Dynamical structure of water by Raman spectroscopy

Fluid Phase Equilibria 144 Ž1998. 323–330

Dynamical structure of water by Raman spectroscopy Yasunori Tominaga

a, )

, Aiko Fujiwara a , Yuko Amo

b

a

b

Graduate School of Humanities and Sciences, Ochanomizu UniÕersity, Otsuka, Tokyo 112, Japan DiÕision of AdÕanced Technology for Medical Imaging, National Institute of Radiological Sciences, Anagawa, Chiba 263, Japan Received 13 January 1997; accepted 27 June 1997

Abstract Raman spectra of liquid water have a broad background extended to 4000 cmy1 as well as molecular vibrational modes. Depolarized Raman spectra below 250 cmy1 in liquid water are well interpreted with a superposition of two damped harmonic oscillators and one Cole–Cole type relaxation mode. Two damped harmonic oscillators are interpreted as stretching and bending vibration modes of a temporal tetrahedral-like structure of five water molecules. High-frequency Raman spectra between 1600 cmy1 and 4000 cmy1 in liquid water are well explained by molecular vibration modes of a temporal C2v tetrahedral-like structure around oxygen atom. This interpretation of high frequency spectra is consistent with the interpretation of low-frequency vibrational modes below 250 cmy1 . Moreover, the high frequency tail of the above Cole–Cole type relaxation mode could explain the broad background spectra in liquid water. q 1998 Elsevier Science B.V. Keywords: Raman spectroscopy; Dynamical structure; Tetrahedral-like structure; Relaxation mode; GF matrix method

1. Introduction There have been many investigations on liquid water by various spectroscopic experiments w1x. The most impressive result of them was carried out by X-ray diffraction study w2x. The result indicates that in liquid water the average numbers of nearest neighbor oxygen atoms were 4.4 for each oxygen atom. This means that the average structure of water can be considered as a tetrahedrally coordinated pentamer which is formed by about water molecules through the hydrogen bonds. It must be noted that the dynamical structure of liquid water is also important as well as the static average structure, because the hydrogen bonds between water molecules are not permanent and the

)

Corresponding author.

0378-3812r98r$19.00 q 1998 Elsevier Science B.V. All rights reserved. PII S 0 3 7 8 - 3 8 1 2 Ž 9 7 . 0 0 2 7 6 - 8

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Y. Tominaga et al.r Fluid Phase Equilibria 144 (1998) 323–330

hydrogen bonds are continuously created and destroyed. The details of dynamical structure of liquid water are not still fully understood. Raman spectroscopy has been usually employed to investigate the dynamical structure of water for a long time. In the high-frequency spectral region above 1600 cmy1, internal molecular vibration spectra are measured and these spectra are analyzed and discussed by many researchers w3–10x. On the other hand in the low-frequency region intermolecular vibration bands which are due to the interaction between water molecules through the hydrogen-bonds are observed w7,11–25x. In this low frequency region, there appears a stretching-like band around 190 cmy1 and a bending-like band around 70 cmy1 among water molecules based on a five-molecule cluster model w7,21x. Recently it has been found that besides the above two broad vibrational bands one relaxation mode appears as a central component below 50 cmy1 w11,18–22,25x. This relaxation mode is due to the creation and annihilation process of hydrogen bond among water clusters. Besides these spectra in liquid water there has been a broad background spectrum extended to 4000 cmy1 which is called ‘collision-induced Raman scattering’ w15x. This background spectrum, however, has not yet been fully clarified. In this paper based on a temporal tetrahedral-like structure of five water molecules we propose a consistent interpretation of both high-frequency Raman spectra and low-frequency Raman spectra.

2. Experimental Raman scattering spectra were obtained by a double-grating spectrometer Ž Jobin–Yvon U-1000. . The exciting light source was a NEC Ar-ion laser operating at 488 nm with a power from 100 to 300 mW. A right-angle-scattering geometry is always adopted in the present light-scattering experiments. The depolarized ŽVH. Raman spectra were measured with the configurations of X ŽVH. Y and the polarized ŽVV. Raman spectra were measured with the configuration of X ŽVV. Y, where the XY plane is horizontal and X denotes the direction of incident light and Y denotes the direction of scattered light. The typical spectral resolution was 2.0 cmy1 for the low-frequency region below 250 cmy1 and 4.0 cmy1 for the high frequency region up to 4000 cmy1. The samples of liquid water were natural H 2 O which was deionized and distilled, 99.9% D 2 O, and H 18 2 O which was purchased from Isotec, Japan. All the samples were further purified by removing dust particles through 0.2 mm Millipore filter.

3. Results and discussions Fig. 1 shows a typical high frequency Raman spectral pattern of distilled water at 294 K. This characterizes internal molecular vibrations above 1600 cmy1. Each polarized ŽVV. spectrum and depolarized ŽVH. spectrum is calibrated by the spectrometer efficiency through a florescence of quinine w26x. The spectral pattern above 1600 cmy1 has a characteristic of tetrahedral-like symmetry of C2v , although the spectral line shapes are very broad. From this view point between 1600 cmy1 and 4000 cmy1 we can assign four broad bands which include nine lines. These four groups can be assigned from lower frequency side, as ŽA1, B1., ŽA2, B2, A1. , Ž A1. , and Ž B2, A1, B1. . It is noticeable that the ŽA1. mode of 3193 cmy1 in the polarized ŽVV. spectrum drastically disappears in

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Fig. 1. High-frequency Raman spectra of distilled water at 294 K. Large dots are VV spectrum and small dots are VH spectrum. These spectral intensities are calibrated by the spectrometer efficiency through a florescence of quinine. The bars between 1600 cmy1 and 4000 cmy1 are the calculated frequencies by the GF-matrix method in C2v symmetry of a tetrahedral-like structure.

the ŽVH. depolarized spectrum. Therefore this Ž A1. mode is considered as a totally symmetric mode in the tetrahedral-like structure. The bars are the calculated frequencies using by GF-matrix method w27x in C2v symmetry of the tetrahedral-like structure of 2H- - -O 2H, where - - - represents two hydrogen bonds and represents two covalent bonds between oxygen and hydrogens. This configuration around oxygen atom is consistent with the temporal tetrahedral-like structure of five water molecules mentioned above. If we consider molecular vibrations of only one H 2 O molecule, there must exist only three normal vibrations in this frequency region and thus the broad band at 2200 cmy1 cannot be explained. However, the molecular vibrations in the above temporal tetrahedral-like structure naturally explain the whole spectral pattern above 1600 cmy1. To clarify the spectral profile in the low-frequency region below 250 cmy1, we reduced the Raman spectral intensity I Ž n . into the imaginary part of the complex dynamical susceptibility x Ž n . w25x. The x Y Ž n . is given by

x Y Žn . s K Žni y n .

y4

nŽ n . q 1

y1

IŽn .

Ž1.

here nŽ n . q 1 is Bose–Einstein thermal factor with nŽ n . s wexpŽ hcnrkT . y 1xy1. The n is the Raman frequency shift in cmy1, and the n i is the frequency of incident laser light represented by cmy1, and K is an instrumental constant. Fig. 2 shows the depolarized low-frequency reduced Raman spectrum x Y Ž n . of distilled water at 294 K from y50 cmy1 to 250 cmy1 , which is obtained by the Eq. Ž1.. Since the reduced spectrum x Y Ž n . clearly shows the low-frequency Raman modes, we introduced a simple model to analyze the spectral profile of x Y Ž n . for obtaining the quantitative information.

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Fig. 2. Low-frequency reduced spectrum x Y Ž n . of water at 294 K obtained by depolarized Raman spectrum using the Eq. Ž1.. Dots are measured data and solid line is a best fitted curve described in the text. Dotted lines are the components of one Cole–Cole relaxation mode and two damped oscillator modes, a bending mode and a stretching mode.

The model is composed of two damped harmonic oscillator modes and one Cole–Cole type relaxation mode. The formula of Cole–Cole type relaxation is represented as:

x Žv.s

1 1 q Ž i vt .

Ž2.

b

where v s 2p cn and t s 1rŽ2p cg 1 .. The v is an angular frequency, t is the relaxation time, and the parameter b Ž0 - b F 1. represents the distribution of relaxation times. For b s 1, the Eq. Ž 2. reduces to Debye type relaxation mode, and the g 1 corresponds to the spectral half width of the relaxation mode which is expressed by cmy1. The imaginary part of the susceptibility of the damped harmonic oscillator modes is:

v j2g j v

Y n

x Ž v j ,g j , v .

žv

2 j y

2

v 2 / q Ž vg j .

2

Ž3.

where v j s 2p cn j Ž j s 2,3. Ž j s 2,3. and g j s 2p cg j Ž j s 2,3. are the characteristic frequencies and damping constants, respectively. The n j and g j are the characteristic frequencies and damping constants in cmy1 unit. Therefore, the imaginary part of the total susceptibility is represented as:

x Y Ž n . s A1 xrY Ž g 1 , b ;n . q A 2 xnY Ž n 2 , g 2 ;n . q A 3 xnY Ž n 3 , g 3 ;n .

Ž4.

where A1, A 2 and A 3 are the strength of each mode. Using the Eqs. Ž 1. and Ž 4. , the reduced spectrum x Y Ž n . was fitted by a nonlinear least squares method. We fitted each "250 cmy1 spectrum and "50 cmy1 spectrum separately and adjusted all the parameters consistently. The solid curves in

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Table 1 Best fit parameters of liquid water at 295 K g1

H 2 O Žcmy1 .

Ž y1 . H 18 2 O cm

D 2 O Žcmy1 .

8.3 69.3 194.1

7.4 64.8 184.9

6.5 64.4 194.7

The n 3 mode frequency of H 2 O and D 2 O are almost the same and the n 2 mode frequency of H 18 2 O and D 2 O are almost the same and that of H 2 O is higher than the others.

Fig. 2 are the best fitting curves. In Fig. 2, the spectral components of one relaxation mode and two damped oscillator modes are also shown by dotted curves. From the nonlinear least squares fitting method we can extract physical parameters which could describe the dynamic structure of water. Table 1 shows the three important fitting parameters of Ž .y1 is the spectral line width of the isotopic waters H 2 O, H 18 2 O and D 2 O at 295 K. The g 1 s 2 p ct central component which corresponds to the inverse relaxation time of the Cole–Cole relaxation mode. The n 2 and n 3 are the characteristic frequencies of two damped harmonic oscillators. On the basis of the temporal distorted tetrahedral-like structure of five water molecules the n 3 mode corresponds to the stretching mode of the tetrahedron and the n 2 mode corresponds to the bending mode among at least three water molecules w7x. From the Table 1 it is remarkable that in the n 3 mode only oxygen atoms vibrate, because the frequency of H 2 O and D 2 O are almost the same and that of H 18 2 O is lower than the others. On the other hand in the n 3 mode the whole water molecule vibrates, because the frequency of H 18 2 O and D 2 O are almost the same and that of H 2 O is higher than the

Fig. 3. Reduced Raman spectrum of depolarized ŽVH. spectral intensity of distilled water at 294 K with log–log representation. The dots are the measured data which is overlapped with a high-frequency spectrum and a low-frequency spectrum. Upper solid curve is the extrapolation of the fitting curve of the low-frequency spectrum described in the text. Lower solid curve is the fitting component of the Cole–Cole relaxation mode. It is noticeable that the background spectrum of water can be explained by the high frequency tail of the Cole–Cole relaxation mode.

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others. This vibration pattern is consistent with the result of the incoherent inelastic neutron scattering experiment which can selectively observe the motion of hydrogen atoms w27x. Fig. 3 shows the Ž VH. reduced Raman spectral intensity of distilled water at 294 K with log–log representation. The dots are the measured data which are overlapped with a high-frequency spectrum and a low-frequency spectrum. The log–log representation exaggerates the low-frequency region and clarifies the background spectrum. The upper solid curve and the lower solid curve are the extrapolation of the fitting curve of the low-frequency spectrum and the Cole–Cole relaxation component as shown in Fig. 2, respectively. It is remarkable that the high-frequency tail of the Cole–Cole relaxation mode could explain the background spectrum extended to 4000 cmy1. This is an important suggestion of the origin of so called collision-induced background in liquid water. Fig. 4 shows the reduced Raman spectral intensity x Y Ž n . in the O–H stretching region. The ISOTROPIC spectrum is obtained by the standard equation ISOTROPICs VV y 4r3)VH. The isotropic spectrum includes essentially the polarized modes. From the isotropic spectrum in Fig. 3 we can see at least two polarized modes in this frequency region. The highest mode of 3627 cmy1 has been assigned as a free O–H vibration. We also adopt this conventional assignment in this paper. Other four modes A1, B2, A1, and B1 are obtained by the GF matrix method in the C2v tetrahedral-like structure around oxygen atom. This temporal structure is made by two covalent bonds among the oxygen and two hydrogens, and two hydrogen bonds among the same oxygen and another two hydrogens. Solid curves are the results of a nonlinear least squares fitting where the starting frequencies are set to the frequencies obtained by the GF calculation. The fitting frequencies and damping constants are shown in Table 2. From Table 2 we can see that the calculated frequencies by GF matrix method in C2v tetrahedron agree well with the results by the

Fig. 4. Reduced Raman spectral intensity x Y Ž n . in the O–H stretching region. The ISOTROPIC spectrum is obtained by the standard equation ISOTROPIC sVVy4r3)VH. The isotropic spectrum includes essentially the polarized modes. The bars are the calculated frequencies by GF matrix method in C2v tetrahedron. Dots are the measured data and solid curves are the results of a nonlinear least squares fitting where the starting frequencies are set to the frequencies obtained by the GF calculation. Free_OH is the stretching vibration mode of a free H 2 O molecule.

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Table 2 Characteristic frequencies and damping constants in O–H vibration region in liquid water GF Žcmy1 . freq.

ŽVV. Žcmy1 . freq.rdamp.

ŽVH. Žcmy1 . freq.rdamp.

ŽISO. Žcmy1 . freq.rdamp.

A1 B2 A1 B1 OH

3193 3283 3421 3464 3627

3320r236 3221r65 3196r89 3450r130 3627r48

3320r232 3221r167 3196r76 3450r167 3627r31

Mode names A1, B2, A1, B1, and OH correspond to Fig. 3. In ŽVV., ŽVH., and ŽISO. spectra ‘xxxxryyy’ means ‘frequencyrdamping constant’, respectively.

fitting analysis. This means the reduced Raman spectra in the O–H vibration region of liquid water are well explained by a temporal tetrahedron around oxygen atom, not a single H 2 O molecule and some coupling effects.

4. Concluding remarks In this paper, we have proposed a new interpretation of Raman spectra in liquid water. Both high-frequency regions above 1600 cmy1 and low-frequency region below 250 cmy1 are consistently explained by the temporal tetrahedral-like structure of five water molecules. Ž1. In the high-frequency region, we can assign the spectral pattern as normal vibrations of a part of the temporal tetrahedral-like pentamer. The vibration unit is composed by two covalent bonded hydrogen atoms and two hydrogen bonded hydrogen atoms around one oxygen atom. Since the symmetry of this unit is C2v , we can calculate the mode frequencies by an ordinary GF matrix method. This calculated spectral pattern well explain the high-frequency Ž VV. and Ž VH. spectra. Ž2. In the low-frequency region, we can assign two broad vibration bands as follows; the higher band around 190 cmy1 is a stretching vibration of oxygen in the temporal tetrahedron of five water molecules and the lower band around 70 cmy1 is a bending vibration of the whole water molecule among at least three water molecules. Ž3. In the very low-frequency region below 20 cmy1, we can assign the central component as the Cole–Cole relaxation mode due to the creation and annihilation of hydrogen bond. Ž4. Moreover, the broad background spectra extended to 4000 cmy1 could be well explained by the higher frequency tail of above Cole–Cole relaxation mode associated with the central component. These pictures are all consistent with the temporal tetrahedral-like structure composed by the hydrogen bond in liquid water. Thus, from the Raman spectroscopic point of view, the dynamical structure of water is essentially a distorted temporal tetrahedral-like structure of five water molecules.

Acknowledgements This work is partially supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science, Culture, and Sport. We also thank to Dr. Kohji Mizoguchi of Osaka University for stimulating discussion.

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