Formation of Periodic Layered Pattern of Tetrahydrofuran Clathrate

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J. Phys. Chem. B 2008, 112, 9876–9882

Formation of Periodic Layered Pattern of Tetrahydrofuran Clathrate Hydrates in Porous Media Kazushige Nagashima,* Takahiro Suzuki, Masaki Nagamoto, and Tempei Shimizu Dept. of Physics, School of Science and Technology, Meiji UniVersity, 1-1-1 Higashimita, Tama-ku, Kawasaki 214-8571, Japan ReceiVed: March 21, 2008; ReVised Manuscript ReceiVed: June 3, 2008

Directional growth of tetrahydrofuran (THF) clathrate hydrates was studied in a mixture of glass beads and a stoichiometric THF-water solution. Results showed that disseminated pore space type hydrates formed in a mixture containing 50-µm beads. However, a pure hydrate layer formed pushing the beads in a mixture containing 2-µm beads (frost heaving of hydrates). As the growth proceeded, new layers were formed repeatedly, leading to the eventual formation of a periodic layered pattern. It was found that as the growth rate increased, both the thickness of a hydrate layer and the interval between the neighboring layers decreased according to power laws. The effects of the applied temperature gradient and the weight ratio of the solution and glass beads were also systematically studied. Further, the possibility of applying our model experiments to the formation of natural methane hydrates was discussed. 1. Introduction Clathratehydrates are ice-like crystals composed of a network of hydrogen-bonded water molecules that contain guest molecules in cavities. A huge amount of methane hydrates have been found globally in sediments under the ocean floor. These methane hydrates are of significant interest both as a possible cause of global climate change and as a potential energy resource.1,2 Cores recovered from the ocean floor have been reported to have a variety of patterns (textures) and sizes of hydrates in the sediments. These hydrates were classified into four categories by Malone:3 disseminated (fine hydrates in the pore space of sediments), nodular (hydrates up to 5 cm in diameter), layered (parallel hydrate layers), and massive (as thick as 3-4 m and containing 95% hydrates and less than 5% sediments), as shown in Figure 7.7 of ref 1. On the other hand, freezing of water in soil causes frost heave. Growing ice crystals absorb water in the pore space, pushing the soil particles and forming a pure ice layer called an ice lens.4–6 The frost heave phenomenon is not unique to water; it has also been reported during the growth of He crystals7 and Ar crystals8 in porous media. Although the formation of hydrates has been studied extensively, the effect of porous media on the formed patterns and sizes has not been clarified. Chuvlin et al.9 conducted laboratory experiments on the simultaneous formation of methane hydrates and ice crystals in soil. Frozen-hydrate-containing samples showed a variety of crystal patterns, depending on the mixing ratio of sand and clay. It is important to note that these samples were in the frost heave condition for ice (permafrost), and the sole effect of hydrate formation has therefore not been determined. A typical experimental procedure for forming gas hydrates in water involves the boundary between a gas bubble and water. Hydrates form preferentially at the boundary. Therefore, the formed pattern depends strongly on the bubble shape and is different from the four types of patterns described. Suess et al. reported that cores recovered from the near-surface marine * Corresponding author. E-mail: [email protected].

sediments show a globular pattern, in which hydrates form on only the surface of the cavities.10 Shoji et al.11 investigated the process of formation of the globular type hydrates by introducing multiple gas bubbles into water in a high-pressure vessel. Buffett et al.12 experimentally studied the formation of CO2 hydrates from the dissolved gas in water in soil in the absence of both gas bubbles and ice crystals, in order to confirm commonly proposed models of marine hydrate formation.13,14 Their results showed successfully that gas hydrates can nucleate at a dissolved gas concentration less than the concentration when free gas is present. However, once the dissolved gas was depleted, hydrate formation stopped. This resulted from the time limitation of an experimental run to diffuse the dissolved gas into the hydrates. In this sense, the THF-water solution system is useful as an idealized model system without the diffusion effect of guest molecules. Numerous in situ observations of growing THF hydrates have been performed in solution (without soil).15–20 THF is miscible with water at all molar ratios. A stoichiometric THF-water solution (THF-17H2O) forms a structure-II hydrate21 at atmospheric pressure below 4.4 °C.22 Interferometric observation has confirmed that the concentration distribution of THF near the growing hydrate remains unchanged when the stoichiometric solution is used.18 Our preliminary report23 and that of Watanabe et al.24 involved growth experiments of THF hydrates in porous media (the mixture of glass beads and the stoichiometric THF-water solution). Results of both studies revealed that layered patterns of pure hydrates were formed in the mixture as the growth of hydrate pushed the glass beads (frost heaving of hydrates). In these experiments, the growth temperature was above 0 °C (no ice crystals) and no bubbles existed. Therefore, formation of the layered patterns was solely attributed to growth of the hydrates in porous media. According to studies on the formation of patterns of growing crystals (without soil), such as dendrite patterns, typical size scales of growth patterns were well characterized as a function of growth rate.25 The size scales of self-organized patterns of methane hydrates in recovered cores may provide information

10.1021/jp802487d CCC: $40.75  2008 American Chemical Society Published on Web 07/22/2008

Tetrahydrofuran Clathrate Hydrates concerning the formation rates and formation time scales as the patterns formed. Therefore, the relationship between the growth rate and the typical size scales of the hydrate patterns must be established. Our previous investigations demonstrated that a directional growth technique, which was originally used for studying the pattern formation of ice crystals,26 was able to control the growth rate of THF hydrates in solution (without soil) at arbitrary constant rates. This was achieved by controlling the velocity of the growth cell toward the colder region under an applied temperature gradient.18,19 This type of compulsory growth technique is advantageous in the observation of growth patterns as a function of growth rate. In the present work, the directional growth of THF hydrates was observed in situ in the mixture of glass beads and a stoichiometric THF-water solution. The effect of the glass bead diameter was tested using two sizes of glass bead (diameters: 2 and 50 µm). The pattern formation of layered hydrates in the mixture of 2-µm glass beads was systematically studied as a function of the growth rate, applied temperature gradient, and weight ratio of the solution and the glass beads (the solution content in the mixture). Finally, the possibility of applying our model experiments to the formation of natural methane hydrates in oceanic sediments was discussed. 2. Experimental Section 2.1. Materials. The model system consists of a mixture of spherical glass beads and a stoichiometric THF-water solution (THF-17H2O). The mean diameter of the glass beads was 2 µm (silica microbeads P-600, Catalysts and Chemicals Ind. Co. Ltd.). These glass beads were identical to those used by Watanabe et al.6 in their investigation of ice lens formation. In addition, large 50-µm diameter glass beads (Unibead SPL-50, Union Co. Ltd.) were used to test the effect of size of porous media. Note that the present study primarily used 2-µm glass beads, which formed the layered hydrates. All sample solutions were prepared by mixing a dehydrated stabilizer-free THF reagent (99.5% purity, Kanto Chemical Inc., Japan) with ultrapure water at the stoichiometric composition. These solutions were mixed with dry glass beads. The weight ratio of the solutions and the glass beads (solution content in the mixture), ws/wg, was unity for experiments studying growth as a function of growth rate and applied temperature gradient. The effect of solution content in the mixture was studied in the range of 0.75 e ws/wg e 1.0. Note that the viscosity of the sample at ws/wg < 0.75 was too high to inject it into the growth cell. 2.2. Methods. Figure 1 shows schematic illustrations of the growth cell designed for the present experiments, as well as the directional growth apparatus which was the same as that used in previous studies.18,19 The growth cell consisted of two microscope slides (26 mm × 76 mm × 1 mm) and Teflon spacers (thickness: 1 mm) inserted between the two slides. A solution reservoir formed from scientific cleaning tissue (20 mm × 10 mm × 1 mm) was inserted into one side of the growth cell. As the hydrate grows, the solution reservoir supplies additional solution to the mixture of glass beads and solution if necessary, and shrinks so that the glass cell is not destroyed due to frost heaving of hydrates. Three capillaries (inner diameter: 0.5 mm; length: 10 cm) were connected to the growth cell, as shown in the figure. Capillary 1 was used to inject the sample solution mixed with glass beads, capillary 2 was used to inject the solution into the solution reservoir, and capillary 3 provided air relief during sample injection. Note that in order to confirm uniform

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Figure 1. Schematic illustrations of the growth cell and the directional growth apparatus.

distribution of glass beads in the solution as an initial condition, both the growth cell and the sample were made newly for each experimental run. The growth cell filled with the sample was placed horizontally in two copper blocks; one of the blocks was maintained at a temperature lower and the other, higher than the equilibrium temperature Teq, using thermoelectric modules. A temperature gradient G was applied to the growth cell along its long side. Then, hydrate crystals were nucleated by contact with a chilled wire at the edge of the growth cell in the colder region. The growth cell was moved at a constant velocity (V g 0.4 µm s-1) toward the cold block. The growth interface was forced to locate between two blocks owing to the applied temperature gradient. Thus, the growth of hydrates could be controlled by the velocity of the growth cell. The velocity was controlled precisely by a translational stage connected to a PC-controlled pulse motor. The temperature profile in the growth cell between the cold and hot blocks was measured using a thermocouple attached to the growth cell. As the growth cell was moved from the hot block toward the cold block, the temperature was recorded as a function of the position of the thermocouple tip. The temperature profile was linear. The slope, the temperature gradient G, was found to be 1.3 K mm-1 for runs in which V and ws/wg were varied. The effect of G was examined at fixed V ) 1 µm s-1 and ws/wg ) 1.0 in the range of 0.52 e G e 3.7 K mm-1. 3. Results 3.1. Formation of Periodic Layered Pattern. Figure 2 shows images of the hydrates formed in the mixture of the solution and the glass beads of diameter (a) 2 and (b) 50 µm. Each growth condition was identical: V ) 1 µm s-1, G ) 1.3 K mm-1, and ws/wg ) 1.0. The growth cell was cooled from the left to right in the figure. The hydrate formed a layered pattern in the mixture containing 2-µm beads (Figure 2a). The bright vertical lines in the image represent pure hydrates, and the dark lines represent the glass-bead-rich region. The initial hydrate layer was formed at the extreme left, as can be seen in the image. As the growth proceeded, new layers were formed repeatedly, leading to the formation of multilayered patterns. The thickness of the hydrate layer and the interval between the neighboring layers decreased gradually. After more than 20 layers had formed, the thickness and interval became almost constant. Thus, a periodic layered

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Figure 4. Relationship between Lth and t at V ) 1 µm s-1, G ) 1.3 K mm-1, and ws/wg ) 1.0.

Figure 5. Relationship between R and V at G ) 1.3 K mm-1 and ws/wg ) 1.0.

Figure 2. Images of the hydrates formed in glass beads of diameter (a) 2 and (b) 50 µm, under the same growth conditions: V ) 1 µm s-1, G ) 1.3 K mm-1, and ws/wg ) 1.0. (a) Layered type, and (b) disseminated pore space type.

Figure 3. Sequential images of the formation of the periodic layers at V ) 1 µm s-1, G ) 1.3 K mm-1, and ws/wg ) 1.0. The growth times after appearance of the hydrate layer labeled “1” are (a) 30, (b) 90, (c) 150, and (d) 210 s.

pattern formed in steady-state growth conditions where the size scales were time-independent. On the other hand, in the mixture containing 50-µm beads (Figure 2b), typical patterns for frost heaving were not observed. Note that the small white dots were observed prior to cooling and can be attributed to light transmission through some of the glass beads. The contrast in the image before and after cooling was the same. Consequently, hydrates grew in the pore space of the mixture of glass beads without pushing the glass beads (disseminated type).

Figure 6. Images of the periodic hydrate layers at G ) 1.3 K mm-1 and ws/wg ) 1.0. The velocities of the growth cell are (a) 1, (b) 3, (c) 7, and (d) 12 µm s-1.

Hereafter, the results for periodic hydrate layers during the steady-state growth in the case of the 2-µm beads will be shown. Figure 3 shows sequential images of the formation of periodic layers. The growth time after the appearance of the hydrate layer labeled “1” is (a) 30, (b) 90, (c) 150, and (d) 210 s. The layer

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Figure 9. Relationship between Lth and G, and Li and G, at fixed values of V ) 1 µm s-1 and ws/wg ) 1.0. The solid lines indicate the best-fit lines.

Figure 7. Relationship between Lth and V, and Li and V, at G ) 1.3 K mm-1 and ws/wg ) 1.0. The values of Lth and Li were obtained by averaging ten measured values. The solid lines indicate the best-fit lines.

Figure 8. Images of the periodic hydrate layers as a function of G at fixed values of V ) 1 µm s-1 and ws/wg ) 1.0. The values of G are (a) 0.87, (b) 1.6, and (c) 3.6 K mm-1.

“1” grew with each elapse of time, as shown in Figure 3a-c. The growing layer shifted gradually toward the colder region (left side in the image) under the applied temperature gradient. Note that if the growth interface is located at the same position in the image, the growth rate R is equal to V. Therefore, the shift in the growing layer toward the left side indicates that R was lower than V. Finally, in Figure 3d, a new layer labeled “2” started to grow.

Figure 4 shows the relationship between the thickness of the hydrate layer, Lth, and the growth time t. The hydrate layer grew at almost a constant rate. When the new layer started growing, the former hydrate layer suddenly stopped growing. Figure 5 illustrates the relationship between R and V. The result shows that, although the velocity controlled the cooling rate, R was smaller than V. As a result, the growing hydrate layer was supercooled compared with the equilibrium temperature in the porous media, as reported by Watanabe et al.24 3.2. Effect of the Growth Rate R. Figure 6 shows images of the periodic hydrate layers at a velocity of (a) 1, (b) 3, (c) 7, and (d) 12 µm s-1. It was determined that Lth and the interval between the neighboring layers, Li, decreased as V increased. At V ) 12 µm s-1 (Figure 6d), the layers were undulated and the contrast in the image was weakened. When V was further increased, a layered pattern was not observed. Moreover, the contrasts between the bright and dark areas completely disappeared (not shown). These results therefore indicate that increase in V caused a change in the hydrate pattern from the layer type to the disseminated pore space type. Figure 7 shows the relationship between Lth and V, and between Li and V. The values for Lth and Li were obtained by averaging ten measured values. The results show that Lth and Li can be well characterized by power laws as a function of V, such as Lth ) 88.3 V-1.20 (R2 ) 0.996) and Li ) 250 V-1.16 (R2 ) 0.976). The relationships were rewritten in terms of R as Lth ) 24.2 R-1.19 and Li ) 71.5 R-1.16. Results suggest that both size scales were nearly inversely proportional to R. Watanabe et al.6 also reported an identical dependence of the ice lens thickness on R. However, the interval between the ice lenses was not found to be dependent on R (the size scales of THF hydrate layers were not shown24). The results in the present study were obtained by measuring periodic hydrate layers during steady-state growth. This difference may be attributed to the difference in measurement conditions. 3.3. Effect of the Applied Temperature Gradient G. The temperature gradient applied was G ) 1.3 K mm-1, which is four or 5 orders of magnitude larger than the typical geothermal gradient under the ocean floor (∼50 K km-1). In this section, we present the study into the effect of G on the size scales. Figure 8 shows images of the periodic layers grown at V ) 1 µm s-1 and ws/wg ) 1.0. The temperature gradients applied were (a) 0.87, (b) 1.6, and (c) 3.6 K mm-1. Figure 9 shows the

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Figure 10. Relationship between R and G at V ) 1 µm s-1 and ws/wg ) 1.0.

averaged values of Lth and Li as a function of G. The results show that, as G increased, both Lth and Li decreased. However, G had a smaller effect on Lth than on Li. Figure 10 shows the relationship between R and G at constant values of V ) 1 µm s-1 and ws/wg ) 1.0. Results indicate that R was almost constant, independent of G. Therefore, the experimental relationship between Lth and R mentioned above was found to be nearly independent of G. 3.4. Effect of the Solution Content ws/wg. In frost heaving, one of the most critical processes is water transport through the porous media. In the present study, growth experiments were performed as a function of ws/wg at fixed values of V ) 1 µm s-1 and G ) 1.3 K mm-1. Figure 11 shows images of the periodic layers at solution content values of (a) 1.0, (b) 0.90, and (c) 0.75. Figure 12 shows averaged values of Lth and Li as a function of ws/wg. Lth and Li decreased with a decrease in ws/wg. The best-fit lines indicate that both Lth and Li decrease to zero when ws/wg decreases to 0.65. 4. Discussion 4.1. Effects of Growth Conditions on Size Scales of Periodic Layers. In this section, the effects of growth conditions on the size scales of periodic hydrate layers are discussed. When a hydrate layer grows, it pushes the glass beads, absorbing the solution from the pore space between the glass beads. As a result, the solution content in the glass bead region decreases gradually near the growing layer (consolidation). Figure 12 shows results suggesting that when the solution content decreased to a critical value (≈0.65), the hydrate layer could not continue growing. This causes pore space type growth, and a new hydrate layer thus emerges in the solution-rich region. At a larger R, Lth, and Li were observed to decrease, as shown in Figure 7. The typical length scale of the solution-poor region in soil is predicted theoretically for frost heaving and is inversely proportional to R.27 The hydrate layer absorbs the solution closer to the growing layer at a higher R, and therefore, the solution content near the interface rapidly reaches the critical value. This may result in a thinner layer. In addition, the shortened length of the solution-poor region at higher R may lead to a shorter interval of formation for a new layer. Figure 13 shows the relationship between Lth and Li, obtained from the results shown in Figure 7. Results indicate that the interval is well characterized by the thickness as a best-fit line of Li ) 2.4 Lth (R2 ) 0.99), as shown in the figure by a solid line. (Note that the fitting line was obtained while neglecting the outlier at Li ≈ 730 µm.) This indicates that the interval is strongly dependent on the growth of a hydrate layer characterizing the length of the solution-poor region. Both theoretical and experimental studies on ice growth have revealed that there exists a critical growth rate, RC, below which an isolated single foreign particle in water is pushed by the growing ice crystal, and above which the particle is encapsulated

Figure 11. Images of the periodic hydrate layers as a function of ws/ wg at fixed values of V ) 1 µm s-1 and G ) 1.3 K mm-1. The values of ws/wg are (a) 1.0, (b) 0.90, and (c) 0.75.

Figure 12. Relationship between Lth and ws/wg, and Li and ws/wg, at fixed values of V ) 1 µm s-1 and G ) 1.3 K mm-1. The solid lines indicate the best-fit lines.

in the crystal.28,29 Furthermore, these studies also showed that RC is inversely proportional to the diameter of the particle. In the present study, both an increase in R greater than 12 µm s-1 in the mixture of 2-µm glass beads and an increase in the glass bead diameter (50 µm) resulted in a disseminated pore space type. This is thought to be due to exceeding the critical conditions for pushing the glass beads. When the applied temperature gradient increased, Li decreased, as shown in Figure 9, although it had a smaller effect

Tetrahydrofuran Clathrate Hydrates

Figure 13. Relationship between Lth and Li, obtained from the results in Figure 7. Note that the fitting line was obtained while neglecting an outlier at Li ≈ 730 µm.

on Lth. The hydrate layer jumped into the solution-rich region where the temperature was higher due to an applied temperature gradient. Since the temperature to form a new layer must be lower than the equilibrium temperature, the increase in the temperature gradient shortened the distance for jump, and thus decreased Li. 4.2. Application to the Natural System. In the present study, the thickness of the hydrate layer Lth (µm) was found to be well characterized as a function of the growth rate R (µm s-1) such as Lth ) 24.2 R-1.19 at G ) 1.3 K mm-1 and ws/wg ) 1.0. Since the results (Figures 9a and 10) indicate that both Lth and R were nearly constant and independent of G, it was assumed that the relationship between Lth and R could be extrapolated to the size scale of natural gas hydrates, neglecting the effect of G. The relationship between R (cm years-1) and Lth (cm) was derived as R ) 20 Lth-0.84. The time scale of formation, t (years), of a single hydrate layer as a function of Lth (cm) was derived as t ) 5.0 × 10-2 Lth1.84. The result estimates that the formation of single hydrate layers of thicknesses 10 cm and 1 m takes about 3.4 and 240 years, respectively. It is noted that this result is based on the idealized model experiments in which the diffusion effect of guest molecules was neglected using the stoichiometric THF-water solution. The time scale of the formation of methane hydrates is expected to be extremely longer than the present result, as numerically predicted by considering the mass transport of methane.30 The formation process of methane hydrates is strongly controlled by the diffusion of guest molecules in water. In order to consider the diffusion effect, future studies must employ a THF-poor solution. In addition, in the present study, the growth front of hydrates was localized by moving the growth cell under the applied temperature gradient and thus nucleation of hydrates away from the growth interface was prevented. Zatsepina et al.31 estimated the nucleation rate in marine environments and showed the importance of considering the induction time for nucleation. Furthermore, Moudrakovski et al.32 observed the localized growth of methane hydrates using a technique of NMR microimaging, and suggested that hydrate growth occurs by renewed nucleation away from the hydrate-water interface as long as gas can diffuse into the pore water. Our future study must also employ a nearly isothermal condition where additional nucleations can occur widely in the sample. The relative effects of nucleation and diffusion will be studied, and the validity using the model system will be examined by comparison with the results obtained from gas hydrate experiments. 5. Conclusions THF hydrates were grown in a mixture of glass beads and a stoichiometric THF-water solution using a directional growth

J. Phys. Chem. B, Vol. 112, No. 32, 2008 9881 apparatus. Results indicated that a periodic layered pattern formed in the mixture containing 2-µm glass beads, whereas disseminated pore space type hydrates formed in the mixture containing 50-µm glass beads. Both the thickness Lth of the hydrate layer and the interval Li between the neighboring layers decreased according to the power laws as the growth rate R increased. When the applied temperature gradient G increased, Li decreased, although it had a smaller effect on Lth. When the initial solution content ws/wg in the mixture decreased, Lth and Li also decreased. The best-fit lines suggested that when ws/wg decreases to a critical value of 0.65, the hydrate layers stop growing and a new layer forms in the solution-rich region. The experimental relationship between Lth and R was extrapolated to the size scale of natural gas hydrates. The time scale of formation, t (years), of a single hydrate layer as a function of Lth (cm) was derived as t ) 5.0 × 10-2 Lth1.84, neglecting the diffusion effect of guest molecules. Note that the present model system was found to be advantageous regarding the characterization of the frost heaving of THF hydrates in porous media; however, our model system must be improved to better emulate the natural system for the formation of methane hydrates. Studies using improved model systems are currently under way. References and Notes (1) Sloan, E. D., Jr. Clathrate hydrates of natural gases, 2nd ed.; Marcel Dekker: New York, 1998. (2) Kvenvolden, K. A. Chem. Geol. 1988, 71, 41–51. (3) Malone, R. D. Gas Hydrate Topical Report, DOE/METC/SP-218; U.S. Department of Energy: Washington, DC, April 1985. (4) Taber, S. J. Geology 1929, 37, 428–461. (5) Taber, S. J. Geology 1930, 38, 303–317. (6) Watanabe, K. J. Cryst. Growth 2002, 237-239, 2194–2198. (7) Hiroi, M.; Mizusaki, T.; Tsuneto, T.; Hirai, A.; Eguchi, K. Phys. ReV. B 1989, 40, 6581–6590. (8) Zhu, D-M.; Vilches, O. E.; Dash, J. G.; Sing, B.; Wettlaufer, J. S. Phys. ReV. lett. 2000, 85, 4908–4911. (9) Chuvilin, E. M.; Perlova, E. V.; Makhonina, N. A.; Yakushev, V. S. In Ground Freezing; Thimus, J. F. Ed.; Balkema: Rotterdam, The Netherlands, 2000, pp. 9-14. (10) Suess, E.; Torres, M. E.; Bohrmann, G.; Collier, R. W.; Rickert, D.; Goldfinger, C.; Linke, P.; Heuser, A.; Sahling, H.; Heeschen, K.; Jung, C.; Nakamura, K.; Greinert, J.; Pfannkuche, O.; Trehu, A.; Klinkhammer, G.; Whiticar, M. J.; Eisenhauer, A.; Teichert, B.; Elvert, M. Natural Gas Hydrates: Occurrence, Distribution, and Detection. Geophys. Monogr. 2001, 124, 87–98. (11) Shoji, H.; Hachikubo, A.; Miyamoto, A.; Hyakutake, K.; Abe, K.; Bohrmann, G.; Kipfstuhl, S. Proc. Fourth Int. Conf. Gas Hydrates (ICGH4) 2002, 839, 843. (12) Buffett, B. A.; Zatsepina, O. Y. Marine Geol. 2000, 164, 69–77. (13) Hyndman, R. D.; Davis, E. E. J. Geophys. Res. 1992, 97B5, 7025– 7041. (14) Soloviev, V.; Ginsburg, G. D. Bull. Geol. Soc Denmark 1994, 41, 86–94. (15) Makogon, T. Y.; Larsen, R.; Knight, C. A.; Sloan, E. D., Jr J. Cryst. Growth 1997, 179, 258–262. (16) Larsen, R.; Knight, C. A.; Sloan, E. D., Jr Fluid Phase Equilib. 1998, 150, 353–360. (17) Knight, C. A.; Rider, K. Philos. Mag. A 2002, 82, 1609–1632. (18) Nagashima, K.; Yamamoto, Y.; Takahashi, M.; Komai, T. Fluid Phase Equilib. 2003, 214, 11–24. (19) Nagashima, K.; Orihashi, S.; Yamamoto, Y.; Takahashi, M. J. Phys. Chem. B 2005, 109, 10147–10153. (20) Zeng, H.; Wilson, L. D.; Walker, V. K.; Ripmeester, J. A. J. Am. Chem. Soc. 2006, 128, 2844–2850. (21) Jeffrey, G. A. In Inclusion Compounds; Atwood, J. L., Davies, J. E. D., MacNicol, D. D. Eds.; Academic Press: New York, 1984; Vol. 1, pp. 135. (22) Gough, S. R.; Davidson, D. W. Can. J. Chem. 1971, 49, 2691– 2699. (23) Nagashima, K.; Nagamoto, M.; Shimizu, T.; Suzuki, T. Proc. Fifth Int. Conf. Gas Hydrates (ICGH5) 2005, 573, 579. (24) Watanabe, K.; Yokokawa, K.; Muto, Y. Proc. Int. Symp. Cold Regions Eng. 2006, 13, 1211–1216. (25) Glicksman, M. E.; Marsh, S. P. In Handbook of Crystal Growth 1; Hurle, D. T. J. Ed.; Elsevier North-Holland: Amsterdam, 1993; p 1075.

9882 J. Phys. Chem. B, Vol. 112, No. 32, 2008 (26) Nagashima, K.; Furukawa, Y. J. Cryst. Growth 1997, 171, 577– 585. (27) Takashi, T.; Ohrai, T.; Yamamoto, H. J. Jpn. Soc. Snow Ice 1977, 39, 53–64. (28) Po¨tschke, J.; Rogge, V. J. Cryst. Growth 1989, 94, 726–738. (29) Lipp, G.; Ro¨dder, M.; Ko¨rber, Ch.; Rau, G. Cryo-Lett. 1992, 13, 229–238.

Nagashima et al. (30) Rempel, A. W.; Buffett, B. A. J. Geophys. Res. 1997, 102, 10151– 10164. (31) Zatsepina, O. Y.; Buffett, B. A. Geophys. Res. Lett. 2003, 30, 1451. (32) Moudrakovski, I. L.; Ratcliffe, C. I.; McLaurin, G. E.; Simard, B.; Ripmeester, J. A. J. Phys. Chem. B 2004, 108, 17591–19595.

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