Temperature dependence of the optical constants for liquid H2O and D2O in the far IR region

Journal of

MOLECULAR STRUCTURE ELSEVIER

Journal of Molecular Structure 350 (1995) 95-114

Temperature dependence of the optical constants for liquid H 2 0 and D 2 0 in the far IR region Hans R. Zelsmann 1 CEA/D~partement de Recherche Fondamentale sur la Mati~re Condens~e, SESAM/Physico-Chimie Mol~culaire, 17, avenue des Martyrs, 38 054 Grenoble Cedex 9, France

Received 8 July 1994;in final form 7 November 1994

Abstract Calibrated thin films of ordinary and heavy liquid water have been measured over the temperature range -5.6 to 81.4°C in the spectral region extending from 25 to 450 cm -1 by classical absorption techniques with an FTIR interferometer. From these experimental spectra, the optical constants n and k were calculated by iteration using the Kramers-Kronig transformation which has been especially adapted to the problem of fringe correction for a fiat absorbing sample in contact with highly refractive silicon substrates. As the principal result, we show that this method yields new quantitative data for the optical constants n and k of liquid H20 and D20 in the cited spectral region and temperature range. A comparison with earlier data for H20 at 19°C, measured by dispersive FT spectrometry, shows very good agreement. Further results are given concerning the parameters of the FIR bands, namely the evolution of band positions and band widths with temperature. Analysis of the shape of the librational band led us to suppose the existence of a second IR active component of this band which has hitherto only been reported in Raman and inelastic neutron scattering (INS) spectra. Finally, we confirm the different relaxation behavior of H20 and D20 in the high temperature range found in a recent Raman study.

1. Introduction Far I R spectroscopy provides a valuable tool for gaining insight into the processes of the liquid state on a molecular scale. These processes concern, besides the intramolecular vibrations at low frequency, mainly the translational and rotational motions of the molecules which can generally be seen from about a few cm -l to some 1000 cm 1. With improved experimental techniques we may get better and quantitative far I R spectra which can give us a lot of information about the behavior 1Member of the Universit6 Joseph Fourier Grenoble.

of molecules, especially the intermolecular forces. This knowledge leads to a better understanding of hydrogen-bonded liquids in general. Of all liquids, water presents a special case, not only because of its exceptional physical properties, but also because the most widespread chemical compound on earth is still not understood as regards its structure and dynamics on a molecular scale. In the past, considerable experimental work has been done on liquid water, using in particular the optical methods of investigation such as I R and Raman spectroscopy and neutron diffraction. The former results are summarized in [1] and [21.

0022-2860/95/$09.50 © 1995 Elsevier Science B.V. All rights reserved S S D I 0022-2860(94)08471-8

96

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

A lot of newer contributions studying the O - H stretching region come from mid IR and Raman spectroscopy, whereas the librational and translational motions of the water molecule have been investigated, essentially by Raman spectroscopy [3-10]. For the IR region below 1000 cm 1, and particularly for the far IR, there is undoubtedly a lack of reliable results and only a few studies can be cited [11-17]. The major reason for this situation is most probably the experimental difficulties in performing accurate measurements in the far IR region. The two major FIR experimental approaches consist of either measuring the attenuation of the intensity of a light beam by a wellcalibrated sample or measuring the reflectance of a sample with precision at normal incidence. In either case, the true quantitative spectrum has to be calculated - - an operation that is feasible only if the measured data are sufficiently precise. The most relevant FIR spectroscopical work is that of Draegert et al. [11] and, more recently, of Afsar and Hasted [15]. Draegert et al. studied the liquid spectra of H20 and D20 from 50 to 2600 cm z at temperatures of 25, 50 and 75°C. However, in spite of careful calibration of the sample thicknesses, the data obtained were of limited photometric accuracy owing to insufficiencies of the instruments at this time. The measurements of Afsar and Hasted were made using a dispersive FT spectrometer, giving spectra for H20 (5-450 cm -1) and D20 (5-250 c m -1) of very good accuracy for the optical constants n and k, but only at a single temperature of 19°C. The primary object of the present study is to complete these fragmentary FIR data by giving new quantitative data for the optical constants n

a) the Si substrate

and k for both H20 and D20 over an extended temperature range.

2. Experimental procedure For this experiment, we choose to measure directly the transmittance of a thin liquid film with parallel faces.

measurement of the absorption spectrum of a thin liquid film

Io

It

~

Si

water sample

Si

Form 1.

As the sample thicknesses required in the FIR region are roughly ten times higher than those in the mid IR region, this type of set-up could be adequate. The sample cell was equipped with silicon windows because this material not only permits good optical surfaces, but also shows good resistance to water and has an acceptable transmission over the whole FIR spectrum. Other characteristics of the silicon flats are: index of refraction, nsi = 3.4213; thickness 3.00 mm; an absorption coefficient, ~, well below 0.1 neper cm 1. A major drawback of silicon as window material is its high refractive index which leads to high reflectivities and thus to high losses and pronounced interference fringes. The general description of stratified absorbing media is rather complicated, even more so as we should take into account multiple reflections and all the possible combinations of interferences arising from the four interfaces in our case.

b) the sample

c) combinations of a) and b)

Interference fringes in the transmitted intensity I t due to reflections on the surfaces

Form 2.

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

97

FLOW OF HEAT EXCHANGE LIQUID

I

SAMPLE CELL WITH SILICON WINDOWS ---

~ii!!i~i!il;:i!

SAMPLE FLOW

-I

i ° /

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"//////

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~

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, / / / / / t

N

~

Pt

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TEMPERATURE SENSORS

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I

1 cm

SAMPLE COMPARTMENT OF THE INTERFEROMETER

Fig. 1. Variable temperature device with stainless steel sample cell, equipped with silicon windows.

In order to reduce the complexity of the problem, it is useful to cancel the observation of the fringes caused by the thickness of the silicon windows. This can be done by an appropriate choice of this thickness with respect to the instrumental resolution desired for the spectrum. In practice with a 3 mm silicon flat we have a fringe spacing Agf,inge ~ 0,5 cm -1, which is no longer visible if the spectra are run under a resolution of A~re~olu~on= 2 cm -1. Thus, the fringes arising from the external faces of the cell are suppressed as well. In consequence the spectra need to be corrected only by a constant which is given by the simplified Fresnel formula for the mean R and T power values.

The different spectroscopical measurements required are: (1) the intensity of a background spectrum without the cell; (2) the intensity of a reference spectrum of the empty cell from which we can deduce (with (1)) the sample thickness to an accuracy of + 0.2 #m; (3) the intensity of the spectrum of the cell containing the sample, which gives (with (1)) the raw transmittance or absorbance spectrum of the water sample. This latter spectrum needs to be corrected for the reflection losses of the two interfaces vacuum/Si and Si/ vacuum and eventually for absorption of the silicon substrate. As the refractive index of silicon shows no appreciable variation in this region and

98

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114 2.5

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H.R. Zelsmann/Journal o f Molecular Structure 350 (1995) 95 114

as one may neglect the absorption losses of silicon, which have been verified by calculation, this correction reduces to a constant scaling factor for the spectrum or simply a constant shift on the absorbance scale. By this simplification, there are only the interference fringes left created by the parallel water sample in contact with the two silicon surfaces. As the intensity of the fringes depends on the values of n and k of water, it is useful to include their evaluation in the iterative method described in the next section. The spectrometer we used was a Polytec FIR30 interferometer operating under vacuum, equipped with a liquid helium cooled bolometer from Infrared Laboratories. All spectra were recorded in the 30-450 cm -1 range under an apodized resolution of A~ = 2 cm -1 with an upper sampling limit at 1000 cm -1. The vacuum tight sample cell that could be filled from outside was mounted on a heat exchanger device. This variable temperature set-up, as shown in Fig. l, was connected to a thermal bath which allowed for control of the sample temperature.

3. Calculations of the optical constants n and k 3.1. Definitions The complex optical constants and the dielectric constant are defined by

h(f/) = n(~) + ik(g,)

(1)

~(~) = e'(~) + ie"(~)

(2)

All these quantities depend on the wavenumber ~. The real part of the complex refractive index is the usual refractive index n and the imaginary part is the absorption index k. Eq. (1) is related to Eq. (2) by

~2(19) = ~(/~)

99

which gives us in detail e'(~) = n2(~) - k2(~) = n2(~) - [a(v)] 2 L47r~J

(4a)

e"(D) = 2n(D)k(D)

(4b)

For the representation of a spectrum generally one uses a plot of the transmittance T or of the absorbance A versus wavenumber. T and A are expressed for a given sample thickness I as: r =

I° = exp ( - a l )

(5)

A = -cdlogl0(e ) where a is the absorption coefficient of the sample. The corresponding absorption index k may be obtained from Eq. 5 by k(~) - a(ts)

In (10)lo f 1"~ 2.303 A - ~-ff~ gl0 \ ~ ) - 47rM

(6)

This expression shows the relation of the absorption index k to the measured quantities T and A which permits us to calculate a value for k from the spectra in zeroth approximation. For a more exact evaluation ofk(~) we need its related quantity n(~). In other words, we have either to measure a spectrum of n(~), which may be done by dispersive Fourier transform spectrometry, or to calculate it. Writing a complex refractive index or a complex dielectric constant is not a mathematical convenience, but rather fundamental physical reasons compel us to do so. The real part n(~) is connected to the imaginary part k0) ) by the Principle of Causality which is formulated mathematically by the Kramers-Kronig dispersion relations. An analog statement holds for e' and e". These relations define each quantity in terms of its related quantity by the integrals

2 [~

~k(~)

n(~') - n~ = ~Jo ~ 5 - t)-52dr)

(7a)

and

(3) 7r j0

(7b)

Fig. 2. Raw experimental H20 spectra (a) and D20 spectra (b) for several temperatures without any other correction than for the reflectedintensity on the outer faces of the silicondisks.

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

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H20 spectra

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H.R. Zelsmann/Journalof Molecular Structure 350 (1995) 95-114 The Cauchy principal values of these two integrals are equal to the principal values of the Hilbert transform given by

1 [+~ k(~)

n(P') - n~ . . . . . 7rJ-o~ D

-

d~

(8a)

1 [+~ n(~)

_

(8b)

with the symmetry properties n(D)= n(-D) and k(~) = - k ( - ~ ) , which imply k(0) = 0. For practical purposes of numerical calculation, it is useful to convert Eqs. (8a) and (8b) into Fourier integrals n(~') - n~ = 2

I?

X " (6) cos (2rrD'6) d6

with

X"(6)

-= 2 [+oc k(~/) sin (2~r~'6) d~' j0

(9a)

and k(~') = 2

J:

X'(6) sin (2~r~'6) d6

with X'(6) = 2

j0

reflectance (ATR) technique was done by Mar6chal [24].

3.2. Procedure for calculation

D~

and

k(~') =

101

n(~') cos (27r~'6) d~'

(9b)

This means that one can calculate n(~) from k(~) by two successive Fourier transforms given by Eq. (9a), where the complex quantity 2 ( 6 ) = X'(6) + iX"(6) is the generalized response function. This fundamental method for determination of the optical constants from transmission measurements of a thin liquid film was initially developed by Jones and co-workers. An exhaustive discussion of the different aspects may be found in Refs. [18-21]. A complementary outline for the exploitation of attenuated total reflection measurements on water and other liquids in the mid IR range has been given by Bertie et al. [22,23] and a more recent quantitative study of water based on the same attenuated total

For this type of procedure, we need smooth and well-defined absorbance spectra in the widest spectral range available, which means that we have to extend the spectra in a plausible way to the lower limit of ~ = 0 and to the upper limit /~max~/~Nyquist, as defined in the sampling theorem. This extension beyond the measured spectral interval was done by fitting the spectra with Gaussian line-shapes with the primary intention of getting the best reproduction of the measured absorbance values. Beyond the limits of the measured interval of our spectra, we should get a valid accordance with the earlier results of Draegert et al. [11], and Afsar and Hasted [15]. This kind of procedure may be criticized; however, it can be shown that any other alternative, for instance a violent cut-off or an indetermination arising from a zero by zero division, introduces far more artifacts into the resulting spectra of n(tS) and k(~). From these extended smoothed absorbance spectra, we calculate in a first step by using Eq. (6) a k(D) spectrum, which serves as starting point for the two Fourier transforms, as defined by Eq. (9a). So we obtain a spectrum of n(~), if we assume a value for n~, which is usually deduced from the high frequency limit of an experimental spectrum. In the present case we found the most coherent results in taking n~ = 1.45 for both H20 and D20. With this spectrum for n(tS) we can now calculate, using Eqs. (10a) and (10b), a new transmittance and absorbance spectrum of the sample, including the fringes coming from the sample thickness, given by the Fresnel formula Tsample

Fig. 3. Fittedexperimentalspectra for H20 (a) and D20 (b); see text.

(1 - RSi/water) 2 exp [-47rDk(D)l] -- l -- 2Rsi/water exp [-4~rgk(D)/] cos [ 47rgn(9)l] +

4R2i/waterexp [-8:r~k(9)/]

00a)

102

H.R. Zelsmann/Journal

of Molecular Structure 350 (1995) 95-114

Band positions for H 2 0 and D 2 0 700

600

......................

i. . . . . . . . . . . . . . . . . . . . . . . . . . .

~. . . . . . . . . . . . . . . . . . . . . . . . . .

~ .....................

500

D20 . ~" ~ ~ ~ ........................................ ~ .............. "-~ . . . . ~ ' -

400

......H

~ ..........................

~i ~~ i

"7,

e;"

2

0

~

I

i

:

................. ~ L2 band

......~i...................... ~:..........................i........................

i i i ! D20 ~' :*" ~ ~ ~'-

300

~~

, ...................

i i i

i

~

i i

L1 band

i i

i

" ~

L 1

band

H20 200

..............

~..................................................................... ~. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

D

~

100 -20

0

-i 20

40

i 60

-~

S band

i 80

100

temperature 0 / °C Fig. 4. Evolution of the band positions for the most prominent bands of the far IR spectrum of water with temperature. The notation of the bands is in accordance with the labeling of the recent Raman spectra by Mizoguchi et al. [10].

with [nsi -- n(/~')]2 q- k 2 ( ~ ' ) Rsi/water = [nsi --b n ( ~ ) ] 2 + k 2 ( F )

(10b)

The new absorbance spectrum is compared with the original experimental spectrum and the k values are updated for the next loop of the iteration. For the present water spectra the calculation converged very rapidly and after a few loops only, the n(~) and k(~) spectra did not vary any more.

absorbance representation of the water spectra. These data were completed by the results from Afsar and Hasted [15] for extrapolation towards the low wavenumber limit, whereas the result from Draegert et al. [11] served to establish a tendency of the spectra towards the high wavenumber limit. The subsequent line fit with Gaussian line-shapes appeared to be very Table 1 Fitted bands for H20 and D20 at 0°C Type of band

Position (cm-l)

4. Results and discussion

In Figs. 2(a) and 2(b), we show respectively the raw experimental spectra for H20 and DzO at several temperatures. The only mathematical treatment to these spectra was a subtraction of the reflected intensity on the outer faces of the silicon disks. In doing so, we get the best approach for the

B S LI L2

Widths (HWHM) (cm 1)

Height in absorbance"

H20

D20

~0.17 0.86 0.85 3.20

~0.18 0.83 0.79 2.40

H20

D20

H20

D20

~50 183.4 395.5 686.3

m50 176.7 315.3 520.4

~40 74.0 149.5 172

~40 69.5 104.0 124

a For a sample thickness of 19.3/~m.

103

H.R. Zelsmann/Journal o f Molecular Structure 350 (1995) 95-114

Band widths for H 2 0 and D20 200 ..................................................................................................................................................... ~..............................

i180

............................... i.............................................................

H

"7.

i 2

,:band

......................................................

i ........................

0

160 .......................... i.................................... [....................................... i....................... band H20~ .~~--.---"-'--~ ix L1 140 ............................................................................................................................ ~........................... i -- ~ L: band 120

. . . . . . . . . . . . .

D20

~ ~

i

:

'i

... ~ ~ - - -- "'-~ -- -- -D20

x-- -- -- ~ ~

i

,oo ................ii..................................................... 80- H:o 60 -20

i ~

i i

i ..........................

~

i ~ -

i ...................

i .........................

S band -- "-~ Sband

-

.....

0

~. L1 band

............

I 20

i 40

i 60

80

i i

i

t 100

temperature 0 / °C

Fig. 5. Evolution of the band widths (HWHM) for the most prominent bands of the far IR spectrum of water with temperature. satisfactory for the effectively m e a s u r e d spectral interval, so t h a t the fitted spectra, as given in Figs. 3(a) a n d 3(b), really reflect the e x p e r i m e n t in this region. L o o k i n g at the e v o l u t i o n o f the p a r a m e t e r s o b t a i n e d for the characteristic lines o f the spectra with t e m p e r a t u r e ( b a n d p o s i t i o n a n d b a n d width), we c o n c l u d e t h a t these d a t a are a m e a n i n g f u l refinement o f the f o r m e r values f o u n d by D r a e g e r t [11]. A s u m m a r y o f these p a r a m e t e r s is given in T a b l e 1. W e have used here the s a m e n o t a t i o n for the b a n d s as m a y be f o u n d in the recent R a m a n w o r k o f M i z o g u c h i et al. [10]. T h e B b a n d corres p o n d s to the b e n d i n g o f the i n t r a m o l e c u l a r h y d r o gen b o n d , the S b a n d arises f r o m the stretching o f the i n t r a m o l e c u l a r h y d r o g e n b o n d a n d the L b a n d s are due to the l i b r a t i o n a l m o t i o n s o f the w a t e r molecules. Because o f the chosen s a m p l e thicknesses, the B b a n d r e m a i n s very faint in o u r case,

SO t h a t the n u m e r i c a l analysis c o u l d n o t be very accurate. F o r the l i b r a t i o n a l b a n d we get clear i n d i c a t i o n s o f the existence o f two I R c o m p o n e n t s a l r e a d y o b s e r v e d by R a m a n [25,26] a n d n e u t r o n spectros c o p y [27] where m o r e t h a n one L b a n d has been r e p o r t e d . W e s h o u l d note here t h a t this L1 b a n d should n o t be I R active a c c o r d i n g to W a l r a f e n ' s analysis [25] which is b a s e d on a structure o f the five-molecule m o d e l o f h y d r o g e n - b o n d e d w a t e r with C2v s y m m e t r y . In this context, it is useful to r e m e m b e r t h a t the a s s u m p t i o n o f Cev s y m m e t r y relies on the p o l a r i z a t i o n p r o p e r t i e s o f the R a m a n b a n d s which seem to be n o t so well-established as usually a d m i t t e d , because o t h e r a u t h o r s [3,7] f o u n d d e p o l a r i z a t i o n r a t i o s for the l i b r a t i o n a l region well below 0.75 which w o u l d n o t s u p p o r t this statement. Even if a h y d r o g e n - b o n d e d w a t e r p e n t a m e r has a m e a n structure c o r r e s p o n d i n g a p p r o x i m a t e l y

Fig. 6. Calculated H20 spectra (a) and D20 spectra (b) of the refractive index n for several temperatures. Fig. 7. Calculated H20 spectra (a) and D20 spectra (b) of the absorption index k for several temperatures.

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

104 2 . 5

°

H20 spectra

- refraction

index n

2.25

temperature:

81.4 ........................

°C

57.2 38.7 20,2 8.4

1.75 -5.

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1.5n Infinity

: 1.45

1.25 + Rfsar

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H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

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"

"

H.R, Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

106

Table 2 Refraction and absorption index data for H 2 0 Wavenumber (cm -1)

n values for H 2 0

k values for H 2 0

-5.6°C

0.4°C

20.2°C

38.7°C

57.2°C

81.4°C

-5.6°C

0,4°C

20.2°C

38.7°C

57.2°C

81.4°C

19.531 23.437 27.344 31.250 35.156 39.062 42.969 46.875

2.1049 2.0663 2.0387 2.0181 2.0023 1,9902 1.9810 1.9743

2.1431 2.1018 2.0719 2.0489 2.0308 2.0164 2.0048 1.9957

2.2657 2.2138 2.1750 2,1442 2.1188 2.0974 2.0792 2.0630

2.3732 2.3097 2.2617 2.2229 2.1903 2,1621 2.1373 2.1153

2.4335 2.3644 2.3125 2.2707 2.2356 2.2051 2.1781 2.1539

2.5491 2.4633 2.3990 2.3471 2.3034 2.2652 2.2313 2.2006

0.5534 0.4922 0.4474 0.4132 0.3861 0.3642 0.3463 0.3316

0.5843 0.5229 0.4784 0.4447 0.4183 0,3970 0.3797 0.3655

0.7107 0.6424 0.5935 0.5571 0.5288 0.5063 0.4880 0.4740

0.8336 0.7572 0.7029 0.6626 0.6314 0.6066 0.5863 0.5692

0,9114 0.8269 0.7671 0.7229 0.6891 0.6625 0.6409 0.6231

1.1016 0.9992 0.9263 0.8723 0.8308 0,7979 0.7711 0.7486

50,781 54.687 58.594 62.500 66.406 70.312 74.219 78.125 82.031 85.937 89.944 93.750 97.656

1.9699 1.9673 1.9663 1.9665 1.9665 1.9691 1.9708 1.9723 1.9734 1.9736 1.9730 1.9713 1.9683

1.9888 1.9837 1.9802 1.9781 1,9769 1.9763 1,9760 1,9756 1.9748 1.9740 1.9706 1.9671 1.9625

2.0488 2.0369 2.0267 2.0180 2.0105 2.0040 1.9981 1.9926 1.9871 1,9814 1.9753 1.9687 1.9613

2.0958 2.0785 2,0631 2.0495 2.0374 2.0265 2.0166 2.0074 1.9985 1.9898 1.9810 1,9719 1.9624

2.1320 2.1122 2.0943 2,0779 2.0630 2.0492 2.0365 2.0244 2.0128 2.0016 1.9904 1.9791 1.9677

2.1726 2.1471 2.1237 2.1022 2.0823 2.0640 2,0469 2.0309 2.0157 2.0012 1.9871 1.9732 1.9594

0.3197 0.3104 0,3037 0.2994 0.2975 0.2979 0.3006 0.3053 0.3119 0.3201 0.3298 0.3406 0.3524

0.3540 0.3449 0.3381 0.3336 0.3314 0.3314 0.3334 0.3375 0.3433 0.3508 0.3601 0,3698 0.3804

0.4612 0,4508 0.4423 0.4358 0.4312 0.4283 0.4272 0.4278 0.4300 0.4335 0.4383 0.4441 0.4508

0.5547 0.5424 0.5319 0,5231 0.5161 0.5106 0.5068 0.5045 0.5037 0.5043 0.5060 0.5087 0.5123

0.6082 0.5955 0.5847 0.5756 0.5681 0.5620 0.5573 0.5539 0.5517 0.5506 0.5506 0.5513 0.5528

0.7295 0.7129 0.6984 0.6856 0.6744 0.6647 0.6563 0.6491 0.6432 0.6383 0.6344 0.6314 0.6291

101.563 105.469 109.375 113.281 117.188 121.094 125.000 128.906 132.813 136.719 140.625 144.531 148,437 152.344

1.9641 1.9587 1.9519 1.9438 1.9343 1.9232 1.9110 1.8975 1.8828 1.8670 1.8502 1.8324 1.8137 1,7943

1.9567 1.9497 1.9416 1.9321 1.9214 1.9096 1.8965 1.8823 1.8671 1.8509 1.8339 1,8160 1.7976 1.7785

1.9531 1.9440 1.9339 1,9230 1.9110 1,8982 1,8846 1,8701 1,8549 1.8391 1.8228 1.8060 1.7890 1.7717

1.9523 1.9416 1.9302 1.9180 1.9052 1.8916 1.8774 1,8627 1.8474 1.8317 1.8157 1.7994 1.7831 1.7668

1.9559 1.9438 1.9312 1.9182 1.9047 1.8908 1.8765 1.8619 1.8470 1.8319 1.8168 1.8015 1.7864 1.7714

1.9457 1.9318 1.9178 1.9036 1.8892 1.8746 1.8599 1.8450 1.8301 1.8152 1.8003 1.7856 1.7711 1,7569

0.3649 0.3779 0.3912 0.4047 0.4187 0.4320 0.4449 0.4573 0.4691 0.4801 0,4901 0.4991 0.5069 0.5134

0.3917 0.4034 0.4154 0.4274 0.4393 0.4510 0.4622 0.4729 0.4829 0.4920 0,5001 0.5072 0.5131 0.5177

0.4580 0.4657 0.4737 0.4817 0.4896 0.4972 0.5045 0.5111 0.5171 0.5223 0.5267 0.5301 0.5325 0,5338

0.5165 0.5212 0.5262 0.5313 0.5363 0.5410 0.5454 0.5493 0.5526 0.5552 0.5570 0.5580 0.5581 0.5573

0.5548 0.5572 0.5598 0.5624 0.5650 0.5674 0.5694 0.5711 0.5722 0.5727 0.5726 0.5719 0.5704 0.5682

0.6274 0.5261 0.6252 0.6243 0.6235 0.6226 0.6215 0,6200 0.6182 0.6160 0.6133 0.6100 0.6063 0.6020

156.250 160.156 164,062 167.969 171.875 175.781 179.687 183.594 187.500 191.406 195.312 199.219

1.7744 1.7541 1.7334 1.7127 1.6921 1.6717 1.6517 1.6323 1.6135 1.5956 1.5787 1.5628

1.7592 1.7396 1.7199 1.7002 1.6808 1.6618 1.6432 1.6253 1.6081 1.5918 1.5765 1.5622

1.7544 1.7372 1.7201 1.7033 1.6869 1.6710 1.6557 1,6411 1.6273 1.6142 1.6021 1.5909

1.7505 1.7345 1.7188 1.7035 1.6887 1.6745 1.6609 1.6480 1.6360 1.6247 1.6143 1.6048

1.7566 1,7421 1.7281 1.7144 1.7013 1.6888 1.6769 1.6656 1.6551 1.6453 1.6362 1.6279

1.7430 1.7295 1.7165 1.7040 1.6921 1.6808 1.6700 1.6600 1.6506 1.6419 1.6338 1.6265

0.5185 0.5222 0.5244 0.5250 0.5241 0.5217 0.5178 0.5124 0.5057 0.4976 0.4884 0.4782

0.5210 0,5230 0.5235 0.5227 0.5204 0.5168 0.5119 0.5057 0.4983 0.4899 0.4804 0.4701

0,5341 0.5333 0.5314 0.5285 0.5245 0,5195 0.5136 0.5068 0.4993 0.4910 0.4821 0.4727

0.5556 0.5530 0,5494 0.5450 0,5398 0,5339 0.5272 0.5198 0.5119 0.5035 0,4948 0.4856

0.5653 0.5618 0.5575 0.5526 0.5472 0.5412 0.5347 0.5277 0.5204 0.5128 0.5049 0.4969

0.5972 0.5919 0.5861 0.5799 0.5733 0.5663 0.5590 0.5515 0.5438 0.5359 0.5279 0.5200

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

107

Table 2 Continued Wavenumber (cm -l)

n values for H20

k values for H20

-5.6°C

0.4°C

20.2°C

38.7°C

57.2°C

81.4°C

-5.6°C

0.4°C

20.2°C

38.7°C

57.2°C

81.4°C

203.125 207.031 210.937 214.844 218.750 222.656 226.562 230.469 234.375 238.281 242.187 246.094

1.5480 1.5345 1.5223 1.5114 1.5019 1.4938 1.4871 1.4817 1.4777 1.4750 1.4736 1.4735

1.5491 1.5371 1.5263 1.5168 1.5086 1.5016 1.4959 1.4915 1.4883 1.4863 1.4854 1.4856

1.5807 1.5715 1.5633 1.5562 1.5501 1.5449 1.5408 1.5377 1.5354 1.5340 1.5334 1.5335

1.5962 1.5885 1.5817 1.5758 1.5708 1.5667 1.5634 1.5609 1.5591 1.5580 1.5575 1.5575

1.6204 1.6136 1.6076 1.6024 1.5978 1.5939 1.5907 1.5881 1.5860 1.5844 1.5833 1.5826

1.6198 1.6138 1.6084 1.6037 1.5995 1.5959 1.5929 1.5903 1.5881 1.5863 1.5849 1.5838

0.4669 0.4549 0.4221 0.4288 0.4151 0.4011 0.3869 0.3728 0.3587 0.3450 0.3316 0.3187

0.4590 0.4472 0.4349 0.4222 0.4092 0.3960 0.3828 0.3697 0.3568 0.3442 0.3320 0.3204

0.4628 0.4526 0.4421 0.4315 0.4209 0.4103 0.3998 0.3896 0.3797 0.3703 0.3613 0.3529

0.4763 0.4667 0.4571 0.4475 0.4381 0.4288 0.4197 0.4110 0.4027 0.3948 0.3875 0.3807

0.4887 0.4806 0.4724 0.4644 0.4565 0.4489 0.4415 0.4345 0.4279 0.4216 0.4159 0.4106

0.5120 0.5041 0.4964 0.4888 0.4815 0.4744 0.4677 0.4613 0.4553 0.4497 0.4445 0.4397

250.0O0 253.910 257.812 261.719 265.625 269.531 273.437 277.344 281,250 285.156 289.062 292.969 296.875

1.4744 1.4764 1.4794 1.4831 1.4875 1.4923 1.4975 1.5028 1.5082 1.5135 1.5186 1.5234 1.5280

1.4868 1.4889 1.4917 1.4952 1.4992 1.5036 1.5081 1.5128 1.5175 1.5220 1.5264 1.5305 1.5344

1.5343 1.5356 1.5373 1.5394 1.5418 1.5443 1.5469 1.5495 1.5521 1.5546 1.5569 1.5591 1.5611

1.5580 1.5589 1.5600 1.5614 1.5630 1.5646 1.5662 1.5678 1.5693 1.5707 1.5720 1.5731 1.5740

1.5822 1.5820 1.5820 1.5822 1.5825 1.5828 1.5832 1.5835 1.5837 1.5839 1.5840 1.5839 1.5837

1.5829 1.5821 1.5815 1.5811 1.5806 1.5802 1.5798 1.5794 1.5789 1.5783 1.5777 1.5769 1.5760

0.3065 0.2950 0.2844 0.2747 0.2661 0.2585 0.2519 0.2464 0.2418 0.2381 0.2353 0.2331 0.2315

0.3095 0.2993 0.2900 0.2816 0.2741 0.2675 0.2619 0.2572 0.2534 0.2504 0.2480 0.2463 0.2451

0.3451 0.3380 0.3316 0.3259 0.3209 0.3166 0.3129 0.3099 0.3075 0.3056 0.3042 0.3032 0.3026

0.3745 0.3689 0.3639 0.3596 0.3558 0.3526 0.3500 0.3479 0.3463 0.3452 0.3444 0.3440 0.3439

0.4057 0.4014 0.3976 0.3943 0.3914 0.3890 0.3871 0.3855 0.3844 0.3835 0.3830 0.3828 0.3828

0.4354 0.4315 0.4281 0.4250 0.4224 0.4202 0.4183 0.4167 0.4155 0.4145 0.4139 0.4134 0.4132

300.781 304.687 308,594 312.500 316.406 320.312 324.219 328.125 332.031 335.937 339.844 343.750 347.656

1.5322 1.5362 1.5398 1.5431 1.5461 1.5488 1.5513 1.5536 1.5557 1.5577 1.5595 1.5612 1.5627

1.5379 1.5412 1.5442 1.5469 1.5493 1.5516 1.5535 1.5553 1.5569 1.5584 1.5597 1.5609 1.5619

1.5629 1.5644 1.5658 1.5670 1.5680 1.5688 1,5694 1,5699 1,5702 1.5703 1.5703 1.5701 1.5698

1.5748 1.5754 1.5758 1.5760 1.5760 1.5758 1.5755 1.5749 1.5742 1.5734 1.5724 1.5712 1.5698

1.5834 1.5829 1.5823 1.5815 1.5805 1.5794 1.5781 1.5767 1.5752 1.5734 1.5716 1.5695 1.5674

1.5750 1.5739 1.5726 1.5712 1.5697 1.5681 1.5663 1.5644 1.5624 1.5602 1.5580 1.5556 1.5531

0.2305 0.2299 0.2297 0.2297 0.2300 0.2305 0.2312 0.2320 0.2329 0.2339 0.2351 0.2363 0.2377

0.2443 0.2439 0.2439 0.2441 0.2445 0.2451 0.2459 0.2468 0.2479 0.2490 0.2502 0.2515 0.2529

0.3024 0.3024 0.3027 0.3033 0.3040 0.3049 0.3060 0.3072 0.3085 0.3099 0.3114 0.3130 0.3147

0.3441 0.3445 0.3452 0.3461 0.3471 0.3483 0.3497 0.3511 0.3527 0.3543 0.3561 0.3578 0.3597

0.3831 0.3836 0.3843 0.3852 0.3862 0.3873 0.3886 0.3899 0.3914 0.3929 0.3945 0.3961 0.3978

0.4132 0.4134 0.4137 0.4142 0.4148 0.4155 0.4164 0.4173 0.4182 0.4193 0.4204 0.4215 0.4227

351.562 355,469 359,375 363.281 367.187 371.094 375.000 378,906 382.812

1.5641 1.5655 1.5667 1.5679 1.5690 1.5699 1.5708 1.5716 1.5723

1.5628 1.5637 1.5644 1.5650 1.5655 1.5660 1.5663 1.5666 1.5667

1.5694 1.5688 1.5681 1.5673 1.5664 1.5653 1.5642 1.5629 1.5616

1.5683 1.5667 1.5649 1.5630 1.5610 1.5589 1.5566 1.5542 1.5517

1.5651 1.5627 1.5601 1.5574 1.5546 1.5517 1.5487 1.5456 1.5424

1.5505 1.5478 1.5450 1.5421 1.5391 1.5360 1.5328 1.5296 1.5262

0.2391 0.2406 0.2423 0.2440 0.2458 0.2478 0.2498 0.2520 0.2542

0.2544 0.2560 0.2576 0.2594 0.2612 0.2631 0.2651 0.2671 0.2693

0.3164 0.3182 0.3201 0.3220 0.3239 0.3259 0.3280 0.3300 0.3321

0.3616 0.3635 0.3654 0.3673 0.3693 0.3712 0.3732 0.3751 0.3770

0.3995 0.4012 0.4029 0.4047 0.4064 0.4081 0.4098 0.4115 0.4132

0.4239 0.4251 0.4263 0.4276 0.4288 0.4301 0.4313 0.4325 0.4337

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

108 Table 2 Continued Wavenumber (cm -l)

n values for H20

k values for H20

-5.6°C

0.4°C

20.2°C

38.7°C

57.2°C

81.4°C

-5.6°C

0.4°C

20.2°C

38.7°C

57.2°C

81.4°C

386.719 390.625 394.531 398.437

1.5729 1.5734 1.5737 1.5740

1,5668 1,5667 1,5666 1,5664

1.5601 1.5585 1.5569 1.5551

1.5492 1.5465 1.5437 1.5409

1.5391 1.5357 1.5322 1.5287

1.5228 1.5193 1.5158 1.5122

0.2566 0.2590 0.2616 0.2642

0.2715 0.2738 0.2761 0.2785

0.3341 0.3362 0.3384 0.3405

0.3789 0.3808 0.3827 0.3845

0.4148 0.4164 0.4179 0.4194

0.4349 0.4361 0.4372 0.4384

402.344 406.250 410.156 414.062 417.969 421.875 425.781 429.687 433.594 437.500 441.406 445.312 449.219

1.5741 1.5742 1.5741 1.5739 1.5736 1.5732 1.5727 1.5720 1.5713 1.5705 1.5696 1.5686 1.5675

1.5660 1.5656 1.5651 1.5644 1.5637 1.5629 1.5620 1.5610 1.5599 1.5587 1.5575 1.5562 1.5547

1.5533 1.5514 1.5494 1.5474 1.5453 1.5431 1.5408 1.5385 1.5361 1.5337 1.5312 1.5286 1.5259

1.5380 1.5380 1.5320 1.5289 1.5257 1.5225 1.5192 1.5159 1.5125 1.5091 1.5057 1.5022 1.4986

1.5251 1.5214 1.5177 1.5139 1.5100 1.5061 1.5022 1.4982 1.4941 1.4901 1.4860 1.4818 1.4776

1.5085 1.5048 1.5010 1.4971 1.4933 1.4893 1.4853 1.4813 1.4772 1.4731 1.4689 1.4647 1.4605

0.2669 0.2696 0.2725 0.2754 0.2783 0.2813 0.2843 0.2874 0.2905 0.2936 0.2968 0.3001 0.3033

0.2810 0.2835 0.2861 0.2887 0.2913 0.2940 0.2967 0.2995 0.3023 0.3051 0.3080 0.3109 0.3138

0.3426 0.3447 0.3469 0.3490 0.3511 0.3533 0.3554 0.3576 0.3597 0.3619 0.3641 0.3662 0.3684

0.3863 0.3880 0.3898 0.3915 0.3932 0.3948 0.3964 0.3980 0.3996 0.4012 0.4027 0.4042 0.4057

0.4209 0.4223 0.4237 0.4251 0.4264 0.4277 0.4289 0.4301 0.4312 0.4323 0.4334 0.4344 0.4354

0.4395 0.4405 0.4416 0.4426 0.4436 0.4446 0.4455 0.4464 0.4473 0.4482 0.4490 0.4498 0.4506

453.125 457.031 460.937 464.844 468.750 472.656 476.562 480.469 484.375 488.281 492.187 496.094

1.5663 1.5651 1.5637 1.5623 1.5607 1.5591 1.5574 1.5556 1.5536 1.5516 1.5495 1.5472

1.5532 1.5517 1.5500 1.5483 1.5464 1.5445 1.5425 1.5404 1.5382 1.5359 1.5335 1.5310

1.5233 1.5205 1.5177 1.5148 1.5119 1.5088 1.5057 1.5026 1.4993 1.4960 1.4925 1.4890

1.4950 1.4914 1.4877 1.4840 1.4802 1.4763 1.4724 1.4685 1.4645 1.4604 1.4563 1.4521

1.4734 1.4691 1.4648 1.4604 1.4560 1.4516 1.4471 1.4426 1.4380 1.4334 1.4288 1.4241

1.4562 1.4518 1.4474 1.4430 1.4385 1.4340 1.4294 1.4247 1.4200 1.4153 1.4105 1.4056

0.3066 0.3100 0.3134 0.3168 0.3203 0.3238 0.3274 0.3310 0.3347 0.3384 0.3422 0.3460

0.3168 0.3198 0.3228 0.3259 0.3290 0.3321 0.3353 0.3385 0.3418 0.3451 0.3485 0.3519

0.3706 0.3728 0.3750 0.3773 0.3795 0.3818 0.3840 0.3863 0.3886 0.3909 0.3932 0.3955

0.4072 0.4086 0.4100 0.4115 0.4129 0.4143 0.4157 0.4170 0.4184 0.4197 0.4211 0.4224

0.4364 0.4373 0.4382 0.4391 0.4399 0.4407 0.4415 0.4422 0.4429 0.4436 0.4442 0.4448

0.4514 0.4521 0.4528 0.4535 0.4541 0.4547 0.4553 0.4559 0.4564 0.4568 0.4573 0.4577

500.000 503.906 507.812 511.719 515,625 519.531 523.437 527.344 531.250 535.156 539.062 542.969 546.875

1.5448 1.5423 1.5396 1.5368 1.5339 1.5307 1.5275 1.5240 1.5204 1.5166 1.5126 1.5084 1.5041

1.5283 1.5256 1.5227 1.5197 1.5165 1.5132 1.5097 1.5061 1.5024 1.4984 1.4944 1.4901 1.4857

1.4854 1.4816 1.4778 1.4739 1.4698 1.4657 1.4617 1.4571 1.4526 1.4479 1.4432 1.4383 1.4333

1.4478 1.4435 1.4391 1.4346 1.4300 1.4254 1.4207 1.4159 1.4111 1.4061 1.4011 1.3960 1.3908

1.4193 1.4145 1.4096 1.4047 1.3997 1.3947 1.3896 1.3845 1.3793 1.3741 1.3688 1.3635 1.3581

1.4007 1.3958 1.3908 1.3857 1.3806 1.3754 1.3701 1.3648 1.3595 1.3541 1.3486 1.3431 1.3376

0.3499 0.3538 0.3578 0.3618 0.3658 0.3699 0.3740 0.3782 0.3823 0.3865 0.3906 0.3948 0.3989

0.3553 0.3588 0.3623 0.3658 0.3693 0.3729 0.3765 0.3800 0.3836 0.3872 0.3908 0.3943 0.3978

0.3979 0.4002 0.4025 0.4048 0.4071 0.4094 0.4117 0.4139 0.4161 0.4183 0.4204 0.4225 0.4245

0.4236 0.4249 0.4261 0.4273 0.4285 0.4296 0.4307 0.4317 0.4327 0.4336 0.4345 0.4353 0.4360

0.4453 0.4458 0.4463 0.4467 0.4470 0.4473 0.4476 0.4477 0.4478 0.4479 0.4478 0.4477 0.4475

0.4580 0.4583 0.4586 0.4587 0.4589 0.4590 0.4590 0.4589 0.4588 0.4586 0.4584 0.4580 0.4576

550,781 554.687 558.594 562.500

1.4995 1.4948 1.4898 1.4846

1.4811 1.4763 1.4714 1.4662

1.4282 1.4230 1.4176 1.4122

1.3856 1.3803 1.3749 1.3694

1.3527 1.3472 1.3417 1.3362

1.3320 1.3263 1.3206 1.3149

0.4030 0.4071 0.4111 0.4151

0.4013 0.4047 0.4081 0.4114

0.4265 0.4284 0.4302 0.4320

0.4367 0.4373 0.4378 0.4382

0.4473 0.4469 0.4465 0.4459

0.4571 0.4565 0.4559 0.4551

H.R. Zelsmann/Journal o f Molecular Structure 350 (1995) 95 114

109

Table 2 Continued Wavenumber (era - l )

566.406 570.312 574.219 578.125 582.031 585.937 589.844 593.750 597.656 601.562

n values for H 2 0

k values for H 2 0

-5.6°C

0.4°C

20.2°C

38.7°C

57.2°C

81.4°C

-5.6°C

0.4°C

20.2°C

38.7°C

57.2°C

81.4°C

1.4793 1.4737 1.4680 1.4620 1.4558 1.4495 1.4430 1.4362 1.4293 1.4222

1.4609 1.4555 1.4498 1.4440 1.4381 1.4319 1.4256 1.4192 1.4126 1.4058

1.4066 1.4009 1.3950 1.3891 1.3830 1.3769 1.3706 1.3643 1.3579 1.3513

1.3639 1.3583 1.3526 1.3469 1.3411 1.3353 1.3294 1.3235 1.3175 1.3116

1.3306 1.3250 1.3194 1.3137 1.3081 1.3024 1.2967 1.2910 1.2853 1.2796

1.3091 1.3033 1.2974 1.2915 1.2856 1.2797 1.2737 1.2677 1.2617 1.2557

0.4189 0.4228 0.4265 0.4301 0.4337 0.4371 0.4403 0.4435 0.4465 0.4493

0.4146 0.4178 0.4209 0.4238 0.4267 0.4294 0.4320 0.4345 0.4369 0.4391

0.4336 0.4352 0.4366 0.4380 0.4392 0.4404 0.4413 0.4422 0.4429 0.4435

0.4386 0.4388 0.4389 0.4390 0.4389 0.4387 0.4384 0.4380 0.4375 0.4369

0.4453 0.4446 0.4437 0.4428 0.4418 0.4406 0.4394 0.4380 0.4365 0.4350

0.4542 0.4532 0.4522 0.4510 0.4497 0.4483 0.4468 0.4452 0.4434 0.4416

to a C2v point group, there remains some doubt about the absolute validity of this model. The most evident result of the temperature effect on the different bands is the behavior of the S band. It shows only a small isotope effect of about 1.040 at 0°C - - a quantity which is at this temperature slightly less than the square root of the mass ratio

of the molecules - - whereas it obviously tends to unity at higher temperatures, for instance, 1.006 at 81.4°C. The temperature coefficients for the band positions were calculated by a linear fit from the data plotted in Fig. 4. The evolution of these band parameters with temperature are shown in Figs. 4 and 5.

........................................................................................................................

i

cm "I

constant of water

dielectric

4

................................................................... ~. .

H20

•

D20

•

20.2°C 81"4°C

+

2o.ooc

74.2

~ 6Ol.6

0

.... 0

I . 1

~x× 0

i

,+

, ........................ .i=................... ~+ 203.1 •+

•!

O ~

~ :

%:i

~

I

•

** i ××xA+

.,o~

296 1

.............

•

125°i . I r.................

!

ii 39.1 ©

i

..........

.

{

i

2

27.30 i

81.2°C •* ~× + ~........................... k'~...........© . . . . . . .

× .......................................................................

3

.

i

....................................................................

t .

.

.

. 2

.

.

.

.

.

.

.

3

.

. . 4

. 5

E' Fig. 8. C o l e - C o l e representation of the complex dielectric constant for H 2 0 and D 2 0 at two selected temperatures. Some of the data points are labeled with their wavenumbers in cm -1 .

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

110

Table 3 Refraction and absorption index data for D20 Wavenumber (cm - I )

n values for D20

k values for D20

4.0°C

20.2°C

38.7°C

57.2°C

81.2°C

4.0°C

20.2°C

38.7°C

57.2°C

81.2°C

19.531 23.437 27.334 31.250 35.156 39.062 42.969 46.875

2.1625 2.1128 2.0784 2.0530 2.0336 2.0184 2.0066 1.9975

2.2193 2.1639 2.1249 2.0955 2.0724 2.0537 2.0383 2.0258

2.2975 2.2419 2.2001 2.1666 2.1388 2.1146 2.0933 2.0749

2.3667 2.3057 2.2582 2.2200 2.1880 2.1603 2.1359 2.1142

2.4509 2.3818 2.3297 2.2876 2.2520 2.2209 2.1932 2.1682

0.5645 0.5073 0.4648 0.4323 0.4068 0.3864 0.3698 0.3563

0.6189 0.5593 0.5154 0.4821 0.4560 0.4352 0.4182 0.4043

0.7383 0.6704 0.6222 0.5862 0.5585 0.5374 0.5192 0.5042

0.8131 0.7399 0.6894 0.6510 0.6215 0.5982 0.5793 0.5636

0.9064 0.8256 0.7689 0.7274 0.6959 0.6714 0.6519 0.6360

50.781 54.687 58.594 62.500 66.406 70.312 74.219 78.125 82.031 85.937 89.844 93.750 97.656

1.9906 1.9858 1.9826 1.9806 1.9797 1.9793 1.9791 1.9788 1.9781 1.9768 1.9748 1.9712 1.9665

2.0156 2.0075 2.0012 1.9963 1.9920 1.9887 1.9859 1.9833 1.9805 1.9772 1.9734 1.9687 1.9630

2.0588 2.0448 2.0327 2.0222 2.0131 2.0050 1.9978 1.9911 1.9845 1.9779 1.9711 1.9638 1.9558

2.0949 2.0777 2.0624 2.0487 2.0364 2.0253 2.0152 2.0057 1.9966 1.9877 1.9787 1.9695 1.9599

2.1455 2.1248 2.1058 2.0884 2.0724 2.0575 2.0436 2.0304 2.0178 2.0055 1.9933 1.9811 1.9688

0.3456 0.3372 0.3312 0.3276 0.3261 0.3269 0.3298 0.3346 0.3412 0.3494 0.3590 0.3701 0.3816

0.3930 0.3839 0.3770 0.3729 0.3700 0.3691 0.3702 0.3731 0.3777 0.3838 0.3912 0.3996 0.4089

0.4915 0.4810 0.4723 0.4653 0.4601 0.4566 0.4548 0.4546 0.4560 0.4587 0.4627 0.4677 0.4735

0,5504 0,5392 0,5298 0.5221 0.5159 0,5112 0.5081 0,5064 0,5061 0,5070 0,5090 0,5120 0.5166

0.6227 0.6117 0.6024 0.5946 0.5882 0.5832 0.5794 0.5769 0.5754 0.5750 0.5754 0.5767 0.5786

101.563 105.469 109.375 113.281 117.188 121.094 125.000 128.906 132.813 136.719 140.625 144.531 148.437

1.9606 1.9535 1.9450 1.9352 1.9241 1.9117 1.8981 1.8833 1.8675 1.8507 1.8331 1.8148 1.7959

1.9563 1.9485 1.9396 1.9296 1.9184 1.9062 1.8930 1.8788 1.8638 1.8481 1.8317 1.8148 1.7975

1.9471 1.9376 1.9273 1.9160 1.9040 1.8911 1.8775 1.8631 1.8482 1.8328 1.8169 1.8008 1.7845

1.9498 1.9391 1.9278 1.9159 1.9033 1.8901 1.8763 1.8620 1.8473 1.8323 1.8170 1.8016 1.7861

1.9562 1.9433 1.9300 1.9163 1.9022 1.8877 1.8729 1.8579 1.8426 1.8272 1.8117 1.7963 1.7809

0.3938 0.4064 0.4192 0.4320 0.4447 1.4570 0.4687 0.4798 0.4900 0.4992 0.5073 0.5142 0.5198

0.4189 0.4292 0.4398 0.4504 0.4608 0.4709 0.4805 0.4895 0.4978 0.5051 0.5115 0.5169 0.5211

0.4800 0.4870 0.4942 0.5015 0.5086 0.5155 0.5220 0.5279 0.5331 0.5376 0.5413 0.5441 0.5459

0,5203 0.5251 0.5302 0.5354 0.5405 0.5453 0.5499 0.5539 0.5574 0.5603 0.5624 0.5638 0.5645

0.5810 0.5837 0.5866 0.5896 0.5924 0.5951 0.5974 0.5993 0.6007 0.6016 0.6018 0.6014 0.6004

152.344 156.250 160.156 164.062 167.969 171.875 175.781 179.687 183.594 187.500 191.406 195.312 199.219

1.7766 1.7571 1.7375 1.7180 1.6988 1.6800 1.6618 1.6442 1.6275 1.6117 1.5970 1.5833 1.5708

1.7800 1.7624 1.7447 1.7273 1.7102 1.6935 1.6773 1.6617 1.6470 1.6330 1.6199 1.6078 1.5967

1.7682 1.7519 1.7358 1.7200 1.7046 1.6897 1.6753 1.6616 1.6486 1.6363 1.6249 1.6143 1.6045

1.7707 1.7554 1.7404 1.7257 1.7114 1.6976 1.6843 1.6717 1.6597 1.6483 1.6377 1.6279 1.6187

1.7658 1.7509 1.7364 1.7223 1.7086 1.6955 1.6829 1.6710 1.6596 1.6489 1.6388 1.6294 1.6207

0.5241 0.5269 0.5282 0.5282 0.5267 0.5238 0.5197 0.5143 0.5077 0.5002 0.4917 0.4824 0.4725

0.5242 0.5261 0.5268 0.5263 0.5247 0.5219 0.5181 0.5134 0.5077 0.5012 0.4940 0.4862 0.4779

0.5468 0.5467 0.5457 0.5437 0.5408 0.5371 0.5325 0.5273 0.5214 0.5150 0.5080 0.5007 0.4931

0.5643 0.5633 0.5616 0.5591 0.5559 0.5520 0.5475 0.5424 0.5369 0.5310 0.5247 0.5181 0.5114

0.5987 0.5964 0.5934 0.5899 0.5858 0.5813 0.5763 0.5709 0.5652 0.5592 0.5530 0.5467 0.5403

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

111

Table 3 Continued Wavenumber (cm-1)

n values for D20

k values for D20

4.0°C

20.2°C

38.7°C

57.2°C

81.2°C

4.0°C

20.2°C

38.7°C

57.2°C

81.2°C

203.125 207.031 210.937 214.844 218.750 222.656 226.562 230.469 234.375 238.281 242.187 246.094

1.5595 1.5495 1.5407 1.5331 1.5267 1.5215 1.5175 1.5145 1.5125 1.5115 1.5113 1.5118

1.5866 1.5775 1.5694 1.5624 1.5564 1.5513 1.5472 1.5440 1.5415 1.5397 1.5386 1.5381

1.5956 1.5876 1.5805 1.5742 1.5687 1.5640 1.5601 1.5568 1.5541 1.5520 1.5504 1.5492

1.6103 1.6027 1.5957 1.5895 1.5839 1.5790 1.5747 1.5709 1.5676 1.5647 1.5623 1.5601

1.6126 1.6051 1.5982 1.5920 1.5862 1.5810 1.5762 1.5719 1.5679 1.5643 1.5610 1.5579

0.4620 0.4512 0.4401 0.4289 0.4177 0.4066 0.3958 0.3854 0.3754 0.3660 0.3572 0.3491

0.4693 0.4603 0.4513 0.4421 0.4331 0.4242 0.4156 0.4073 0.3994 0.3921 0.3853 0.3791

0.4852 0.4773 0.4693 0.4614 0.4536 0.4460 0.4387 0.4317 0.4252 0.4191 0.4135 0.4084

0.5046 0.4976 0.4908 0.4840 0.4773 0.4709 0.4648 0.4589 0.4535 0.4484 0.4437 0.4394

0.5339 0.5276 0.5213 0.5152 0.5093 0.5036 0.4982 0.4930 0.4882 0.4838 0.4797 0.4760

250.000 253.910 257.812 261.719 265.625 269.531 273.437 277.344 281.250 285.156 289.062 292.969 296.875

1.5130 1.5146 1.5166 1.5189 1.5214 1.5238 1.5263 1.5286 1.5308 1.5328 1.5345 1.5360 1.5372

1.5380 1.5382 1.5388 1.5395 1.5403 1.5411 1.5419 1.5426 1.5432 1.5437 1.5439 1.5440 1.5438

1.5484 1.5478 1.5474 1.5471 1.5469 1.5468 1.5466 1.5463 1.5459 1.5454 1.5447 1.5439 1.5429

1.5583 1.5566 1.5551 1.5537 1.5523 1.5510 1.5496 1.5482 1.5468 1.5452 1.5435 1.5416 1.5397

1.5549 1.5522 1.5495 1.5469 1.5443 1.5418 1.5391 1.5365 1.5338 1.5310 1.5280 1.5250 1.5219

0.3419 0.3354 0.3297 0.3249 0.3209 0.3176 0.3150 0.3131 0.3118 0.3110 0.3107 0.3107 0.3111

0.3736 0.3687 0.3645 0.3609 0.3579 0.3556 0.3538 0.3525 0.3517 0.3513 0.3513 0.3516 0.3522

0.4039 0.3999 0.3965 0.3936 0.3912 0.3893 0.3879 0.3869 0.3863 0.3861 0.3862 0.3866 0.3872

0.4356 0.4323 0.4294 0.4269 0.4248 0.4232 0.4219 0.4210 0.4203 0.4200 0.4200 0.4202 0.4206

0.4726 0.4696 0.4670 0.4647 0.4627 0.4611 0.4597 0.4586 0.4578 0.4572 0.4568 0.4565 0.4565

300.781 304.687 308.594 312.500 316.406 320.312 324.219 328.125 332.031 335.937 339.844 343.750 347.656

1.5382 1.5389 1.5394 1.5396 1.5396 1.5395 1.5391 1.5386 1.5380 1.5372 1.5363 1.5352 1.5340

1.5434 1.5428 1.5420 1.5410 1.5397 1.5383 1.5367 1.5350 1.5330 1.5309 1.5287 1.5263 1.5237

1.5417 1.5403 1.5387 1.5369 1.5349 1.5327 1.5303 1.5278 1.5250 1.5221 1.5190 1.5157 1.5122

1.5375 1.5352 1.5328 1.5302 1.5274 1.5244 1.5213 1.5179 1.5145 1.5108 1.5070 1.5030 1.4988

1.5186 1.5152 1.5116 1.5080 1.5041 1.5002 1.4961 1.4919 1.4875 1.4830 1.4783 1.4736 1.4686

0.3118 0.3127 0.3138 0.3151 0.3165 0.3181 0.3198 0.3215 0.3234 0.3254 0.3274 0.3295 0.3317

0.3531 0.3541 0.3554 0.3568 0.3583 0.3600 0.3617 0.3636 0.3655 0.3675 0.3696 0.3717 0.3739

0.3881 0.3892 0.3905 0.3919 0.3934 0.3951 0.3969 0.3988 0.4007 0.4027 0.4048 0.4049 0.4091

0.4216 0.4221 0.4230 0.4241 0.4254 0.4267 0.4281 0.4296 0.4312 0.4329 0.4345 0.4363 0.4380

0.4566 0.4568 0.4571 0.4575 0.4580 0.4585 0.4591 0.4598 0.4604 0.4611 0.4619 0.4626 0.4633

351.562 355.469 359.375 363.281 367.187 371.094 375.000 378.906 382.812

1.5328 1.5313 1.5298 1.5282 1.5264 1.5245 1.5224 1.5201 1.5177

1.5210 1.5181 1.5151 1.5119 1.5086 1.5051 1.5014 1.4976 1.4936

1.5085 1.5047 1.5006 1.4964 1.4920 1.4874 1.4826 1.4776 1.4724

1.4944 1.4899 1.4852 1.4803 1.4752 1.4699 1.4645 1.4589 1.4530

1.4636 1.4584 1.4531 1.4476 1.4420 1.4362 1.4303 1.4243 1.4181

0.3341 0.3365 0.3390 0.3417 0.3444 0.3473 0.3505 0.3534 0.3566

0.3761 0.3784 0.3808 0.3832 0.3856 0.3881 0.3906 0.3931 0.3957

0.4113 0.4135 0.4158 0.4180 0.4202 0.4225 0.4247 0.4269 0.4290

0.4398 0.4415 0.4433 0.4450 0.4468 0.4485 0.4502 0.4518 0.4533

0.4640 0.4647 0.4654 0.4660 0.4666 0.4671 0.4676 0.4680 0.4683

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

112 Table 3 Continued Wavenumber (cm -1)

n values for D20

k values for D20

4.0°C

20.2°C

38.7°C

57.2°C

81.2°C

4.0°C

20.2°C

38.7°C

57,2°C

81.2°C

386.719 390.625 394,531 398,437

1.5151 1.5123 1,5092 1.5059

1.4894 1.4849 1.4803 1.4755

1.4670 1.4614 1.4556 1,4495

1.4470 1.4408 1.4345 1.4279

1.4118 1.4054 1.3988 1.3921

0.3599 0.3634 0.3669 0.3705

0.3983 0.4009 0.4036 0.4062

0.4311 0.4332 0.4351 0.4370

0.4548 0.4562 0.4574 0,4586

0.4686 0.4687 0.4687 0.4687

402.344 406.250 410.156 414.062 417.969 421.875 425.781 429.687 433.594 437.500 441.406 445.312 449.219

1.5023 1.4985 1.4944 1,4900 1.4854 1.4803 1.4749 1.4693 1.4633 1.4570 1.4503 1.4434 1.4361

1.4704 1.4651 1.4596 1.4538 1.4478 1.4415 1,4350 1.4283 1.4213 1.4141 1,4067 1,3990 1.3912

1.4433 1.4369 1.4303 1.4235 1,4164 1.4092 1,4018 1.3942 1.3864 1,3785 1.3705 1.3623 1.3539

1.4211 1.4142 1.4071 1.3998 1.3924 1.3847 1.3770 1.3691 1.3610 1.3528 1.3446 1.3362 1.3278

1.3852 1.3782 1.3711 1.3639 1,3565 1.3491 1.3415 1.3338 1.3261 1.3183 1.3104 1.3025 1.2945

0.3742 0.3779 0.3817 0.3855 0.3893 0.3930 0,3968 0.4004 0.4040 0.4075 0,4108 0.4139 0.4169

0.4087 0,4113 0.4138 0.4162 0.4185 0.4208 0.4229 0.4248 0.4266 0.4283 0.4297 0.4309 0.4319

0.4388 0,4404 0.4420 0.4434 0,4446 0,4457 0,4466 0,4472 0,4477 0,4479 0.4478 0.4475 0.4470

0.4597 0.4606 0.4613 0.4619 0.4623 0.4625 0.4625 0.4623 0.4618 0.4611 0.4601 0.4588 0.4573

0,4684 0.4681 0.4676 0.4669 0.4660 0.4650 0.4637 0.4623 0.4606 0.4587 0.4565 0.4541 0.4514

453.125 457.031 460.937 464.844 468,750 472.656 476.562 480.469 484.375 488.281 492.187 496.094

1.4285 1.4206 1.4125 1.4040 1.3953 1.3864 1.3773 1.3680 1.3585 1.3488 1.3391 1.3293

1.3831 1.3748 1.3664 1.3578 1.3491 1.3403 1.3314 1.3224 1.3133 1,3043 1.2952 1.2862

1.3455 1.3369 1.3283 1.3196 1.3109 1.3021 1.2934 1.2847 1.2760 1.2673 1.2588 1.2503

1,3192 1.3107 1.3021 1.2935 1.2849 1.2763 1.2677 1,2592 1.2508 1.2425 1.2344 1.2263

1.2866 1.2786 1.2706 1.2627 1.2548 1.2470 1.2392 1.2316 1.2240 1.2166 2.2094 1.2023

0,4196 0.4220 0.4242 0.4261 0.4277 0.4290 0.4298 0.4303 0.4304 0.4301 0.4294 0.4282

0.4326 0.4330 0.4331 0.4329 0.4324 0.4316 0.4304 0.4288 0.4269 0.4245 0.4218 0.4187

0.4461 0.4450 0.4435 0.4417 0.4396 0.4371 0.4343 0.4311 0.4276 0.4238 0.4196 0.4150

0.4555 0.4534 0.4509 0.4482 0,4451 0.4417 0.4380 0.4339 0.4295 0,4248 0.4197 0.4144

0.4485 0.4453 0.4418 0.4380 0.4340 0,4296 0.4250 0.4201 0.4149 0.4094 0.4036 0.3976

500.000 503.906 507.812 511.719 515.625 519.531 523.437 527.344 531.250 535.156 539.062 542.969 546.875

1.3194 1.3095 1.2996 1.2897 1,2799 1.2702 1.2606 1.2512 1.2420 1.2330 1.2243 1.2158 1.2076

1.2772 1.2682 1.2594 1.2507 1.2422 1,2338 1.2257 1.2177 1.2101 1.2026 1.1955 1,1887 1.1822

1.2420 1.2339 1.2259 1.2181 1.2105 1.2031 1.1960 1.1891 1.1826 1.1763 1.1704 1.1647 1.1594

1.2185 1.2108 1.2023 1.1960 1.1890 1.1822 1.1757 1.1695 1.1636 1.1580 1.1527 1.1478 1,1432

1.1954 1.1887 1,1822 1,1759 1,1699 1,1642 1,1587 1.1535 1A486 1.1440 1.1398 1.1358 1.1322

0.4265 0,4224 0.4219 0.4189 0.4154 0.4115 0.4071 0.4023 0.3970 0.3913 0.3852 0.3787 0.3719

0.4153 0.4114 0.4071 0.4025 0.3974 0,3920 0.3863 0.3802 0.3737 0.3670 0,3599 0.3525 0,3449

0.4102 0.4049 0.3994 0.3935 0.3873 0.3808 0.3740 0.3669 0.3596 0.3520 0.3442 0.3363 0.3281

0,4087 0.4027 0.3964 0.3898 0.3830 0.3759 0.3685 0.3609 0.3531 0.3451 0.3368 0.3285 0.3200

0.3913 0.3847 0.3779 0.3708 0.3636 0.3561 0.3484 0.3405 0.3325 0,3243 0.3160 0.3075 0.2990

550.781 554.687 558.594 562.500

1.1998 1,1923 1.1851 1.1783

1.1760 1.1702 1.1648 1.1597

1.1545 1.1499 1.1457 1.1418

1.1389 1.1350 1.1315 1.1283

1.1289 1.1260 1,1234 1.1211

0.3647 0.3571 0.3493 0.3411

0.3371 0.3290 0.3207 0.3123

0.3197 0.3112 0.3026 0.2939

0.3113 0.3025 0.2937 0.2848

0.2903 0.2816 0.2729 0,2641

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

113

Table 3 Continued Wavenumber (cm-I)

566.406 570.312 574.219 578.125 582.031 585.937 589.844 593.750 597.656 601.562

k values for D20

n values for D20 4.0°C

20.2°C

38.7°C

57.2°C

81.2°C

4.0°C

20.2°C

38.7°C

57.2°C

81.2°C

1.1720 1.1660 1.1605 1.1554 1.1507 1.1465 1.1428 1.1395 1.1366 1.1342

1.1550 1.1507 1.1468 1.1434 1.1403 1.1376 1.1354 1.1335 1.1321 1.1310

1.1384 1.1353 1.1326 1.1302 1.1283 1.1267 1.1256 1.1248 1.1243 1.1243

1.1255 1.1230 1.1210 1.1193 1.1180 1.1171 1.1165 1.1163 1.1164 1.1169

1.1192 1.1177 1.1165 1.1157 1.1152 1.1150 1.1152 1.1158 1.1167 1.1179

0.3328 0.3242 0.3154 0.3064 0.2973 0.2880 0.2787 0.2693 0.2600 0.2506

0.3036 0.2949 0.2861 0.2771 0.2682 0.2592 0.2502 0.2412 0.2323 0.2234

0.2851 0.2762 0.2673 0.2583 0.2494 0.2405 0.2317 0.2229 0.2143 0.2058

0.2758 0.2668 0.2578 0.2488 0.2399 0.2310 0.2222 0.2135 0.2050 0.1966

0.2553 0.2465 0.2378 0.2291 0.2204 0.2119 0.2035 0.1952 0.1871 0.1791

For the different bands we get the values of: B, -0.303 cm 1 deg-I for H 2 0 and -0.225 cm -1 deg -~ for D20; L1, -0.565 cm -1 deg -1 for H 2 0 and -0.300 cm -l deg 1 for D20; L2, -0.713 cm -1 deg -1 for H 2 0 and -0.442 cm 1 deg-l for D20. In Figs. 6(a) and 6(b), we have represented the calculated spectra of the refractive index n for several temperatures. To the H 2 0 spectra we have added the earlier available data for comparison. It can be seen that there is very good agreement between the present data and those of Afsar and Hasted [15], whereas there is some variance with the n values given by Downing and Williams [13]. This same discrepancy is even more obvious on the spectra of the absorption index k which are shown in Fig. 7(a). The lack of corresponding data for D 2 0 does not permit a similar comparison. Due to the fact that our results confirm the findings of Afsar and Hasted [15] within a few percent by a different method of measurement, we may consider these n and k spectra of D 2 0 to be actually the most reliable ones. The numerical values used for the plots of Figs. 6 and 7 are summarized in Tables 2 and 3. From these latter spectra of n and k, we can deduce the real and imaginary parts of the dielectric constant for both the H 2 0 and the D 2 0 molecule by using Eqs. (4a) and (4b). For their representation it is useful to choose a Cole-Cole plot, which shows more clearly the differences between H 2 0 and D 2 0 than would a simple

spectrum of e' and e" plotted versus wavenumber (see Fig. 8). The principal information we may draw from Fig. 8 is that H 2 0 and D 2 0 behave similarly at temperatures of 20°C and below, whereas we notice a fundamental difference in the principal relaxation process between HzO and D 2 0 at high temperatures. Qualitatively we see that the relaxation times decrease more rapidly with rising temperature for light water, than they do for heavy water; a finding which has been independently quantified by low frequency Raman spectroscopy [10]. This behavior seems to merit further attention for new quantitative experiments over an extended frequency and temperature range.

5. Conclusion We have shown in this paper that conventional absorption spectroscopy may be a valid approach to quantitative results, namely the optical constants n and k of a parallel film of a highly absorbing liquid, which are obtained otherwise by dispersive F T spectroscopy in the far IR region or by the A T R technique in the mid IR region. One of the major advantages of the chosen method of data exploitation is the possibility of including all contributions from the interference signals into the iterative K r a m e r s - K r o n i g procedure which in the context of quantitative results is an essential clue. Thus we overcome the

114

H.R. Zelsmann/Journal of Molecular Structure 350 (1995) 95-114

principal drawback of conventional absorption spectroscopy which is rather pronounced in the far IR region. The statement of validity of this method stems from the very good agreement obtained with the H20 spectrum at 19°C of Afsar and Hasted [15]. From our water spectra we conclude the probable existence of a second IR component of the librational band which in the past has only been observed by Raman spectroscopy or neutron scattering. The observation of this band by IR implies that the actually claimed structure of the hydrogenbonded pentamer with C2v symmetry certainly needs some refinements. Only forthcoming experiments and a deeper analysis may help to clarify this point and its consequences on the structure of water.

Acknowledgment The author would like to thank Dr. Y. Mar6chal for his unfailing advice, his encouragement and careful reading of the manuscript. References [1] D. Eisenberg and W. Kauzmann, The Structure and Properties of Water, Clarendon, Oxford, 1969. [2] G.E. Walrafen, in F. Franks (Ed.), Water: A Comprehensive Treatise, Vol. 1, Plenum, New York, 1972. [3] M. Moskovits and K.H. Michaelian, J. Chem. Phys., 69 (1978) 2306. [4] Y. Yeh, J.H. Bilgram and W. K~inzig, J. Chem. Phys., 77 (1982) 2317. [5] S. Krishnamurthy, R. Bansil and J. Wiafe-Akenten, J. Chem. Phys., 79 (1983) 5863.

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