Temperature effects on the C–H symmetric stretching vibrational frequencies of guest hydrocarbon molecules in 512, 51262 and 51264 cages of sI and sII clathrate hydrates

C–H symmetric stretching vibrational frequencies of CH4, C2H4 and C2H6 molecules encapsulated in 512, 51262 and 51264 cages of structures I (sI) and II (sII) clathrate hydrates measured by Raman spectroscopy in the temperature range of 93–183 K was analysed. The slopes of the symmetric stretch vibrational frequencies under changing temperatures (Δv/ΔT) for CH4, C2H4 and C2H6 molecules encapsulated in sII 51264 cages were smaller than those for molecules in sI 51262 cages, although sI 51262 cages are smaller than sII 51264 cages. We compared the results of Δv/ΔT in this study with the geometrical properties of each host water cage, and these comparisons suggest that the geometry of host water cages affects Δv/ΔT.


Introduction
Clathrate hydrates, commonly known as gas hydrates, are crystalline inclusion compounds consisting of guest molecules of suitable sizes and shapes encapsulated in well-dened cages formed by water molecules. Gas hydrates with encapsulated hydrocarbon gases, which exist in sea/lake bottom sediments, have attracted considerable interest as a potential source of natural gas. [1][2][3] There are three common crystallographic structures of hydrates, structure I (sI), structure II (sII) and structure H (sH). [4][5][6] The unit cell of sI hydrates comprises two pentagonal dodecahedral (5 12 ) and six tetrakaidecahedral (5 12 6 2 ) water cages. 4 For sII hydrates, the unit cell is formed by sixteen 5 12 cages and eight hexakaidecahedral (5 12 6 4 ) water cages. 5 Small guest molecules such as methane (CH 4 ), ethylene (C 2 H 4 ) and ethane (C 2 H 6 ) form sI hydrates, whereas larger molecules such as propane (C 3 H 8 ) or 2-methylpropane (C 4 H 10 ) form sII hydrates. C 2 H 4 and C 2 H 6 are encapsulated in sI 5 12 6 2 cages, while sI 5 12 cages remain almost empty at equilibrium pressure conditions except at high-pressure conditions ($100 MPa). 7-10 A mixture of CH 4 + C 2 H 6 hydrates can form both sI and sII hydrates, depending on the gas composition of CH 4 and C 2 H 6 . 11 Coexisting states of both sI and sII CH 4 + C 2 H 6 hydrates have also been observed in natural settings. 12 Moreover, in environments where larger hydrocarbons, e.g., C 3 H 8 or C 4 H 10 are present, smaller hydrocarbon molecules can also be encapsulated in the sII hydrate. 13 Thus, accumulating knowledge about hydrocarbon hydrates in sI and sII structures is important.
Raman spectroscopy has been frequently used for gas hydrates to identify the type of crystal structure 11,14,15 or to analyse cage occupancy 14 and type of guest molecule. 15 The Raman spectra of the C-H symmetric stretch region of encapsulated CH 4 and C 2 H 6 have been used to identify the types of crystal structures and guest molecules. 16,17 Raman spectra of hydrocarbon hydrates have shown that the C-H stretching frequencies of hydrocarbon molecules in large cages are generally lower than those of molecules in small cages. 11,14,15 Subramanian and Sloan rationalised this observation in terms of the guest-host intermolecular interactions using the loose cage-tight cage (LCTC) model as an explanation for matrixisolation IR experiments. 15,18 The variation in the C-H stretching frequencies of various hydrocarbons with varying types of water cages has been computed by quantum chemical computations. 19 Investigating the C-H stretching frequencies of guest hydrocarbons in water cages is important for understanding the fundamental properties of gas hydrates. In addition, the guesthost interactions in gas hydrates play a role in the thermal expansion ratio of different types of guests and crystallographic structures 20 and in the expression of a unique phenomenon known as self-preservation. 21 In earlier studies, the temperature dependence of the C-H symmetric stretching frequencies of encapsulated CH 4 as a guest molecule were investigated using Raman spectroscopy. [22][23][24] In the case of sI CH 4 hydrate, the thermal variation in the frequencies of CH 4 in larger cages (sI 5 12 6 2 cages) is greater than that of frequencies of CH 4 in smaller cages (sI 5 12 cages). 24 In another earlier study, the neutron diffraction experiments for sI deuterated CD 4 hydrate showed that CD 4 in the sI 5 12 6 2 cage distributes longitudinally within the cage at temperatures higher than 80 K, whereas CD 4 in the 5 12 cage distributes spherically around the center of the cage even at higher temperatures. 25 These results suggest that the distance between the guest and host molecules in the sI 5 12 6 2 cage is smaller than that in the sI 5 12 cage. We proposed the idea that the difference in the thermal variations of the C-H symmetric stretching frequencies of CH 4 in sI 5 12 and 5 12 6 2 cages is caused by the difference in distribution changes of guest CH 4 under changing temperature. 24 The trend of the variations of the C-H vibrational frequencies of the encapsulated hydrocarbon molecules in the gas hydrate under changing temperature is useful for better understanding the trends of the temperature change of the distribution of guest molecules. However, these trends for hydrocarbons encapsulated in sII hydrate have not been investigated. It has also been reported that the distribution of guest molecules differs depending on the geometry of guest molecules. 9,10,26,27 Hence, additional investigation for the C-H vibrational frequencies of encapsulated hydrocarbon molecules in various combinations of host cages and guest molecules are expected.
In this study, we observed the variations in the Raman shi of C-H symmetric stretching vibrations for various guest hydrocarbon molecules in sI 5 12 and 5 12 6 2 cages and in sII 5 12 and 5 12 6 4 cages under changing temperatures. Gas hydrates of sI C 2 H 4 hydrate, sII Kr + C 2 H 4 hydrate, sI C 2 H 6 hydrate, sI CH 4 + C 2 H 6 hydrate and sII CH 4 + C 2 H 6 hydrate were investigated. From these results, we discuss the variations in the Raman shi of the C-H symmetric stretching vibrations and the geometric dependence of the intermolecular interaction energies within the water cages of sI and sII hydrates with varying temperature.

Sample preparation
To synthesise gas hydrate samples, research-grade CH 4 , C 2 H 4 and C 2 H 6 (purities of 99.99, 99.9 and 99.99%, respectively; Takachiho Chemical Industry, Japan) and Kr (99.9% purity; Air Liquide Japan Ltd.) were used as the guest gases. These gas hydrate samples were formed from ne ice powder at 273.2 K and high-pressure conditions. For C 2 H 4 hydrate and C 2 H 6 hydrate, 1.2 MPa of C 2 H 4 and C 2 H 6 gas pressure was applied. The Kr + C 2 H 4 hydrate was prepared from a gas mixture containing 9 mol% C 2 H 4 and 91 mol% Kr at 1.6 MPa. sI CH 4 + C 2 H 6 hydrates were prepared from a gas mixture containing 70 mol% C 2 H 6 and 30 mol% CH 4 at 2.0 MPa. sII CH 4 + C 2 H 6 hydrates were prepared from a gas mixture containing 15 mol% C 2 H 6 and 85 mol% CH 4 at 2.0 MPa.
Fine ice powder (1.0 g) was prepared for preparing highpurity hydrate sample and was loaded into a high-pressure cell (internal volume: $30 mL), which was precooled in a freezer at 253 K. Aer loading at 253 K, the high-pressure cell was cooled to below 90 K, and pure CH 4 , C 2 H 4 , C 2 H 6 or Kr gas was slowly introduced into the cell. The high-pressure cell was then transferred into a water bath kept at 273.2 K for hydrate formation. As the hydrates formed, the pressure decreased.
When the pressure stabilised more than 12 hours later, the cell was cooled below 90 K, and the sample was retrieved from the cell.

Raman spectroscopy
A Raman spectrometer (Jasco Corporation, RMP-210) equipped with a 532 nm excitation source (100 mW), a single holographic diffraction grating (1800 grooves per mm) and a CCD detector were used. The spectrum pixel resolution, which is the sampling interval of the spectrum, was 0.9 cm À1 per pixel in the range of 2500-3100 cm À1 . The wave number was calibrated using atomic emission lines from a neon lamp. The Raman spectra for the C-H symmetric stretch region (2500-3100 cm À1 ) of the encapsulated hydrocarbon molecules in the gas hydrate water cages were obtained at ambient pressure within a temperature range of 93-183 K at 15 K intervals. The measured temperature was conrmed by using a thermocouple (Type T, 01-T, Ninomiya Electric Wire Co. Ltd., Japan). The calibrated thermocouple had an accuracy within 0.1 K. The peak positions could be rigorously analysed by tting the data to a mixed Gaussian-Lorentzian function, which allowed us to obtain a high positional accuracy. We measured the C-H symmetric stretch of the sI C 2 H 6 hydrate 18 times at 123 K at the same sample position. From these measurements, the standard deviation of the peak positions was found to be approximately 0.1 cm À1 .

Powder X-ray diffraction (PXRD)
Temperature-dependent PXRD measurements were performed using an X-ray diffractometer (40 kV, 40 mA; Rigaku model Ultima-III) with parallel beam optics and a low-temperature chamber. Finely powdered hydrate samples were mounted on a PXRD sample holder made of 2.5 mm thick Cu at a temperature of around 100 K. Each measurement was performed in a q/ 2q step scan mode with a step width of 0.02 using Cu Ka radiation (l ¼ 1.541 A).

Gas chromatography
Molecular compositions of CH 4 and C 2 H 6 in gas hydrate samples were determined using a gas chromatograph (Shimadzu Corporation, GC-2014) equipped with a packed column (Shimadzu Corporation, Sunpak-S), along with a thermal conductivity detector and fame ionisation detector. Fig. 1 depicts the Raman spectra of the C-H stretching region of sI C 2 H 4 hydrate, sII Kr + C 2 H 4 hydrate, sI C 2 H 6 hydrate, sI CH 4 + C 2 H 6 hydrate and sII CH 4 + C 2 H 6 hydrate at a temperature range of 93-183 K. We conrmed the crystal structures of sI C 2 H 4 hydrate and sII Kr + C 2 H 4 hydrate and their lattice constants by the PXRD method ( Fig. S1 and S2 †).
For sI C 2 H 4 hydrate, the Raman spectrum of the C-H symmetric stretch of encapsulated C 2 H 4 in sI 5 12 6 2 cages were observed at 3011.3 cm À1 at 93 K. This result was consistent with an earlier study. 7 The Raman shi of the C-H symmetric stretch of encapsulated C 2 H 4 in larger sII 5 12 6 4 cages (3007.0 cm À1 at 93 K) was red-shied relative to that of the encapsulated C 2 H 4 in smaller sI 5 12 6 2 cages. Furthermore, the Raman shi of the C]C symmetric stretch of the encapsulated C 2 H 4 in sII 5 12 6 4 cages of sII Kr + C 2 H 4 hydrate (1340.7 AE 0.4 cm À1 at 93 K) was red-shied relative to that of sI 5 12 6 2 cages of sI C 2 H 4 hydrate (1342.6 AE 0.4 cm À1 at 93 K) (Fig. 2). These results agree with the LCTC model. This is also the rst report of the Raman spectrum of C 2 H 4 encapsulated in sII hydrate.
In the case of sI C 2 H 6 hydrate, sI CH 4 + C 2 H 6 hydrate and sII CH 4 + C 2 H 6 hydrate, the Raman spectrum of the C-H symmetric stretch of encapsulated C 2 H 6 in the water cages of gas hydrate were observed at 2942.1 cm À1 , 2941.9 cm À1 and 2940.1 cm À1 at 93 K, respectively. The attribution of this vibrational mode was Fig. 1 Raman spectra of the C-H stretching region of (a) sI C 2 H 4 hydrate, (b) sII Kr + C 2 H 4 hydrate, (c) sI C 2 H 6 hydrate, (d) sI CH 4 + C 2 H 6 hydrate (yC 2 H 6 : 79.7%) and (e) sII CH 4 + C 2 H 6 hydrate (yC 2 H 6 : 35.3%) at a temperature range of 93-183 K.
based on the previous literature. 28 Furthermore, structures of sI C 2 H 6 hydrate, sI CH 4 + C 2 H 6 hydrate and sII CH 4 + C 2 H 6 hydrate samples were conrmed from the Raman spectra of the C-C symmetric stretch of encapsulated C 2 H 6 in each gas hydrate (1002.2 AE 0.4 cm À1 , 1001.9 AE 0.4 cm À1 and 992.4 AE 0.4 cm À1 , respectively, at 93 K; see Fig. 2). 11 Here, the notation Dv/DT refers to the temperaturedependent slope of the Raman shis of the C-H symmetric stretching vibrations in guest hydrocarbon molecules encapsulated in the gas hydrate water cages. Fig. 3 shows Dv/DT of the encapsulated CH 4 , C 2 H 4 and C 2 H 6 in water cages of various gas hydrates in a temperature range of 93-183 K. In the case of CH 4 , Dv/DT of encapsulated CH 4 in sI 5 12 6 2 cages (sI CH 4 + C 2 H 6 hydrate) were greater than that of encapsulated CH 4 in sII 5 12 and 5 12 6 4 cages. We observed that Dv/DT of CH 4 in the larger sI 5 12 6 2 cages was greater than that of CH 4 in 5 12 cages of sI hydrates. 24 Our measurements for the encapsulated CH 4 in the sI CH 4 + C 2 H 6 hydrate agree with this trend. In the case of C 2 H 4 , Dv/DT of C 2 H 4 in sI 5 12 6 2 cages (sI C 2 H 4 hydrate) was greater than that of C 2 H 4 in sII 5 12 6 4 cages (sII Kr + C 2 H 4 hydrate). Furthermore, in the case of C 2 H 6 , Dv/DT of C 2 H 6 in sI 5 12 6 2 cages (sI C 2 H 6 hydrate and sI CH 4 + C 2 H 6 hydrate) was greater than that of C 2 H 6 in sII 5 12 6 4 cages (sII CH 4 + C 2 H 6 hydrate). For CH 4 , C 2 H 4 and C 2 H 6 as guest molecules, Dv/DT for molecules in the sI 5 12 6 2 cages were greater than that for molecules in sII 5 12 6 4 cages. Moreover, we found that Dv/DT of CH 4 in sII 5 12 cages was almost the same as that of CH 4 in sII 5 12 Table 1.
The Raman spectra of sI and sII CH 4 + C 2 H 6 hydrates having different cage occupancies of large cages were obtained for verication of the effect of cage occupancies of large cages on Dv/DT. The cage occupancies of large cages of sI and sII CH 4 + C 2 H 6 hydrates were estimated from yC 2 H 6 (see Table S1 †). 30 The Raman spectra of sI and sII CH 4 + C 2 H 6 hydrates which have different guest composition are shown in Fig. 1 and S3, † and these Dv/DT are compared in Fig. S4. † We observed the consistent trends of Dv/DT of encapsulated CH 4 and C 2 H 6 in sI and sII CH 4 + C 2 H 6 hydrates regardless of different cage occupancies of large cages: Dv/DT for guest molecules in the 5 12 6 2 cages were greater than that for molecules in 5 12 and 5 12 6 4 cages (see Fig. S4 and Table S1 †). Although different distortion and thermal expansion in sII hydrates dependent on the guest Fig. 2 Raman spectra of C-C stretching region of sI C 2 H 4 hydrate, sII Kr + C 2 H 4 hydrate, sI C 2 H 6 hydrate, sI CH 4 + C 2 H 6 hydrate (yC 2 H 6 : 79.7%) and sII CH 4 + C 2 H 6 hydrate (yC 2 H 6 : 35.3%) at 93 K. We compared the geometrical properties of 5 12 , 5 12 6 2 and 5 12 6 4 cages. sI 5 12 , sII 5 12 and 5 12 6 4 cages are known to be almost spherical, although they are slightly distorted, depending on the type of guest molecule. sI 5 12 6 2 cages, however, are known to be spheroidal and extend along the equatorial plane (Fig. 4). Dv/DT values of CH 4 in both sII 5 12 and 5 12 6 4 cages were equivalent, although these two host water cages were the smallest and largest cages in this study, respectively (see Table  1). Dv/DT of guests in the sI 5 12 6 2 cages was greater compared with the 5 12 cages and sII 5 12 6 4 cages. The earlier study indicated that distributions and reorientations of guest molecules were affected by the distortion of the shapes of the host cages. For instance, C 2 H 6 and carbon dioxide (CO 2 ) molecules within the sI 5 12 6 2 cage lie near the equatorial plane of the cages, with the long axis of the guest molecules lying in the plane. 9,10 By contrast, the spherically extended distribution of C 3 H 8 and C 4 H 10 molecules in the sII 5 12 6 4 cages obtained by the X-ray diffraction structure analysis was apparent. 26,27 In addition, in the case of sI CD 4 hydrate, the CD 4 in sI 5 12 cages showed a spherical density distribution at the centre of the 5 12 cage at temperatures of 7.7-185 K, while CD 4 in sI 5 12 6 2 cages showed only a longitudinal density distribution between the two hexagonal faces of the sI 5 12 6 2 cages. 25 These differences in the distributions of guest molecules encapsulated in the different host water cages of gas hydrates may cause thermal vibrations in the guest molecules and variations in guest-host and guestguest interactions due to varying temperatures.
In our previous study, we considered the effect of the size of the host cages on Dv/DT and found that the slope increased with Table 1 Raman shifts of C-H symmetric stretch of CH 4 in sI 5 12 , 5 12 6 2 , sII 5 12 and 5 12 6 4 cages; C 2 H 4 and C 2 H 6 in sI 5 12 6 2 and sII 5 12   increasing host water cage volume. 24 In this study, we revealed that Dv/DT depends on the geometry as well as the volume of host water cages. For a discussion about the effect of the conformation of guest molecules on Dv/DT, more studies of various combinations of guest molecules and host water cages are needed. These experimental trends of Dv/DT for the various water cages of gas hydrates may advance our understanding of the fundamental properties of sI and sII hydrocarbon gas hydrates.

Conclusions
In this work, we investigated the slopes of C-H symmetric stretching vibrational frequencies under changing temperatures (Dv/DT) for various hydrocarbon molecules in 5 12 , 5 12 6 2 and 5 12 6 4 cages of sI and sII hydrates. Dv/DT values of CH 4 , C 2 H 4 and C 2 H 6 molecules encapsulated in sII 5 12 6 4 cages were smaller than those for molecules in sI 5 12 6 2 cages. In our previous study, we suggested that Dv/DT is greater with increasing volume of host water cages. In this study, we revealed that Dv/DT is dependent on the geometry, as well as the volume of host water cages and guest molecules.
In the future, we intend to investigate the effects of the conformation of guest molecules on Dv/DT. For a discussion about the effect of the conformation of guest molecules on Dv/ DT, more studies of various combinations of guest molecules and host water cages are required.

Conflicts of interest
There are no conicts to declare.