Raman Peak Frequencies of Fluoromethane Molecules Measured in

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J. Phys. Chem. A 2010, 114, 317–323

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Raman Peak Frequencies of Fluoromethane Molecules Measured in Clathrate Hydrate Crystals: Experimental Investigations and Density Functional Theory Calculations 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 and EnVironmental Engineering, Faculty of Engineering, Kitami Institute of Technology, 165, Koencho, Kitami 090-8507, Japan ReceiVed: August 26, 2009; ReVised Manuscript ReceiVed: September 27, 2009

Systematic observations of fluoromethane clathrate hydrates were carried out by Raman spectroscopy. The series of fluoromethanes, i.e., methane (CH4), fluoromethane (CH3F), difluoromethane (CH2F2), trifluoromethane (CHF3), and tetrafluoromethane (CF4), were used as standard guest molecules to investigate the vibration modes of the guest molecules in the hydrate phase, since all of these fluoromethanes are included in the same crystal structure and share similar functional groups. In this study, both the C-H and C-F vibration modes of the guest molecules were systematically collected and assigned each peak based on the density functional theory (DFT) calculations. The Raman peak table obtained by the DFT calculations was useful for assigning the Raman peaks measured by the experiments. The assignment of the Raman peaks of the C-H stretching mode of each fluoromethane hydrate coincided well with those estimated both experimentally and theoretically in previous studies. The empirical “loose cage-tight cage” model of the Raman peak shifts allowed us to estimate the unperturbed frequencies of the C-H symmetric stretching mode on CH3F molecules in the clathrate structure. Clathrate hydrates formed with deuterated water molecules indicated that the deuterium had little effect on the Raman spectra of the intramolecular vibration modes of the guest molecules within the experimental uncertainties. Introduction Raman spectroscopic measurements have been carried out to observe the vibrational modes of guest and host molecules in the clathrate hydrate phase. Sum et al.1 showed the double peak of methane (CH4) molecules occupying both the pentagonal dodecahedron (512) and tetrakaidecahedron (51262) cages in the cubic structure I (sI) CH4 hydrates. Both peak frequencies are shifted lower than that of the vapor phase. Since the frequency difference between these peaks is sufficient to be distinguished, it allows us to classify the type of cage in which the guest molecules are included. This technique was originally studied in several gas hydrates by infrared spectroscopy2,3 and used for the clathrate hydrate measurements by nuclear magnetic resonance (NMR).4 The Raman peak frequency difference in different cage types is sometimes used for the crystal structure characterization of clathrate hydrates instead of X-ray diffraction or neutron diffraction methods. For example, Subramanian et al.5 showed the structural transition of methane-ethane mixed gas hydrates by combining NMR and Raman spectra. Hester et al.6 developed a new seagoing Raman spectrometer and observed the in situ Raman spectra in the deep sea to characterize the gas hydrate properties. Raman spectroscopy has become a useful technique, especially for field analyses, since the experimental apparatus is simple and compact. However, the shifts in the Raman peak frequencies of the molecules encaged in the clathrate hydrates * Corresponding author: telephone, +81-11-706-6635; fax, +81-11-7066635; e-mail, [email protected]. † Hokkaido University. ‡ Keio University. § Kitami Institute of Technology.

(guest molecules) have been experimentally interpreted with few theoretical supports. Therefore, it is noted that the application of Raman spectroscopic measurements for structural characterization should be restricted to a system that has been well characterized in the laboratory. In order to apply the Raman spectroscopic measurements to the structural characterization of any clathrate hydrates, a theoretical explanation is required. One empirical model for the shift of the Raman peak frequencies in clathrate hydrates has been proposed by Subramanian and Sloan.7 Their “loose cage-tight cage” model was based on the principle that uses the perturbation treatment developed by Pimental and Charles,8 which was based on a solvation model proposed by Buckingham9 to explain the shifts in the vibrational frequencies of a diatomic solute molecule due to its interaction with a liquid solvent. They checked the validity of the model by the experimental measurements of various gas hydrates of hydrocarbons. However, these gas hydrates included several crystallographic structures and a large range of guest molecular sizes. To investigate the validity of the model, other systematic evidence on clathrate hydrates is required. Fluorocarbon molecules such as monofluoromethane (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) are confirmed to form sI clathrate hydrates as is the case for CH4.10 Most of the equilibrium conditions were milder than that of the CH4 hydrate; the dissociation pressures at 273.5 K were 2.65, 0.27, 0.16, and 0.25 MPa for the CH4 hydrate,11 CH3F hydrate,12 CH2F2 hydrate (extrapolation of Imai et al.13), and CHF3 hydrate (extrapolation of Mooijer-van den Heuvel, et al.14), respectively, except for 3.6 MPa for the CF4 hydrate.14,15

10.1021/jp908263s  2010 American Chemical Society Published on Web 11/16/2009

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TABLE 1: Fluorocarbon Hydrate Formation Conditions guest molecule

host molecule

temperature (K)

pressure (MPa)

CH4 CH3F CH2F2 CHF3 CF4

H2 O H2O H2O, D2O H2O, D2O H2 O

274.4 273.5 273.5, 278.2 273.5, 278.2 273.5

4.2 1.0 0.7, 0.8 1.0, 1.0 7.5

In our previous paper,16 we reported that the cage occupancy ratio between the small and large cages of these guest molecules depended on their molecular size and demonstrated that the series of the fluoromethanes was suitable for the studies of guest molecule vibration depending on the molecular size. In the present study, we focused on summarizing both the C-F and C-H intramolecular vibrational modes of the fluoromethane molecules in clathrate structures in order to obtain the Raman spectroscopic data sets for the fluoromethanes encaged in the 512 and 51262 cages of the type I structure. The observed Raman peak frequencies were assigned by comparison to the results of the density functional theory (DFT) calculations. On the basis of the completed Raman peak frequency table of the fluoromethane hydrates, we investigated the validity of the empirical model for the Raman spectroscopic measurements on the general clathrate hydrates. We also found that the Raman peak frequencies of the guest molecules in the clathrate hydrates formed with deuterated water coincided well with those with normal water. Experimental Procedures The clathrate hydrates of the fluoromethanes were prepared by stirring guest gases and water in a high-pressure vessel. CH4, CH3F, CH2F2, CHF3, and CF4 were selected as the guest molecules, whereas H2O and D2O were used as the host molecules. Originally, D2O was used for both the CH2F2 and CHF3 hydrates to precisely measure the C-H stretching-mode Raman intensities, since the use of D2O allowed the elimination of the background signal of the O-H stretching mode of water. In the present study, we compared their Raman peak frequencies with those of H2O in order to investigate the effect of the deuterated host molecules on the guest molecule vibrations. The experimental apparatus used to form the hydrate samples is the same as that used in our previous studies.17,18 The main part of the apparatus is a stainless-steel cylinder with the inner dimensions of 80 mm diameter and 40 mm height. A magnetic stirrer was driven through its lid at 400 rpm to agitate the fluids and hydrate crystals inside the vessel. The vessel was immersed in a temperature-controlled bath to maintain the temperature inside the vessel, T, at a prescribed value to (0.1 K. Two platinum wire resistance thermometers were inserted into the vessel to measure T. The pressure in the vessel, p, was measured by a strain-gauge pressure transducer (model PH 100 KB, Kyowa Electric Co., Ltd.). Each hydrate crystal sample was prepared with liquid water and gaseous guests under higher pressures than the equilibrium one at the formation temperature. The pressure and temperature were set at the conditions specified in Table 1. The line connecting the test cell and the high-pressure cylinder of each guest was opened during the hydrate formation in the test cell to keep p constant by continuously supplying the gaseous component to compensate for the pressure reduction in the test cell due to hydrate formation, so that a sufficient amount of hydrate crystals would be stored in the cell. p and T were kept constant for over 200 h along with continuous agitation in the vessel at 400 rpm after nucleation of the hydrate.

The vessel was subsequently taken out of the temperaturecontrolled bath and then immediately immersed into a liquid nitrogen pool in a stainless steel container. We allowed 20 min for T to decrease below approximately 120 K and then disassembled the vessel to remove the formed hydrate crystals. These prepared samples were stored in a container kept at a temperature of approximately 100 K and then subjected to Raman spectroscopy measurements. The Raman spectra were collected using a triple-monochronic Raman spectrometer (Jobin Yvon Ramanor T64000) with gratings of 1800 mm-1. The specimen was set below the objective lens, and the scattered radiation was collected through a slit with a 180° geometry and with a 45× long-distance objective lens; the incident laser beam (514.5 nm Ar-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 measurement by controlling the flow rate of the nitrogen gas vaporized from the liquid nitrogen. For calibration, the shape of the neon emission lines indicated that the wavenumbers of peak positions were determined within (0.6 cm-1. We measured the Raman spectra of the intermolecular C-H vibrational mode (2700-3200 cm-1) and the C-F vibrational mode (800-1600 cm-1); five or six measurements were carried out at different sites on each sample in order to allow the signal to accumulate for averaging. The data accumulated for each spectrum were fitted by the Voigt curve to estimate the half-width of full maximum (hwfm). The initial condition of the fitting is the number and frequency of the peaks which was suggested by the Raman spectra of the guest molecules in the vapor phase. In the present study, we used the structure data of the CH4 hydrate reported by Gutt et al.22 as the initial structures of the CH4 hydrate for the cluster calculations mentioned below. However, there are no published structure data for the fluoromethane hydrates. To obtained the initial structures of the fluoromethane hydrates, after the substitutions of the H atoms in the CH4 molecules of the optimized CH4 hydrate structure with F atoms, we carried out geometry optimization calculations for solids under the periodic boundary condition using the DMOL3 Solid State program package in the Materials Studio (version 4.0 and 4.2) of Accelrys, Inc.,19–21 on personal computers. The frequency calculations were conducted for three states: (1) a fluoromethane molecule in a vacuum, (2) 512, and (3) 51262 water clusters including fluoromethane molecules. States 2 and 3 are the mimic of the two-cage structures of the sI clathrate hydrate. The calculated C-F and C-H vibrational modes were assigned by the visualization of the intramolecular vibrations using GaussView 3.0.23 The geometry optimization calculations for these clusters were performed at the B3LYP/ 6-31G(d) level with Gaussian0324 and then the frequency calculations for the optimized structures were also performed at the B3LYP/6-31G(d) level with Gaussian03. The Raman peak frequencies of the CH4 and fluoromethane molecules were also calculated in the same way. The calculated frequencies were multiplied by the scaling factor of 0.9613 for comparison with the experimentally obtained results.25 Results and Discussion (a) Raman Spectra of Fluoromethane Molecules in Various Phases Calculated by the DFT Method. The calculated results are summarized in Table 2. The listed vibrational modes were selected in order to compare the experimental Raman spectra mentioned later. Since these calculations were performed on a single molecule or on the isolated cluster, the absolute

Raman Spectra of HFC Hydrates

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TABLE 2: Summary of Raman Peak Positions of Various Guest Molecules Estimated by the DFT Calculationsa guest molecule CH4

CH3F

CH2F2

CHF3

CF4

in 51262 cage in 512 cage in vacuum νLC (cm-1) νSC (cm-1) νmolC (cm-1) assignment 1315.7 1324.8 1343.6 1535.6 1538.6 2924.8 3021.2 3037.3 3044.3 1002.4 1155.7 1169.6 1464.9 1481.1 1474.5 2934.7 3014.2 3040.5 495.6 1002.4 1033.8 1055.6 1071.8 1149.8* 1160.2 1247.2 1265.9 1449.7 1525.9 2974.6 3047.6 475.8* 477.9 479.7 662.3 1068.4* 1079.3 1084.8 1091.2* 1103.6 1123.0 1133.7 1379.4 1385.5* 3056.9* 3059.7 407.3* 408.0 408.7 590.3 591.2 593.1* 869.0 1210.7 1251.1 1265.6

1318.1 1319.5 1342.1 1537.7 1539.7 2943.0 3041.8 3057.2 3059.4 1019.3 1158.9 1164.1 1458.0 1468.8 1475.8 2959.8 3041.8 3050.5 500.6 1044.6 1068.9* 1085.5 1134.8 1157.3 1165.1* 1217.7 1240.8 1437.7 1506.7 2997.9 3080.0 482.9 484.4* 486.3 667.0 1088.0* 1119.5

1320.3

1110.8* 1132.2* 1150.5 1165.8 1381.0* 1391.9 3076.5

1136.9

410.7 412.8

407.3

596.3 596.9 598.8 880.7 1231.9 1247.3 1261.0

593.0

1532.3 2935.4 3041.5 1049.8 1158.3 1464.5 1472.4 2921.2 2992.0 498.5 1085.4 1086.5 1149.5 1227.0 1444.1 1507.4 2941.9 3001.7 477.9 667.8 1105.6

1376.5 3023.0

871.7 1254.7

T2 T2 T2 E E A1 T2 T2 T2 A1 E E E E A1 A1 E E A1 B2 A1 A1 B1 B1 B1 A2 A2 B2 A1 A1 B1 E E E A1 A1 A1 A1 E E E E E E A1 A1 E E E T2 T2 T2 A1 F2 F2 F2

a The asterisk indicates the major frequency of the vibrational mode for the guest molecule.

frequencies would be different from those obtained on the actual solid crystal. Therefore we qualitatively used this table for the assignment of the experimentally obtained Raman peaks and for the estimation of the Raman peak frequency shifts in the different phases of the fluoromethane molecules. In the vacuum phase, some vibrational modes of the fluoromethane molecule showed a degeneracy. For example, the ν3 mode of the CF4 molecule is found at 1254.0 cm-1, which

includes three different molecular vibrations (all of which are assigned as the triply degenerate asymmetry stretching modes, but calculated with different atoms). These modes have different frequencies in the water clusters. On the other hand, some vibrational modes having a single frequency in a vacuum are found to be separated into multiple frequencies in the water clusters. For example, the ν1 mode of the CHF3 molecule is found at 3023.6 cm-1 in a vacuum. This mode is shifted to 3076.5 cm-1 in the 512 cluster. However, it shifted to two different frequencies, 3053.3 and 3055.3 cm-1, in the 51262 cluster. The visual analysis indicated that the former frequency of the CHF3 molecule in the 51262 cluster (3053.3 cm-1) is the ν1 mode of the guest molecule alone in the cluster, whereas the latter (3055.3 cm-1) is the vibration of the CHF3 molecule oscillating by the intermolecular vibrations of several surrounding H2O molecules. This kind of satellite frequency would make the actual Raman peak broader. Some of satellite frequencies are also listed in Table 2 with the major frequency marked by an asterisk. We conducted the DFT calculations for clusters in order to investigate the molecular vibrations of the guest molecules encapsulated in the cage structures. In the optimized structures, the positions of the central carbon atoms were found to be different from those of the cluster centers. The distances between these positions were approximately 0.1-0.3 Å in the 512 cluster and about 0.2-0.5 Å in the 51262 cluster. The CF4 molecule was located almost at the center of both clusters. On the basis of our calculations, we obtained information on the stretching and the bending modes of the molecules, but we could not find any rotational vibration of the guest molecules. For a better understanding of the molecular vibrations, another method, for example, molecular dynamics, should be performed for the solids. (b) C-H and C-F Modes of Raman Frequencies of Various Fluoromethane Molecules in the Hydrate Phase. Figures 1 and 2 show the Raman spectra of C-H and C-F vibrational modes for the four fluoromethane clathrate hydrates plus the CH4 hydrate, respectively. In the C-H vibrational mode of the Raman spectra for the fluoromethane hydrates, these are several large and sharp peaks in the observed range. Most of them are recognized to be split into two peaks; the larger peak was at a lower frequency than the smaller one. The numerical data of these peak frequencies are listed along with the hwfm values in Table 3. A comparison of these values for the CH4 hydrate with the previously obtained ones1,26,32 indicated the accuracy of the Raman spectrum measurements in the present study. On the other hand, in the C-F vibrational mode of the Raman spectra for the fluoromethane hydrates, there are several common peak patterns. One or two large and sharp (hwfm’s are smaller than 10 cm-1) peaks, each of which is overlapped with a broad peak, are observed at frequencies lower than 1200 cm-1. In some spectra, several other broad peaks are observed at frequencies higher than 1200 cm-1. All of these peak frequencies are also tabulated along with the hwfm values in Table 3. Each peak frequency observed in the present study was then checked and assigned by comparison with the DFT calculated data (Table 2). The obtained Raman peak frequencies in the C-F vibrational mode for the CF4 hydrate coincide well with those obtained in a previous study,15 which also indicates the accuracy of the Raman spectrum measurements in the present study. Since most of the C-H stretching mode peaks split into high and low frequency peaks with a Raman shift of 10-20 cm-1

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Figure 2. C-F stretching mode spectra of fluoromethane hydrates: (a) CH3F hydrate, (b) CH2F2 hydrate, (c) CHF3 hydrate, and (d) CF4 hydrate. The dots and thin lines indicate the measured data and fitted curves, respectively. Figure 1. C-H stretching mode spectra of fluoromethane hydrates with H2O molecules: (a) CH4 hydrate, (b) CH3F hydrate, (c) CH2F2 hydrate, and (d) CHF3 hydrate. The dots and thin lines indicate the measured data and fitted curves, respectively. The large peak around 3150 cm-1 is assigned to the O-H stretching mode of the host H2O molecules.

that is larger than the experimental uncertainty, they are attributed to the guest molecules present in the different cages. For example, the CH4 hydrate has large and small peaks at 2904 and 2915 cm-1, respectively. The DFT calculation shows that the peak shift in the vibrational mode of the CH4 molecule in the 512 cluster from that in a vacuum is smaller than that in the 51262 cluster. The peak position difference between in these clusters is approximately 18 cm-1, which is on the same order of the experimental value of 11 cm-1. Consequently, each peak of the C-H stretching mode of the CH4 hydrate was assigned to the CH4 molecule encaged in the 51262 and 512 cages. This result coincides with the experimental assignments by the NMR and Raman measurements.32 All the split peaks in the C-H stretching mode observed in the present study were then assigned by the DFT calculation. Since all of them were consistent with the previous assumptions made by the relative intensity ratio,16 our conclusions in Table 3 confirmed their assignments to be correct. On the other hand, the C-F stretching mode Raman spectra of the fluoromethane hydrates were different in each hydrate. Only one large and sharp peak was observed, which was overlapped by a broad peak. Unfortunately, we did not find any obvious peak splittings as observed in the C-H stretching modes. The DFT calculation indicates that, in the C-F

stretching mode region, the peak shift of the vibrational mode of the guest molecules in the 512 cluster from that in a vacuum is smaller than that in the 51262 cluster for all the A1 mode frequencies in the present study. The peak position differences between these clusters are greater than 10 cm-1, which is large enough to observe the experimental uncertainties. Therefore, it is difficult to assign the experimentally observed peaks only from the DFT calculations. The main reason for this problem would result from the fact that several vibrational and bending modes of a guest molecule exist within the observed range, each of which has a different shift of the peak frequency depending on both the vibrational mode and cage types. Furthermore, as predicted by the DFT calculations, the vibrational frequency of the guest fluoromethane molecules in a cage was slightly changed by the vibration of the surrounding host water molecules which might be induced by the guest molecule vibration. There are only a few reports about the C-F vibrational modes of the Raman spectra in clathrate hydrates. Cleaver et al.33 reported that the C-F vibrational mode in the Raman spectrum of the CH3F molecule in the β-quinol clathrate was 1022 cm-1, which well coincided with the 1025 cm-1 of the large peak in the present study. Since the cavity size of the β-quinol clathrate is similar to that of the 51262 cage of the hydrate structure, the coincidence of the Raman shift is feasible. However, this result is not enough to determine the enclathration cage types. Only assignment of the guest molecules in different cages was done for the CF4 hydrate.15 One large peak observed at 908 cm-1 for the CF4 hydrate was assigned as the ν1 C-F symmetric stretching mode of the CF4 molecules encaged in the 51262 cage of the sI structure, whereas the peak at 920 cm-1 in the Raman

Raman Spectra of HFC Hydrates

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TABLE 3: Summary of Raman Peak Positions of Various Guest Moleculesa in H2O hydrate

in D2O hydrate

guest molecule (re(C-H) (Å))b

νL (cm-1)

νS (cm-1)

νL (cm-1)

νS (cm-1)

CH4 (1.087)

2904 (4.4)

2915 (6.6)

2904 (4.2)

2915 (5.5)

CH3F (1.086)

2852 (2.9) 2860 (4.0) 2955 (4.8) 2967 (7.4) 1025 (5.0) 1035 (broad) 1180 (broad) 1469 (broad) 1469 (broad) 2830 (3.2) 2837 (6.0) 2947 (11) 2961 (8.9) 3016 (6.3) 3025 (17) 1097 (7.3) 1082 (broad) 1254 (broad) 1436 (broad) 1513 (broad) 3043 (12) 3062 (5.7) 1128 (3.7) 1137 (broad) 1370 (9.6), 1383 (broad) 867 908 (2.7) 919 1272 (broad)

CH2F2 (1.084)

CHF3 (1.090)

CF4

2831 (2.3) 2839 (4.5) 2948 (11) 2963 (14) 3018 (5.2) 3026 (6.9) 1096 (12) 1082 (broad) 1256 (broad) 1438 (broad) 1513 (broad) 3043 (11) 3062 (5.6) 1127 (7.4) 1136 (broad) 1372 (13) 1372 (broad)

vaporc νvap (cm-1)

assignment

2917

ν1 (A1)

2864 2964 1049 1049 1182 1460 1467

νν+ ν3 (A1) ν3 (A1) ν6 (E) ν2 (A1) ν5 (E) unknown ν1 (A1) ν6 (B1) ν3 (A1) ν9 (B2) ν5 (A2) ν8 (B2) ν2 (A1) ν1 (A1) ν2 (A1) ν4 (E) ν5 (E) ν5 (E) 2ν2 (E) ν1 (A1) ν3 (F2)

2949 3012 1111 1090 1262 1435 1508 3036 1117 1152 1372 1372 869 908 ∼1283

a The numbers in parentheses in the νL and νS columns are the measured hwfm. The assignment shows the vibrational mode and symmetry in parentheses. b The equilibrium C-H bond length of the guest molecules was found in previous studies.36,37 c The Raman peak positions of each vapor phase were found in previous studies: CH4 for Sum et al.1 and Uchida et al.,26 CH3F for Wu et al.27 and Duncan et al.,28 CH2F2 for Wu et al.,29 CHF3 for Wu et al.,30 and CF4 for Clark and Rippon31 and Sugahara et al.15

spectra was for the CF4 molecules in the 512 cages under highpressure conditions. Therefore, the C-F vibrational mode of the Raman spectra for the CH3F, CH2F2, and CHF3 hydrates could support the existence of clathrate structures but was not useful for the estimation of the cage type holding the guest molecules as performed in the C-H stretching mode. The peak assignments with encaged classifications for all the observed Raman peaks are listed in Table 3. This table also indicated that both the C-H and C-F stretching modes of the Raman frequencies of the guest molecules in the clathrate hydrates formed with deuterated water coincided well with those for normal water within our experimental uncertainties. (c) Raman Peak Position Shifts of C-H Vibrational Mode on Fluoromethane Molecules in Clathrate Hydrates: Comparison with ‘Loose Cage-Tight Cage’ Model. The Raman peak frequencies of guest molecules encaged in clathrate structures typically differ from the frequencies in the vapor phase. Such differences between the Raman peak frequencies in 51262 and 512 cages are defined as ∆νL and ∆νS, respectively, by the following equations.

∆νL ) νL - νvap

(1a)

∆νS ) νS - νvap

(1b)

where νi indicates the observed Raman frequency for the guest molecule included in the i cage and νvap indicates the Raman frequency for the guest vapor. Since the Raman peak frequencies of the CH3F molecules are perturbed due to the Fermi resonance of the ν1 + 2ν5 modes,27 we estimated ∆νi from the perturbed νvap.

The Raman peak shifts vary with the different environments around the guest molecule, and this variation was interpreted by the empirical model referred to as the “loose cage-tight cage” model by Subramanian and Sloan.7 The loose cage-tight cage model for the stretching vibrational mode of the guest molecules in the clathrate hydrates was accounted for by the equation7

∆ν ) νguest - νvap ) 0.5 ωek-1(U′′-3Aωe-1U′)re-2

(2) where ωe is the “classical” frequency of the harmonic oscillator; U′ and U′′ are, respectively, the first and second derivatives of the solute-solvent (or guest-host) interaction potential with respect to the dimensionless displacement coordinate (r - re)/ re, averaged over all the solvent configurations, where re is the equilibrium bond length and (r - re) is the displacement from the equilibrium position; A is the anharmonicity constant expressed in inverse centimeters; and k is the harmonic force constant corresponding to the vibrational mode of the trapped molecule. This model has been used to predict the trends in the stretching vibrational frequencies of several hydrocarbon molecules in clathrate hydrate cages.34,35 The series of fluoromethanes used in the present study was expected to be useful for investigating the feasibility of this empirical model because they have the same C, H, and F atoms in different ratios and hence they have systematically different values of re. When we examined the C-H stretching mode of the Raman spectra, eq 2 indicates that ∆ν depends on re(C-H)-2, where re(C-H) is the equilibrium C-H bond length of the guest molecule. The experimental results ∆νi for each of the fluoromethanes in the ν1 mode obtained by eqs 1a and 1b were then related to

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Uchida et al. linear relation observed for the CH3F hydrate would be the result of the perturbation by the Fermi resonance with the 2ν5 mode. We then estimated the unperturbed peak frequencies of the CH3F molecules in clathrate structures. The unperturbed peak frequencies ν1 and ν5 are represented by the following equations:39

Figure 3. Variation in Raman peak position shift with intramolecular C-H distance. The open and solid circles indicate ∆νS and ∆νL, respectively. re(C-H)-2 was calculated from the previous studies.36,37

re(C-H)-2,36,37 as shown in Figure 3. This figure indicates that all the ∆νS values are larger than ∆νL. Since all of these guest molecules are encaged in both the 51262 and 512 cages,16 this result coincides well with the first general trend of the loose cage-tight cage model,7 namely, the larger the cavity, the lower the frequency of the stretching vibration. On the other hand, the C-F vibration mode is difficult when simply applying the “loose cage-tight cage” model. This is because each large peak of the C-F stretching mode is in a different vibration mode, such as the ν3 mode at 1025 cm-1 in the CH3F hydrate, the ν3 mode at 1097 cm-1 in the CH2F2 hydrate, the ν2 mode at 1128 cm-1 in the CHF3 hydrate, and the ν1 mode at 908 cm-1 in the CF4 hydrate (see Table 3). The obtained results also indicated that both ∆νS and ∆νL increased with increases in re(C-H) of the molecule occupying a cage. This result supports the second general trend suggested by the loose cage-tight cage model,7 i.e., the larger the guest size, the higher the frequency of the stretching vibration. However, this general trend is not observed when we investigated the relation between ∆ν and the “molecular size” (such as the van der Waals radius). This is feasible since the model is derived from the C-H stretching vibration motion affected by the guest-host molecular interaction energy. Therefore, it is noted that the critical parameter for this general trend is not the “molecular size”, but the observed bond length (re(C-H)). The CH2F2 molecule has an intermediate molecular size between those of CH3F and CHF3,16 but it has the shortest C-H bond length of all four fluoromethanes.36,37 The short C-H bond length may cause the so-called “looser” cage circumstances, due to the relative distance between the hydrogen of the guest and the oxygen of the host. The free rotational motion of a guest molecule in each cage would make this relative distance constant in the whole hydrate phase. (d) Estimation of Unperturbed Peak Frequency of CH3F Molecules in Clathrate Hydrates by Applying the Loose Cage-Tight Cage Model. In the previous section, we concluded that the general trends in the Raman peak frequencies obtained in the present study qualitatively coincided with the empirical loose cage-tight cage model.7 Since this series of fluoromethanes are beneficial for evaluation of the microenvironments of the investigated molecules in clathrate structures,38 we discussed the variation in the ∆ν in the ν1 C-H stretching vibrational mode for each fluoromethane in quantitative terms, since the loose cage-tight cage model was found to be feasible for high-frequency and large-force-constant stretching vibrations. Figure 3 also shows that ∆νi for the C-H stretching mode of the Raman spectra is linearly related to re(C-H)-2, with the exception of ∆νS and ∆νL for CH3F. The deviations from the

ν1 ) (ν+ + ν-)/2 - ∆/2

(3a)

2ν5 ) (ν+ + ν-)/2 + ∆/2

(3b)

δ2 ) ∆2 + 4W2

(3c)

where ν+ and ν- are the Raman frequencies perturbed by the Fermi resonance; δ ) ν+ - ν- is the difference between the perturbed frequencies; ∆ ) ν1 - 2ν5 is the difference between the unperturbed frequencies; and W is the Fermi coupling constant. We obtained two independent sets of perturbed frequencies for CH3F molecules in the 512 and 51262 cages and, therefore, could estimate the value of W and then those of ν1 and ν5. Using the experimentally obtained values in Table 3, we estimated that W ) 51.21 cm-1, ν1 ) 2898 cm-1, and ν5 ) 1454.5 cm-1. These values are slightly lower but comparable to those reported for the infrared spectroscopic measurements (ν1 ) 2910 cm-1 and ν5 ) 1467.8 cm-1).28 Since we obtained linear relations between ∆ν and re(C-H)-2 in the fluoromethane molecule series, we assumed they would be possible to correct for the Fermi resonance affecting the perturbed Raman frequencies. The linear relations of ∆νi and re(C-H)-2 can be estimated using three molecules (CH4, CH2F2, and CHF3), as

∆νL ) 3.66 × 103 - (4.23 × 103)re(C-H)-2

(4a)

∆νS ) 3.99 × 103 - (4.71 × 103)re(C-H)-2

(4b)

The correlation for each line-fitting R2 was 0.99 and 0.98, respectively. The interpolation of eqs 4a and 4b for the CH3F molecule indicated that ∆νL and ∆νS were -19.4 and -4.4 cm-1, respectively. We then estimated the perturbed Raman frequencies in the vapor phase instead of using the previously reported values.27 Substituting the collected perturbed Raman frequencies in the vapor and the obtained value of W into eqs 3, we obtained ν1 ) 2909 cm-1 and ν5 ) 1466 cm-1. These values coincide well with the reported values measured according to the infrared spectroscopic measurements.28 Therefore, the obtained relations between ∆ν and re(C-H)-2 appear to hold for the present fluoromethane molecule series. As shown in Figure 3, the Raman peak frequency is found not only in the red shift but also in the blue shift compared with those in the vapor phase. Equations 4a and 4b then show the critical C-H bond length 〈re(C-H)〉 of fluoromethanes enclathrated in each cage, which allows the zero shift of the symmetric stretching vibration from that in the vapor phase. For guest molecules in the 512 cage and the 51262 cage, the values would be 〈re(C-H)〉 ) 1.087 and 1.089 Å, respectively. Table 3 shows that the former is equivalent to the value of re(C-H) for CH4 (re(C-H) ) 1.087 Å), and the latter is similar to that for CHF3 (re(C-H) ) 1.090 Å). It is of interest that these coincidences remain consistent with the suitable cage occupations for the 512 and 51262 cages, respectively.16

Raman Spectra of HFC Hydrates Conclusions Raman spectra for five fluoromethanes in clathrate hydrate structures were obtained. In the present study, both the C-H and C-F vibrational modes of the guest molecules were tabulated and assigned by considering the vibrational analysis of the DFT calculations. The summary of the Raman peak frequencies of guest molecules would be useful not only for detecting the clathrate hydrates but also for investigating the cage type including guest molecules, especially in the C-H stretching vibrational mode. The comparison of the Raman spectra of fluoromethane hydrates formed from H2O and D2O indicated that the influence of the deuterated host molecules on the intramolecular vibrational frequencies was less than that suggested by the experimental uncertainty. The obtained summary of the Raman peak frequencies was used to generalize one of the empirical models for the clathrate hydrates, the loose cage-tight cage model, which had been previously applied for the hydrocarbon hydrates.7 The difference in the peak frequencies of the C-H symmetric stretching modes of the guests, ∆ν, was then found to linearly depend on re(C-H)-2, where re(C-H) is the equilibrium C-H bond length. On the basis of the model predicting the relation between ∆ν and re(C-H)-2, we were able to estimate the unperturbed ν1 stretching frequency of the CH3F molecule. These results quantitatively confirmed the validity of the empirical model for the Raman peak frequencies of clathrate hydrates, which would support the application of Raman spectroscopy for the noncontact or nondestructive investigations of clathrate hydrates. 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 would also like to thank Dr. Satoshi Takeya (AIST) for his fruitful discussions and Dr. Hiroshi Ohno and Mr. Toshimitsu Sakurai (Hokkaido University) for providing experimental support during the Raman spectroscopic measurements. The peak fitting software was supported by Dr. Hideo Fujii (OriginLab Co.). Note Added after ASAP Publication. This article was published ASAP on November 16, 2009, with minor text errors in Table 3. The correct version was reposted on November 18, 2009. References and Notes (1) Sum, A. K.; Burruss, R. C.; Sloan, E. D., Jr. J. Phys. Chem. B 1997, 101, 7371. (2) Richardson, H. H.; Wooldridge, P. J.; Devlin, J. P. J. Chem. Phys. 1985, 83, 4387. (3) Fleyfel, F.; Devlin, J. P. J. Phys. Chem. 1988, 92, 631. (4) Collins, M. J.; Ratcliffe, C. I.; Ripmeester, J. A. J. Phys. Chem. 1988, 94, 157. (5) Subramanian, S.; Kini, R. A.; Dec, S. F.; Sloan, E. D., Jr. Chem. Eng. Sci. 2000, 55, 1981. (6) Hester, K. C.; Dunk, R. M.; White, S. N.; Brewer, P. G.; Peltzer, E. T.; Sloan, E. D. Geochim. Cosmochim. Acta 2007, 71, 2947.

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