Surface Transformation of Methane–Ethane sI and sII Clathrate Hydrates

Article pubs.acs.org/JPCC

Surface Transformation of Methane−Ethane sI and sII Clathrate Hydrates Steven F. Dec* Department of Chemistry and Geochemistry, Colorado School of Mines, Golden, Colorado 80401, United States S Supporting Information *

ABSTRACT: The reaction of methane, ethane, and water to form structure I (sI) and structure II (sII) clathrate hydrates at 268 K was studied using solid-state 13C NMR. The reaction can be described in terms of four stages: stage 1, the simultaneous formation of methane−ethane sI and sII clathrate hydrates; stage 2, cessation of sI hydrate formation and enhanced sII hydrate formation; stage 3, decomposition of sI hydrate and continued enhanced sII hydrate formation; stage 4, approach to a final steady state of the system. The rates of formation and decomposition of the various methane and ethane sites obtained from analysis of the time-resolved 13C MAS NMR intensity data provide strong evidence that the sI ↔ sII transformation occurs at surfaces and is dominated by two simultaneous reactions; methane−ethane sI hydrate decomposes to gas phase methane, gas phase ethane, and water while forming methane−ethane sII hydrate from gas phase methane, gas phase ethane, and water. The results of a 2D exchange 13C MAS NMR experiment are consistent with these concurrent methane−ethane sI hydrate decomposition and methane−ethane sII hydrate formation surface reactions. The 2D exchange 13C MAS NMR spectrum also provides conclusive evidence that methane−ethane sI and sII hydrates are not intimately mixed.

■

INTRODUCTION Gas hydrates are solid inclusion compounds, often only stable at low temperatures and high pressures, consisting of molecules encapsulated by cages formed from networks of hydrogenbonded water molecules.1,2 Gas hydrates are abundant in permafrost3 and deep sea environments.4 These naturally occurring deposits are a possible energy resource5 and a potential environmental hazard6 and are also considered a means to sequester carbon to mitigate global warming.7−12 The temperatures and pressures in industrial pipelines used for the production of oil and gas are conducive to gas hydrate formation, which can result in costly remediation efforts.13 Small molecules such as methane, ethane, propane, and carbon dioxide can react with water in its various phases to form structure I14 and structure II14 clathrate hydrate (sI hydrate and sII hydrate, respectively), and large molecules such as adamantane can form structure H15 clathrate hydrate (sH hydrate) when a small helper molecule, such as methane, is also present. The sI and sII hydrate structures are of interest in this work. The water-lattice cages that form the unit cells of sI and sII hydrates are depicted in Figure 1. The sI hydrate unit cell consists of two dodecahedra (512 cages) and six tetrakaidecahedra (51262 cages).16 The sII hydrate unit cell contains sixteen 512 cages and eight hexakaidecahedra (51264 cages).17 Methane (C1) and ethane (C2) are two of the components of natural gas and are particularly interesting because C1−C2 mixtures form both sI and sII hydrate; the stable phase depends on the C1−C2 gas phase composition.18 The structural © 2012 American Chemical Society

Figure 1. Number and structure of cages of sI and sII hydrate unit cells.

transformations between C1−C2 sI and sII hydrates are readily observed.19−21 Studies of the reactions in the C1−C2 gas hydrate system provide not only an understanding of the reaction mechanisms of the C1−C2 gas hydrate system but also insight into other clathrate hydrate reactions, such as the exchange of carbon dioxide for methane in C1 sI hydrate, a strategy suggested for the sequestration of the greenhouse gas carbon dioxide.22,23 While it is clear that the early stages of gas hydrate formation occur at surfaces,24−31 no definitive reaction scheme has been developed for structural transitions such as the C1−C2 sI ↔ sII Received: February 22, 2012 Revised: April 9, 2012 Published: April 10, 2012 9660

dx.doi.org/10.1021/jp301766y | J. Phys. Chem. C 2012, 116, 9660−9665

The Journal of Physical Chemistry C

Article

corresponds to stage 3 (see below) of the C1−C2 clathrate hydrate reaction. NMR Spectroscopy. The 13C MAS NMR spectra were recorded on a Chemagnetics Infinity 400 NMR spectrometer. A Chemagnetics double-resonance, magic-angle spinning probe equipped with 7.5 mm outer diameter zirconia Pencil rotors was used to record all spectra. The 13C observation frequency was 100.5 MHz. The 1H decoupling field was 50 kHz, and the MAS speed was about 2 kHz in all experiments. The 13C 90° pulse was 5 μs. Both time-resolved, single-pulse excitation and 2D exchange 13C MAS NMR experiments were performed. The 2D exchange pulse sequence is shown in Figure S2 (Supporting Information), where t1 is the evolution time, tm is the mixing time or time where chemical or spin exchange may occur, and t2 is the detection or acquisition time. Pulse delays of 60 and 10 s were used in time-resolved, single-pulse excitation experiments and 2D exchange experiments, respectively. Each spectrum in the time-resolved, single-pulse excitation experiment corresponds to the addition of 32 transients. The 2D exchange experiment used a tm of 5 s and 256 evolution times with an increment of 200 μs. The total number of acquisitions for each t1 increment was 24. The 13C spin−lattice relaxation times at 268 K for C1 and C2 in the gas phase and sI and sII hydrate sites are provided in Table SI (Supporting Information). The methylene carbon resonance line of adamantane was used as an external chemical shift standard and was assigned a value of 38.83 ppm.34,35 Chemagnetics solid-state MAS speed and temperature controllers were used. The temperature at the position of the sample was calibrated using methanol.34

gas hydrate transformation. The initial replacement of C2 sI hydrate by C1−C2 sII hydrate has recently been shown to be a regrowth process occurring at surfaces,32 whereas Ohno and coworkers, while not completely discounting a surface reaction, suggest that mature C1−C2 sI and sII hydrates primarily undergo sI ↔ sII structural transitions in the bulk sI or sII hydrate phases.21 In this work high-resolution 13C NMR techniques are used to study the C1−C2 gas hydrate system in order to ascertain possible reaction pathways for the sI ↔ sII transformation. In particular, the transformation of C1−C2 sI hydrate to C1−C2 sII hydrate at 268 K is reported and discussed.

■

EXPERIMENTAL SECTION Sample Preparation. A schematic diagram of the sample preparation apparatus is shown in Figure S1 (Supporting Information). The sample was prepared in a Pyrex glass tube with a constriction at one end that defines the sample bulb. A brass 0.125 cm Swagelok fitting was glued to the glass tube using epoxy. The volumes of the bulb and tube were approximately 0.2 and 1.0 cm3, respectively. About threequarters of the bulb was filled with about 50 mg of powdered ice (250−500 μm), and the tube was pressurized to about 5.0 MPa with 60% 13 CH 4 (99% 13 C, Cambridge Isotope Laboratory) and 40% 13CH3CH3 (99% 13C at one carbon, Isotec). During hydrate formation the pressure drop was measured within ±0.007 MPa using a Sensotec pressure transducer. After pressurizing, the tube was placed in temperature bath at 271 K for 1 day. The bath temperature was then increased to 273 K, and the temperature was maintained within ±0.1 K of 273 K until the ice and gas converted into hydrate as evidenced by a final stable pressure reading of the pressure transducer (∼7 days). After the methane−ethane hydrate formation was complete, all unreacted free gas was removed from the glass tube using a vacuum pump while keeping the hydrate portion submersed in an ice−water bath. The glass bulb was immediately submerged into liquid nitrogen after evacuating the glass tube. The glass bulb, with the hydrate portion submerged in liquid nitrogen, was sealed using a flame torch and transferred to a freezer at a constant temperature of 253 K. Some hydrate always melts during the sealing procedure yielding an unknown amount of methane and ethane in the gas phase of the sealed sample. After initial hydrate formation and sealing of the ampule, the hydrate was melted and allowed to re-form while stored in a freezer at 253 K for 1 year. The C1−C2 hydrate sample was removed from the freezer and completely melted at 291 K in the NMR probe while undergoing magic-angle spinning (MAS); the pressure in the sealed sample was about 1 MPa. The temperature of the probe at the sample position was then lowered to 273 K, and C1−C2 hydrate was allowed to re-form for 17.6 h; the time-resolved 13 C MAS NMR spectra for this time period were reported earlier.30,31 The temperature of probe at the sample position was subsequently lowered to 268 K, and 13C MAS NMR spectra were recorded as a function of time for 45.9 h; the timeresolved 13C MAS NMR spectra recorded during the first 26.2 h at 268 K were reported previously.30,31 For the 2D exchange 13C MAS NMR experiment,33 the C1− C2 hydrate was prepared by melting at 291 K, re-forming at 273 K for 17.6 h, and re-forming at 268 K for 29.9 h, at which time the 2D exchange experiment was recorded; this

■

RESULTS AND DISCUSSION Figure 2 shows one of the 13C MAS NMR spectra recorded during the C1−C2 clathrate hydrate reaction of interest in this

Figure 2. Typical 100.5 MHz 13C MAS NMR spectrum of C1−C2 sI and sII hydrate at 268 K.

work. Noting that a single C1 molecule may occupy any cage in sI and sII hydrates and a single C2 molecule may only occupy the 51262 and 51264 cages,36 structural assignments for each resonance line of Figure 2 are provided in the figure, and the peak positions are listed in Table 1. Figure 3 shows a plot of the 13C MAS NMR relative intensities recorded as a function of time at 268 K. Figure 3 also shows the time dependence of the C1(g) mole fraction. The relative intensities were obtained from the spectra shown in Figure S3 (Supporting Information) and are provided in tabular form in Table SII (Supporting Information). The C1−C2 clathrate hydrate reaction will be discussed below in terms of the four reaction stages denoted in Figure 3. The time rate of change of intensity for each 13C MAS NMR resonance line at 9661

dx.doi.org/10.1021/jp301766y | J. Phys. Chem. C 2012, 116, 9660−9665

The Journal of Physical Chemistry C

Article

Table 1. Structural Assignments and Chemical Shiftsa of the 13C Resonance Lines of Figure 2 and Time Rate of Change of Intensities from Figure 3 rate × 103 (h−1)b site C2 C2 C2 C1 C1 C1 a

sI 51262 sII 51264 gas sI and sII 512 sI 51262 gas

chemical shift (ppm)

stage 1

stage 2

stage 3

stage 4

7.8 6.5 3.7 −3.8 −6.0 −10.6

3.73(0.04) 1.23(0.03) −5.39(0.03) 1.83(0.02) 0.60(0.03) −2.01(0.03)

0.2(1) 6(1) −4.9(0.7) 6.9(0.8) 0.7(0.7) −8.9(0.7)

−3.4(0.2) 3.7(0.2) 0.2(0.1) 2.1(0.2) −0.3(0.1) −2.2(0.2)

−0.6(0.4) 0.9(0.2) −0.1(0.3) 0.2(0.3) 0.1(0.4) −0.5(0.2)

References 30 and 31 and references therein. bNumbers in parentheses correspond to one standard error of the linear fit of the data.

Table SII (Supporting Information) show that the transition point occurs at a C1(g) mole fraction of about 0.74, essentially equal to the value of 0.726 predicted by one equilibrium-based model for the lower sI ↔ sII hydrate transition point at 268 K.36 Stage 3 of the clathration reaction was characterized by the decrease in the number of C2−51262 cages, indicating that the decomposition of C1−C2 sI hydrate was occurring. The rate of formation of C2-sII 51264 cages in stage 3 was about 3 times that observed in stage 1, consistent with the fact that C1−C2 sII hydrate is the stable phase during stage 3.19,36 The relative intensity of the C2(g) resonance line marginally increased in this time period. The number of C1−51262 cages also decreased during stage 3, consistent with the above observation that C1− C2 sI hydrate decomposed during this time period. The ratio of the C2−51264 to C1−512 (sII hydrate only in this case) formation rates of 1.8 is larger than the equilibrium value of 1.5,36 which suggests that the formation of C1−C2 sII hydrate is controlled by the formation of C2−51264 cages as noted in previous work.30,31 Stage 4 of the clathration reaction corresponds to the approach to a final steady state of this system as indicated by the significantly reduced rates of change of the number of C1 and C2 molecules in each of the various C1 and C2 sites, respectively. The C1(g) mole fraction approached a final value of 0.74 after passing through a maximum value during stage 2. The intensity data of stage 2 demonstrates for the first time the existence of a time lag between the onset of a dramatic increase of C1−C2 sII hydrate formation and the decomposition of C1−C2 sI hydrate as the C1 gas phase composition crosses the lower sI ↔ sII phase transition. During stage 2, the invariance of the C2−51262 relative intensity and the equality, within experimental error, of the magnitudes of the time rate of change of the relative intensities of the C2−51264 and C2(g) 13 C NMR resonance lines are strong evidence that the formation of C1−C2 sII hydrate occurs at ice or C1−C2 sII hydrate surfaces from C1(g) and C2(g) as facilitated by the existence of a quasi-liquid layer.30,31 The rate of consumption of C1(g) during stage 2 is more than 4 times that of stage 1 and is therefore also consistent with a surface reaction; the rate of hydrate growth and hence gas phase consumption are significantly reduced once ice crystal surface sites have been covered with a gas hydrate layer, and the reaction is limited by diffusion of guest/water molecules through the layer.27−29 Stage 3 of the C1−C2 clathration reaction is of special interest. This time period is where C1−C2 sI hydrate is first observed to decompose while C1−C2 sII hydrate continues to form. Notably, the time rate of change of the C2(g) intensity is ∼0, indicating that the source of C2 in C2−51264 cages is C2 from the decomposition of C2−51262 cages. Focusing on

Figure 3. Time rate of change of 13C MAS NMR intensities and C1 gas phase mole fraction. Each spectrum used to obtain the intensities required 32 min to record. Time values are assigned as the midpoint of the time required to record each spectrum; for example, spectrum 1 is 16 min, spectrum 2 is 16 + 32 min, and so on. Vertical lines denote start and end points of reaction stages.

each stage of the clathration reaction is approximated with a linear function; the various rates are listed in Table 1. Stage 1 corresponds to the formation of both C1−C2 sI hydrate and sII hydrate at surface sites.30,31 Briefly, the initial formation of C1−C2 sI and sII hydrates was found to be significantly reduced when a quasi-liquid water layer or water layer could not be detected. The existence of mobile water permits the dissolution of C1 and C2 at ice and gas hydrate surfaces, which facilitates gas hydrate growth at these surfaces at 268 and 273 K.30,31 The C1−C2 sII hydrate is a metastable state in stage 1.36 In addition to the C2−51262 and C2−51264 data presented in the earlier work,30,31 new data for the C1(g), C2(g), C1−512, and C1−51262 resonance lines are shown in Figure 3 for stage 1 of the reaction. During stage 2, the number of C2−51262 cages of sI hydrate reached a steady-state value. The number of C1−51262 cages also stabilized during this time period. The C1(g) mole fraction continued to increase during stage 2. The stage 2 rate of C2(g) consumption equals that of stage 1 within experimental error while the stage 2 consumption rate of C1(g) is significantly larger than that of stage 1. The formation rates of C2−51264 and C1−512 cages during stage 2 of the clathration reaction dramatically increased over those rates observed in stage 1. These observations suggest that the initial point of stage 2 roughly corresponds to the sI hydrate to sII hydrate transition point, that is, the point where sII hydrate becomes the stable phase and sI hydrate the metastable phase.19 Figure 3 and 9662

dx.doi.org/10.1021/jp301766y | J. Phys. Chem. C 2012, 116, 9660−9665

The Journal of Physical Chemistry C

Article

Figure 4. 2D exchange 13C MAS NMR of C1−C2 sI and sII hydrate. The mixing time was tm = 5 s. ν1 and ν2 are the frequencies corresponding to the times t1 and t2, respectively.

Figure 5. Left-hand side of (a) and (b) shows schematic diagrams of the six 51262 cages of the sI hydrate unit cell. For simplicity, sI 512 cages are not shown. Right-hand side of (a) and (b) shows hypothetical formation of C2−51264 cages within the sI hydrate unit cell at surface sites. As discussed in the text, reactions depicted in (a) and (b) do not occur as indicated by the X.

C2(g) ↔ C2(sII512 64 , crystal surface)

reactions involving C2 molecules, three reaction schemes for the formation of C1−C2 sII hydrate from C1−C2 sI hydrate consistent with these observations are as follows:

Equations 1 and 2 both correspond to a direct conversion of C1−C2 sI hydrate to C1−C2 sII hydrate, that is, rearrangement of molecules within C1−C2 sI hydrate unit cells to form C1− C2 sII hydrate unit cells. Equations 3a and 3b should be interpreted as two simultaneous, not sequential, reactions. A significant contribution to the sI ↔ sII transformation reaction corresponding to eq 1 is unlikely on the basis of the enhanced rate of consumption of C1(g) in stage 3 and because C1−C2 sII hydrate growth significantly increases in stage 3 relative to stage 1 as indicated by the increased formation rates

C2(sI512 62 , bulk crystal) ↔ C2(sII512 64 , bulk crystal) (1)

C2(sI512 62 , crystal surface) ↔ C2(sII512 64 , crystal surface) (2)

C2(sI512 62 , crystal surface) ↔ C2(g)

(3b)

(3a) 9663

dx.doi.org/10.1021/jp301766y | J. Phys. Chem. C 2012, 116, 9660−9665

The Journal of Physical Chemistry C

Article

of the C2−51264 and C1−512 cages. These consumption and formation rates are consistent with a surface reaction, for example, stages 1 and 2, as well as previous studies where it has been shown that gas hydrate growth rapidly decreases when limited by diffusion of guest/water molecules through a bulk gas hydrate phase.27−29 The results presented thus far indicate that C1−C2 sII hydrate growth during stage 3 is a surface reaction, eq 2 or eq 3. On the basis of the principle of microscopic reversibility,37 the observation that the magnitudes of the stage 1 formation of C2−51262 cages and the stage 3 decomposition of C2−51262 cages are equal suggests that eq 3 is the dominant reaction pathway. That is, C1−C2 sI gas hydrate decomposes to water, C1(g), and C2(g) while C1−C2 sII gas hydrate simultaneously forms from water, C1(g), and C2(g). Further evidence to distinguish the relative importance of eqs 2 and 3 in the C1−C2 sI ↔ sII transformation is provided by the 2D exchange 13C MAS NMR spectrum performed with a mixing time tm = 5 s, shown in Figure 4. The peaks occurring along the diagonal of the 2D plot correspond to the 1D 13C MAS NMR spectrum except that the resonance lines due to C1(g) and C2(g) sites are not observed because of the short spin−lattice relaxation times (less than 1 s) and small peak intensities of these two gas phase sites. The appearance of cross-peaks, especially between C1 and C2 sites, indicates that spin exchange (due to dipolar coupling of the 13C spins) between C1 and C2 has occurred during the mixing time.33 Note that the C1−512 sI hydrate and C1−512 sII hydrate resonance lines are resolved in the 2D exchange 13C MAS NMR experiment with measured chemical shifts of −3.9 and −3.8 ppm, respectively. Most importantly, however, is the absence of a cross-peak between the C2−51262 and C2−51264 resonance lines that indicates that the C1−C2 sI hydrate and C1−C2 sII hydrate phases are not intimately mixed.38 The conclusion that the C1−C2 sI and sII hydrate phases are not intimately mixed is consistent with identifying eq 3 as the dominant reaction pathway for the C1−C2 sI ↔ sII hydrate transformation observed in this work. The validity of this statement is justified by first considering the stage 3 average relative intensity ratio of the C2−51262 to C1−51262 cages, which is 6.5. This value of 6.5 corresponds approximately to the structure depicted schematically on the left-hand side of Figure 5a, which shows all 51262 cages of the sI unit cell occupied by a guest molecule, the typical situation for sI gas hydrates at or near equilibrium.36 Cross-peaks between the C2−51262 and C1−51262 cages are readily observed in the 2D exchange 13C MAS NMR experiment (Figure 4). The increase of 0.04 in the relative intensity of the C2−51264 cage during stage 3 is twothirds of the average stage 3 relative intensity of the C1−51262 cage of 0.06. If eq 2 dominates C1−C2 sI ↔ sII transformation reaction, then, as depicted on the right-hand side of Figure 5, nearly as many sI unit cells would contain a C2−51264 cage as those that contain a C1−51262 cage. Therefore, cross-peaks between the C2−51262 and C2−51264 peaks should be readily observed; that this is not the case is consistent with the conclusion that eq 3 is the dominant reaction pathway for the C1−C2 sI ↔ sII gas hydrate transformation.

Stage 1 corresponds to the simultaneous formation of both C1−C2 sI and sII gas hydrates. Stage 2 shows enhanced formation of C1−C2 sII gas hydrate and an invariant quantity of C1−C2 sI gas hydrate. During stage 3, C1−C2 sI gas hydrate decomposes while C1−C2 sII gas hydrate continues to form at an enhanced rate. Stage 4 exhibits a gradual approach to a final steady state. Analysis of the rates of formation and decomposition of the various C1 and C2 species present as well as 2D exchange NMR yields the significant conclusion that the C1−C2 sI ↔ sII transformation is dominated by the reaction where C1−C2 sI hydrate decomposes to C1(g), C2(g), and water while simultaneously forming C1−C2 sII hydrate from C1(g), C2(g), and water.

■

ASSOCIATED CONTENT

* Supporting Information S

Schematic depictions of synthesis and measurement systems. 13 C spin−lattice relaxation times; methane gas, ethane gas, and methane−ethane clathrate hydrate 13C MAS NMR relative intensities used to generate Figure 3. This material is available free of charge via the Internet at http://pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel 303-664-1054; e-mail [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was partially fund by NSF Grant CTS-0419204. Kristen E. Bowler and Laura L. (Stadterman) Roberts synthesized the methane−ethane clathrate hydrate used in this study.

■

REFERENCES

(1) von Stackelberg, M.; Muller, H. R. Z. Electrochem. 1954, 58, 25. (2) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2008; pp45−111. (3) Collett, T. S.; Dallimore, S R. Permafrost-Associated Gas Hydrate. In Natural Gas Hydrate in Oceanic and Permafrost Environments (Coastal Systems and Continental Margins); Max, M. D., Ed.; Kluwer Academic Publishers: Boston, MA, 2000; pp 43−60. (4) Dillon, W. P; Max, M. D. Oceanic Gas Hydrate. In Natural Gas Hydrate in Oceanic and Permafrost Environments (Coastal Systems and Continental Margins); Max, M. D., Ed.; Kluwer Academic Publishers: Boston, MA, 2000; pp 61−76. (5) Collett, T. S. Natural Gas Hydrate as a Potential Energy Resource. In Natural Gas Hydrate in Oceanic and Permafrost Environments (Coastal Systems and Continental Margins); Max, M. D., Ed.; Kluwer Academic Publishers: Boston, MA, 2000; pp 123−136. (6) Haq, B. U. Climate Impact of Natural Gas Hydrate. In Natural Gas Hydrate in Oceanic and Permafrost Environments (Coastal Systems and Continental Margins); Max, M. D., Ed.; Kluwer Academic Publishers: Boston, MA, 2000; pp 137−148. (7) Brewer, P. G.; Friederich, C.; Peltzer, E. T.; Orr, F. M., Jr. Science 1999, 284 (5416), 943. (8) Yoon, J. H.; Kawamura, T.; Yamamoto, Y; Komai, T. J. Phys. Chem. A 2004, 108, 5057. (9) Lee, H.; Seo, Y.; Seo, Y. T.; Moudrakovski, I. L.; Ripmeester, J. A. Angew. Chem., Int. Ed. 2003, 42, 5048. (10) Komai, T.; Kawamura, T.; Kang, S.; Nagashima, K.; Yamamoto, Y. J. Phys.: Condens. Matter 2002, 14, 11395. (11) Ota, M.; Abe, Y; Watanabe, M.; Smith, R. L.; Inomata, H. Fluid Phase Equilib. 2005, 228/229, 553.

■

CONCLUSIONS Time-resolved and 2D exchange 13C MAS NMR spectroscopy were used to follow the formation and transformation of C1− C2 sI and sII clathrate hydrates. Four separate reaction stages were identified as the gas phase C1 and C2 composition varies. 9664

dx.doi.org/10.1021/jp301766y | J. Phys. Chem. C 2012, 116, 9660−9665

The Journal of Physical Chemistry C

Article

(12) Park, Y.; Kim, D. Y.; Lee, J. W.; Huh, D. G.; Park, K. P.; Lee, J.; Lee, H. Proc. Natl. Acad. Sci. U. S. A. 2006, 103 (34), 12690. (13) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2008; pp643−683. (14) Davidson, D. W. Clathrate Hydrates. In Water, A Comprehensive Treatise, Plenum: New York, 1973; Vol. 2, pp 115−234. (15) Ripmeester, J. A.; Tse, J. S.; Ratcliffe, C. I.; Powell, B. M. Nature 1987, 325, 135. (16) McMullan, R. K.; Jeffrey, G. A. J. Chem. Phys. 1965, 42, 2725. (17) Mak, T. C. W.; McMullan, R. K. J. Chem. Phys. 1965, 42, 2732. (18) Hendriks, E. M.; Edmonds, B.; Moorwood, R. A. S.; Spcpepanski, R. Fluid Phase Equilib. 1996, 117, 193. (19) Subramanian, S.; Kini, R. A.; Dec, S. F.; Sloan, E. D., Jr. Chem. Eng. Sci. 2000, 55, 1981. (20) Uchida, T.; Takeya, S.; Kamata, Y.; Ikeda, I. Y.; Nagao, J.; Ebinuma, T.; Narita, H.; Zatsepina, O.; Buffett, B. A. J. Phys. Chem. B 2002, 106, 12426. (21) Ohno, H.; Strobel, T. A.; Dec, S. F.; Sloan, E. D., Jr.; Koh, C. A. J. Phys. Chem. A 2009, 113, 1711. (22) Yoon, J. H.; Kawamura, T.; Yamamoto, Y; Komai, T. J. Phys. Chem. A 2004, 108, 5057. (23) Lee, H.; Seo, Y.; Seo, Y. T.; Moudrakovski, I. L.; Ripmeester, J. A. Angew. Chem., Int. Ed. 2003, 42, 5048. (24) Pietrass, T.; Gaede, H. C.; Bifone, A.; Pines, A.; Ripmeester, J. A. J. Am. Chem. Soc. 1995, 117, 7520. (25) Moudrakovski, I. L.; Sanchez, A. A.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. B 2001, 105, 12338. (26) Wang, X; Schultz, A. J.; Halpern, Y. J. Phys. Chem. A 2002, 106, 7304. (27) Klapproth, A.; Goreshnik, E.; Staykova., D.; Klein, H.; Kuhs, W. F. Can. J. Phys. 2003, 81, 503. (28) Staykova, D. K.; Kuhs, W. F.; Salamatin, A. N.; Hansen, T. J. Phys. Chem. B 2003, 107, 10299. (29) Genov, G.; Kuhs, W. F.; Staykova, D. K.; Goreshnik, E.; Salamatin, A. N. Am. Mineral. 2004, 89, 1228. (30) Dec, S. F. J. Phys. Chem. C 2009, 113, 12355. (31) Dec, S. F. J. Phys. Chem. C 2012, 116, 6504. (32) Murshed, M. M.; Schmidt, B. C.; Kuhs, W. F. J. Phys. Chem. A 2010, 114, 247. (33) Szeverenyi, N. M.; Sullivan, M. J.; Maciel, G. E. J. Magn. Reson. 1982, 47, 462. (34) Gupta, A.; Dec, S. F.; Koh, C. A.; Sloan, E. D., Jr. J. Phys. Chem. C 2007, 111, 2341−2346. (35) Dec, S. F.; Bowler, K. E.; Stadterman, L. L.; Koh, C. A.; Sloan, E. D., Jr. J. Phys. Chem. A 2007, 111, 4297−4303. (36) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press: Boca Raton, FL, 2008; pp685−692 plus included CSMGem software. (37) Tolman, R. C. Proc. Natl. Acad. Sci. U. S. A. 1925, 11, 436. (38) Linder, M.; Henrichs, M; Hewitt, J. M.; Massa, D. J. J. Chem. Phys. 1985, 82, 1585.

9665

dx.doi.org/10.1021/jp301766y | J. Phys. Chem. C 2012, 116, 9660−9665