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Far-infrared absorption in liquid water
Volume
118, number
CHEMICAL
6
FAR-INFRARED J.B. HASTED, E~rxTbechCollege, Received
24 April
ABSORPTION SK
HUSAIN,
Maler Sreer, 1985;
London
PHYSICS
IN LIQUID F.A.M. WCJE
m final form 25 May
LFTITERS
WATER
FRESCURA 7NX.
16 August 1985
and J.R
BIRCH
’
UK
1985
The results of new measuremems of the far-infrared opticalconstant OFhquld waler out 10 4 cm-’ a~ 293 K are presented. The+= together with previously published submillimetre wavelength measuremen&. are analysed to show that it is possible to lip the continuous far-infrared-tcrmicrowave absorption spectrum LO classical polar-molecule relaxation theory with added conlribuuons rrom Gaussian oscillator close to 200 and 50 cm- ‘_ Bolh of these oscillators ha\e been observed in Raman sludles. The 100 cm- ’ band is well characLerised in infrared measuremenls. but the presenL work represents the first unambiguous identirlcalion of the 50 cm-’ band in mrrared observations.
The far-infrared absorption spectrum of liquid water is so intense that quantitative studies of its optical constants are best made by the technique of reflectron dispersrve Fourier transform spectroscopy [l] (reflection DFTS). In this the complex reflection spectrum of an interface between a transparent wiudow and the liquid is directly dcterrnmed and used to calculate the optical constants. Previous measurements on water by various forms of this technique [2--71 have characterised the spectral region between 15 and 400 cm-l and have shown that although the principal dielectnc relaxation mechanism was well known [S], the anomalously high value of the limiting highfrequency permittivity [9], E,, had posed difficultres of interpretation [lo,1 11. The present work draws on recent experimental developments in reflection DFTS that have mcluded improved measurement method [ 121 and Improved cell construction [13]. It presents the re&Its of near mrllimetre vave!cngth studies on water that have allowed its optical constants to be determined with improved accuracy and to lower wavenumbers than were attained by other DFTS measurements. These results are discussed in association with some of the previous results [6]- This complete far-infrared-to-
’
Pemanerrt addmss: Division or Electrical Science, National Physical Laboratory. Teddingion. Mrddlesex TWll OLW. UK.
622
data set is fitted to classical polar-molecule relaxation theory with additional contrrbutions from Gaussian oscillators at about 200 and 50 cm-l. The 50 cm-l band 1s clearly resolved in the measurements and this represents its first unambiguous identification in infrared measurements, although rt has been observed in Raman studres [I 41. The new measurements were made by reflection DOTS using a polarising interferometer [13] and a liquid-helium-cooled indium antimonide hot electron bolometer as detector_ Measurements were made in the spectral range between 4 and 40 cm-l at temperatures between 277 and 317 K, although only data at 293 K are reported here_ Above 15 cm-1 the present results are in good agreement with those of Afsar and Hasted [6], while at Iower wavenumbers the present refraction spectrum has somewhat lower values than the earlier work. For the purposes of the present work the optical constant data is most conveniently expressed as the complex relative permittivity, S, and &splayed on a Cole-Cole plot as iu fig. 1. At the lowest wavenumbers measured both the real, l‘,and the imaginary, E”, parts of @ increase as the wavenumber decreases towards values corresponding to the principal relaxation time (9.33 ps 181). In the present treatment of the principal relaxation process, 5 is described as a function of angular frequency, o, by the Cole-Cole equation microwave
yw)
= e,
0 009-2614/85/S (North-Holland
+ (e, - E,)/[
1+ (iwT)l-h]
-
(1)
03.30 0 Elsevier Science Publishers B.V. Physics Publishing Division)
CHEMICAL PHYSICS LEITERS
Volume 118, number 6
16 August 1985
and found that at 293 and 294 K the extrema values of E, were 5.62 f 0.19 and 4.13 * 0.38. Thus, the present value for E, falls almost midway between these values. However, this agreement is probably fortuitous as it is apparent from the full results of Kaatze
lo-
and Uhlendorf
for E, as a function of temperature that there are systematic errorsin their results at levels
e-6.0
-7
0
6-
k!;?
. . . 13.7
i
Fig. 1. Cole-Cole representation of the spectral variation of the complex relative permittitity of water at 293 K. The ticles represent the new data, the crosses the previous data of Afsar and Hasted [6]. The continuous curverepresents the mntriblhon to the complex perrmttlvity of the principal relaxation process. as destibed in eq. (1). The data points are labelled with their corresponding wavenumbers in cm-l_
In this E, and E, are the static and lugh-frequency limits of the real part of the permittivity, respectively, r is the principal relaxation time, and the parameter h represents the effect of a small distribution of relaxation times about the central value 7. The results of fittmg this to the present low-wavenumber data is represented by the continuous curve in fig. 1. The only adjustable parameter was E,, the parameters of the principal relaxation process being taken from previous work [8]. The value of E, obtained from the fit was 4.86, considerably above that obtained (4.2) from only fitting to lower-frequency data [S]. Kaatze and Uhlendorf [IS] have reported a determination of the complex relative permittivity of water in the I -60 GHz region at temperatures between 269 and 333 IL They analysed their data by fittingthem to a Debye form
of the order of, or somewhat above, the quoted !evels of random uncertainty_ It is interesting to note that Kaatze and Uhlendorf were unable to find any clear evidence for a dtstnbution of relaxation tunes such as that assumed in the present work by the use of the Cole-Cole formulation. Thus, one can sensibly compare the E, data derived from these two different models as, in the hmit of no distribution of relaxation times, the two models are equivalent. The principal relaxation process and the measured data can also be compared in the form of their corresponding power absorption spectra,as shownin fig. 2. The contxibutron of the principal relaxation process rapidly tends to the constant Debye plateau value, while the real data rise into the wing of a higher-wavenumber process. The important feature of these data is the presence of a small shoulder m the regton of 8-10 cm-1 that is superimposed on this wing absorption_ It is resolved in the measurements at a level well above the random uncertainties of the measuremen t process. This will be considered in more detail in a subsequent presentation after further measurements. Fig. 3 presents the complete absorption spectrum of water up to 230 cm- 1, drawing on both the new low-wavenumber data and the previous higher-wavenumber values [6]. The continuous curve represents the best fit to the data of the sum, Q(P), as a function of wavenumber, P, of the contribution of the principal relaxation process, a,(ir), and a Gaussian oscillator: a(P) = o&J)
+ C, exp [-(J
- PJ2/r,2]
_
(2)
In this ‘Jsis the oscillator wavenumber, 7s the damping term and C, the oscillator strength. The principal relaxation, Cole-Cole, contribution to this was calculated from eq. (1) using the previously referred to parameters [8]. The best-fit values of these were ‘75 = 199 cm-r, -ys = 102 cm-l and C, = 1078 cm-r. Between RO and 210 cm b-1 the agreement between measurement and calculation is very close, far better than corresponding Lorentzian frttmgs Above 210 cm-l no 623
Volume
CHFMICAL
118, number 6
PHYSlCS
lJXll’EI%S
16
August 1985
I +
+
I
I._
10
I 30
20 Wavenumber
I
LO
(cm-‘)
Fig_ 2. The measured spectral variation of the power absorption coefficient up to 40 cm -l. Circles represent the new &Ix. the uosscs t>e previous data of Afsar and Hasted [6] The continuous curye represents the contribution to the absorption spectrum of the principal relaxanon profess. as desabed in cq. (1).
claim is made concemmg the symmetry of the band (see ref_ [14]), whch m any case is obscured by the strong 685 cm-l band. Below 80 cm-l it is clear that the measurements reveal the presence of an additional band in the region I
I
looO-
mm1 a-acme
-
(Cm-‘)
0
100
ci (cm-‘)-
zoo
Fig_ 3 The measured power absorption speclrum of water up to 230 cm+ at 293 K shown plotted as circles The continuous curve represents the best fit of eq (2) to the data set.
624
Fig. 4. ‘The 49 cm-t absorption band in wat& at 293 K. The aosses represent the Merenoe spectrum between the measured data points and the best-fit curve shown m kig. 3 The continuous curve represents the best fit of a Gaussian oscilk tar to the differen= spectrum.
Volume 118, number 6
CHEMICALPHYSICS LEl-EFS
of 50 cm-l, superimposed on the low-frequency wing of the 199 cm-l band. The difference between the measurements and the best-fit calculation in this spectral region is represented by the plotted points in fig. 4. These clearly reveal an absorption band centred close to 50 cm-l with a full width at half height of about 40 cm-l. This band has been observed in the Raman spectrum of water [ 141, but not previously in its absorption spectrum, although Simpson et al. [16] have interpreted structure at 5.5 m-1 in the refraction spectrum derived from power reflection measurements on water as evidence for tlus feature. However, their data, both in absorption and refraction, show other sin&r small-scale structure that is not assigned. Hence their assignment may have been fortuitous. The smooth curve in fig. 4 represents the best fit of a further Gaussian oscillator to this second feature The best fit parameters were ir = 49.4 cm-l, y, = 25.3 cm-l and C, = 37.5 cm- ls It is of relevance here to note that in the present measurements that have been made at other temperatures, this band virtually disappears by a temperature of 303 K. This agrees with the Raman measurements [ 141 which were taken both in water and supercooled water, where the band was found to be more pror@nent. It is encouragmg that the milbmetre and submillimetre wavelength electrical properties of liquid water should be susceptible to interpretation along such well established lines, without recourse to new postulations and hypotheses_ The uniquely high value of E, has been a source of controversy for many years. NOW it seems probable that the breadth of the 50 and 200 cm-1 bands contnbute most of the E, - n2 difference through the Kramers-Kronig relations. Thus, in
16 August
1985
the treatment of dlpcle relaxatior?, n* rather than c_ must be used in Kirkwood-Frbhlich or other formalisms
References [I] J.R Birch and TJ. Parker, in: Tnfra~ed and millimeter
[2] [3] [4] [5]
[6] [7] (81 [9] [lo] (111
[ 121 [13] [14] [ 15) [16]
waves, Vol. 2. ed. K.J. Button (Aademic Press, New York, 1979) ch I J. Chamberlain, MS. Zafar and J-B. Hasted, Nature 243 (1973) 116. MS. Zafar, J.B. Hasted and J. Chamberlain, Nature 243 (1973) 106. J-E. Cl-Amberlain, M.N. A&r, J.B. Hasted, M_S. Afar and GJ. Davies, Nature 255 (1975) 319. M.N. Afsar, J.B. Ha_sted and J. Chamberlain. Infrared Fhys. 16 (1976) 301. M.N.Afsar and J.B. Hasted, J Opt. Sot. Am 67 (1977) 902. MN. Afsar and J.B. Hasted. Infrared Phys. 18 (1978) 835. P.R. Mason, J B. Hasted and L. Moore, Advan Mel Relaxation Processes 6 (1974) 217. C.H. Collie, J.B Hasted and D.M. Ritson, Rot Phys. Sot. (London) 60 (1948) 71. E WhaUey,Nature 251 (1974) 217. J.B. Harted, M S. Afar and J Chamberlain, Nature 251 (1974) 218. J.R. Birch and M. Bennouna. Infrared Phys. 21 (1981) 229. J R. Birch, G.P. OWeilI, J Yarwood and M. Bennouna. J. Phys El5 (1982) 6e4. S. Krishnamurthy, R. Bansil and J. Wiafe-Akezten, J. Chem. Phys. 79 (1983) 5863. U. Kaatze and V Uhlendorf, Z. Physik Chem N F 126 (1981) 151 0-A. Simpson, B.L. Bean and S. Perkowitz, J. Opt. Sot. Am. 69 (1979) 1723.
625
118, number
CHEMICAL
6
FAR-INFRARED J.B. HASTED, E~rxTbechCollege, Received
24 April
ABSORPTION SK
HUSAIN,
Maler Sreer, 1985;
London
PHYSICS
IN LIQUID F.A.M. WCJE
m final form 25 May
LFTITERS
WATER
FRESCURA 7NX.
16 August 1985
and J.R
BIRCH
’
UK
1985
The results of new measuremems of the far-infrared opticalconstant OFhquld waler out 10 4 cm-’ a~ 293 K are presented. The+= together with previously published submillimetre wavelength measuremen&. are analysed to show that it is possible to lip the continuous far-infrared-tcrmicrowave absorption spectrum LO classical polar-molecule relaxation theory with added conlribuuons rrom Gaussian oscillator close to 200 and 50 cm- ‘_ Bolh of these oscillators ha\e been observed in Raman sludles. The 100 cm- ’ band is well characLerised in infrared measuremenls. but the presenL work represents the first unambiguous identirlcalion of the 50 cm-’ band in mrrared observations.
The far-infrared absorption spectrum of liquid water is so intense that quantitative studies of its optical constants are best made by the technique of reflectron dispersrve Fourier transform spectroscopy [l] (reflection DFTS). In this the complex reflection spectrum of an interface between a transparent wiudow and the liquid is directly dcterrnmed and used to calculate the optical constants. Previous measurements on water by various forms of this technique [2--71 have characterised the spectral region between 15 and 400 cm-l and have shown that although the principal dielectnc relaxation mechanism was well known [S], the anomalously high value of the limiting highfrequency permittivity [9], E,, had posed difficultres of interpretation [lo,1 11. The present work draws on recent experimental developments in reflection DFTS that have mcluded improved measurement method [ 121 and Improved cell construction [13]. It presents the re&Its of near mrllimetre vave!cngth studies on water that have allowed its optical constants to be determined with improved accuracy and to lower wavenumbers than were attained by other DFTS measurements. These results are discussed in association with some of the previous results [6]- This complete far-infrared-to-
’
Pemanerrt addmss: Division or Electrical Science, National Physical Laboratory. Teddingion. Mrddlesex TWll OLW. UK.
622
data set is fitted to classical polar-molecule relaxation theory with additional contrrbutions from Gaussian oscillators at about 200 and 50 cm-l. The 50 cm-l band 1s clearly resolved in the measurements and this represents its first unambiguous identification in infrared measurements, although rt has been observed in Raman studres [I 41. The new measurements were made by reflection DOTS using a polarising interferometer [13] and a liquid-helium-cooled indium antimonide hot electron bolometer as detector_ Measurements were made in the spectral range between 4 and 40 cm-l at temperatures between 277 and 317 K, although only data at 293 K are reported here_ Above 15 cm-1 the present results are in good agreement with those of Afsar and Hasted [6], while at Iower wavenumbers the present refraction spectrum has somewhat lower values than the earlier work. For the purposes of the present work the optical constant data is most conveniently expressed as the complex relative permittivity, S, and &splayed on a Cole-Cole plot as iu fig. 1. At the lowest wavenumbers measured both the real, l‘,and the imaginary, E”, parts of @ increase as the wavenumber decreases towards values corresponding to the principal relaxation time (9.33 ps 181). In the present treatment of the principal relaxation process, 5 is described as a function of angular frequency, o, by the Cole-Cole equation microwave
yw)
= e,
0 009-2614/85/S (North-Holland
+ (e, - E,)/[
1+ (iwT)l-h]
-
(1)
03.30 0 Elsevier Science Publishers B.V. Physics Publishing Division)
CHEMICAL PHYSICS LEITERS
Volume 118, number 6
16 August 1985
and found that at 293 and 294 K the extrema values of E, were 5.62 f 0.19 and 4.13 * 0.38. Thus, the present value for E, falls almost midway between these values. However, this agreement is probably fortuitous as it is apparent from the full results of Kaatze
lo-
and Uhlendorf
for E, as a function of temperature that there are systematic errorsin their results at levels
e-6.0
-7
0
6-
k!;?
. . . 13.7
i
Fig. 1. Cole-Cole representation of the spectral variation of the complex relative permittitity of water at 293 K. The ticles represent the new data, the crosses the previous data of Afsar and Hasted [6]. The continuous curverepresents the mntriblhon to the complex perrmttlvity of the principal relaxation process. as destibed in eq. (1). The data points are labelled with their corresponding wavenumbers in cm-l_
In this E, and E, are the static and lugh-frequency limits of the real part of the permittivity, respectively, r is the principal relaxation time, and the parameter h represents the effect of a small distribution of relaxation times about the central value 7. The results of fittmg this to the present low-wavenumber data is represented by the continuous curve in fig. 1. The only adjustable parameter was E,, the parameters of the principal relaxation process being taken from previous work [8]. The value of E, obtained from the fit was 4.86, considerably above that obtained (4.2) from only fitting to lower-frequency data [S]. Kaatze and Uhlendorf [IS] have reported a determination of the complex relative permittivity of water in the I -60 GHz region at temperatures between 269 and 333 IL They analysed their data by fittingthem to a Debye form
of the order of, or somewhat above, the quoted !evels of random uncertainty_ It is interesting to note that Kaatze and Uhlendorf were unable to find any clear evidence for a dtstnbution of relaxation tunes such as that assumed in the present work by the use of the Cole-Cole formulation. Thus, one can sensibly compare the E, data derived from these two different models as, in the hmit of no distribution of relaxation times, the two models are equivalent. The principal relaxation process and the measured data can also be compared in the form of their corresponding power absorption spectra,as shownin fig. 2. The contxibutron of the principal relaxation process rapidly tends to the constant Debye plateau value, while the real data rise into the wing of a higher-wavenumber process. The important feature of these data is the presence of a small shoulder m the regton of 8-10 cm-1 that is superimposed on this wing absorption_ It is resolved in the measurements at a level well above the random uncertainties of the measuremen t process. This will be considered in more detail in a subsequent presentation after further measurements. Fig. 3 presents the complete absorption spectrum of water up to 230 cm- 1, drawing on both the new low-wavenumber data and the previous higher-wavenumber values [6]. The continuous curve represents the best fit to the data of the sum, Q(P), as a function of wavenumber, P, of the contribution of the principal relaxation process, a,(ir), and a Gaussian oscillator: a(P) = o&J)
+ C, exp [-(J
- PJ2/r,2]
_
(2)
In this ‘Jsis the oscillator wavenumber, 7s the damping term and C, the oscillator strength. The principal relaxation, Cole-Cole, contribution to this was calculated from eq. (1) using the previously referred to parameters [8]. The best-fit values of these were ‘75 = 199 cm-r, -ys = 102 cm-l and C, = 1078 cm-r. Between RO and 210 cm b-1 the agreement between measurement and calculation is very close, far better than corresponding Lorentzian frttmgs Above 210 cm-l no 623
Volume
CHFMICAL
118, number 6
PHYSlCS
lJXll’EI%S
16
August 1985
I +
+
I
I._
10
I 30
20 Wavenumber
I
LO
(cm-‘)
Fig_ 2. The measured spectral variation of the power absorption coefficient up to 40 cm -l. Circles represent the new &Ix. the uosscs t>e previous data of Afsar and Hasted [6] The continuous curye represents the contribution to the absorption spectrum of the principal relaxanon profess. as desabed in cq. (1).
claim is made concemmg the symmetry of the band (see ref_ [14]), whch m any case is obscured by the strong 685 cm-l band. Below 80 cm-l it is clear that the measurements reveal the presence of an additional band in the region I
I
looO-
mm1 a-acme
-
(Cm-‘)
0
100
ci (cm-‘)-
zoo
Fig_ 3 The measured power absorption speclrum of water up to 230 cm+ at 293 K shown plotted as circles The continuous curve represents the best fit of eq (2) to the data set.
624
Fig. 4. ‘The 49 cm-t absorption band in wat& at 293 K. The aosses represent the Merenoe spectrum between the measured data points and the best-fit curve shown m kig. 3 The continuous curve represents the best fit of a Gaussian oscilk tar to the differen= spectrum.
Volume 118, number 6
CHEMICALPHYSICS LEl-EFS
of 50 cm-l, superimposed on the low-frequency wing of the 199 cm-l band. The difference between the measurements and the best-fit calculation in this spectral region is represented by the plotted points in fig. 4. These clearly reveal an absorption band centred close to 50 cm-l with a full width at half height of about 40 cm-l. This band has been observed in the Raman spectrum of water [ 141, but not previously in its absorption spectrum, although Simpson et al. [16] have interpreted structure at 5.5 m-1 in the refraction spectrum derived from power reflection measurements on water as evidence for tlus feature. However, their data, both in absorption and refraction, show other sin&r small-scale structure that is not assigned. Hence their assignment may have been fortuitous. The smooth curve in fig. 4 represents the best fit of a further Gaussian oscillator to this second feature The best fit parameters were ir = 49.4 cm-l, y, = 25.3 cm-l and C, = 37.5 cm- ls It is of relevance here to note that in the present measurements that have been made at other temperatures, this band virtually disappears by a temperature of 303 K. This agrees with the Raman measurements [ 141 which were taken both in water and supercooled water, where the band was found to be more pror@nent. It is encouragmg that the milbmetre and submillimetre wavelength electrical properties of liquid water should be susceptible to interpretation along such well established lines, without recourse to new postulations and hypotheses_ The uniquely high value of E, has been a source of controversy for many years. NOW it seems probable that the breadth of the 50 and 200 cm-1 bands contnbute most of the E, - n2 difference through the Kramers-Kronig relations. Thus, in
16 August
1985
the treatment of dlpcle relaxatior?, n* rather than c_ must be used in Kirkwood-Frbhlich or other formalisms
References [I] J.R Birch and TJ. Parker, in: Tnfra~ed and millimeter
[2] [3] [4] [5]
[6] [7] (81 [9] [lo] (111
[ 121 [13] [14] [ 15) [16]
waves, Vol. 2. ed. K.J. Button (Aademic Press, New York, 1979) ch I J. Chamberlain, MS. Zafar and J-B. Hasted, Nature 243 (1973) 116. MS. Zafar, J.B. Hasted and J. Chamberlain, Nature 243 (1973) 106. J-E. Cl-Amberlain, M.N. A&r, J.B. Hasted, M_S. Afar and GJ. Davies, Nature 255 (1975) 319. M.N. Afsar, J.B. Ha_sted and J. Chamberlain. Infrared Fhys. 16 (1976) 301. M.N.Afsar and J.B. Hasted, J Opt. Sot. Am 67 (1977) 902. MN. Afsar and J.B. Hasted. Infrared Phys. 18 (1978) 835. P.R. Mason, J B. Hasted and L. Moore, Advan Mel Relaxation Processes 6 (1974) 217. C.H. Collie, J.B Hasted and D.M. Ritson, Rot Phys. Sot. (London) 60 (1948) 71. E WhaUey,Nature 251 (1974) 217. J.B. Harted, M S. Afar and J Chamberlain, Nature 251 (1974) 218. J.R. Birch and M. Bennouna. Infrared Phys. 21 (1981) 229. J R. Birch, G.P. OWeilI, J Yarwood and M. Bennouna. J. Phys El5 (1982) 6e4. S. Krishnamurthy, R. Bansil and J. Wiafe-Akezten, J. Chem. Phys. 79 (1983) 5863. U. Kaatze and V Uhlendorf, Z. Physik Chem N F 126 (1981) 151 0-A. Simpson, B.L. Bean and S. Perkowitz, J. Opt. Sot. Am. 69 (1979) 1723.
625