J. Phys. Chem. 1902, 86, 4897-4905
ular detection applications, it is unfortunate that sharp Rydberg structure was not observed. In future experiments we intend to extend the search for Rydberg states to lower enerm, usinn a third fixed-waveleneth ionizinn beam. However, recent calculations by Biriez3for poc (23) R. Birge, private communication, 1981.
4097
yacenes suggest that, in general, resonance-enhanced transitions, involving valence-Rydberg dipole matrix elements, are exceedingly weak for extended molecular systems.
Acknowledgment. This work was supported by the Office of the Environment, Department of Energy, under Contract 79EV10239.000.
Vibrational Spectral Studies of Solutions at Elevated Temperatures and Pressures. 5. Raman Studies of Liquid Water up to 300 O C C. I. Ratcllffe and D. E. Irlsh' Gueiph-Waterloo Centre for Greduate Work In Chemlstty, Waterloo Campus, Depanment of Chemlstty, Unlverslty of Waterloo, Waterloo, Ontario, Canada N2L 3Gl (Received: May 4, 1982; In Flnal Form: July 14, 1982)
The Raman spectra of the stretching-mode regions of liquid H20, DzO, and HDO in a 10% solution with H20 or DzO, and the bending-mode regions of H2O and D20, have been obtained in the temperature range 4-300 "C. The results have been interpreted in detail in terms of a continuum-typemodel, the distribution of oscillator pairs, and considerationsof a high-frequency band edge, but it is not proposed that a mixture model is untenable. Increasing temperature reduces the complexity of the stretching-mode spectra of HzO and D20; the main distribution of intensity narrows and shifts to higher frequency, overlap with the overtone of the bending mode is reduced, and intermolecular coupling decreases. All the changes appear to reflect a steady decrease in the strength of the intermolecular hydrogen-bonding interactions. For D20 at high temperatures a resolution of the symmetric and asymmetric stretching modes (vl and VQ) is observed for the fist time in the Raman spectrum. The bending mode v2 does not shift with increasing temperature, but the combination band of the bending mode with a librational mode (v2 + v ~ shows ) a dramatic reduction in frequency.
Introduction We recently described a new apparatus' designed to allow observation of Raman spectra of electrolyte solutions at elevated temperatures and pressures where, among other different properties, the drastically reduced dielectric constant of water might be expected to enhance ion association. The spectroscopy of liquid water itself at high temperatures is an important starting point in the study of such systems, yet apart from the excellent work of Lindner and Franck2%there is no other report of Raman spectra above 100 "C. Hence, although we originally intended obtaining spectra of water at several temperatures merely for purposes of comparison with solution spectra, we felt that the quality of the new spectra and the lack of information warranted a more extended study. The available literature on water is extensive, and for this reason only those works with immediate relevance wilI be referred to. The standard and ongoing collection of work on water is the series edited by Franks,* but the recent review by Scherer on the vibrational spectroscopy of water: which includes an extensive bibliography, is the most relevant in the current context. Studies of the temperature variation of the IR and Raman spectra of water have generally been confined to the region below 100 "C (1) D. E. Irish, T.Jarv, and C. I. Ratcliffe, Appl. Spectrosc., 36, 137 (1982). (2) H. A. Lindner, Ph.D. Thesis, University of Karlsruhe, Karlsruhe, West Germany, 1970. (3) E. U. Franck in 'Structure of Water and Aqueous Solutions", W. A. P. Luck, Ed., Verlag Chemie, Weinheim, West Germany, 1974, p 49. (4) F. Franks, Ed., 'Water: A Comprehensive Treatise", Vols. 1-7, Plenum Press, New York, 1970-82. (5) J. R. Scherer in "Advancesin Infrared and Raman Spectroscopy", Vol. 5, R. J. H. Clark and R. E. Heater, Eds., Heyden, London, 1978, Chapter 3, p 149. 0022-3654/82/2086-4897$01.25/0
(ref 6 and 7 to mention recent examples), with the following exceptions: (1)In the early work of Saumagne and Josien8v9IR spectra of HzO were obtained up to 374 "C; (2) Falk and Fordlo have studied HDO up to 130 "C in the IR; (3) Franck and Roth" have studied the IR of the 0-D stretching mode of HDO up to 400 "C and 400 MPa; (4) Bondarenko and Gorbatyi12 studied the IR of the 0-H stretching mode of HDO up to 550 "C and 450 MPa; (5) Luck and DitterI3 have studied the IR 0-H stretching overtone region of HDO up to the critical point under saturation conditions; and (6) Franck and Linder,2,3as mentioned above, have studied the Raman spectra of the stretching regions of 0-H in H 2 0 and 0-D in HDO up to 400 "C and 400 MPa. Controversy has raged over the type of molecular model to be adopted for liquid water. The two extremes may be classed broadly (1)mixture, involving two or more kinds of water, or intact and broken hydrogen bonds, in equilibrium, and (2) continuum, involving a continuous distribution of intermolecular interactions; some viewpoints fall between these two. In the area of spectroscopy, for instance, and in particular Walrafen,lGwho did (6) L. W. Pinkley, P. P. Sethna, and D. Williams, J. Opt. SOC. Am., 67, 494 (1977). (7) J. R. Scherer, M. K. Go, and S. Kint, J. Phvs. Chem., 78, 1304 (1974). (8) P. Saumagne and M. L. Josien, Bull. SOC.Chim. Fr., 813 (1958). (9) M. L. Josien, Discuss. Faraday Soc., 43, 142 (1967). (10) M. Falk and T.A. Ford, Can. J. Chem., 44, 1699 (1966). (11) E. U. Franck and K. Roth, Discuss. Faraday SOC.,43,108 (1967). (12) G. V. Bondarenko and Yu. E. Gorbatyi, Dokl. Akad. Nauk SSSR, 210, 132 (1974). (13) W. A. P. Luck and W. Ditter, 2.Naturforsch. B , 24,482 (1969). (14) W. A. P. Luck in 'Structure of Water and Aqueous Solutions", W. A. P. Luck, Ed., Verlag Chemie, Weinheim, West Germany, 1974, p 221.
0 1982 American Chemical Society
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a large number of Raman studies on water, and Murphy and Bernsteinl’ have argued the case for a mixture model, whereas Schiffer and Hornig,18 Falk et al.,’o~’*2’ and Carnutte et al.22g23 have argued for a continuum. Scherer’s model5,’ is intermediate, arguing distributions for different types of water molecules. Efimov and N a b e r ~ k h i nhave ~~ met with reasonable success in simulating the infrared and Raman spectra of H 2 0 and D20, based on the spectra of HDO and assuming a continuum model. As yet there clearly is no consensus, since no evidence has been sufficient to prove entirely any particular model, and frequently spectroscopic evidence which has been interpreted by some as favoring one model or excluding another has been shown by others to have a conflicting interpretation. However, as Scherer has taken pains to point there is a great deal of information which can be extracted from the spectra. We would also draw attention to some results from an entirely different technique; in a recent report Vernon et al.25have shown vibrational predissociation spectra (crossed laser and molecular beams) of hydrogenbonded clusters of three to six water molecules. These spectra show a sharp band at 3715 cm-l, which is attributed to “free” OH oscillators, and which decreases rapidly in intensity as the cluster size increases (as might be expected). What is perhaps of most interest, however, is that even for such small clusters there is also a very broad distribution of intensity in the range 3100-3600 cm-’, which could arise from a broad range of hydrogen-bonding interactions. Theoretical calculations simulating water at various temperatures (reviewed recently26) are also of great importance, particularly the molecular dynamics calculations of Stillinger et al.,27728Wood et a1.,26Impey et and Jorgen~en.~~ These ? ~ ’ calculations have not provided evidence to support “two-state” or “iceberg” type models, and the water pair interaction distribution is found to be continuous over the energy range considered.28 The calculations also show that, as the temperature increases, the distribution of pair interaction energies shifts toward weaker interactions. There is still, however, an element of ambiguity in the way these results may be interpreted; in particular, the use of the terms “broken hydrogen bond” and “intact hydrogen bond” is dependent on an arbitrary fixing of an energy division. This can produce quite different pictures of the “structure” de(15)W. A. P. Luck, Angew. Chem., Int. Ed. Engl., 19, 28 (1980). (16)G. E. Walrafen in “Structure of Water and Aqueous Solutions“, W. A. P. Luck, Ed., Verlag Chemie, Weinheim, West Germany, 1974,p 301,and many references cited therein. (17)W. F. Murphy and H. J. Bernstein, J . Phys. Chem., 76, 1147 (1972). (18)J. Shiffer and D. F. Hornig, J. Chem. Phys., 49,4150 (1968). (19)T. A. Ford and M. Falk, Can. J . Chem., 46,3579 (1968). (20)H. R.Wyss and M. Falk, Can. J. Chem., 48,607 (1970). (21) M.Falk in ‘Chemistry and Physics of Aqueous Gas Solutions”, W. A. Adams, G. Greer, J. E. Desnoyers, G. Atkinson, G. S. Kell, K. B. Oldham, and J. Walkley, Eds., Electrochemical Society, Princeton, NJ, 1975,p 19. (22)B. Curnutte and J. Bandekar, J. Mol. Spectrosc., 41,500(1972); 49.314 (1974). ’(23)J. B.Bryan and B. Curnutte, J. Mol. Spectrosc., 41,512 (1972). (24)Y.Y.Efimov and Y. I. Naberukhin, Mol. Phys., 36,973 (1978). (25)M. F. Vernon, D. J. Krajnovich, H. S. Kwok, J. M. Lisy, Y. R. Shen, and Y. T. Lee, J . Chem. Phys., 77,47 (1982). (26)D.W. Wood in “Water: A Comprehensive Treatise”, Vol. 6,F. Franks, Ed., Plenum Press, New York, 1979,p 279. (27)F. H. Stillinger, Science, 209, 451 (1980),and references cited therein. (28) F. H. Stillinger and A. Rahman, J. Chem. Phys., 60,1545(1974). (29)R.W. Impey, M. L. Klein, and I. R. McDonald, J . Chem. Phys., 74,647 (1981). (30)W. L. Jorgensen, J. A m . Chem. SOC.,101,2016 (1979). (31)W. L.Jorgensen, Chem. Phys. Lett., 70,326 (1980).
Ratcliffe and Irish pending on where this broken-intact boundary is taken. When it comes down to fundamentals, this is also the basic distinction between some mixture models and continuum models, in that the latter do not introduce a boundary in the first place. One might even suggest that the two approaches are saying essentially similar things, except for this one distinction. Recently a “correlated site polychromatic percolation” model has been developed by Stanley and T e i ~ e r aand ~ ~a random network model by Rice and though these are both essentially continuum approaches. A number of properties of water, other than its spectra, have also been studied at high t e m p e r a t ~ r e . ~ Of? partic~ ular interest here is the X-ray work of Narten et al.% The radial distribution functions show that the nearest-neighbor (0-0) distance increases from 2.82 A, at 4 “C and atmospheric pressure, to 2.94 A, at 200 “C and the vapor pressure of the sample. The radial distribution functions also show that peaks due to second and higher neighbors at 4.5 and 8 A, clearly visible at 4 “C, slowly disappear as the temperature increases. This indicates a decrease in between the distance of short-range order from =8 to ;.7 4 and 200 “C.
Experimental Section Raman spectra were obtained by using a digitally driven Jarrell-Ash 25-100 spectrometer (1-m double CzernyTurner monochromator), with an RCA 3134 photomultiplier and an SSR Model 1105/1120 photon counting system. The 4880- and 5145-A lines of a Spectra Physics argon ion laser, Model 165-03, were used for excitation. Instrument control and data collection were performed by means of a 32K byte PET Commodore computer, which has recently been interfaced to the spectrometer. The samples used were H20 distilled in glass stills and 99.7% D20 courtesy of A.E.C.L. All samples were filtered through 0.6-pm Millipore filters before injection into the capillary sample tubes. To obtain spectra at 4 and 25 “C samples were contained in sealed, thin-walled capillary tubes which were held in a thermostated copper block. The thick-walled, Pyrex glass capillary cells, the highpressure system, and the furnace, used to obtain spectra at high temperatures, have been described earlier.’ For temperatures up to 250 “C a hydrostatic pressure of 6-8 MPa (and sometimes higher) was applied and for 300 “C 10-11.5 MPa was applied. These pressures are sufficient to maintain the liquid state.35 It is not possible with this equipment to maintain a constant density as the temperature increases. Lindner, for instance, used a pressure of 400 MPa to maintain a density of 0.9 g cm-3 at 400 0C.2 An attempt to take water to 350 “C at 18 MPa resulted in attack of the Pyrex as described earlier’ although it was possible to obtain what appeared to be a good spectrum during the first 0.5 h at this temperature. There was evidence for very slight attack of the Pyrex even at 250 “C, in that the weak spectrum of silica caused by scattering from the tube sides showed some increase in intensity after sustained periods of high temperature. This increased intensity was not lost on recooling. The strongest band of silica occurs at =440 ~ m - ’ . ~ ~ Spectra of the 0-H and 0-D stretching regions were measured under parallel (11) and perpendicular (I) po(32)H.E. Stanley and J. Teixera, J . Chem. Phys., 73,3404 (1980). (33)S. A. Rice and M. G. Sceata, J. Phys. Chem., 85, 1108 (1981). (34)A. H.Narten, M. D. Danford, and H. A. Levy, Discuss. Faraday Soc., 43,97 (1967). (35)U. K. Committee on the Properties of Steam, ‘U.K. Steam Tables in S.I. Units”, Arnold, London, 1970. (36)R. H. Stolen and G. E. Walrafen, J. Chem. Phys., 64,2623(1976).
Raman Studies of Liquid Water up to 300
The Journal of Physical Chemistry, Vol. 86, No. 25, 1982
OC
indicated that some properties of the Raman spectra, such as the polarizability derivative and the ratio of mean bond polarizability to anisotropy derivatives, do vary with hydrogen-bond strength. (5) Inasmuch as one trusts molecular selection rules when applied to the liquid state, there can be two types of water symmetry: C2",where there are two equivalent OH (or OD) groups, or C, for all other cases. The three modes of vibration are
larizations, to permit calculation of the depolarization ratios and the isotropic and anisotropic components of the s p e ~ t r a , ~given ' by Iiso
= I,,- 411/3
= 41, / 3 For the spectra of HDO in H 2 0 , however, it is necessary to subtract a background spectrum of H 2 0 or DzO before these calculations can be performed. This was attempted but the final results were not very satisfactory (as compared with Scherer's results), and consequently we prefer to show the untreated parallel and perpendicular spectra. It is always a problem in Raman spectroscopy to obtain good relative intensities between spectra, and in the present case the problems are compounded by the large changes in temperature, which cause changes in the glass components of the assembly and changes in the density and optical properties of the sample itself. Nor is it feasible to add an intensity standard such as ClO,, which is frequently used at room temperature in studies of other electrolytes in solution, since (a) the water would no longer be pure and (b) the intensity changes of the standard with temperature would also have to be known. Consequently, we have discussed most of our results without reference to relative intensity changes with temperature, and the different spectra shown in Figures 1-3 and 6 do not have common intensity scales. The effect of decreasing density can be taken into account, however; thus, notwithstanding the other problems mentioned above, we have attempted to obtain some idea of the relative intensity behavior of HzO and HDO in HzO, in two experiments where all the conditions were carefully maintained constant as temperature was varied. After a complete series of spectra up to 300 "C had been obtained, spectra were repeated at several temperatures and the reproducibility was found to be excellent. Ianiso
Results and Discussion There are a number of relevant features of water, its vibrational spectrum, and the effect of temperature which can be emphasized without making reference to any particular model: (1) Hydrogen-bonding interactions in liquid water are very important and, together with the geometry of the molecules, these induce a tetrahedral ordering (as in ice). (2) As the temperature increases, translational and hindered rotational motions will increase in amplitude, and, since the hydrogen-bonding interactions have both distance and angular dependence, the effect will be to reduce, on average, the strength and ordering effects of these interactions. (3) Correlations between the O-H.--O distance and the 0-H stretching frequency uOH in HDO in crystals are w e l l - k n o ~ n . ~ As , ~ ~the > ~distance ~ increases, and the interaction weakens, the frequencies approach asymptotically their gas-phase values of 3707 (OH) or 2727 (OD) cm-le5 (4) An inverse linear correlation between band intensity and frequency of uOH has been found from IR spectraa (Le., intensity increases with increasing strength of interaction). It is not yet known whether Raman spectra show any kind of intensity-frequency relationship although Scherer5 has (37)J. R. Scherer, S. Kint, and G. F. Bailey, J.Mol. Spectrosc., 39, 146 (1971). (38)A. Novak in "Structure and Bonding", Vol. 18,J. D. Dunitz, P. Hemmerich, R. H.Holm, J. A. Ibers, C. K. Jsrgensen, J. B. Neilands, D. Reinen, and R. J. P. Williams, Ed., Springer-Verlag, Berlin, 1974,p 177. (39)M.Falk and 0. Knop in "Water: A Comprehensive Treatise", Vol. 2, F. Franks, Ed., Plenum Press, New York, 1972,Chapter 4. (40)D. N. Glew and N. S. Rath, Can. J. Chem., 49, 837 (1971).
4899
,
uI
symmetric stretch
u 2 bending
u 3 asymmetric stretch
CZ"
c,
AI A,
A' A' A'
B,
Note that u1 and u2 belong to the totally symmetric species no matter which point group applies, whereas u3 does not when the symmetry is C2u.In terms of the Raman spectra this means that any molecules which have equivalent OH groups should cause an increase in the depolarization ratio in the region of u3 and make a contribution to the anisotropic spectrum which has no equivalent in the isotropic spectrum. This can be extended to molecules with almost similar groups, since, although u3 should be polarized (A'), it may have a depolarization ratio only slightly less than 3/4 in such cases. (6) In H 2 0 and DzO the overtone of the bending mode falls in the stretching-mode region and thus may complicate the spectrum, because of the possibility of Fermi resonance. (7) Intramolecular coupling of the two 0-H stretching vibrations is quite significant for symmetric, or nearly symmetric, molecules. As a consequence u1 and u3 are well separated; in the gas u1 and u3 have values of 3656.7, 3755.8 (H20), and 2671.5, 2788.1 (D20) cm-'. (8) Anharmonicity constants for H 2 0 and DzO in the vapor phase and in various c ~ m p l e x e s ~suggest l - ~ ~ that strong asymmetry in the molecule decouples the two stretching modes. HDO is strongly decoupled, although not totally so since uOD has a slightly lower depolarization ratio than uOH. (9) Intermolecular coupling is significant in HzO and D20, at least at low temperatures, but for dilute solutions of HDO in HzO or D 2 0 this complication is removed for the dilute OD or OH oscillators, respectively. This will be discussed, in context, later. Spectra of HDO in the Stretching-Mode Region. We will concentrate first on the spectra of the dilute OH or OD oscillators of HDO in D 2 0 since these are not complicated by overlap with 2u2 or inter- and intramolecular couplings. It is immediately obvious from Figure 1 that the behavior of the OH and OD bands is similar although the OD bands are somewhat narrower. We note also that the Ill OD spectra are essentially identical with those obtained by LindnerP2who also demonstrated that the effect of decreasing density at high temperature is a gradual and slight shift of the peak maximum to higher frequency. At 300 "C in the present work the density of water has dropped to about 0.718 g ~ m - ~ . At the lower temperatures the Ill spectra show a pronounced high-frequency shoulder, which increases in intensity, relative to the rest of the band, as the temperature increases. Recently recorded Raman spectra of the OD oscillator of HDO in H 2 0 in the supercooled liquid@show ~
~
~
~
(41)W. S. Benedict, N. Gailar, and E. K. Plyler, J. Chem. Phys., 24, 1139 (1956). (42)N. M.Gailar and F. P. Dickey, J . Mol. Spectrosc., 4, 1 (1960). (43)A. Burneau and J. Corset, J. Chim. Phys. Phys.-Chim. Biol., 69, 171 (1972).
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The Journal of Physical Chemistry, Vol. 86, No. 25, 1982
-CD
HDO
r------r-----
'
-OF
H2G
020
v 7 -
I I
\
4c
I
/
I
\
lS0C
'
I
200c
1 200c
250C
CV-
:
/
ZM-:
Flgure 1. Parallel and perpendicular Raman spectra (upper and lower traces, respectively) of the 0-D and 0-H stretching modes of 10% HDO in H,O and D,O, respectively, as a function of temperature (slit width, 15 cm-'; step interval, 5 cm-I).
that this trend commences from temperatures as low as -20 "C. This shoulder has played a key role in the mixture-continuum controversy, since it could be inferred that the band envelope comprises two overlapping bands representing two distinct species in equilibrium.16 This is not, however, sufficient reason for discarding the continuum approach. Wyss and Falkms2lhave presented a mechanism for the development of such a high-frequency shoulder in the continuum picture, which has not been given the prominence that it perhaps deserves, and which could be developed further. In general, as the hydrogen-bond strength decreases, the 0-H or 0-D stretching frequency increases and approaches asymptotically the gas-phase frequency (see feature 3 earlier), where the interaction is effectively zero. In liquid water there must always be interaction since the molecules are densely packed. Hence, while one would still expect an upper frequency limit, this should be at a lower frequency than that for the gas phase. In the continuum picture where there is a continuous distribution of interaction energies this leads, in terms of oscillator frequencies, to a band edge, because the density of states at the frequency limit must be high. As the temperature increases, the distribution shifts to higher frequencies and the population of states with energies close to the band edge must obviously grow. The spectra of Figure 1 are clearly compatible with this viewpoint. We see a distribution shifting with temperature but never going above some high frequency limit. To obtain a consistent measure of the position of the band edge, we took the position of greatest slope on the edge (roughly half way
L-dLA-
2000
CM-1
3000
2500
3500
CM- 1
Flgure 2. Isotropic and anisotropic Raman spectra (upper and lower traces, respectively) of the stretching-mode regions of D,O and H,O as a function of temperature (slit wldth, 9 cm-I; step interval, 5 cm-I).
down). This was determined from a nine-point leastsquares quadratic first-derivative spectrum (method of Savitsky and G01ay~~). The four values are remarkably similar over the range 25-300 O C ; there is a small shift to higher frequency which can be attributed to the fall of density as temperature is increased: 3657-3664 (OH) and 2678-2685 (OD) cm-'. This high-frequency shoulder, or band edge, is also seen in the IR overtone region, but not in the IR fundamental region where its presence is thought to be obscured by the dependence of intensity on hydrogen-bond strength mentioned earlier. It should also be noted that the shoulder is not apparent in the I, (or anisotropic) Raman spectra, which consist of relatively symmetric bands with maxima at lower frequencies than the shoulder. This also implies that the depolarization ratios, which are quite low all across the band, should dip slightly at the position of the ~ shoulder/band edge, as observed by S ~ h e r e r .Although we did not obtain depolarization ratios of similar quality (due to subtraction problems), this dip was confirmed; the current work also indicates that the dip in the ratio falls to lower values as the temperature increases. Spectra of HzO and DZO in the Stretching-Mode Region. In H20and DzO the coupling of the oscillators produces some distinct changes in the stretching-mode regions of the spectra. Their two sets of spectra (Figure 2) are again essentially identical in appearance, but for D20
(44) R. Bansil, J. Wiafe-Akenten,and J. L. Taaffe, J. Chem. Phys., 76, 2221 (1982).
(45) A. Savitsky and M. J. E. Golay, Anal. Chem., 36, 1627 (1964).
The Journal of Physical Chemistry, Vol. 86,
'C
Raman Studies of Liquid Water up to 300
I
2000
3
2500
I
2780
CM- 1
No. 25,
1982 4901
h
3180
3580
CM- 1
3908
,
Flgure 3. Superimposed spectra as a function of temperature of the stretching-mode regions of H,O and D,O: (top) total Raman spectrum ( I iI I); (middle) isotropic; (bottom) anisotropic. All the spectra are plotted on scales so as to effect the rough normalizationon peak displayed in the top figures: this is merely a convenient form of presentation. The dashed lines indicate the calculated position of 2v,; (A) 4, (B) 5O,-(C) 100, (D) 150, (E) 200, (F) 250, and (G) 300 OC.
the bands are narrower and the features more pronounced because of this. The spectra of HzO are again essentially in agreement with those of Lindner.2 The most striking changes seen as the temperature increases are (1) a rapidly decreasing intensity in the low-frequency region and (2) a steady increase in the frequency, and a decrease in the width of the central region as intensity builds (relative to the rest of the spectrum) toward the high-frequency end. This latter behavior is superficially similar to the HDO spectra. We believe our results strengthen the arguments that the presence of 2vz (bending-mode overtone) and its Fermi resonance with the stretching modes are responsible for the low-frequency feature at =3230-3260 cm-I in H20and ~2375-2400cm-' in D20 in the range 4-300 "C (see dashed line, Figure 3). It very definitely does not have a counterpart in the HDO spectra, at any temperature, and hence cannot be regarded as representative of a particular "state" of water as recently suggested.G The frequency of v2 itself does not change significantly with temperature (described later) and from this value and a correction for anharmonicit9 the expected position of 2v2 can be calculated at 3240 (HzO) and 2386 (D20) cm-l, in excellent agreement with the observed feature. It is also worth noting that the frequency of the feature changes very little over the range 4-300 O C as indicated in Figure 3. In supercooled water at -10 "C, it is apparently pushed further down to ~ 3 2 0 0(H20)and =2360 (D20)cm-', but at -24 "C it appears to be at ~ 3 2 2 cm-l.& 0 One can also see from the high-temperature spectra that the width of the feature ~
~
~~
(46) G. D'Arrigo, G . Maisano, F. Mallamace, P. Migliardo, and F. Wanderlingh, J. Chem. Phys., 75, 4264 (1981).
is also compatible with 2v2 since the width of v2 is ~ 1 0 3 (H20) and =66 (DzO) cm-l and the width of 2v2 may be expected to be roughly twice these values. The polarization data are also very informative: The feature only appears in the isotropic spectra, and at low temperatures it lies in a region of very low depolarization ratios (0.1) (Figure 4). The most striking result, however, is the appearance of a very pronounced dip (at 3240 cm-I in H20, 2390 cm-I in D20) in the high-temperature depolarization ratios, which is consistent with the feature being more strongly polarized than the tail of the main spectral band. This also is consistent with 215, because it is a totally symmetric mode. The following interpretation seems plausible: The feature arises from 2u2,which is a totally symmetric mode and hence can interact via Fermi resonance with the totally symmetric stretching modes (vl in all cases and v3 in C, cases). At high temperatures the bulk of the v1 distribution is at a significantly higher frequency than 2v2,the sum of all resonance interactions is not very great, and so the intensity at 2v2 is weakly enhanced. As the temperature decreases, the stretching-mode distribution moves down in frequency and broadens, there is increasing overlap with 2vz, and an increase in the sum of resonance interactions and hence intensity builds at 2vz. At room temperature and below the peaks of the 2v2 and v1 distributions are very close. The whole question of the behavior of two distributions of frequencies in Fermi resonance with each other, and particularly the resulting bandshape, is rather complicated and not well understood. Scherer has attempted to model this problem and tried to relate the result to the case of water.5 There can be little doubt that intramolecular coupling must play a conspicuous role in the spectrum of H 2 0 and
4902
The Journal of Physical Chemistry, Vol. 86, No. 25, 1982
Ratcliffe and Irish
the temperature is expected to cause changes in the magnitude of intermolecular coupling: at low temperatures there exists come degree of ordering of the molecules with respect to each other (as compared to the strict order in the crystal phase) and hence intermolecular coupling of the vibrational modes is strong. The effect of increasing temperature, however, is to transfer more energy into the molecular translations and librations, which weakens the interactions on average, causing a decrease in ordering and hence a decrease in the intermolecular coupling. This kind of effect has been demonstrated for methanol and ethan 0 1 ; ~for ~ instance, ethanol at low temperatures shows a splitting of vOH of =lo0 cm-' but at 400 K the splitting has completely disappeared. Luck et al.55have presented evidence which strongly suggests that an infrared band seen for HDO in D20 in the 6100-cm-' region is due to the combination vOH + vOD where the two oscillators are on neighboring molecules. Furthermore, it is suggested that the two oscillators are hydrogen bonded to each other. The main point of interest here is that, as temperature increases, this band decreases in intensity, suggesting that the strengths of intermolecular interactions are decreasing. Kint and S ~ h e r e have r ~ ~ presented Raman difference spectra of the uncoupled OH and OD oscillators of HDO in H20, which they interpreted as indicative of intermolecular coupling in water in the temperature range -10 to 2e22 22a2 7422 is0z 25E2 322E 70 "C. We can now proceed to discuss the stretching-mode CV- 1 spectra of H20 and D20. It seems reasonable to believe, Figure 4. Depolarizationratios in the stretching-mode regions of H,O from the HDO spectra, that the changes taking place as and D,O as a function of temperature. The spectra were smoothed the temperature increases reflect a continuous process, so before ratioing to improve the clarity at the extremes of the plots. we will chiefly consider the spectra at the two extremes of temperature. Aside from the influence of 2v2 on the D20. Since the angular geometry of the two oscillators is low-frequency end of the spectra, one would expect the fixed under all conditions, the magnitude of intramolecular spectra of H20 and D,O, bearing the effects of coupling, coupling depends mainly on the degree to which the two to derive from exactly the same distribution of oscillator oscillators differ by virtue of intermolecular hydrogen potentials as the simpler HDO spectra. (This idea forms bonding. If identical, the coupling is quite strong (see the basis of the calculations of spectra by Efimov and gas-phase splittings mentioned earlier in feature 7 and the N a b e r ~ k h i n . ~The ~ ) intra- and intermolecular couplings calculations of Burneau and Corset47),but the greater the arise from a distribution of pairs of oscillator potentials, difference between the two, the smaller the coupling (for and consequently there will be a range of different splitinstance in asymmetric complexes5 and the results of tings (ranging from large to small) for all the different pair calculation^^^). combinations. Regardless of the position of the first osFor intermolecular coupling the magnitude again decillator in the distribution of single oscillator potentials, pends on the similarity of the interacting oscillators, but the probability is greatest that it will be paired with an it also depends on their spatial relationship (distance and oscillator at the peak of the distribution. This considerorientation) and the strength of the interaction producing ation has some important implications: the coupling, both of which can obviously vary in the liquid (1) Most pairs will have both oscillators in the region state. These two factors work together, since the greater of the maximum of the distribution of single oscillator the interaction the more likelihood of specific orientations potentials, and hence these will give rise to the main body between the two oscillators. Intermolecular coupling of the spectrum. Since the oscillators will be very similar, manifests itself as a splitting of a mode v into in-phase v+ one expects to see effects due to coupling. and out-of-phase v- components. (It is, in fact, analogous (2) A smaller number of pairs will have one oscillator to correlation splittings in crystals.) It has been clearly in either wing of the distribution while the second is in the seen in the spectra of a l ~ o h o l where s ~ ~ ~intramolecular ~~ region of the maximum of the distribution. Here the coupling does not complicate the issue; for neat alcohol the situation is not so clear but, assuming the two oscillators isotropic Raman spectrum shows the v+OH component and ~ sufficiently different, they will be relatively uncoupled the anisotropic spectrum shows some intensity due to v + ~ are and behave much like HDO. but largely v-OH at higher frequency. v+OH and v-OH lie on (3) Very few pairs will have both oscillators in the wings either side of the single mode VOH observed in a dilute of the distribution of single oscillator potentials, and solution. (Further discussion and examples of intermolecular coupling may be found in ref 50-54.) Increasing ZE?CLj4RiS4TIOh R P I
:OS
(47) A. Burneau and J. Corset, J . Chim.Phys. Phys.-Chim. Biol., 69, 142, 153 (1972). (48) C. Perchard and J. P. Perchard, Chem. Phys. Lett., 27,445 (1974). (49) C. Perchard and J. P. Perchard in "Molecular Spectroscopy of Dense Phases", M. Grosmann, S. G. Elkomoss, J. Ringeissen, Eds., Elsevier, Amsterdam, 1976, p 629. (50) M. L. J o s h in ref 49, p 583. (51) G. Fini and P. Mirone in ref 49, p 633.
(52) V. I. Korsunskii, N. L. Lavrik, and Y. I. Naberukhin, J. Opt. SOC. Am., 41,468 (1976). (53) B. Desbat and P. V. Huong, J. Raman Spectrosc., 8, 1 (1979). (54) J. Yarwood in "Annual Reports on the Progress of Chemistry", Section C, Physical Chemistry, Vol 76, 1979, The Royal Society of Chemistry, London, 1980, p 99. (55) D. Schioberg, C. Buanam-Om, and W. A. P. Luck, Spectrosc. Lett., 12, 83 (1979). (56) S. Kint and J. R. Scherer, J . Chem. Phys., 69, 1429 (1978).
Raman Studies of Liquid Water up to 300
"C
consequently these will make very little contribution to the total spectrum. The spectra at temperatures below 100 "C have already been discussed in detail by S ~ h e r e r There . ~ ~ ~ is one feature which can be considered immediately. The isotropic spectra of both H 2 0 and D20at 4 and 50 "C show a small but pronounced shoulder at the high-frequency end, and it is rather curious that the band edge of this feature is very nearly the same as that in the HDO spectra (=3665 (H,O) and ~ 2 7 0 0(D,O) cm-'1. The most reasonable explanation is that this is due to the small number of highfrequency oscillators which are paired with oscillators of much lower frequency and are relatively decoupled (case 2 above). The same factors then apply which led to the formation of a band edge in HDO. The fact that the new edge is slightly higher in frequency than in HDO is consistent with the fact that the decoupling would not be expected to be as great as for HDO, since the frequency separation is not as great. (This is basically the same interpretation as that given by Scherer in terms of the weakly hydrogen-bonded oscillator in an asymmetric m ~ l e c u l e ~ , When ~ . ) one considers the main part of the spectrum, which we expect to correspond with case 1, it is perhaps best to look at the spectra at 50 "C (or even 100 "C) where the 2v2 feature is no longer dominant. The first observation is that the peak is at lower frequency than the corresponding isotropic spectrum of HDO. This can only be due to coupling. The second observation is that the peak of the anisotropic spectrum is at a higher frequency than the peak of the isotropic (or anisotropic) spectrum of HDO. As we have discussed earlier, this may be indicative of intermolecular coupling. (Note, however, that Efimov and N a b e r ~ k h i nwere ~ ~ able to calculate similar spectra without taking into account any intermolecular coupling. In that case the high-frequency peak in the anisotropic spectrum arose because v3 was more intense than the v1 component.) We might also note here that another obvious effect of the coupling is to broaden the bands, compared to HDO. A shoulder on the high-frequency side of the intensity distribution is noticeable in the lower-temperature anisotropic spectra (particularly for DzO). The most plausible explanation is that this is a v3- component of the main distribution of oscillators, pushed up in frequency by intermolecular coupling. It is, of course, rather difficult to unravel completely the combined effects of intra- and intermolecular coupling on the spectrum. As the temperature increases, there are several general observations: (a) The weak high-frequency shoulder in the isotropic spectrum does not increase in intensity, and, in fact, at 100 "C and above it is not evident. (b) The main band slowly narrows and moves up in frequency, and in the isotropic spectra, clearly seen above 100 "C, intensity builds at the band edge (not to be confused with the high-frequency shoulder (a));the frequency of this band edge is below that observed for HDO. (c) At 300 O C the isotropic spectra resemble those of HDO except that they are still broader and at lower frequency. An important piece of evidence then emerges when we look at the anisotropic spectrum of D20 at 300 "C; there are two maxima, one at the same frequency as the isotropic peak and a second at significantly higher frequency with no counterpart in the isotropic spectrum. The peak of the HDO isotropic spectrum corresponds with the minimum between these two anisotropic maxima. Clearly the components can be attributed to coupling and are sufficiently narrowed that they begin to resolve. One would expect the same behavior for H 2 0 at 300 "C, and, although the
The Journal of Physical Chemistry, Vol. 86, No. 25, 1982 4903
Scheme In 300 "C (band edge) vODIHDOI u,[D20)
2685 +62\
voH(HDO) VI
3664
+6\
2671
117
3707
~
136771 not resolved 3
w 2788
3607
u,(H,OI
a
2727
119
(HZ01
t o t a l splitting:
2628
2747
v3(D20) total splitting:
Y
vapor
p 3657
+4\
3756 99
Frequencies in cm-'.
bands are not resolved, there is additional intensity at the high-frequency end in the anisotropic spectrum which is not present in the isotropic spectrum. In terms of oscillator potentials, the maximum in the distribution at 300 "C has shifted considerably toward the weak-interaction end and consequently most of the oscillators are very similar. Hence, most pairs will have two very similar oscillators (as in case 1again), and a splitting to either side of the HDO band-edge frequency is expected. If the components can be resolved, then they should each also have a high-frequency band edge. If we measure the positions of the band edges in D20 at 300 "C as before (the lower one from the isotropic spectrum and the higher one from the anisotropic spectrum), the values obtained and that for HDO at 300 O C give a surprisingly good parallel with the behavior of the vapor-phase frequencies (see Scheme I). For H 2 0 the comparison for the lower-frequency component is again good but it is not clear that we can see the true band edge of the high-frequency component in the anisotropic spectrum because of the overlap with the low-frequency component. We have already anticipated the disappearance of any intermolecular coupling, as the temperature is increased, earlier in the discussion; as further evidence of this the low-frequency maximum in the anisotropic spectrum of D20at 300 "C is more intense than the high-frequency component. This is opposite to the effect expected if intermolecular coupling alone were responsible for the splitting. The two modes may therefore be assigned as v1 and v3 as indicated. The resolution into v l and v3 components in D20 at 300 "C is the first evidence for such in the Raman spectra. However, the high-temperature IR spectra of H20obtained by Saumagne and J o ~ i e nshowed ~ ? ~ two maxima, which they also suggested was a splitting into vl and v3. They give the approximate peak positions as 3520,3625 cm-' at 300 "C and 3545, 3650 cm-' at 374 "C. The splitting of 105 cm-' is fairly consistent with that in the vapor phase (see above). The reason for the resolution of bands in the IR but not the Raman spectrum may again be connected with the hydrogen-bond strength vs. intensity properties in the IR, which also give rise to a lower peak frequency. (The peak frequency of vl, from the isotropic Raman spectrum, occurs at 3565 cm-' in H 2 0 at 300 "C, 45 cm-' higher than in the IR.) The information contained in the depolarization ratios strengthens the arguments above. These results (Figure 4) are in agreement with the earlier work of Cunningham and Lyons5' but extend the temperature range considerably. In the low-temperature spectra at low frequencies the depolarization ratio is very low, because the modes are (57) K. Cunningham and P.A. Lyons, J.Chem. Phys., 59,2132 (1973).
4004
The Journal of Physical Chemistry, Vol. 86, No. 25, 1982
I
t-i ? (!
2600
2800
3000
3200
3400
3600
3800
Ratcliffe and Irish
w, I
4000
I
I I
-\
303..
2800
2200
2480
2600
2800
3
CM- 1 Figure 5. Densitycorrected total spectra of the stretching-mode regions of H,O and of OD in 10% HDO in H,O.
largely totally symmetric, i.e., ul, 2uz,and ul+ if, as has been suggested, intermolecular coupling is strong a t low temperature. At intermediate frequencies the ratio is higher due to increasing v3 and ul- components. At high frequency the ratio decreases due to the uncoupled oscillators which give rise to the weak high-frequency shoulder; these are totally symmetric and hence similar to HDO which has low depolarization ratios. As the temperature increases, we see that the falling-off trend of the ratio a t the high-frequency end gradually reverses. This shows that the strongly polarized decoupled oscillators have disappeared at high temperature and the ratio rises steadily due to the increasing u3 components of the coupled oscillators. A curious feature of the depolarization ratio plots is the relatively constant point a t the high-frequency end, a t 3660 f 20 cm-' for H 2 0 and 2690 f 20 cm-l for D20. Although one must be careful not to read too much significance into this, its position is a t about the same frequency as the isolated OH or OD oscillator band edge seen in HDO, which perhaps suggests that the feature is associated with the redistribution of modes into u1 and u3 types in this region. Relative Intensities i n the Stretching-Mode Regions. Relative intensity spectra of H 2 0 are shown in Figure 5. The counts were divided by the density of H 2 0 a t the particular t e m ~ e r a t u r and e ~ ~a t 10.5 MPa (this pressure was maintained throughout the experiment), so that to a first approximation this gives the intensity scattered from a fixed number of water molecules per unit volume. For the spectra of HDO in H 2 0 the counts were also divided by the density of pure water. Any further interpretation of these results must then rely on the tentative assumption that other factors affecting intensity are of minor consequence. The total corrected intensity under the bands decreases as a linear function of temperature, although the
I
,
L - L - i -
:200
!6aa
2nm
2400
CY-: Figure 6. Raman spectra of the bending mode u, and combination , as a function of temperature (slit width, 15 cm-'; mode (v, uL) of HO step interval, 5 cm-I).
+
changes of intensity at a particular frequency are generally quite nonlinear. The least-squares linear fits of total band intensity vs. temperature gave correlation coefficients better than 0.999. (Linear base-line corrections, between 2700-3900 em-' for H 2 0 and 2200-2800 cm-' for HDO in H20,were subtracted from the spectra beforehand.) The results of the fits are best expressed by the equation IT/I298 = M ( T - 298) + 1 where the intensities are normalized to the intensity at 298 K (25 "C) and M = (-1.264 f 0.023) X low3K-' for HzO and (-1.117 f 0.023) X K-' for HDO in HzO. The total intensity falls by 30-35% from room temperature to 300 "C. Although the significance of the observed linearity is puzzling, the decrease in itself indicates that the absolute Raman scattering of an OH oscillator decreases as the intermolecular interactions decrease (and the frequency increases). This parallels the reported higher specific infrared intensity associated with strongly hydrogen-bonded OH oscillators. Spectra of the Bending Mode v2 and the Combination Mode (u2 + uL). Initially, interest in the v2 bending mode was centered largely on its frequency, to help in the investigation of 2uz in the stretching-mode region. This band is very much weaker than the bands in the stretching region and for this reason much longer counting times, increased slit width, with no polarization analysis were needed to acquire spectra within a reasonable time period. The most noticeable feature of the band (Figure 6), as mentioned earlier, is that its frequency does not change within experimental error, between 4 and 300 "C (1637.5 f 2.5 (H20)and 1202 f 2.5 (D20)em-'), nor is there any appreciable change in bandwidth, although it is difficult to measure this accurately (103 f 5 (H,O) and 66 f 10
Raman Studies of Liquid Water up to 300
The Joumal of Physical Chemistry, Vol. 86, No. 25, 1982 4905
"C
T ("C)
Figure 7. Plots of A as a function of temperature for H,O and D20. The hear least-squares fits are shown. A = (v, 4) - v2.
+
TABLE I
H,O D,O a
dA/dT, cm-'/"C
intercept at 0 OC, cm-'
Ra
-0.729 * 0.041 -0.513 t 0.040
509.8 t 6.9 359.7 6.2
0.991 0.985
*
Correlation coefficient.
(D20) cm-'). This behavior reflects the peculiarities of water. Normally, as the temperature increases, one expects bands to broaden, and the obvious factor counteracting this in water would be a decreasing width of the distribution of vibrational potentials, i.e., a greater similarity among the individual molecules. Scherer has pointed out that there is no rigorous correlation between v2 frequencies and the hydrogen-bonding interaction strength5 and the present results tend to strengthen this view. Attention is drawn to the even weaker and much broader combination band, at higher frequency than v2, which was found to decrease rapidly in frequency as the temperature increased (Figure 6): from -2132 cm-l at 3 "C to ~ 1 9 2 0 cm-l at 300 "C in H20, and from 1562 cm-' at 4 "C to ~ 1 4 2 0cm-l a t 300 "C in D20. This band is usually assigned to a combination (v2 + vL), where L is a librational mode, chosen in preference to a translational mode because of the larger frequency and the large decrease in A = (v2 + vL) - v2 on deuteration6 Polarization studies (present work and ref 5) show that the band is depolarized and, since v2 is polarized, the combination band must have the same symmetry as the vL fundamental. Unfortunately this is not very informative since the only possibility that this observation excludes is an R, libration for C, cases, which
would be totally symmetric. Plots of A vs. temperature for the combination band are shown in Figure 7. It was found possible to fit the results by linear least squares as shown in Table I. Pinkley et a1.6 have noted that the maximum in the librational region of the infrared spectrum shows a strong temperature dependence (590 cm-l at 1 "C and 555-560 cm-' at 50 "C) and the combination band (v2 + vL) which is also seen in the infrared has been observed to decrease in frequency as the temperature increases.58 The band is of interest since in effect A gives a measure of the changing librational potential with temperature. One word of caution must be mentioned, however, in that this might also reflect, to some extent, the change in density between room temperature and 300 "C. The decreasing frequency, however, is clearly compatible with a decreasing average interaction energy, as expected. In conclusion we might return to the question of the suitability of the various models. We have interpreted the spectra from a continuum viewpoint; however, we would not discard a mixture model of the type which considers strong and weak hydrogen-bonded oscillators as the two components, on the basis of the spectroscopic results. A great many of the arguments and observations could apply equally well to such a model. The results do not seem to be compatible, however, with a two-state type mixture model, where icelike clusters exist in a sea of relatively "free" non-hydrogen-bonded water. The free water in such a system would have virtually identical oscillators and hence intramolecular splitting should produce the split into v1 and v3 at the high-frequency end of the spectrum at all temperatures. There is no indication that this occurs in the lower-temperature spectra. Regardless of model, the changes in the spectra as the temperature increases are quite compatible with the view that the hydrogen-bonding interactions become weaker and the ordering which these impose is reduced. Note Added in Proof. At the 8th International Conference on Raman Spectroscopy, Bordeaux, France, Sept 6-11, 1982, where this paper was presented, Professor Z. Kecki noted that the temperature dependence of the 0-H band intensity was consistent with early measurements in the range 2-90 "C from his laboratory (Roc. Chem., 40,919 (1966)) and work done in collaboration with H. J. Bernstein. Acknowledgment. This research was supported by a grant from the Natural Sciences and Engineering Research Council of Canada. (58) D. A. Draegert, N. W. B. Stone, B. Curnutte, and D. Williams, J. Opt. SOC.Am., 56, 64 (1966).
