1684
J . Phys. Chem. 1987, 91, 1684-1686
phase transition, however, the soft mode is not observed in the high-pressure phase as far as the experimental results we obtained are concerned. It might be possible that we might not have the best experimental arrangement to find a weak band very close to the Rayleigh wing. However, so far we have found no trace of a band below 50 cm-I. The similarity of the pressure-induced phase transition to the temperature-induced phase transition does not seem to hold in the monoclinic crystal, unlike in the case of the orthorhombic crystal. The problem regarding the nature of the pressure-induced phase transition and the structure of the high-pressure phase of
the monoclinic crystal remains to be solved.
Acknowledgment. The authors express their sincere thanks to Prof. T. Yagi, Institute for Solid State Physics, University of Tokyo for his kind guidance in constructing the diamond anvil cell, and to Prof. Y . Shono and Dr. M. Kikuchi, The Research Institute for Iron, Steel and Other Metals, Tohoku University, for their courtesy in permitting us to use various facilities in their laboratory. A part of this study was supported by a Grant-in-Aid for Scientific Research (A) No. 58430005. Registry No. K,Co(CN),, 13963-58-1.
Coupling of SmalEAmplitude Proton Motions in Liquid Water to Density and Temperature J. L. Green, A. R. Lacey, M. G. %eats,* Department of Physical Chemistry, University of Sydney, N.S.W. 2006, Australia
S. J. Henderson, and R. J. Speedy Department of Chemistry, Victoria University, Wellington, New Zealand (Received: October 16, 1986)
The extent of the collective character of small-amplitude proton motions of stretched supercooled water is determined from the OH stretching Raman spectrum. Comparison of data with that obtained previously at 1 atm shows that in supercooled water the collective motions are coupled to the liquid density, whereas at temperatures above 20 O C they are coupled to temperature.
Introduction Green, Lacey, and Sceats (GLS)1-3 have recently developed a measure of the extent of collective character, C, of the smallamplitude proton motions in water from an analysis of the strongly polarized OH stretching Raman spectrum and have reported values of C along the 1-atm isobar from +90 to -25 O C . These studies, on water',* and aqueous s o l ~ t i o n shave , ~ shown that the small-amplitude collective proton motions are sensitive to structural characteristics which affect the resonance coupling between adjacent 0-H oscillators. Experimental studies along the 1-atm isobar are insufficient to elucidate the relationship between C and the underlying changes in the structure of liquid water, although conjectures have been made by GLS. Henderson and Speedy4v5 have developed a technique for stretching liquids which has made it possible to study a sample of water along an approximately isochoric path, from about 500 bar at 100 O C , through the tension maximum at -209.9 bar at 9.12 OC, to about -50 bar at -24 O C . We report the Raman spectrum of one such sample and compare the variation of C along the approximate isochore with its behavior along the 1-atm isobar. Spectroscopic studies of stretched supercooled water have not been previously reported. Studies of supercooled water6-8 have revealed an unusual increase in fluctuations between states of different density and
energy. The structure of the low-density, low-energy states, which give rise to the expansion of water when it is cooled below 4 "C (at 1 atm), has not yet been e~tablished,~-"but low-density amorphous solid water'* and vacant clathrate lattices" provide some possibilities. By stretching the water, we can increase the proportion present in the low-density form. Measures of structural relaxation times in water provided by the shear vis~osity,'~ spin-lattice relaxation times,I4 and the resistivity of dilute electrolyte s01utions~~J~ indicate a rapid slowing down with possible divergences as T T, = -46 "C (at 1 atm). The thermodynamic response functions, which measure density and enthalpy fluctuations, can be extrapolated to infinity6%'at the same T,, suggesting that the relaxation times are coupled to the anomalous fluctuations. GLSI showed that the fractional intensity C(7) of the collective band in the Raman spectrum of water is linear in temperature (from +90 to -25 "C) along the I-atm isobar and that it extrapolates linearly to the value of C in ice near T,. The value of C for ice is independent of temperature and has the same value as that estimated for amorphous solid water.' GLS have conjectured3%"that this value of C is similar to all fully bonded tetrahedral networks. A reasonable interpretation of the temperature dependence of C in liquid water is that the intermolecular
(1) Green, J. L.; Lacey, A. R.;Sceats, M. G. J . Phys. Chem. 1986, 90, 3958. ( 2 ) Green, J. L.; Lacey, A. R.;Sceats, M. G. Chem. Phys. Lett. 1986,130, 67. (3) Green, J. L.; Lacey, A. R.; Sceats, M. G. J . Phys., Actes du Colloque, in press. (4) Henderson, S . J.; Speedy, R.J. J . Phys. E. 1980, 13, 778. (5) Henderson, S. J.; Speedy, R.J., in preparation. (6) Angell, C. A. In Water-A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1983; Vol. 7, Chapter 1 . (7) Speedy, R.J.; Angell, C. A. J . Chem. Phys. 1976, 65, 851. (8) Speedy, R. J. J. Phys. Chem. 1982, 86, 982.
(9) Stillinger, F. H. Science 1980, 209, 451. (IO) Stanley, H. E.; Teixera, J. J . Chem. Phys. 1980, 73, 3404. ( 1 1 ) Speedy, R. J. J. Phys. Chem. 1984, 88, 3364. (12) Sceats, M. G.; Rice, S. A. In Water-A Comprehensive Treatise; Franks, F., Ed.; Plenum: New York, 1983; Vol. 7, Chapter 2. (13) Hallett, J. Proc. Phys. SOC.,London 1963, 82, 1046. (14) Lang, E. W.; Liidemann, H.-D. Angew. Chem., In?. Ed. Engl. 1982, 21, 315. (15) Speedy, R. J. J . Phys. Chem. 1983, 87, 320. (16) Cornish, B. D.; Speedy, R.J. J . Phys. Chem. 1984, 88, 1888. (17) Green, J. L.; Lacey, A. R.; Sceats, M. G . , in preparation.
0022-3654/87 /2091-1684$01.50/0 - , ,
I
-
0 1987 American Chemical Society
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Small-Amplitude Proton Motions in Liquid Water
1685
18.E
18.E
-8
%
Y
>
18.4
18.2
.. -25
18.C 0
25
50
Temperature
75
100
I OC
Figure 1. The temperature dependence of the pressure of the water m
the sealed capillary plotted against temperature. arrangements in water which determine C(T) become the same as those of a fully hydrogen bonded network which forms as T T,. Such an interpretation can be tested by a determination of C along an approximate isochore, in which case the structural rearrangements are suppressed.
I
0
80
40
TEMPERATURE
'C
Figure 2. The temperature dependence of the molar volume of the liquid in the sealed capillary (m) deduced from Kell's equation of state.ls Also
shown is the molar volume along the 1-atm isobar.
-
Experimental Methods and Results A sample of H 2 0 containing 18 mol % D 2 0 was prepared in a Berthelot-Bourdon tube, as described by Henderson and Speed~."3~Briefly, a fine Pyrex capillary (70-pm i.d., 110-pm 0.d.) was wound into a helix of 11 turns with a 4-mm diameter. The inner and outer surfaces of the capillary were etched with dilute hydrofluoric acid to strengthen the glass by removing surface defects. The capillary was then rinsed and filled with the water sample, one end was sealed, and the angular rotation of a small mirror attached to the sealed end was calibrated against known pressures applied through the open end of the capillary. The open end was then sealed, leaving a small vapor gap. On heating the sealed capillary, the gap disappeared at 53.1 OC at 1 bar. At 99.3 OC the pressure in the capillary rose to 509 bar. On cooling the capillary below 53.1 "C, the vapor gap did not reappear and the sample was taken, under tension, through the maximum tension at 9.12 "C of -209.9 bar to -17.3 OC at -107.8 bar, as shown in Figure 1. The data shown in Figure 1 fitted a quartic polynomial in temperature with a maximum deviation of 0.8 bar. The polynomial extrapolates to intersect the 1-bar axis again at -28.1 OC. The volume of water along the p T path shown in Figure 1 was estimated by using equations of state fitted by Ke11I8 in the positive pressure region and extrapolated into the negative pressure region. Figure 2 shows the variation of the volume of the capillary sample with temperature, in comparison to that along the I-atm isobar. In the range +20 to -20 OC the capillary sample volume is nearly constant and the volume increase over the range 0 to 100 OC is only 20% of the change along the isobar. The Raman spectrum in the region of the OD and OH stretching modes was taken as previously described.ls2 The laser, at 514.5 nm, was focused into the capillary at 90" to its axis. The Raman signal was collected at 90°, and the Illand I , spectra were obtained by conventional means. The glass fluorescence is trapped in the capillary by total internal reflection and does not signifi(18) Kell, G . S . In Water-A Comprehensive Treatise; Franks, F., Ed.: Plenum: New York, 1971; Vol. 1, Chapter 10.
WAVENUMBER
WAVENUMBER
Figure 3. The Ill and I , Raman spectra of water (0.18 mol 3'% D,O in HzO)in a sealed capillary at several temperatures.
cantly contribute to the signal. A complete set of data was obtained for only one capillary having poD = 0.18, and the analysis of that data in the OH stretching region is the subject of this paper. and I , spectra are displayed in Figure 3 for several temThe Ill
1686
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
Green et al.
0.4C
0.30.20.1 ~
1
3800
3600
3400
3200
3000
2800
WAVENUMBER
peratures in the range -20 to +90 "C. The spectra were measured at 14 temperatures in this range. The Raman spectra were analyzed by using the spectral stripping procedure developed by GLS.' The collective band is essentially that part of the spectrum characterized by a depolarization ratio which differs from that of uncoupled OH oscillators. Coupling of OH oscillators gives rise to a strongly polarized band on the low-frequency edge of the spectrum. The collective band is defined by ZJw) = Zil(w) - aZ,(w) where a is adjusted to minimize the high-frequency contribution to Zc(w). Values of a-I determined are statistically indistinguishable from the depolarization ratio of decoupled OH oscillators of HDO in D 2 0 , namely 0.21 f 0.02. The spectrum is then refined to remove residual structure at high frequencies by assuming that the spectrum is symmetrical about the peak and using the low-frequency line shape to define the entire line shape. The resulting spectra for ZJw) are plotted in Figure 4. The fractional collective band intensity C is defined by
Jh, dw
Jh) dw
0
20
40
60
80
100
TEMPERATURE O C
Figure 4. The collective band I J w ) deduced from the data of Figure 3 using the spectral stripping procedure of ref 1.
C=
-40 -20
(1)
The results for C are plotted in Figure 5, along with the data previously obtained' at 1 atm for pure H20. The sealed capillary sample that survived the rigors of a complete spectral study was an H 2 0 / D 2 0 mixture, and the presence of mass defects (POD= 0.18) reduces the collective band intensity.2 From a study of the influence of mass defects on the collective band, C varies as (1 - poo)2, where poD is the mole fraction of OD oscillators, approximately independent of temperature.2 For poD= 0.18, this gives a scale factor of 1.48 to provide estimates of C for pure H 2 0 . The statistical error in this scale factor is f5%. The estimates of C( for pure H,O so obtained are also plotted in Figure 5. The estimates at the two temperatures where the pressure in the sealed capillary is 1 atm, namely -28.1 and +53.1 "C, agree within experimental error with those obtained previously along the 1-atm isobar. Note, however, that at low temperatures the shapes of the curves are significantly different from those obtained at 1 atm.' The sealed capillary data clearly exhibit saturation below 10 "C and a significantly larger value of C than that for water at 1 atm for T = 0 "C. For T > 40 "C the values of Care similar for both samples. The implications of the data of Figure 5 will be considered in the following section. Discussion and Conclusions The data of Figure 5 show that there is a significant difference in the behavior of C(7') along the isobar at 1 atm and the approximate isochore of 18.3 f 0.1 cm3 mol-'. The linear behavior with temperature in the region above 30 "C is similar in both cases,
Figure 5. The temperature dependence of the fractional collective band area C deduced from the spectra of Figure 4 plotted (0)along with the data obtained in ref 1 at 1 atm (0). The former data, when corrected for isotopic composition, are also plotted ( 0 ) . The lines are freehand estimates through the data points.
and the small difference in the value of C( T) indicates that C( T ) is primarily determined by temperature in this regime. The immediate implication is that the changes in structure which give rise to the behavior of C( r ) are determined by thermal excitation. The mechanism whereby C is reduced from the value expected for a fully hydrogen bonded network has been suggested'~'' to be related to formation of network defect oscillators whose resonant frequency falls outside the vibron bandwidth. It follows that in this region such defects, broadly identifiable as broken hydrogen bonds, are independently created by thermal excitation. In contrast, the dependence of C( 7') below 0 "C exhibits saturation at approximately constant density. Although data from one capillary are insufficient to draw firm conclusions, it would seem that C(7') has become strongly coupled to the density rather than temperature. At constant volume in the supercooled region the liquid configurations become locked in; i.e., the proportion of low-energy, low-density configurations is unaffected by temperature. The saturation of C(T ) is an important result because it establishes a relationship between the structural characteristics which give rise to the anomalous thermodynamic and transport properties of the liquid and those which influence the resonant coupling of small-amplitude proton motions. While the integrated intensity of Ic(w) saturates below 0 "C, the peak of the spectrum continues to shift toward lower frequency as the water is supercooled. This indicates that the hydrogen bonds which give rise to collective motions continue to become stronger as the temperature is lowered at constant density; Le., those molecules which are incorporated into the low-energy network exhibit a strengthening of their hydrogen bonds as the temperature is lowered. The linear dependences of C( T)' and the proton conductivity16 along the 1-atm isobar indicate that the dynamics of small- and large-amplitude proton motions have a common origin. The results obtained at 1 atm and along the 18.3 f 0.1 cm3 mol-' isochore are consistent with the picture that the low-energy, low-density configuration to which liquid water tends as it is supercooled at 1 atm is a continuous tetrahedral network. The results of this paper are the first spectroscopic studies to be reported for a liquid under tension. More data are required at different densities on pure H,O capillaries in order to establish the underlying structural mechanisms. The data obtained indicate that OH stretching Raman spectroscopy is a useful probe of water structure.
Acknowledgment. This work was supported by the Australian Research Grants Scheme. J.L.G. acknowledges the award of a Commonwealth University Scholarship. Registry No. H 2 0 , 7732-18-5; H ' , 12586-59-3; OH-, 14280-30-9.
