J. Phys. Chem. 1992,96, 8599-8603 temperature scale, ICin pores is more stable than in the bulk phase. Water has often been used as a probe in thermoporometry for characterizing pores in water-wettable materials.8,26The procedure adopted sometimes is to quench the water-saturated material and then heat it at a controlled rate and determine the pore size from the melting curve.38 Obviously, caution should be exercised in the thermal treatment of the samples as formation of ICand its transition to Ih at relatively higher temperatures can mask or alter part of the melting curve.
Acknowledgment. Financial support for this work was received, in part, from the Geological Survey of Canada under Gas Hydrate Project 870021. We thank Dr. J. S. Tse for help with X-ray diffraction measurements, Dr. D. D. Klug for help with the preparation of vapor-deposited ice, and Mr. Mike Stolovitsky for conducting nitrogen adsorption-desorption measurements.
References and Notes (1) Molecular Dynamics in Restricted Geometries; Klafter, J., Drake, J. M., Eds.; Wiley: New York, 1989. (2) Jackson, C. L.; McKenna, G. B. J. Chem. Phys. 1990, 93, 9002. (3) Patrick, W. A.; Kemper, W. A. J . Phys. Chem. 1938,42, 369. (4) Antoniou, A. A. J. Phys. Chem. 1964, 68, 2754. (5) Litvan, G. G. Can. J . Chem. 1966, 44, 2617. (6) Blachere, J. R.; Young, J. E. J . Am. Ceram. Soc. 1972, 55, 306. (7) Rennie, G. K.; Clifford, J. J . Chem. Soc., Faraday Trans 1 1977, 73, 680. (8) Brun, M.; Lallemand, A.; Quinson, J.-F.; Eyraud, C. Thermochim. Acta 1977, 21, 59. (9) Enastiin, B. V.; Sentiirk, H. S.;Yurdakul, 0. J. Colloid Interface Sci. 1978, 65. 509. (10) Awschalom, D. D.; Warnock, J. Phys. Reu. B 1987, 35, 6779. (1 1) Toni, R. H.; Maris, H. J.; Seidel, G. M. Phys. Reu. B 1990,41,7167.
8599
(12) Shirahama, K.; Kubota, M.; Ogawa, S.;Wada, N.; Watanabc, T. Phys. Rev.Lett. 1990, 64, 1541. (13) Jackson, C. L.; McKenna, G. B. J . Non-Crysr. Solids 1991,131-133, 221. (14) Zhang, J.; Liu, G.; Jonas, J. J . Phys. Chem. 1992, 96, 3478. (15) Handa, Y. P.; Klug, D. D. J . Phys. Chem. 1988,92, 3323. (16) Handa, Y. P.; Klug, D. D.; Whalley, E. Can. J . Chem. 1988,66,919. (17) Dore, J. C.; Dunn, M.; Chieux, P. J. Phys. Collogue C1 1987,48,457. (18) Hofer, K.; Mayer, E.; Johari, G. P. J . Phys. Chem. 1990,94, 2689. (19) Wilson, T.W.; Turner, D. T. Macromolecules 1988, 21, 1186. (20) Brzhan, V. S. Colloid J . (USSR) 1959, 21, 621. (21) Kvenvolden, K. A. Chem. Geol. 1988, 71, 41. (22) Nisbet, E. Nature 1990, 347, 23. (23) Handa, Y. P. J. Chem. Thermodyn. 1986, 18, 891. (24) Handa, Y. P.; Hawkins, R. E.; Murray, J. J. J . Chem. Thermodyn. 1984, 16, 623. (25) Defay, R.; Prigogine, I.; Bellemans, A,; Everett, D. H. Surface Tension and Adsorption; Wiley: New York, 1966. (26) Quinson, J. F.; Brun, M. In Characterization of Porous Solids; Un-
ger, K. K., Rouquerol, J., Sing, K. S.W., Kral, K., Eds.; Elsevier: Amsterdam, 1988; p 307. (27) Homeshaw, L. G. J. Thermal Anal. 1980, 19, 215. (28) Levitz, P.; Ehret, G.; Sinha, S.K.; Drake, J. M. J. Chem. Phys. 1991, 95, 6151. (29) Mikhail, R. Sh.; Brunauer, S.;Bodor, E. E. J . Colloid Interface Sei. 1968,26,45. (30) Huber. T. E.: Huber. C. A. J . Phvs. Chem. 1990., 94., 2505. (31 j Speedy, R. J.’ J . Phyi. Chem. 1987, 91, 3354. (32) Lowell, S.Introduction to Powder Surface Area; Wiley: New York, 1979. (33) Dowell, L. G.; Rinfret, A. P. Nature 1960, 188, 1144. (34) Whalley, E. J. Phys. Chem. 1983,87, 4174. (35) Mayer, E.; Hallbrucker, A. Nature 1987, 325, 601. (36) Handa, Y. P.; Klug, D. D.; Whalley, E. J . Chem. Phys. 1986, 84, 7009. (37) Yamamuro, 0. Ph.D. Thesis, Osaka University, 1987. (38) Smolders, C. A.; Vugteveen, E. ACS Symp. Ser. 1985, 269, 327.
Thermodynamic Properties and Dlssociation Characteristics of Methane and Propane Hydrates in 70-A-Radius Silica Gel Porest Y. Paul Handa* and Dmitri Stupin* Institute for Environmental Chemistry, National Research Council of Canada, Ottawa, Ontario, Canada KIA OR6 (Received: May 18, 1992)
The pressuretemperature profiles for the hydrateicegas and hydrateliquid water-gas equilibria were measured for methane and propane hydrates in 70-&radius silica gel pores. In both cases, the equilibrium pressures were 20-100% higher than those for the bulk hydrates. The dissociation characteristics of the gas hydrates in pores were also studied calorimetrically by heating the hydrates under about zero pressure from 100 K to room temperature. It was found that after the initial dissociation into ice and gas the hydrate became totally encapsulated among the pore walls and the ice caps formed at the pore openings. The hydrate thus trapped in the interior of the pore remained stable up to the melting point of pore ice. These results are similar to those obtained in our previous studies on the bulk hydrates which are also stabilized by a shielding layer of ice. However, the apparent increase in the stability of the pore hydrates was found to be much larger than that of the bulk hydrates. The composition of methane hydrate in 70-A pores was determined to be CH44.94H20,and its heat of dissociation into pore water and gas, obtained calorimetrically, was 45.92kJ mol-’; the corresponding values in the bulk phase are 6.00 and 54.19 kJ mol-’, respectively.
Introduction There are worldwide Occurrenw of natural gas hydrates, both on-shore buried under the permafrost and off-shore buried under the oceanic and deep lake sediments.’#* Gas hydrates are often found dispersed in pores of coarse-grained sediments or fractures in g e o ~ t r a t a ,though ~ , ~ occurrence of a massive hydrate bed containing only about 6% by mass sediment has also been reported.5 Gas hydrates are clathrate compounds in which the gas molecules are trapped inside well-defined cages formed by the water molecules! Most of the laboratory work done on the thermodynamics Issued as NRCC No. 34222. *Visitingscientist: Agriculture Institute, St. Petersburg, Russia.
and kinetics of gas hydrates has been limited to hydrates prepared from pure water6*’ and in a few cases from water containing inhibitors such as salts8 and alcohol^.^ Most inferences of the natural Occurrence of hydrates are not based on the recovery of actual samples. Instead, the laboratory results are imposed on the natural systems to draw-up scenarios of Occurrence, accumulation, and dissociation of gas hydrates. In terms of the solidsolution model, the stability conditions of clathrate hydrates depend directly on the activity of water.I0 As the activity decreases, the hydrates form at increasingly higher pressures at a given temperature or at lower temperatures at a given pressure. This is observed in systems containing inhibitors which cause a depression in the freezing point of water, thereby
0022-365419212096-8599$03.00/0 Published 1992 by the American Chemical Society
8600 The Journal of Physical Chemistry, Vol. 96, No. 21, 19‘92
reducing its activity. It is well-known that the freezing point of pure water is also depressed considerably when confined in small pores.” Therefore, the presence of geometrical constraints on the activity of water is equivalent to a change in its activity as caused by the inhibitors. In the natural environment, the activity of water in the sediments is altered due to the presence of dissolved salts and is further altered due to the capillary forces in the compacted sediments. The combined effect of these factors will be that the phase-equilibria and thermodynamic properties of hydrates formed from such water would be different than those of hydrates formed from pure bulk water. Thus, the laboratory results on pure hydrates may not be directly applicable to hydrates in porous media. Moreover, a significant proportion of water in confined spaces is often found to be present as bound water and does not undergo the freezing transition.” This water will not participate in hydrate formation under the same pressuretemperature @-T) conditions as the pore water, and the naturally occurring hydrates will also be associated with bound or unfrozen water. Thus, knowledge of the thermodynamics of hydrate formation-dissociationin porous media will not only help in mapping the natural existence of these materials but also in improving the estimates of their accumulations. Preliminary estimates indicate that such accumulations are quite large and, in fact, hydrates may be the largest reserve of natural gas.2 These hydrates may thus serve as a source of energy but also may contribute to increases in the atmospheric methane content if they become destabilized and release the encaged gas. In spite of the obvious importance of the thermodynamics of hydrates in porous media, very little work has been done in this area. The few earlier studiesI2-” reported in the literature were directed primarily at establishing that gas hydrates can form in actual well cores, sandstones, and compacted sand. In some c a ~ e s , it~ was ~ J ~found that a relatively larger subcooling or elevated pressure was required to induce hydrate formation. From the limited information available in these studies, it is not possible to draw any conclusion on the thermodynamic and kinetic stability of gas hydrates in restricted geometries. Recently, we reported on the thermal and X-ray diffraction characterization of ice” and tetrahydrofuran hydrate18in porous glass and silica gels with mean pore radii in the range 23-70 A. It was found that the melting point and heat of melting of ice decreased as the pores became smaller. Accordingly, as noted above, the thermal properties of hydrates will also be affected the same way. This indeed was found to be the case for tetrahydrofuran hydratela for which the extent of depression in the melting point and the heat of melting was exactly the same as that found for ice. Naturally occurring natural gas hydrates are usually either a structure I hydrate containing almost pure methane3or a structure I1 hydrate where the encaged gas contains a relatively higher proportion of p r ~ p a n e .The ~ kinetic stability of gas hydrates depends not only on heat transfer but also on mass transport, and thus, these hydrates will be expected to behave differently than the tetrahydrofuran hydrate. In this paper, we report on the stability of CH4 and C3Hs hydrates in 70-A-radius silica gel pores.
Experimental Methods Research-grade methane and propane with minimum purities of 99.95 mol 5% were obtained from Matheson. Distilled and degassed water was used. Porous silica gel sold under the name Davisil was obtained from Aldrich. The sample was in the form of a fine powder (particle size 200-425 mesh) and was used without any further treatment. Textural characteristics of the porous material, determined by thermoporometry,were reported previously;” the mean pore radius was 70 A, and the pore volume was 1.11 cm3g-I. Silica gel containing sorbed water was prepared by placing the material in a desiccator containing water, evacuating the desiccator, and allowing a few days for the solid-vapor equilibrium to be established. The sorption was usually complete within 3 days. Methane and propane hydrates in the silica gel pores were prepared using the procedure routinely employed in our laboratory
Handa and Stupin for making hydrates from bulk ~ a t e r The . ~ hydrates ~ ~ ~ are usually synthesized in a Parr reactor by grinding ice under the appropriate gas pressure. The grinding action continually generates a fresh ice surface for reaction with the gas. In the case of the porous material, it was found that no grinding action was necessary, as water in the material is already present in a finely dispersed state. In fact, the hydrates formed quite readily. The porous material containing water was placed in the reaction vessel, cooled to liquid nitrogen temperature, and degassed. An appropriate amount of gas was then introduced such that at completion of the reaction there was enough gas leftover to stabilize the hydrate. The vessel was then warmed to a temperature about 0.5 K above the melting point of pore ice to initiate the reaction. The reaction was usually complete within 3 days. The hydrates were then conditioned under the final p-T conditions (give below) for another 2 days, after which the vessel was cooled in liquid nitrogen and the contents were taken out and stored in liquid nitrogen until further use. All samples of silica gel used for preparing the gas hydrates were fully saturated with respect to water sorbed from the vapor phase, and a few contained a small amount of bulk water as well. As reported previously,” pore ice in the 70-A silica gel melted over a wide temperature range due to a distribution of pore sizes. The most probable melting point was determined to be 267.5 K. Methane hydrate was prepared by cycling the temperature of the vessel between 240 and 260 K. The final pressure at the completion of the reaction was 33.5 atm at 260 K. The initial pressure for the synthesis of C3H8hydrate was its saturation vapor pressure. The temperature was 262 K, and the final pressure was 3.3 atm. All the samples prepared this way were used for calorimetric studies, and a few were used for phase-equilibrium studies. The equilibrium p T profiles for CH4 and C3Hshydrates in the pores were determined using a very simple setup. A highpressure cell about 25 cm3in volume was connected to a pressure transducer (Setra, Model 204, precision f0.1% full scale), a vacuum pump, and a gas source through a manifold. The vapor space volume of the connecting lines was about 24 cm3. Measurements were made in two different ways. In the first method, the cell was packed with 5-mm-diameter glass beads and then loaded with the finely powdered material containing the pore hydrate over boiling liquid nitrogen. The sample was thus spread as a thin coating over the surface of the glass beads. This ensured rapid equilibration among the various phases. The cell was then connected to the manifold and cooled in liquid nitrogen and the whole system evacuated. The cell was then placed in a thermostat controlled at the lowest temperature of the temperature range of interest. At the same time, gas was introduced in the system and its pressure adjusted such that it was slightly below the estimated dissociation pressure of the hydrate. Consequently, as thermal equilibrium was approached, some hydrate dissociated to establish the hydrate-ice-gas (hig) or the hydrate-liquid-gas (hlg) equilibrium to give the first p T measurement. The temperature of the thermostat was then raised by about 0.5-1.0 K and the new equilibrium p-T determined. This was continued until all the hydrate had dissociated. It was found that as more and more hydrate dissociated, longer equilibration times, from several hours up to 1 day, were required for each p-T point determination. Two loadings of the cell were usually required to establish the hig and hlg equilibrium profiles. Temperature measurements were made using a platinum resistance thermometer (Omega, Model 651) with a resolution of fO.l K. Pressure measurements were made with a 204-atm full-scale transducer in the case of CHI hydrate and with a 6.8-atm full-scale transducer in the case of C3H8 hydrate. The two transducers were calibrated by measuring the saturation vapor pressures of ethane and propane (Matheson, purity better than 99.95 mol 5%) at several temperatures to cover the pressure ranges of interest. In the second method, the cell was loaded with glass beads and silica gel saturated with r e s b t to sorbed water and the system assembled as before. The system was then charged with the gas well in excess of the amount required to convert all the water in the pores into hydrate. The sample was then subjected to a few freezethaw cycles and the hydrate allowed to form at a tem-
Properties of Methane and Propane Hydrates in Pores
The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 8601
TABLE I: Equilibrium RessureTemperature Jhta for Methane and Propane Hydrates in 7O-A-Radius Silica Gel Pores
CH, hydrate PI-
TIK 263.0 264.2 264.6 266.2 268.2 270.0 272.0 273.2 274.2 276.2
26.03 26.9 1 27.38 29.08 3 1.88 35.51 40.11 43.47 46.10 5 1.86
I
'O
C3H8hydrate platm
TIK 253.0 261.2 261.2 262.2 262.6 263.2 263.6 264.2 264.6 265.2 265.6 266.0 266.6 267.2 267.6 268.2 268.8 269.6 270.0 270.8 270.8 271.2 27 1.8 272.0
0.777 1.391 1.451 1.487 1.541 1.599 1.632 1.700 1.760 1.846 1.927 2.003 2.105 2.207 2.309 2.440 2.601 2.800 2.964 3.150 3.212 3.336 3.522 3.653
perature about 0.5 K above the melting point of ice in the silica gel. For the synthesis of CH, hydrate, an initial pressure of about 120 atm was used, whereas C3Hs hydrate was synthesized under its saturation vapor pressure. The initial reaction was quite rapid, and then it slowed down exponentially as the pressure decreased due to the consumption of gas. The pressure in the system was increased periodically to maintain a significant reaction rate. Eventually, the gas consumption rate fell to zero. At this stage, the temperature of the thermostat was lowered to the temperature of interest, the gas pressure was reduced just below the estimated dissociation pressure, and a series of p-T measurements were made as described above. Phaseequilibrium measurements on gas hydrates have usually been performed' in the presence of excess water (or ice). Here we have made measurements in exactly the opposite way using a very simple setup. The validity of our technique was checked by making measurements on a sample of pure CHI hydrate in the temperature range 270-274 K. The equilibrium pressures obtained were in good agreement with the literature values. The reproducibility of the results was checked by making measurements on two different samples of pore C3Hs hydrate and was found to be within the precision limits imposed primarily by the transducer. The reproducibility in the pressure measurements was fl-2%. A Tian-Calvet heat-flow calorimeter was used for measuring the thermal properties and dissociation characteristics of the pore hydrates. The details of the calorimeter and the operational procedure are given e l s e ~ h e r e . ' ~Briefly, . ~ ~ 3-4 g of the sample (about 4040% of which was the pore hydrate) was loaded into the calorimeter at about 100 K and the system evacuated until the pressure was reduced to about 0.005 atm. The sample was then heated from 100 to 300 K at the rate 10 or 40 K h-l, and simultaneous measurements of heat flow and the pressure in the system were made. p-V-T measurements on the gas phase allowed determination of the amount of gas released by the hydrate. At least three scans were made for each system.
Results and Discussion The phase-equilibrium data for the pore hydrates are given in Table I and plotted in Figures 1 and 2. A small scatter in the results seen in Figure 2 is from the measurements made on two different samples of C3Hs hydrate. One of these samples was synthesized in situ, whereas the other was prepared in the reactor and then transferred to the equilibrium cell. The agreement between the two sets of data is quite satisfactory. Also shown in Figures 1 and 2 are the smoothed literature data on hig and
O
'
260
l
' I
! :o
i
264
268
272
276
280
TK
F w 1. Equilibrium pressures of CH4hydrate in 70-A-radiussilica gel pores plotted against temperature. The solid curve is for CHI hydrate in the bulk phase. I
5 3
E m
B
I
0 ' 250
256
268
262
274
280
T! K
Figure 2. Equilibrium prcssures of C3H8hydrate in 70-A-radius silica gel pores plotted against temperature. The solid curve is for C3H8hydrate in the bulk phase.
'
30 360
'-05
368
376
384
392
400
~ O ~ K ~ T
Figure 3. Equilibrium fugacities of CH, (curve 1) and C3HB(curve 2) hydrates in 70-A-radiussilica gel pores plotted against reciprocal temperature. The solid lines represent fits of the data to eq 1 .
hlg equilibria for methane21-25and propane22-z6-29 hydrates, respectively. The dissociation pressures of the pore hydrates are higher than those of the bulk hydrates. The relative increase in the dissociation pressure is in the range 2 0 4 % for CH4 hydrate and 40-10096 for C3H8hydrate. These results are consistent with the depressed melting point of ice when confined in small pores." For the bulk hydrate, there is a distinct change in the slope at the quadruple point representing the hilg equilibria. However, in pore hydrates, there is a gradual change in the slope along the p-T envelope. This is mainly because in porous materials water melts over a wide temperature range due to a distribution of pore sizes," and thus, a unique hilg point is not defined. The pressures in Table I were corrected for the vapor pressure of water and then converted into fugacities,f, using the second virial coefficients for CHI and C3H8.30Plots of lnfagainst 1/T are shown in Figure 3 where solid lines represent the fits to the function lnf= a
+ b/T
(1)
8602 The Journal of Physical Chemistry, Vol. 96, No. 21, 1992 TABLE Ik Pnnuoeters for the Fit to Equation 1, Temperature Range of the Data Used for the Fit, and Phase-Equilibrium Type Represented by the Fit system a CH4 hydrate 12.26 19.08 C3Hs hydrate 18.04 27.36
b -2386.2 -4212.6 -4632.4 -71 12.2
temp range 263.0-266.2 268.2-276.2 253.0-263.6 267.6-272.0
equilib type hig hlg hig hlg
0.00 120
156
228
192
264
300
TIK
Figure 4. Plot of calorimeter output (curve 1) and pressure above the hydrate (curve 2) against temperature for the dissociation of CH4 hydrate in 70-&radius silica gel pores.
The parameters for the fit, the temperature range of the data used for the fit, and the equilibrium to which the fit pertains are given in Table 11. For fitting purposes, data points in the mid-temperature range were not used. Instead, a set of four or five data points each at the two extremes of the temperature range was used to generate the hig and hlg equilibrium lines. These lines were then extrapolated to the mid-temperature range. The lines usually passed through the data points not used in the fits, thereby delineating to which equilibria (hig or hlg) these data points belonged to. The point of intersection of the two lines was taken to give the quadruple point. The values obtained are 267.4 and 266.1 K for CH, and C3Hs hydrates, respectively, and are in excellent agreement with the melting point of 267.5 K for pore ice in the 70-&radius silica gel." The quadruple point in the present systems can be interpreted as the temperature at which the smaller pores have either hlg or lg phases only and the larger pores still have hig phases. The heats of dissociation of gas hydrates have generally been obtainedZoby analyzing the phase-equilibrium results in terms of the Clausius-Clapeyron equation d In f/d(l/T) = -AH/R = b where R is the gas constant. Strictly, eq 2 applies to a univariant equilibrium process. The present systems cannot be considered univariant because in each pore a different process may be going on. Consequently, no attempt was made to derive the heats of dissociation for the pore hydrates from the phaseequilibrium data. The dissociation profile of CHI hydrate in the pores prepared in the presence of a small amount of bulk water is shown in Figure 4. At temperatures below 273 K, the hydrate dissociates to give ice and gas. The presence of two kinds of ice in the sample is evidenced by the two melting peaks (curve l), one starting at about 240 K due to pore ice and the second due to bulk ice which appears as a shoulder at about 273 K. Since, as noted above, pore hydrate is less stable than bulk hydrate, the peak in the range 175-200 K can be ascribed to dissociation of pore hydrate and the peak around 210 K to dissociation of bulk hydrate. The two dissociation processes are accompanied by sharp pressure increases in the system as shown by curve 2. In our previous studies on bulk hydrates,I9vmit was found that dissociation of large hydrate crystals at temperatures below 273 K proceeded with the formation of a surface layer of ice which when thick enough prevented further dissociation. It was found that about 30% of the hydrate could remain intact until it was warmed to 273 K. It was also found that if the bulk hydrates were in the form of a very fine powder then the hydrate could
Handa and Stupin dissociate completely below 273 K. In the present case, the bulk hydrate must be present in a finely dispersed state as it completely dissociated at the lower temperature. This is confirmed by the absence of any pressure increase at 273 K. Thermodynamically, the pore hydrates are less stable than the bulk hydrates, and they are obviously present in a finely dispersed state because of the confinement in pores. An interesting phenomenon is observed in the higher temperature region in Figure 4. At the onset of the premelting of pore ice at about 234 K, the pressure starts to increase slowly followed by a steep rise as the pore ice starts to melt. The pressure finally levels off on completion of melting of pore ice. This implies that on initial dissociation at the lower temperature the pores get plugged with ice, thereby stabilizing the hydrates in the interior of the pores. From a comparison of the relative pressure increases at 175 and 234 K, it appears that about 70% of the pore hydrate remains intact up to the melting point of pore ice. For the pore hydrate CH4.nH20,the composition, n, was determined by the data analysis method described p r e v i o u ~ l y . ~ ~ ~ ~ ~ The amount of gas given off by the pore hydrate was determined from p V - T measurements on the gas phase, applying appropriate corrections for the non ideality of the gas phase, and subtracting from this amount the small contribution from the bulk hydrate. The amount of pore water was determined by subtracting bulk water in the sample, determined calorimetrically,from the total water. In the case of the pure watersilica gel system, it was found" that 8.9% by mass of pore water was present as bound water. Assuming this value for the present case, the value obtained for n is 5.94 for the pore hydrate, whereas it is 6.00 for the bulk hydrate.20 The heat of dissociation of the pore hydrate into liquid water and gas, AH(hlg), was obtained by adding up the heat changes associated with all the transitions in Figure 4 and then subtracting out those associated with the bulk hydrate and bulk ice.2o AH(hlg) thus obtained refers to the melting temperature of 267.5 K of pore ice. A part of the pore hydrate dissociated in the range 175-200 K. However, the temperature dependence of the heat of dissociation of hydrate into ice and gas is negligible because the heat capacity change during the process is almost zero.*O The heat capacity change for the dissociation into liquid water and gas is quite significant and for the bulk CH4 hydrate has a value of 230 J K-' mol-'. This value was used to scale the AH(h1g) value to 273.15 K to give the standard heat of dissociation, W ( h l g ) . The standard heat of dissociation of the pore hydrate into ice and gas, W ( h i g ) , was then obtained by subtracting out the heat of melting of pore ice, 281.4 J g-' at 273.15 K," from W ( h 1 g ) . The values obtained were 15.83 and 45.92 W mol-' for W ( h i g ) and AHo(hlg), respectively. For comparison, the corresponding values for the hydrate CH4*6.00H20in the bulk phase are 18.13 and 54.19 kJ mol-', respectively." W ( h l g ) for the pore hydrate is 15.3% smaller than that for the bulk hydrate. This compares well with the 15.6% reduction in the heat of melting of ice in 7 0 4
pores." The calorimetric results shown in Figure 4 are for the samples heated at 10 K h-l. A sample of pore CHI hydrate was also heated under about zero pressure from 100 K to room temperature at the rate 40 K h-I. This experiment was conducted to simulate the conditions under which the naturally occurring hydrates are brought up from the bottom of the ocean to shipboard. In such extractions, the temperature of the sample changes by about 20 K in about 30 min, and its pressure changes from about 25-35 atm to about 1 atm. In fact, our sample was subjected to even more strenuous conditions since its temperature was changed at the same rate but the pressure was kept nearly zero. But again it was found that most of the hydrate remained intact until the shielding layer of ice was melted away. Dissociation characteristia for pore C3Hs hydrate at 10 and 40 K h-' were studied the same way. C3H8hydrate was found to be relatively stable up to the melting point of pore ice. The results obtained here clearly establish that the thermodynamic properties of hydrates are dominated by those of water. When confined in small pores and/or in the presence of interacting
J. Phys. Chem. 1992, 96,8603-8610
8603
(7) Sloan, E. D. Clarhrare Hydrares of Narural Gases; Marcel Dekker:
surfaces, the thermodynamic properties of hydrates change the same way as those of ice. In fact, it is sufficient to know the change in the activity of water in order to predict how the hydrate behavior will change using the solid-solution model. In general, hydrates become less stable when present in confining geometries. However, the results are somewhat surprising in terms of the dissociation characteristics of the pore hydrates. On dissociation below the melting point of ice, the pores become plugged with ice, so,though less stable thermodynamically, the apparent stability of the hydrates is enhanced due to encapsulation among the pore walls and the ice cap. This also implies that when such a system is heated to the melting point of ice the hydrates in the interior of the pores will tend to dissociate explosively.
New York, 1990. (8) (9)
Englezos, P.; Bishnoi, P. R. AIChE J . 1988, 34, 1718. Robinson, D. B.; Ng, H.-J.;Chen, C.-J.Proc. Annu. Conv.GasprocCss.
Assoc. 1987, 66, 154. (10) van der Waals, J. H.; Platteeuw, J. C. A d a Chem. Phys. 1959,2, 1. (1 1) Handa, Y.P.; Zakrzewski, M.; Fairbridge, C. J . Phys. Chem., preceding paper in this issue. (12) Makogon, Y . F. Hydrafes of Narural Gas; Pennwell Books: Tulsa, AL, 1981. (13) Evrenos, A. I. J . Perr. Techno/. 1971, Sepr, 1059. (14) Cheng, W. K.;Pinder, K. L. Can. J . Chem. Eng. 1976, 54, 377. (15) Baker, P. E. In Natural Gases in Marine Sediments; Kaplan, I. R., Ed.; Plenum: New York, 1974; p 227. (16) Stoll, R. D. In Natural Gases in Marine Sediments; Kaplan, I. R., Ed.; Plenum: New York, 1974; p 235. (17) Stoll, R. D.; Bryan, G. M. J . Geophys. Res. 1979, 84, 1629. (18) Handa, P.; Stupin, D.; Zakrzewski, M. IEC Report No.EC-121991S, National Research Council of Canada. (19) Handa, Y.P. J. Chem. Thermodyn. 1986, 18, 891. 120) Handa. Y. P. J. Chem. Thermodvn. 1986. 18.915. (21) Robert$,0. C.; Brownscombe, E.-R.; Howe, L. S.;Ramser, H.Per. Eng. 1941, 12, 56.
Acknowledgment Financial support for this work was provided, in part, by the Geological Survey of Canada under Gas Hydrate Project 870021. Registry No. Methane hydrate, 14476-19-8; propane hydrate, 14602-87-0.
( 2 2 ) Deaton, W . M.; Frost, E. M. US.Bureau of Mines Monograph - . No.
8, 1946. (23) McLeod, H. 0.; Campbell, J. M. J . Per. Technol. 1961, 222, 590. (24) Marshall. D. R.: Saito. S.: Kobavashi. R. AIChE J . 1964. 10. 202. (25) de Roo, J. R.; Peters, C. J:; Lichienthaler, R. N.; Diepen, G. A. M. AIChE J . 1983.29, 651. (26) Frost, E. M.; Deaton, W. M. Oil Gas J . 1946, 45, 170. (27) Reamer, H. H.; Selleck, F. T.; Sage, B. H. Pet. Trans. AIME 1952, 195. 197. (28) Holder, G. D.; Kamath, V. A. J. Chem. Thermodyn. 1982,14, 1119. (29) Holder, G. D.;Godbole, S. P. AIChE J . 1982, 28, 930. (30) Dymond, J. H.; Smith, E. B. The Virial Coefficients ofpure Gases and Mixfures, Clarendon: London, 1980.
References and Notes Judge, A. Proc. 4th Can. Permafrost Conf. 1982, 320. Kvenvolden, K. A. Chem. Geol. 1988, 71, 41. (3) Initial Reports of the Deep Sea Drilling Project. 1982, Leg 67; 1985,
(1) (2)
Leg 84.
(4) Brooks, J. M.; Kennicutt, M. C.; Fay, R. R.; McDonald, T. J. Science 1984,225,409. ( 5 ) Kvenvolden, K. A.; McDonald, T. J. Initial Reports of the Deep Sea Drilling Project. 1985, Leg 84, p 667. (6) Davidson, D.W. In Warm A Comprehensive Treafise;Franks, F., Ed.; Plenum: New York, 1973; Vol. 2, Chapter 3.
Electron Dlffractlon Studles of the Kinetics of Phase Changes in Molecular Clusters. 3. Solld-State Phase Transitions In SeF, and (CHs)SCCI Theodore S. Dibble and Lawrence S. Bartell*
9
Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109 (Received: May 18, 1992; In Final Form: July 14, 1992)
Clusters of SeFd and of (CH3)$2C1 produced by the condensation of vapor in supersonic flow through a Lava1 nozzle were observed to undergo transitions from one crystalline phase to another. Selenium hexafluoride clusters transformed from the body-centered cubic (bbc) to the monoclinic phase with a nucleation rate of 5.5 X lo2*m-' s-l in the vicinity of 105 K whereas clusters of tert-butyl chloride underwent a transition from phase I11 (tetragonal) to phase IV at 6.4 X le7m-3 s-' at approximately 156 K. Results are interpreted in terms of the classical theory of homogeneous nucleation. In the kinetic prefactor, however, where the frequency of the primary molecular motions involved is conventionally ascribbd to translational jumps, we find it necessary to invoke reorientational jumps for the present transitions. Comparisons of heats of transition with interfacial free energies deduced from the nucleation rates indicate that Turnbull's empirical relation for interfacial tensions applies to boundaries between the two crystalline phases as well as to boundaries between solids and liquids. The extrapolation of nucleation rates to deep undercoolings via the formalism of nucleation theory leads to projections that rates as high as m-3 s-l are possible for the present solid-state transformations. Molecular dynamics simulations of phase transitions in clusters of SeFs corroborate this suggestion and help place constraints on aspects of the mechanism involved. The present experiments apparently constitute the fmt measurements of nucleationrates and determinations of the cmeqonding interfacial free energies for transitions between two Crystalline phases in onecomponent systems and in systems of plyatomic molecules.
Iatraduction Transformations between crystalline phases have been studied by scientists in many disciplines and in widely varying materials.1*2 Most of the work in this field examines the overall rate of transformation' or its dependence on thermal history' rather than the nucleation rate itself. This is understandable in view of the experimental and theoretical difficulties surrounding nucleation, in general, and nucleation in crystalline phases, in particular. Additionally, analysis of experimental results requires extensive knowledge of the thermodynamic and physical properties of undercooled materials, information which is seldom available.
Experimental investigations into the nucleation of transitions between solid phases have been carried out for a number of metal alloy^,^*^^^ because of their obvious technological importance. We know of no previous determinations of the nucleation rate of transformations between crystalline phases in one-component systems or in polyatomic species. Neither are we aware of determinations of the interfacial free energy between two crystalline phases in such systems. Research a t the University of Michigan is currently focusing upon the structure and transformations of molecular clusters. Both experimental and computational techniques are being brought to
0022-3654/92/2096-8603S03.00/00 1992 American Chemical Society
