Critical Size for Guest Molecules to Occupy Dodecahedral Cage of

Mar 1, 2008 - Critical Size for Guest Molecules to Occupy Dodecahedral Cage of Clathrate ... composed of two types of cages: two pentagonal dodecahedr...
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J. Phys. Chem. C 2008, 112, 4719-4724

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Critical Size for Guest Molecules to Occupy Dodecahedral Cage of Clathrate Hydrates Tsutomu Uchida,*,† Ryo Ohmura,‡ and Akira Hori§ DiVision of Applied Physics, Graduate School of Engineering, Hokkaido UniVersity, N13 W8 Kita-ku, Sapporo 060-8628, Japan, Department of Mechanical Engineering, Keio UniVersity, Yokohama 223-8522, Japan, and Department of CiVil Engineering, Kitami Institute of Technology, 165, Koen-cho, Kitami 090-8507, Japan ReceiVed: December 4, 2007; In Final Form: January 8, 2008

The five different structure-I hydrates were formed using the following five different guest substances: methane, fluoromethane, difluoromethane, trifluoromethane, and tetrafluoromethane, for the systematic investigation on the relation between the occupancy of the cages in the hydrates and the size of the guest molecules. The hydrate crystal samples were analyzed using Raman spectroscopy. The results revealed that the cage occupancy ratio between small and large cages of these guest molecules depended on their solvent accessible surface area (ASA). The critical ASA for the enclathration of small cages had a relatively narrow range: approximately 1.7 ( 0.2 nm2. It was found that clathrate hydrates formed with guest molecules having ASA in this critical range were expected to show high nonstoichiometric properties. The obtained relation between the cage occupancy ratio and ASA of guest molecules was generalized by comparison with the results on other structure-I hydrate-forming guest molecules reported in the literature.

Introduction Clathrate hydrates have various lattice structures; cubic structure I (SI), cubic structure II (SII), and hexagonal structure H (SH) are three known structures of clathrate hydrates.1 SI is composed of two types of cages: two pentagonal dodecahedral (512) cages and six tetrakidecahedral (51262) cages in a unit cell. A combination of 16 512 cages and eight hexakaidecahedral (51264) cages constitutes the unit cell of SII. SH has three types of cages: two irregular dodecahedral (435663) cages, three 512 cages, and an icosahedral (51268) cage in a unit cell. Therefore, the 512 cage may play important roles in the formation of clathrate hydrate structures because it is included in all three structures as the common unit. The occupation of each cage of the clathrate structure by a guest molecule (cage occupancy) is one of the most interesting properties because it is related to the estimation of the guest molecule density, stability of clathrate hydrates, etc. However, it is known to be a nonstoichiometric property in the case of many clathrate hydrates. For example, methane (CH4) molecules can occupy both the 512 and 51262 cages in SI; however, its occupancy is less than one and varies with its formation conditions.2 This leads to difficulties in the precise estimation of the total amount of natural gases stored in the naturally occurring hydrates in the deep ocean or in permafrost. The cage occupancy of carbon dioxide (CO2) hydrates has also been reported to be in a wide range: CO2 can occupy both the cages, but in comparison with CH4, it finds it more difficult to occupy 512 cages.3 This uncertainty causes difficulties in the density estimation of CO2 hydrates. This is a serious problem in the feasibility study of the CO2 sequestration technique in the deep ocean. * Corresponding author. Telephone: +81-11-706-6635. Fax: +81-11706-6635. E-mail: [email protected]. † Hokkaido University. ‡ Keio University. § Kitami Institute of Technology.

It is well-known that during the clathrate structure formation process, the occupation of 512 cages with guest molecules is important. Pietrass et al.4 have observed that xenon (Xe) molecules initially occupy the 512 cages formed on the surface phase of an ice crystal prior to the bulk hydrate-lattice growth. A similar process has also been reported in the system of CH4 and water.5 Therefore, in order to estimate the critical size of guest molecules occupying 512 cages, it is important to understand both the clathrate-structure formation process and its physical properties. In the present study, we systematically measure the cage occupancy ratio of SI clathrate hydrates with various fluorocarbon guest molecules by Raman spectroscopy. Fluorocarbon molecules such as fluoromethane (CH3F, methyl fluoride or HFC-41), difluoromethane (CH2F2, methylene fluoride or HFC-32), trifluoromethane (CHF3, fluoroform or HFC-23), and tetrafluoromethane (CF4, carbon tetrafluoride or FC-14) can form SI clathrate hydrates. CH4 molecules can fit into both cages of SI and the cage occupancies of a single crystal are close to unity.6 However, under equilibrium conditions, the CF4 molecule can occupy only 51262 cages.7 This molecule is known to occupy 512 cages only at pressures higher than 95 MPa.8 The cage occupancies of CH3F, CH2F2, and CHF3 molecules are considered to be in the intermediate range. By NMR spectroscopy, the cage occupancy ratio of the 512 cage to that of the 51262 cage (θS/θL) in a deuterated fluoromethane (CD3F) hydrate was measured to be 0.61 ((0.15).9 This implies the presence of a few vacant 512 cages in the structure. Both CH2F210,11 and CHF37,12 are reported to form SI hydrate; however, there are no reports on their cage occupation. Therefore, it is necessary to determine whether there is a critical size for the occupation of the 512 cage within the molecular size range of the above-mentioned fluorocarbon molecules. Raman spectroscopic measurement has been developed to estimate the cage occupancies of single-guest hydrates. The peak positions of guest molecules allow us to distinguish them from

10.1021/jp7114274 CCC: $40.75 © 2008 American Chemical Society Published on Web 03/01/2008

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TABLE 1: Formation Conditions of Fluorocarbon Hydrates guest molecule

host molecule

CH3F CH2F2 CHF3 CF4

H2O D2O D2O H2O

temperature [K]

pressure [MPa]

273.5 278.2 278.2 273.5

1.0 0.8 1.0 7.5

other phases and classify them into different cages. The peak intensity would depend on the population of the molecules in a particular cage. Therefore, the population ratio of the guest molecules between two cages can be estimated from their peak intensity ratios. In the present study, we measure the intramolecular symmetric C-H or C-F stretching vibrations of the fluorocarbon molecules in clathrate structures to determine the variation of cage occupancy ratio with the size of the guest molecules, which was scaled by the parameter of the solvent accessible surface area (ASA). To estimate the molecular occupation in 512 cages, we focus on the evaluation of the C-H stretching mode here.

Figure 1. C-H stretching mode spectra of CH3F hydrates. Open squares indicate the measured values and thin solid line is fitted Voigt curves for each peak.

Experimental Procedures Clathrate hydrates of fluorocarbons were prepared by mixing guest gases and water in a high-pressure vessel. The experimental apparatus used for the sample preparations was essentially the same as the previous one.13 CH4, CH3F, CH2F2, CHF3, and CF4 were selected as guest molecules, whereas H2O and D2O were used for water. For both CH2F2 and CHF3 hydrates, D2O was used to precisely measure the Raman C-H stretching-mode peaks since the signal intensities of the guest molecules in the 512 cages of both the hydrates were expected to be very small. The use of D2O as host molecules could eliminate the background signal of the O-H stretching mode of water. The temperature and pressure conditions for hydrate formation are listed in Table 1. These conditions were selected to avoid both the freezing of water and the condensation of guest molecules during the hydrate formation. The formation period of the clathrate hydrates were monitored by changing the temperature and pressure conditions in the reaction vessel. The formation process lasted for several days. After finishing the hydrate formation, the sample was cooled to below 100 K using liquid nitrogen in order to prevent hydrate decomposition that may occur during the gas release process for retrieving the sample from the reaction vessel. Raman spectra were collected by a triple monochromator Raman spectrometer (Jobin Yvon Ramanor T64000) using the gratings of either 1800 or 600 mm-1. The specimen was set below the objective lens, and the scattered radiation was collected through the slit in a 180° geometry with a ×45 longdistance objective lens. The incident laser beam (514.5 nm argon ion laser, 100 mW) was focused to a diameter of approximately 1 µm on the specimen. The temperature of the specimen was maintained at approximately 243 ( 1.5 K during the measurements by controlling the flow rate of nitrogen gas that vaporized from liquid nitrogen. For the calibration of the Raman shift, the line shape of neon emission lines was examined; it revealed that the wave number of a peak was within (0.6 cm-1 (for 1800 mm-1 grating) or (1.8 cm-1 (for 600 mm-1 grating). We measured Raman spectra of the C-H stretching mode (2700∼3200 cm-1), and the C-F stretching mode (800∼1500 cm-1) for the CF4 hydrate five or six times at different locations on one specimen to accumulate the signal intensities and obtain the average peak position and intensity for each stretching mode.

Each accumulate spectrum was fitted by using the Voigt model to estimate the peak wave number and peak intensity (area of the fitting curve). Since there is no systematic study in the literature for the Raman signals of fluorocarbon molecules in clathrate structure, the assignment of the peaks were made based on the data of the pure fluorocarbons that are in a gas, liquid or solid state.14-16 Results and Discussions (a) Analyses of Raman Spectra of Various Fluorocarbon Hydrates. (1) CH4 Hydrates. The Raman spectra exhibit a double peak in the C-H stretching mode region: a large peak at 2904 cm-1 (the full width at half-maximum (fwhm) is approximately 4.4 cm-1) and a small peak at 2915 cm-1 (fwhm ∼ 6.6 cm-1). Both these peaks are red-shifted as compared to the spectrum of the C-H symmetric stretching mode ν1 of CH4 vapor (2917 cm-1). The peak intensity ratio of these two peaks IL/IS is approximately 3.3. These results are consistent with those reported previously.2,17 (2) CH3F Hydrates. The C-H stretching mode of Raman spectra recorded on the CH3F hydrates is shown in Figure 1. There are two sets of peaks for CH3F molecules in this range: at approximately 2860 and 2960 cm-1; they both have a doublepeak structure (total of four peaks). A large broad peak (maximum peak position is approximately 3130 cm-1 (fwhm ∼ 120 cm-1) is the O-H stretching mode of H2O molecules. The larger peaks at 2852 (fwhm ∼ 2.9 cm-1) and 2955 cm-1 (fwhm ∼ 4.8 cm-1) have lower Raman shifts than the smaller peaks at 2860 (fwhm ∼ 4.0 cm-1) and 2967 cm-1 (fwhm ∼ 7.4 cm-1), respectively. This tendency is similar to that observed in CH4 hydrates. Neutron diffraction analysis revealed that the CH3F hydrate formed SI.18 Then, we considered that the CH3F molecules were enclathrated in both the 512 and 51262 cages. The IL/IS values for the 2860 and 2960 cm-1 peaks were IL/IS ∼ 3.5 ((0.2) and 3.1 ((0.6) for, respectively. The two sets of peaks resulted from the Fermi resonance of the C-H stretching modes: ν1 + 2ν5.14 The peak Raman shifts for the CH3F vapor phase were reported as ν+ ) 2964 cm-1 and ν- ) 2864 cm-1, where + and - indicate the higher and lower Raman shifts observed, respectively. Compared to those in the vapor phase, the larger peaks of the hydrate phase were red-shifted, whereas the smaller peaks were slightly blue-shifted.

Critical Guest Size in Dodecahedral Clathrate Cage

Figure 2. C-H stretching mode spectra of CH2F2 hydrates. Open squares indicate the measured values and thin solid line is fitted Voigt curves for each peak.

The peak intensity ratio between these peaks I+/I- in vapor phase was reported to be approximately 2.14 For the hydrate phase, the IL/IS values of both the large peaks I(2955)/I(2852) was approximately 2.3. This is consistent with that observed for the vapor phase. (3) CH2F2 Hydrates. In order to reduce the background signal of the O-H stretching mode of the H2O host molecules so as to obtain the low-intensity signal from the CH2F2 molecules enclathrated in the 512 cages, we measured the CH2F2 hydrates with the D2O host lattice. The C-H stretching mode of the Raman spectra recorded on a CH2F2 hydrate with the D2O host lattice is shown in Figure 2. There are three peaks in this range: at approximately 2830, 2950, and 3020 cm-1; each peak is spit into large and small double peaks. Larger peaks at 2831 (fwhm ∼ 2.3 cm-1), 2948 (fwhm ∼ 11 cm-1), and 3018 cm-1 (fwhm ∼ 5.2 cm-1) are lower Raman shifts than the smaller ones at 2839 (fwhm ∼ 4.5 cm-1), 2963 (fwhm ∼ 14 cm-1), and 3026 cm-1 (fwhm ∼ 6.9 cm-1), respectively. Based on the Raman shift measurements on CH2F2 vapor,15 two of these peaks are considered to be an unknown mode, ν1 C-H symmetric stretching mode (2980 cm-1), and ν6 C-H antisymmetric stretching mode (mixture of both TO mode: 3040 cm-1 and LO mode: 3075 cm-1), respectively. All of the peak positions in the hydrate phase are red-shifted compared to those in the vapor phase. These tendencies are similar to those observed in both the CH4 and CH3F hydrates. The peak at the lowest Raman shift cannot be assigned because there is no Raman-active mode of CH2F2 molecule around 2830 cm-1. Since the 2860 cm-1 peak for the CH3F molecule is assigned as the result of Fermi resonance of C-H stretching modes, the 2830 cm-1 peak for the CH2F2 molecule would be similar contribution. Further detailed investigations are necessary to be clarified. Then, we considered that the CH2F2 molecules were enclathrated in both the 512 and 51262 cages in SI and the larger peaks were the signals from the CH2F2 molecules encaged in the 51262 cages. The IL/IS values of three peaks, 2830, 2950, and 3020 cm-1, in Figure 2 were approximately 4.8, 4.3, and 2.9, respectively. These values were often observed in different parts of the same sample; it varied from 2.9 to 16 for CH2F2 hydrates. This large scattering of IL/IS values were observed significantly on CH2F2 hydrate. Since the D2O molecules were used as host molecules, we could ignore the background signal of the O-H stretching mode, which overlapped the C-H stretching mode of the guest

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Figure 3. C-H stretching mode spectra of CHF3 hydrates. Open squares indicate the measured values and thin solid line is fitted Voigt curves for each peak.

molecules. This allowed us to confirm that the CH2F2 molecules were enclathrated in the 512 cages and obtain their relative population in terms of the IL/IS value. (4) CHF3 Hydrates. Since the CHF3 molecule is expected to be of a critical size to fit in the 512 cage, we used the D2O molecules as host molecules to obtain the precise Raman spectra of the C-H stretching mode for the guest molecules. Figure 3 shows the Raman spectra of the C-H stretching mode of the CHF3 hydrate with the D2O host lattice. There is one large peak at 3043 cm-1 (fwhm ∼ 12 cm-1) in this range. We can find a small peak at 3062 cm-1 (fwhm ∼ 5.7 cm-1) whose Raman shift is higher than that of the large peak. This peak is assigned to the ν1 C-H symmetric stretching mode of the CHF3 molecules by comparison with the Raman spectra of its vapor phase (3036 cm-1).16 It is interesting that the peak Raman shift in the hydrate phase was blue-shifted than that in the vapor phase. Since the CHF3 hydrate forms the SI structure,7,12 we consider that the CHF3 molecules can occupy both the 512 and 51262 cages but their occupancy in 512 will be very small. The IL/IS value is approximately 69. (5) CF4 Hydrates. CF4 molecules do not have a C-H stretching mode; therefore, we observed the C-F stretching mode for a CF4 hydrate. One large peak was observed at 908 cm-1 (fwhm ∼ 2.7 cm-1). This is assigned to be the C-F symmetric stretching mode of CF4 molecules encaged in the 51262 cage of the SI structure.8 The results obtained in the present study are consistent with those obtained previously. Sugahara et al.8 suggested that the Raman spectrum of CF4 molecules in 512 cages at high pressure was observed at 920 cm-1. In the present study, the peak-fitting analysis indicated the existence of a very small peak at approximately 919 cm-1; however, the intensity ratio IL/IS was in the range of 102. Therefore, we considered that most of the CF4 molecules were enclathrated in the 51262 cages in SI. We also observed the 2ν2 mode of the CF4 molecules at 867 cm-1 (fwhm ∼ 2.9 cm-1), which was slightly red-shifted as compared with that of the vapor phase (869 cm-1).19 (b) Relationship between Peak Intensity Ratio and Guest Molecular Size. We observed that all of the guest molecules measured in the present study had double peaks for each mode. Larger peaks had lower Raman shifts than the smaller ones. Based on the “loose cage-tight cage” model of clathrate

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Figure 4. Peak intensity ratio IL/IS of double peaks for each Raman spectrum of guest molecules depending on the solvent accessible surface area (ASA).

structures,20 we considered the smaller peaks to be the signals of the guest molecules enclathrated in the 512 cages. Then, we compared the IL/IS value with the guest molecular size in order to estimate the critical molecular size for enclathration into 512 cages. The guest molecular size was characterized by the solvent accessible surface area (ASA) of the molecule that was estimated by Winmostar program.21 This is the surface area of a molecule that is accessible to a solvent; here it is a water molecule (specifically which has the van der Waals radius of 0.14 nm).22 Since the maximum guest molecule fitting to the 512 cage would have the critical ASA, no guest molecules having larger ASA than this critical value can be encaged in the 512 cage. Figure 4 shows the IL/IS values for various fluorocarbon hydrates measured in the present study. This figure indicates that IL/IS becomes constant at the minimum value 3 for guest molecules with ASA less than approximately 1.7 nm2, which is expected for the full cage occupation with guest molecules. For larger molecules, IL/IS suddenly increases with the ASA within the narrow range (approximately 0.2 nm2) and it reaches 102 for larger molecules as ASA > 1.9 nm2. Therefore, we concluded that the critical molecular ASA for the occupation of the 512 cage in SI is approximately 1.8 ( 0.1 nm2. This critical value of ASA is slightly smaller than the surface area of a sphere having the average cavity radius of the 512 cage in the SI hydrate (0.395 nm),1 approximately 1.96 nm2. Therefore the obtained result is reasonable, and it is noted that the critical molecular ASA exists within very narrow range. The parameter for the molecular size fitting to the vacancy of the cages has been sometimes discussed with the van der Waals radius of guest molecules, as mentioned previously (for example, ref 1). However, the ASA is better scaling parameter since it involves the shape information of a guest molecule. (c) Dependency of Cage Occupancy Ratio on Guest Molecular Size. To understand the general feature of guest molecular ASA dependence on the 512 cage occupation, we estimated the cage occupancy ratio between the small and large cages in SI from our experimental results. SI has two 512 cages and six 51262 cages in a unit cell. Each cage occupancy, θS and θL, respectively, can be estimated by assuming that the peak intensity of the Raman spectra is linearly proportional to the population of the molecules in the same conditions. Then, the cage occupancy ratio is related to the peak intensity ratio by the following equation:

θS/θL ) 3(IS/IL)

(1)

Figure 5. Cage occupancy ratio θS/θL of various SI hydrates depending on guest molecular ASA. Circles are obtained in the present study and the dotted line is the fitting curve (2) for these data. Squares are reported in previous works with some variations (shown in an error bar). Triangles are speculated in previous works.

This assumption would be favorable because the measured clathrate hydrate samples were all single-guest hydrates.23 Several fluorocarbon hydrates measured in previous studies have also been investigated in the present study. CD3F was measured by 19F magic angle spinning NMR.24 The cage occupancy ratio was estimated to be θS/θL ) 0.61 ( 0.15 using the 19F spectra or θS/θL ) 0.53 ( 0.15 using the 2H spectra. These results were consistent with those of CH3F observed in the present study. On the other hand, the cage occupancies of chloromethane (CH3Cl, or methyl chloride) were estimated by the thermodynamic estimation from the equilibrium condition measurements.25 The results indicated that the CH3Cl hydrate had SI and the cage occupancies of the 512 and 51262 cages were θS ) 0.052 and θL ) 0.9759, respectively. Since the molecular volume of CH3Cl is larger than that of CH3F, or similar to that of CHF3, θS would be close to zero. These results support our result that the Raman intensity ratio, or the resulting cage occupancy ratio, is mainly dependent on guest molecular size rather than on the functional group. Figure 5 shows the value of θS/θL observed for the measured fluorocarbon hydrates (marked with solid squares) with ASA. The dotted line is the sigmoid curve fitted to these results

θS/θL ) 1/(1 + (s/s0) p )

(2)

where s is the value of ASA, s0 ) 1.68 ( 0.03 nm2, and p ) 25 ( 10 is the fitting parameter obtained by using the correlation R2 ) 0.818. This figure indicates that θS/θL is approximately unity at s < 1.5 nm2. The guest molecules in this ASA range, such as CH4, can fully occupy both the 512 and 51262 cages. On the other hand, θS/θL becomes zero at s > 1.9 nm2. Guest molecules having ASA larger than 1.9 nm2, such as CF4, are considered to occupy only the 51262 cages, and θS approaches zero under the formation conditions in the present study. This is consistent with the fact that this value is equivalent to the surface area of a sphere having the average cavity radius of the 512 cage in the SI hydrate as mentioned in the previous section. At the molecular ASA between these values, that is, 1.5 < s < 1.9 nm2, the guest molecules can occupy both the 512 and 51262 cages but the small cage occupancy varies significantly. This may be related to the high nonstoichiometric properties of these hydrates. For example, the measured θS/θL value of the CH2F2

Critical Guest Size in Dodecahedral Clathrate Cage

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TABLE 2: Cage Occupancy Ratio θS/θL in Various Guest Molecules for SI Hydratesa

a

guest molecules

ASA [nm2]

θS/θL

reference, remarks

CO H2S CO2 C2H2 Xe Cl2 C2H4 NF3 COS CH3Cl ClO3F SO2 ethylene oxide C2H6 CH3SH CH3Br CF4 (CH2)2S cyclopropane CHClF2 SO2F2

1.30 1.45 1.54 1.57 1.59 1.64 1.70 1.71 1.72 1.74 1.77 1.79 1.82 1.84 1.84 1.93 1.94 1.95 1.96 1.97 2.03

NA 0.93∼1 0.71 0.6 0.67∼0.77 0.14 0 0.55 NA 0.05 NA 0.26 0.19∼0.4 0.058 NA 0.01 0 NA 0 0.005 NA

6, 26 25, 27, 28: calculated 29 30 25, 27, 31 25, 27, 32 33, 34: pressure induced occupation at P > 10 MPa 27, 35 27: speculated 25, 27, 32 27: speculated 25, 27, 32 36, 37, 38 39, 40: pressure induced occupation at P > 20 MPa 27: speculated 25, 27, 32 27, 8: pressure induced occupation at P > 95 MPa 27: speculated 34: pressure induced occupation at P > 200MPa 25, 27, 32 27: speculated

Each ASA is calculated by Winmostar21 with the solvent radius of 0.14 nm.

hydrate varies from 0.2 to 0.7. The cage occupancy of the CH3F hydrate is approximately unity, but that of the similar ASA of molecule CD3F is approximately 0.6.9 These variations or differences cannot be investigated by the small difference in the guest ASA. The vacancy of the 512 cage is known to be rather spherical. The structure determinations based on the X-ray diffraction measurements indicate that the minimum distance between the center of the cage and a cage-forming oxygen atom was 0.383 nm,10 which is approximately 3% smaller than the average distance mentioned previously. Even if we assume that the cage is spherical having the minimum radius, the surface area of this sphere is approximately 1.84 nm2 that is slightly larger than the critical ASA value of 1.8 ( 0.1 nm2 or s0 ∼ 1.68 nm2. Therefore it is feasible that the fitting curve in Figure 5 indicates the cage occupancy ratio θS/θL of the guest molecule having the ASA smaller than this value to be unity. To investigate the general feature of the relation between θS/ θL and ASA, we examined various guest molecules forming SI from the literature. Their ASA values ranged from 1.5 to 1.9 nm2 and they are plotted in Figure 5 with open squares. Table 2 lists the guest molecules along with their references. The figure shows that most of the guest molecules generally follow the relationship between θS/θL and ASA obtained in the present study. Although these molecules have various functional groups, various shapes of molecules, or various interactions with the surrounding water molecules, their cage occupancy ratios are mainly dependent on their ASA. This result strongly suggests that the cage occupation of guest molecules is mainly determined by their size. Based on the relationship, we can estimate the unknown cage occupancies of guest molecules forming SI. For example, H2S cage occupancy of a hydrate formed in the shallower part of deep sea sediments or in chemical plants would be comparable to that of CH4 hydrates. This estimation coincides well with that predicted by the calculations.28 Larger guest molecules predicted to form SI hydrates, such as SO2F2 and ClO3F, ..., etc., would form a SI hydrate; however, they cannot occupy 512 cages. Ohgaki and co-workers have reported some large-guest molecule occupation of 512 cages under high-pressure conditions. This pressure-induced cage occupation can be classified by the

molecular ASA relation obtained in the present study. They have reported the minimum pressures of the pressure-induced cage occupation to be approximately 10 MPa for an ethylene hydrate (s ∼ 1.70 nm2),33,34 20 MPa for an ethane hydrate (s ∼ 1.84 nm2),40 95 MPa for a CF4 hydrate (s ∼ 1.94 nm2),8 and 200 MPa for a cyclopropane hydrate (s ∼ 1.96 nm2).34 The size of these molecules is less than the average surface area of the 512 cage (1.96 nm2) but larger than the preferable ASA for 512 cage occupation (less than 1.5 nm2). The pressure required for the pressure-induced cage occupation increases with the increasing guest molecular ASA. Therefore, it is considered that if the molecular ASA is in the range of high nonstoichiometric properties (that is, approximately 1.7 ( 0.2 nm2), the required pressure for 512 cage occupation would be rather small. However, if the molecular ASA is larger than this value, the required pressure would be considerably higher. Conclusions Systematic investigations of Raman spectra on various fluorocarbon hydrates revealed the molecular size variations of cage occupancies in the structure I (SI). When the molecular size is smaller than 1.5 nm2 in the solvent accessible surface area (ASA), the guest molecule would fully occupy both 512 and 51262 cages. On the other hand, when the molecule ASA is greater than 1.9 nm2, it can occupy the 51262 cage only. Molecules having an intermediate ASA, that is, 1.7 ( 0.2 nm2, may provide high nonstoichiometric properties since they can occupy both the cages but do not fully occupy 512 cages. These guest size dependences on the cage occupancy ratio were found to be widely applicable for guest molecules forming SI of clathrate hydrates. The 512 cage appears in all three clathrate hydrate structures of SI, SII, and SH. Therefore the conclusions obtained for SI hydrates mentioned above would be also applied to SII and SH hydrates, although the experimental investigations are required. The series of fluoromethane molecules used in the present study is favorable for the scaling of 512 cage occupation with Raman spectroscopic observations. This is the first systematic approach to investigate the guest size dependence on the 512 cage occupancy experimentally. This approach can be applied to other structures of clathrate hydrates if the suitable series of guest molecules for SII and SH hydrates are available.

4724 J. Phys. Chem. C, Vol. 112, No. 12, 2008 Acknowledgment. This work was partly supported by the Keio Gijuku Academic Development Funds, a grant of the Keio Leading-edge Laboratory of Science and Technology (KLL) specified research projects, and the Industrial Technology Research Grant Program in 2003 (Grant 03B64003c) from the New Energy and Industrial Technology Development Organization (NEDO) of Japan. The authors also thank Dr. S. Takeya for the fruitful discussions and Dr. H. Ohno and Mr. T. Sakurai for providing experimental supports during the Raman spectroscopic measurements. References and Notes (1) Sloan, E. D., Jr. Clathrate Hydrates of Natural Gases; Dekker: New York, 1998. (2) Uchida, T.; Hirano, T.; Ebinuma, T.; Narita, H.; Gohara, K.; Mae, S.; Matsumoto, R. AIChE J. 1999, 45, 2641. (3) Ripmeester, J. A; Ratcliffe, C. I. Energy Fuels 1998, 12, 197. (4) Piatrass, T.; Gaede, H. C.; Bifone, A.; Pines, A.; Ripmeester, J. A. J. Am. Chem. Soc. 1995, 117, 7520. (5) Subramanian, S.; Sloan, E. D., Jr. Fluid Phase Eq. 1999, 158160, 813. (6) Davidson, D. W.; Desando, M. A.; Gough, S. R.; Handa, Y. P.; Ratcliffe, C. I.; Ripmeester, J. A. Nature 1984, 311, 142. (7) Moojer van den Heuvel, M. M.; Peters, C. J.; de Swaan Arons, J. Fluid Phase Eq. 2000, 172, 73. (8) Sugahara, K.; Yoshida, M.; Sugahara, T.; Ohgaki, K. J. Chem. Eng. Data 2004, 49, 326. (9) Collins, M. J.; Ratcliffe, C. I.; Rimpeester, J. A. J. Phys. Chem. 1990, 94, 157. (10) Davidson, D. W. In Water a comprehensiVe treatise; Franks, F., Ed.; Plenum: New York, 1973; Vol. 2, p 115. (11) Akiya, T.; Shimazaki, T.; Oowa, M.; Matsuo, M.; Yoshida, Y. Int. J. Thermophys. 1999, 20, 1753. (12) von Stackelberg, M.; Jahns, W. Z. Electrochem. 1954, 58, 162. (13) Takeya, S.; Hori, A.; Uchida, T.; Ohmura, R. J. Phys. Chem. B 2006, 110, 12943. (14) Wu, Y. H.; Shimizu, H. J. Chem. Phys. 1995, 102, 1157. (15) Wu, Y. H.; Onomichi, M.; Sasaki, S.; Shimizu, H. J. Phys. Soc. Jpn. 1994, 63, 934. (16) Wu, Y. H.; Onomichi, M.; Sasaki, S.; Shimizu, H. J. Raman Spectro. 1993, 24, 845.

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