessed. Thermal conductivity data on hydrates containing monatomic guests are therefore quite desirable. To that end we have measured the thermal conductivity of structure I xenon hydrate.
Experimental Methods Xenon was obtained from Matheson and has a specified purity of 99.995 mol %. Water used was distilled, deionized, and degassed. The hydrate sample was prepared in a Parr pressure vessel equipped with stainless steel rods and a pressure gauge. The vessel containing the components was mounted on a set of rollers and rotated along its long axis for several days at 240 K. The rods provided the grinding action required for speeding up the reaction between ice and xenon. A steady pressure reading for 48 h indicated the completion of the reaction. At this stage rolling was stopped and the vessel kept at 240 K for another day. The final pressure in the vessel was 9.5 bar, which is considerably higher than the dissociation pressure of 1.5 bar of xenon hydrate at 273 K.9 The vessel was subsequently cooled to liquid nitrogen temperature, and the finely powdered sample was recovered and stored in liquid nitrogen until further use. The composition of the hydrate was determined by weighing about 2 g of the sample in a gas-tight bottle, allowing the hydrate to decompose slowly, and weighing again the liquid water left behind. The composition was found to be Xe.6.2H20. This can be compared with the equilibrium composition of Xe-6.29H20 at 273 K;Io the sample prepared in this work was richer in xenon because of the excess pressure intentionally used to convert all ice into hydrate. A guarded hot-plate cell was used to measure thermal conductance. The cell accepts sample in the form of a circular disk of 3.7-cm diameter and 1.7-cm length. The apparatus, the measurement technique, and test measurements on grade 7740 Pyrex and ice Ih have been described before.lI The measurements are estimated to be accurate to *lo%. A disk was pressed from xenon hydrate powder in a pistoncylinder assembly with a hydrostatic pressure of about 1 kbar. At all stages the sample was handled either in liquid nitrogen or (5)
Ashworth, T.; Johnson, L. R.; Lai, L. P. High Temp.-High Pressures
1985, 17, 413.
(6) White, M. A. J . Phys., Colloq. 1987, C1-565. (7) Ross, R. G.; Andersson, P. Can. J . Chem. 1982, 60, 881. (8) Andersson, P.; Ross, R.G.J . Phys. C 1983, 16, 1423. (9) Ewing, G. J.; Ionescu, L. G. J . Chem. Eng. Data 1974, 19, 367. (IO) Davidson, D. W.; Handa, Y .P.; Ripmeester, J. A. J . Phys. Chem. 1986, 90, 6549. (11) Cook, J. G.;Leaist, D. G.Geophys. Res. Lett. 1983, 10, 397.
Letters above boiling nitrogen in order to avoid condensation of moisture on the disk. During thermal measurements the disk was kept in contact with Xe at a pressure about 0.5 bar higher than the dissociation pressure of the hydrate. After completion of the measurements the composition of the disk was determined and found to be the same as the original composition mentioned above, thus ensuring the integrity of the sample.
Results and Discussion Thermal conductivity measurements were made at 235, 245, and 255 K. Two measurements were made at each temperature, and the mean value of six data points is 0.36 f 0.01 W m-l K-' and showed little if any temperature dependence over the limited temperature range studied. This value is consistent with the low thermal conductivities previously observed for other clathrate hydrates as recorded in Table I. This also indicates that our sample did not contain any ice; since the thermal conductivity of ice is relatively large, the presence of a small amount of ice can change the results significantly. As seen in Table I, the thermal conductivities of the hydrates are much smaller than that of ice Ih. This has been explained* in terms of the coupling of the (hindered) rotational vibrations of the guest molecules with the lattice vibrations which leads to more efficient phonon scattering. However, it is interesting to note that xenon hydrate has the lowest thermal conductivity in spite of the fact that xenon does not have any rotational degree of freedom. It is possible that the interaction of the lattice vibrations with the translational modes of the guest also plays an important role in the phonon transport mechanism. The uncertainties associated with the results in Table I are of the order of 3-10%. It, therefore, appears that the thermal conductivities of the hydrates are nearly the same regardless of the nature of the guest or the hydrate structure. The translational and rotational motions of the guest molecule are associated with rather low energy modes in the range 10-100 cm-' as determined from an analysis of the heat capacity data,2 by infrared spect r o ~ c o p y , ' ~and ? ' ~ by molecular dynamics simulation^.'^,'^ Thus, at higher temperatures the energy dissipation due to excitation of the localized modes of the guest is fully saturated, and if we assume that the motion of the guest is mainly responsible for the anomalous thermal conduction in hydrates, then their thermal conductivities should be nearly the same regardless of the nature of the guest. An alternative implication of the results is that the guest molecule may have no role at all to play in determining the thermal conductivities of the hydrates. This observation led Dharma-wardana16 to suggest a model in which the phonon mean free path in ice Ih is scaled to a constant limiting value for the hydrates because of their relatively much larger unit cell sizes. This is equivalent to suggesting that the fully excited guest molecule has already made whatever contribution it was going to make in affecting the phonon mean free path and any further role of the guest molecule can thus be ignored. Acknowledgment. The authors thank Mr. D. Brown for his assistance with the thermal conductivity measurements. (12) (13) (14) 2096. (15) 6146. (16) (17) 5.
Klug, D. D.; Whalley, E. Can. J . Chem. 1973, 51, 4062. Bertie, J. E.; Jacobs, S. M. Can. J . Chem. 1977, 55, 1777. Tse, J. S.; Klein, M. L.; McDonald, I. R. J . Chem. Phys. 1983, 78, Tse, J. S.; Klein, M. L.; McDonald, I. R. J . Chem. Phys. 1984, 81,
Dharma-wardana, M. W. C. J. Phys. Chem. 1983,87, 4185. Hobbs, P. V. In Ice Physics; Clarendon: Oxford, U.K., 1974; Chapter
(18) Cook, J. G.; Laubitz, M. J. In Thermal Conductiuity; Hust, J. G., Ed.; Plenum: New York, 1983; Vol. 17, p 745.
