THz spectroscopy of liquid H2O and D2O

Abstract

We have measured and analyzed the dielectric (0.1–2 THz) response of liquid H2O and D2O from 270 to 368 K. The response has been modeled using a Debye model with a fast and a slow decay time. By shifting the temperature scale for the slow decay time of D2O by 7.2 K we find identical behavior for D2O and H2O. The temperature dependence and isotope shift of the intermolecular structural relaxation characterized by the slow decay time can be modeled with a singular point at 228 K for H2O and 235 K for D2O.

Full text

VOLUME 82, NUMBER 14 PHYSICAL REVIEW LETTERS 5A
PRIL 1999
THz Spectroscopy of Liquid H2Oand D2O
Cecilie Rønne,1Per-Olof Åstrand,2and Søren R. Keiding1
1Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Århus C, Denmark
2Condensed Matter Physics and Chemistry Department, Risø National Laboratory, DK-4000 Roskilde, Denmark
(Received 15 May 1998)
We have measured and analyzed the dielectric (0.1–2 THz) response of liquid H2O and D2O from
270 to 368 K. The response has been modeled using a Debye model with a fast and a slow decay time.
By shifting the temperature scale for the slow decay time of D2O by 7.2 K we find identical behavior for
D2O and H2O. The temperature dependence and isotope shift of the intermolecular structural relaxation
characterized by the slow decay time can be modeled with a singular point at 228 K for H2O and 235 K
for D2O. [S0031-9007(99)08896-1]
PACS numbers: 61.25.Em, 77.22.–d
The structure and dynamics of liquid water constitute
a central theme in contemporary natural science [1–10].
In biological systems, liquid water defines the environ-
ment for biological activity by supporting and mediating
biochemical reactions. Understanding the physical and
chemical properties of liquid water, and, in particular, the
intermolecular hydrogen bonds, is therefore often consid-
ered a prerequisite for understanding biology and chem-
istry in aqueous solutions on a molecular level. Liquid
water and ice possess many unusual properties compared
with the majority of liquids and solids, and it is often spec-
ulated whether the unique role of water in defining bio-
logical activity is caused by these anomalous properties.
Consequently, liquid water is perhaps the most studied
chemical system, with numerous experimental and theo-
retical studies [1]. In spite of these efforts, the properties
of liquid water are still far from being understood at a
molecular level. For instance, large isotope effects are
seen in some properties, such as the temperature of maxi-
mum density, which occur at 277.2 K in H2Osldand at
284.4 K in D2Osld[11], while other properties, such as
the static dielectric constant, show little difference for the
two isotopes [12,13].
The relaxational response due to intermolecular fluctua-
tions of polar liquids can be observed in the microwave
and far-infrared (FIR) region of the electromagnetic
spectrum. We have previously used THz time-domain
spectroscopy (TDS) to measure the complex dielectric
function of H2Osldin the region from 100 GHz to 2 THz
(3 to 67 cm21) as a function of temperature from a su-
percooled state (271 K) to near the boiling point (366 K)
at ambient pressure [14]. In agreement with a study
combining several microwave techniques sn,100 GHzd
with conventional FIR spectroscopy sn.176 GHzd[15],
we observed that the time correlation function of the
macroscopic polarization of liquid water is well described
by a biexponential decay, with a Debye relaxation time
stD.2psdas well as a fast st2.50 fsdrelaxation time.
A description of the TDS technique, a careful examina-
tion of the H2Oslddata and data processing together with
a comparison of the resulting relaxation times with relax-
ation times obtained in various spectroscopic studies as
well as molecular dynamics simulations can be found in
Ref. [14]. In this Letter we present the results from an
equivalent investigation of D2Osld. We focus on the tem-
perature dependence and the isotope shift of the H2Osld
and D2Osldrelaxation times and discuss the dielectric re-
laxation in view of the prevailing models of the tempera-
ture dependence of liquid water properties.
In 1976 Speedy and Angell constructed a model, where
the temperature dependence of several anomalous thermo-
dynamic properties of H2Osldcould be extrapolated from
a singular point at 228 K [16]. Many glass forming liq-
uids experience diverging structural relaxation times when
supercooled. This gives rise to a temperature dependence
for the structural relaxational predicted by the mode cou-
pling theory [7] to t~jT2T
S
j
2g, where the structural
relaxational will diverge at TS. Accordingly, the observa-
tions of Speedy and Angell have inspired a wealth of theo-
retical and experimental investigations focusing on the
behavior of supercooled/metastable water as the origin of
the anomalous properties of water at ambient temperature
and pressure. Among the water models, recently reviewed
in Ref. [10], two involve a singular/critical temperature
where the thermodynamic response functions of water di-
verge. One is the “stability limit” hypothesis that assumes
a spinodal temperature line in the P-Tphase diagram be-
yond which the liquid phase becomes mechanically unsta-
ble [17]. The other is the “liquid-liquid phase transition”
hypothesis [4,18–20]. This model assumes a line of co-
existence between two liquid phases, a low-density liquid
(LDL) phase at the low-pressure side and a high-density
liquid (HDL) phase at the high-pressure side. This co-
existence terminates in a second critical point, C0, whose
location has been suggested to be at temperatures below
0±C and at either a slightly negative pressure [21] or at
a high positive pressure [18–20]. However, as discussed
by Mishima and Stanley [10], the location of a critical
point in a model will be extremely dependent on the pa-
rameters used in the model as, for example, the simula-
tion potential. Furthermore, Poole et al. [18] have shown
that their two-component model can reproduce both a
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VOLUME 82, NUMBER 14 PHYSICAL REVIEW LETTERS 5A
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spinodal line and the second critical point depending on
the parameters used. Generally, two-component models
provide a simple way of accounting for many thermo-
dynamic anomalies of liquid water. A common feature
among the most recent two-component models is that wa-
ter can be considered exhibiting a two-state temperature-
dependent equilibrium between a LDL with high local
tetrahedral ordering and a HDL [18,20,22]. An alternative
approach is based on percolation theory and contains thus
no singular point [23,24]. The main experimental diffi-
culty in establishing a consistent phase diagram is that ho-
mogeneous crystallization occurs before the hypothesized
point of divergence of the response functions is reached,
and in order to determine if there really exists a singular
point experiments very close to TSare required. Accord-
ingly, it has not yet been possible to definitively decide
which is the preferred model. In the present investigation
of the temperature dependence of the dielectric relaxation
we use the isotope shift between H2Osldand D2Osldto
examine how the two relaxation processes are related to
the liquid structure. The slow relaxation process is found
to be the relaxation of the liquid structure, and this process
is analyzed in terms of the existing models.
The experiments utilized reflection mode TDS, where
ultrashort THz pulses were reflected from a Si window
in the sample cell containing the liquid. Each THz pulse
would be divided into a pulse reflected from the front of
the silicon window and a delayed pulse reflected from the
silicon-liquid interface. Measurement of the frequency-
dependent change in phase and amplitude of the second
pulse with respect to the first pulse permitted the complex
dielectric function of the liquid to be obtained over the
entire 0.1 to 2 THz spectral range of the THz pulses [14].
The dielectric function of H2Osldat 315 K is shown in
Fig. 1 as circles. The amplitude spectrum of the THz
pulse used in the experiment is shown overlaid as crosses.
The imaginary part of the dielectric function increases by
approximately 30% when the temperature is raised from
271 to 367 K, and the real part is most sensitive to the
temperature changes at frequencies below 0.5 THz. A
Debye model including two relaxation times, a slow stDd
and a fast st2d,
ˆ´svd´`1´S2´
1
11ivtD
1´12´
`
11ivt2
,(1)
has previously been found to give a satisfying fit of
the complex dielectric function of H2Osld[25] between
273 and 303 K [15]. The slow relaxation process has
been found to have simple Debye character down to
221 ±C [26]. We find that the dielectric response for
both H2Osldand D2Osldbetween 271 and 368 K is
successfully represented by a biexponential model (solid
line in Fig. 1). The resulting relaxation times show that
both the slow [Fig. 2(a)] and the fast [Fig. 2(b)] processes
for H2Osldand D2Osldspeed up as the temperature is
raised. The slow process is faster in H2Osldthan in
FIG. 1. The imaginary and the real part of the dielectric
constant for H2Osldat 315 K is shown ssdin (a) and (b),
respectively. The solid line is a fit to the double Debye
model described in Eq. (1), where the static dielectric constant,
´SsTf±Cgd, was constrained to 87.91e20.00458Tand 78.25f12
4.617 31023Tp11.22 31025T2
p22.7 31028T3
pgwith
TpsT225d, for H2Osld[12] and D2Osld[13], respectively,
and the individual data points were weighted according to the
amplitude spectrum of the THz pulse s3dgiving less weight to
the low and high frequency limits of the spectrum. The contri-
butions from the two modes, with relaxation strength ´S2´
1
for the slow process stDdand ´12´
`for the fast process
st2d, are shown with dashed and dotted lines, respectively.
D2Osldat a given temperature. In contrast, within the
experimental uncertainty no isotope shift is observed for
the fast process. The temperature dependence of Debye
relaxation times obtained in this work is very similar
to what is observed in previous microwave studies [27]
[e.g., inset of Fig. 2(a)]. Since our discussion of the
experimental data will be based on the relation between
the temperature dependence of the relaxation times for the
two isotopes a small systematic deviation observed in the
numerical values will not influence the conclusions.
We have previously shown that the temperature de-
pendence of tDcan be correlated with the viscosity via
the Einstein-Stoke-Debye relation [14], thus the Debye
process corresponds to a relaxation of the liquid struc-
ture and not to a single-molecule motion. Assuming that
the temperature of maximum density (TMD) can be used
as a fingerprint for the structure, we can explore the role
of temperature dependence of the liquid structure. For
instance, it has been noted that properties of H2Osldand
D2Osldthat depend solely on the liquid structure, e.g.,
density, show a constant isotope ratio if they are shifted
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FIG. 2. Temperature dependence of the slow (a) and fast (b)
relaxation time in H2Osldand D2Osld. The error bars indicate
the 95% confidence limit. The inset in (a) shows single Debye
model relaxation times, tMW , obtained by Yastremskii [27]
using microwave spectroscopy.
with the TMD [28]. Since the TMD for H2Osldand
D2Osldis separated by 7.2 K at atmospheric pressure, we
have compared tDfor H2Osldat Twith tDfor D2Osldat
T27.2 K [Fig. 3(a)]. We find that the slow relaxation
times are equal within the experimental uncertainty for the
isotopes on this “shifted” temperature scale. A qualita-
tive background for shifting the temperature according to
TMD can be found within the two-component model [28]:
The temperature-dependent mole fraction, fsTd, describ-
ing the partition between the LDL sfdand HDL s12fd
water structures, can be assumed to be equal for the two
isotopes at the density maximum, fT277.2
H2OfT284.4
D2O.
Thus, according to the different TMD the hypothesized
singular temperature, TS288 K for H2Osld, will corre-
spond to TS235.2 K for D2Osld. We have correspond-
ingly plotted lnstDdvs 2lnsTyTS21din Fig. 3(b) for
both isotopes. We observe the same linear dependence for
both H2Osldand D2Osldwith g1.57s0.03dfor a linear
fit to the merged isotope data set. This is in good agree-
ment with the temperature dependence observed using
microwave relaxation times of H2Osldwith TS228 K
determined to g1.55 (Ref. [29]) or g1.791s0.02d
(Ref. [16]). The observed power law dependence is not
sufficient to decide among the current water models, but
the observed connection between TMD and TSmakes
clear that a proper model of liquid water should provide a
combined explanation of both the isotope and temperature
FIG. 3. (a) Temperature dependence of the slow relaxation
times in H2Osldand D2Osldcompared on a shifted scale
where the D2Osldrelaxation times measured at Tare shown
at temperature T27.2 K. (b) Angell plot of the slow re-
laxation times, lntDplotted versus 2lnsTyTS21d, where
TS228 K (235.2 K) for H2OsldfD
2
Osldg. The linear fit,
lntD0.11s0.03d11.57s0.03dx, shows the power depen-
dence. The inset in (b) shows the Yastremskii [27] relax-
ation times, tMW , plotted the same way. Also tMW for H2Osld
and D2Osldcoincidence when TSis shifted by 7.2 K [inset of
Fig. 3(b)].
dependence. We find that a two-component model with
a liquid-liquid phase transition [30] is consistent with our
observations. The temperature-dependent equilibrium be-
tween HDL and LDL provides a simple rationale for the
TMD and power dependence observed for both isotopes,
with a difference in singular temperature corresponding to
the difference in TMD.
We have performed a comparison between the fast re-
laxation times of H2Osldat Tand D2Osldat T27.2 K,
but contrary to the slow relaxation times, we do not
find a correlation within the experimental uncertainty.
This indicates that the fast relaxation process is not re-
lated to fluctuations in the liquid structure, but rather
to a molecular relaxation process. Furthermore, we ob-
served that the relative contribution to the fast relax-
ation time, C2s´12´
`
dys´S2´
`
d, increases from
approximately 2.5%(0.3%) to 4%(1%) from the lowest to
the highest temperature in the measurement. Recently,
Woutersen et al. [8] found two relaxation times for the
rotational anisotropy in a femtosecond study of the vibra-
tional spectrum of DOH in D2Osld. They interpreted the
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VOLUME 82, NUMBER 14 PHYSICAL REVIEW LETTERS 5A
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observations in terms of a two-component (HDL/LDL)
model and assigned the fast decay time of 0.7 ps to the
LDL component. In contrast, the slow decay time of
13 ps was assigned to both states. Our results are consis-
tent with the results of Woutersen et al. [8]. The relative
contribution of the fast relaxation process is indeed in-
creasing with increasing temperature, which is consistent
with that of the relative contribution of the LDL com-
ponent increases with temperature [10]. Futhermore, the
overall small contribution from the fast relaxation process
indicates that the Debye relaxation is present in both com-
ponents. A small contribution from the fast relaxation
process to the LDL component may thus be important for
a model of the temperature dependence of liquid water.
To summarize, we have measured and analyzed the
dielectric response function for both H2Osldand D2Osld
as a function of temperature between 0.1 and 2 THz.
The dielectric relaxation was successfully represented
by a biexponential model with a fast s,300 fsdand a
slow s.2psddecay time. The temperature dependence
and isotope shift observed in this experiment for the
intermolecular relaxation characterized by slow decay
times are consistent with structural relaxation, where the
structural properties of H2Osldand D2Osldbecome equal
when compared on a temperature scale shifted by 7.2 K
for D2Osld. Furthermore, the temperature dependence of
the slow relaxation times can be modeled from a singular
point at 228 K for H2O and 235 K for D2O.
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