Water dynamics at the nanoscale
The recent construction of an Inelastic UltraViolet Scattering (IUVS) beamline at the ELETTRA Synchrotron Light Laboratory opens new possibilities for studying the density fluctuation spectrum, S(Q,E), of disordered systems in the mesoscopic momentum (Q) and energy (E) transfer region not accessib...
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| Цитувати: | Water dynamics at the nanoscale / C. Masciovecchio, F. Bencivenga, A. Gessini // Condensed Matter Physics. — 2008. — Т. 11, № 1(53). — С. 47-56. — Бібліогр.: 28 назв. — англ. |
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Masciovecchio, C. Bencivenga, F. Gessini, A. 2017-06-03T03:06:41Z 2017-06-03T03:06:41Z 2008 Water dynamics at the nanoscale / C. Masciovecchio, F. Bencivenga, A. Gessini // Condensed Matter Physics. — 2008. — Т. 11, № 1(53). — С. 47-56. — Бібліогр.: 28 назв. — англ. 1607-324X PACS: 78.35.+c, 62.60.+v, 62.50.+p DOI:10.5488/CMP.11.1.47 https://nasplib.isofts.kiev.ua/handle/123456789/118993 The recent construction of an Inelastic UltraViolet Scattering (IUVS) beamline at the ELETTRA Synchrotron Light Laboratory opens new possibilities for studying the density fluctuation spectrum, S(Q,E), of disordered systems in the mesoscopic momentum (Q) and energy (E) transfer region not accessible by other spectroscopic techniques. As an example of possible application of IUVS technique we will discuss the new insights provided in the case of water dynamics. From the analysis of IUVS spectra we were able to measure the temperature and pressure dependencies of structural relaxation time (τ) in water. In the case of room-pressure water the values of τ, as derived by IUVS, are fairly consistent with previous determinations and, most important, its temperature dependence agrees with Mode Coupling Theory (MCT) predictions. Moreover we found that τ decreases with increasing pressure at fixed temperature. The observed trend demonstrates that the structural relaxation phenomenology is strongly affected by the applied pressure. However, further investigations are necessary in order to clarify the physical meaning of these preliminary experimental results. Недавня побудова лiнiї непружнього розсiяння ультрафiолетових променiв (НРУП) у синхротроннiй лабораторiї ELETTRA вiдкриває новi можливостi для дослiдження спектру флуктуацiй густини, S(Q,E), у невпорядкованих системах у мезоскопiчнiй областi передачi iмпульсу (Q) та енергiї (E), яка є недоступною для iнших спектроскопiчних методик. Як приклад можливого застосування методу НРУП ми обговорюємо новi результати для випадку динамiки води. З аналiзу спектрiв НРУП ми мали можливiсть вимiряти залежнiсть вiд температури та тиску для часу структурної релаксацiї (τ) у водi. Для випадку нормального тиску значення τ, визначене з НРУП, добре узгоджується з попереднiми розрахунками та, що є бiльш важливо, його температурна залежнiсть узгоджується з передбаченнями теорiї взаємодiючих мод. Крiм того, ми знайшли, що τ зменшується зi зростанням тиску при фiксованiй температурi. Спостережувана тенденцiя демонструє, що явище структурної релаксацiї має сильну залежнiсть вiд прикладеного тиску. Однак, для того, щоб вияснити фiзичне значення цих попереднiх експериментальних результатiв, необхiднi подальшi дослiдження. en Інститут фізики конденсованих систем НАН України Condensed Matter Physics Water dynamics at the nanoscale Динамiка води на наномасштабах Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Water dynamics at the nanoscale |
| spellingShingle |
Water dynamics at the nanoscale Masciovecchio, C. Bencivenga, F. Gessini, A. |
| title_short |
Water dynamics at the nanoscale |
| title_full |
Water dynamics at the nanoscale |
| title_fullStr |
Water dynamics at the nanoscale |
| title_full_unstemmed |
Water dynamics at the nanoscale |
| title_sort |
water dynamics at the nanoscale |
| author |
Masciovecchio, C. Bencivenga, F. Gessini, A. |
| author_facet |
Masciovecchio, C. Bencivenga, F. Gessini, A. |
| publishDate |
2008 |
| language |
English |
| container_title |
Condensed Matter Physics |
| publisher |
Інститут фізики конденсованих систем НАН України |
| format |
Article |
| title_alt |
Динамiка води на наномасштабах |
| description |
The recent construction of an Inelastic UltraViolet Scattering (IUVS) beamline at the ELETTRA Synchrotron
Light Laboratory opens new possibilities for studying the density fluctuation spectrum, S(Q,E), of disordered
systems in the mesoscopic momentum (Q) and energy (E) transfer region not accessible by other spectroscopic
techniques. As an example of possible application of IUVS technique we will discuss the new insights
provided in the case of water dynamics. From the analysis of IUVS spectra we were able to measure the temperature
and pressure dependencies of structural relaxation time (τ) in water. In the case of room-pressure
water the values of τ, as derived by IUVS, are fairly consistent with previous determinations and, most important,
its temperature dependence agrees with Mode Coupling Theory (MCT) predictions. Moreover we found
that τ decreases with increasing pressure at fixed temperature. The observed trend demonstrates that the
structural relaxation phenomenology is strongly affected by the applied pressure. However, further investigations
are necessary in order to clarify the physical meaning of these preliminary experimental results.
Недавня побудова лiнiї непружнього розсiяння ультрафiолетових променiв (НРУП) у синхротроннiй лабораторiї ELETTRA вiдкриває новi можливостi для дослiдження спектру флуктуацiй густини, S(Q,E), у невпорядкованих системах у мезоскопiчнiй областi передачi iмпульсу (Q) та енергiї (E), яка є недоступною для iнших спектроскопiчних методик. Як приклад можливого застосування методу НРУП ми обговорюємо новi результати для випадку динамiки води. З аналiзу спектрiв НРУП ми мали можливiсть вимiряти залежнiсть вiд температури та тиску для часу структурної релаксацiї (τ) у водi. Для випадку нормального тиску значення τ, визначене з НРУП, добре узгоджується з попереднiми розрахунками та, що є бiльш важливо, його температурна залежнiсть узгоджується з передбаченнями теорiї взаємодiючих мод. Крiм того, ми знайшли, що τ зменшується зi зростанням
тиску при фiксованiй температурi. Спостережувана тенденцiя демонструє, що явище структурної релаксацiї має сильну залежнiсть вiд прикладеного тиску. Однак, для того, щоб вияснити фiзичне значення цих попереднiх експериментальних результатiв, необхiднi подальшi дослiдження.
|
| issn |
1607-324X |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/118993 |
| citation_txt |
Water dynamics at the nanoscale / C. Masciovecchio, F. Bencivenga, A. Gessini // Condensed Matter Physics. — 2008. — Т. 11, № 1(53). — С. 47-56. — Бібліогр.: 28 назв. — англ. |
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2025-11-26T00:08:26Z |
| last_indexed |
2025-11-26T00:08:26Z |
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| fulltext |
Condensed Matter Physics 2008, Vol. 11, No 1(53), pp. 47–56
Water dynamics at the nanoscale
C.Masciovecchio, F.Bencivenga, A.Gessini
Sincrotrone Trieste, S.S. 14 km 163,5 in AREA Science Park 34012 Basovizza, Trieste, Italy
Received November 12, 2007
The recent construction of an Inelastic UltraViolet Scattering (IUVS) beamline at the ELETTRA Synchrotron
Light Laboratory opens new possibilities for studying the density fluctuation spectrum, S(Q, E), of disordered
systems in the mesoscopic momentum (Q) and energy (E) transfer region not accessible by other spectro-
scopic techniques. As an example of possible application of IUVS technique we will discuss the new insights
provided in the case of water dynamics. From the analysis of IUVS spectra we were able to measure the tem-
perature and pressure dependencies of structural relaxation time (τ ) in water. In the case of room-pressure
water the values of τ , as derived by IUVS, are fairly consistent with previous determinations and, most impor-
tant, its temperature dependence agrees with Mode Coupling Theory (MCT) predictions. Moreover we found
that τ decreases with increasing pressure at fixed temperature. The observed trend demonstrates that the
structural relaxation phenomenology is strongly affected by the applied pressure. However, further investiga-
tions are necessary in order to clarify the physical meaning of these preliminary experimental results.
Key words: water, inelastic scattering, relaxation
PACS: 78.35.+c, 62.60.+v, 62.50.+p
1. Introduction
The physics of systems without translational invariance, such as liquids, dense fluids and glasses,
has been fascinating scientists for many years. The understanding of the liquid-to-glass transition
mechanisms, thermal anomalies at low temperatures, divergence of transport properties and re-
laxation phenomena, is a challenge that is motivating strong experimental and theoretical efforts.
In contrast to the crystalline case, in disordered systems the comprehension of atomic dynamics
is complicated both due to the difficulties associated with the absence of translational invariance
and due to the presence of other degrees of freedom, such as diffusion and relaxation processes
in fluids. The presence of these processes automatically introduces different time-scales, τ , which
are usually strongly dependent on the specific thermodynamic state. These timescales affect the
collective dynamical properties differently, depending on their value as compared to the time scale,
tD, characterizing the vibrational dynamics of particles around their quasi-equilibrium positions.
This is of the order of the inverse Debye frequency, i.e. comparable to that of a corresponding
crystal with similar density and sound velocity. Moreover, one has to consider that the topological
disorder introduces a second length scale, ξ, beside the interparticle distance, α. As a matter of
fact, the rich phenomenology observed in the dynamics of disordered systems can be ascribed to
the interplay between these different structural (ξ, α) and dynamical (τ , tD) scales. An exhaustive
understanding of dynamics in disordered systems in the so-called “mesoscopic region” (defined
by length and time scales comparable to ξ and τ) is still not available and it represents a real
challenge to modern physics [1]. A large amount of information can be experimentally deduced by
determining the density-density correlation function, F (Q, t), or, equivalently, of its time Fourier
transform, the dynamic structure factor, S(Q,E), in the largest momentum (Q) and energy (E)
transfer region. Naturally, special attention should be paid to the portion of the (Q,E)-plane cor-
responding to the characteristic length-scales (ξ, α) and time-scales (τ , tD) of the system. In most
materials ξ and α are about a few tens and tenths of nanometers, respectively, while tD is usually
in the sub-picosecond range. On the other hand, τ can assume rather disparate values, since it
strongly depends both on the specific nature of the relaxation process under consideration and on
the thermodynamic conditions. However, the experience accumulated so far in this field points out
c© C.Masciovecchio, F.Bencivenga, A.Gessini 47
C.Masciovecchio, F.Bencivenga, A.Gessini
that the relaxation processes that mainly influence the physical behavior of disordered systems are
those with characteristic timescale of about ξ/cS (cS being the sound velocity). In most materials
such a time scale falls in the 1÷ 10 picosecond range. It is then natural to infer that, for studying
the physics of disordered systems, the most important (Q,E)-range is the 0.05 ÷ 50 nm−1 and
0.01 ÷ 10 meV ranges. In bulk materials S(Q,E) can be directly measured by means of inelas-
tic photon or thermal neutrons scattering experiments [2–5]. However, a single technique cannot
completely cover, by itself, the entire range from inter-atomic distances to the continuum scale.
Figure 1. Kinematic regions accessible by existing techniques: Inelastic Light (LS), Ultra Violet
(IUVS), X-ray (IXS) and thermal Neutron (INS) Scattering. The two dotted lines indicate
energies of collective excitations with characteristic sound velocities of 500 m/s and 7000 m/s.
Figure 1 displays the portion of the (Q,E)-plane where the major part of the condensed matter
dynamics takes place, together with the regions where different experimental methods are currently
available. The lines depict the characteristic energies of collective excitations propagating with two
different sound velocities, typical of disordered systems. As can be evinced inspecting figure 1, the
recently developed IUVS beamline at the ELETTRA synchrotron laboratory contributes to the
reduction of the existing gap in the (Q,E) regions accessed by LS and IXS/INS, thus enabling us
to perform new investigations on the physics of liquid and glasses towards the mesoscopic region
being of utmost interest. In the next section we will briefly describe the IUVS instrument. The
following section reports the results of our recent investigations on liquid water, performed by IUVS
as function of temperature and pressure at Q-values around 0.07 nm−1, a region of great interest,
where peculiar dynamical behaviors are expected, as inferred by the results obtained through the
complementary BLS and IXS techniques [6–10].
2. The instrument
In order to perform IUVS spectroscopy several requirements had to be fulfilled. Among them
we cite the most demanding ones: incident photon flux on the sample larger than 1011 photons/s
in the photon energy region from 4 to 10 eV, and energy resolving power of about 106. Due to the
high photon flux, the radiation source has to keep the power harmful on the first optical elements.
For such a reason we decided to use an exotic insertion device as radiation source, a Figure-8
undulator [11], as an alternative to the standard vertical field devices. The main advantage of
this solution is a much reduced on-axis power density, which is obtained with no penalty on the
useful photon flux. Using a 32 mm period figure-8 undulator with maximum deflection parameters
Kx = 3.4 and Ky = 9.4, at the exit of a 600×600 mrad2 pinhole the total power of the synchrotron
radiation is as low as 20 W while the first harmonic delivers 2·1015 photons/s/0.1%BW . The beam
48
Water dynamics at the nanoscale
coming from the source has to be cleaned from the high order undulator harmonics and, for this
reason, three reflections are used. More specifically the beam impinges on a gold coated GLIDCOP
mirror internally water-cooled, which deviates the photons in the vertical plane with an angle of
6o. A second externally water-cooled silicon mirror is used to bring back the beam parallel to
the floor. The beam is then focused by a spherical silicon mirror onto the entrance slits of the
monochromator with a demagnification 20:1 and with an incident angle of 85◦. Being the source
size roughly 1× 1 mm2 (Horizontal × Vertical), a spot of 50× 20 µm2 (vertically the astigmatism
makes the focus larger) is obtained on the entrance of the monochromator. The only possible choice
concerning the optical design of the monochromator, when a 106 resolving power is needed at about
10 eV, is the Czerny-Turner model [12]. This design has the most desirable features, namely: better
resolution, higher light-gathering power, simpler scanning mechanism and, furthermore, it presents
the advantage of having fixed exit and entrance slits with no deviation in the direction of the exit
beam. In this design light from the entrance slit is made parallel by a spherical concave mirror and
is reflected onto an echelle plane grating. The grating used has 52 lines/mm and works at a blaze
angle of 690. A second spherical mirror collects the diffracted beam and focuses it on the exit slit.
The relative energy resolution, assuming that the intrinsic contribution coming from the grating
is negligible, is given by the formula:
∆E/E = δ cot θ/2F
where δ is the slit opening, F is the focal length of the spherical mirror and θ is the blaze angle.
We decided to built 8 m focal length monochromator to match the best compromise between the
needed resolving power and mechanical feasibility, in fact, using δ = 50 µm, F = 8 m and θ = 690,
we get a relative resolution of ∆E/E = 1.1 · 10−6. At the exit of the monochromator the beam
impinges on a spherical mirror, which focuses the radiation onto the sample in a spot the size
of about 30 × 100 µm2. A second spherical mirror is used to collect the radiation scattered from
the sample and to send it into the entrance slit of the analyzer unit, having the same design as
the monochromator. The inelastic scattering spectra are then collected by a low noise Peltier-
cooled CCD camera placed at the focal plane of the analyzer, which allows us to register the
inelastic spectrum in one single shot, thus avoiding time-consuming monochromator scans of the
diffraction angle. The quantum efficiency of the detector is larger than 10% for incident energies in
the 5÷15 eV. The momentum transfer can be experimentally set either by changing the scattering
angle, θ, or the wavelength of the incident photons, λ, since it is given by the formula:
Q =
4πn
λ
sin
(
θ
2
)
, (1)
where λ and n are the wavelength of the incident photons and the refraction index, respectively. The
instrumental energy resolution has been measured by collecting the isotropic scattered intensity
from a rough copper surface tilted with respect to the beam of about 400. The measured instru-
mental energy resolution is ∆E/E = 2 ·10−6, very close to the theoretical expectation of 1.6 ·10−6,
given by the convolution of the energy resolutions of the analyzer and of the monochromator [13].
3. The case of water
Water has always occupied a unique role in the physics of liquids. Nevertheless its peculiar
properties (such as the negative melting volume, the density maximum in the normal liquid range
– which makes this substance so fundamental in life and earth – as well as the apparent divergence
of the transport properties in the supercooled liquid region) depict an intriguing scenario still
far from being well settled [14]. Different models have been proposed to explain this anomalous
behavior: e.g., i) the existence of two liquid phases where a second critical point is located in
the “no man’s land” temperature region [15,16]; ii) the retracting spinoidal hypothesis, where
thermodynamic anomalies are ascribed to the vicinity of the spinoidal line [17]; iii) a singularity-
free scenario where thermodynamic anomalies can be ascribed to structural heterogeneities [18],
and iv) the Mode Coupling Theory (MCT) which describes water features without resorting to
49
C.Masciovecchio, F.Bencivenga, A.Gessini
an underlying thermodynamic singularity [19]. In this context, the need of experimental evidence,
which can discriminate among these interpretative models, is evident. Although measurements of
S(Q,E) were performed by IXS [6,7] and BLS [8], a conclusive point was not reached. Basically, the
reasons for that are twofold: a) the best sensitivity condition (ωpτ ≈ 1, where ωp is the frequency
of the sound waves probed in the experiment and τ is the relaxation time) was never matched in
BLS because of the low ωp values probed by this technique, while b) the lower ωp values probed by
IXS are often too large in order to fulfil the ωpτ ≈ 1 condition, especially in the most interesting
case of supercooled water. On the other hand, in the latter case, IUVS frequency window matches
the condition ωpτ ≈ 1, allowing a precise determination of the relaxation parameters. Finally, in
the case of IXS, the low throughput of the spectrometers does not allow us to reliably perform a
detailed study of water as a function of thermodynamic parameters. Using IUVS we systematically
measured S(Q,E) of high purity water as a function of temperature (between 260 and 340 K) and
pressure (between 1 and 4000 bar). The latter measurements were performed at 5.1 eV incident
photon energy (Q ≈ 0.07 nm−1), while room pressure measurements were performed both at 5.1 eV
and 6.7 eV, corresponding to Q-values of about 0.09 nm−1 [20]. In what follows we will discuss
two examples of the results one can obtain by using IUVS in the study of water. In particular,
the temperature (pressure) dependence of the structural relaxation time in water at fixed pressure
(temperature) is discussed.
3.1. Room pressure water vs. temperature
In figure 1 we show a selection of IUVS spectra of liquid and supercooled water at room pres-
sure. The clear broadening of the Brillouin peak – which is not resolution limited, as emphasized
by superimposing the resolution function on the spectrum at 287.1 K – strongly increases with
decreasing temperature, suggesting the presence of a relaxation process whose time scale matches
the experimental frequency window. We analyzed the measured spectra, I(Q,E), by fitting the
experimental data with a model function properly convoluted with the intrinsic energy resolu-
tion function of the spectrometer, R(E), scaled by an overall intensity factor, A. Finally, a flat
background contribution, B, was added:
I(Q,E) = A · S(Q,E) ⊗ R(E) + B, (2)
where ⊗ is the convolution integral. The model function used in describing S(Q,E) was derived
within the memory function formalism, in this framework S(Q,E) can be written as [2]:
S(Q,E) =
(~csQ)2m′(Q,E)
[(E2 − (~csQ)2 − E m′′(Q,E)]2 + [E m′(Q,E)]2
, (3)
where cs is the adiabatic sound velocity while m′(Q,E) and m′′(Q,E) are the real and imaginary
part of the time Fourier transform of the so-called memory function: m(Q, t). In deriving equa-
tion (3) the assumption that the specific heat ratio, γ, is equal to 1 has been made. In this case the
effect of thermal diffusion process on the shape of S(Q,E) can be neglected [21]. Such an approx-
imation is particularly suited for water since in this case γ is only a few percent different from 1;
further details regarding this kind of data analysis are reported elsewhere [6,7]. The analytical
form we used for the memory function was chosen to be consistent with the viscoelastic frame-
work, which has been already proved in order to satisfactorily describe the collective dynamics
of water [6–10,22] and other fluid systems: from supercooled glass formers [23] up to compressed
gases [24,25]. Within this framework the time dependence of the memory function has, at least,
one time decay (i.e. a relaxation) with a finite time scale. The simpler choice is thus as follows:
m(Q,E) = ∆exp(−t/τ), (4)
where ∆ and τ are usually referred to as relaxation strength and time, respectively. The relaxation
function reported in equation (4) is quite a crude approximation being the relaxation process
characterized by a single time scale. A continuous distribution of relaxation times is, indeed, a
50
Water dynamics at the nanoscale
Figure 2. Selection of IUVS spectra of liquid and supercooled water (dots), taken at 6.7 eV
incident photon energy (Q ≈ 0.09 nm−1), at the indicated temperatures. The fit results are
superimposed (red lines). The blue line in the spectra at 287.1 K is the experimental energy
resolution function.
more reliable approximation. In particular, according to MCT, the relaxation behavior of m(Q, t)
can be approximated by the following equation:
m(Q,E) = ∆exp
(
−(t/τMCT)β
)
, (5)
that represents a distribution of relaxation functions as the one reported in equation (4). τMCT
is the τ -value corresponding to the case when the distribution assumes its maximum while β,
commonly referred to as stretching parameter, is related to the broadening of such a distribution.
The average relaxation time, 〈τ〉, associated to the relaxation function reported in equation (5) is
given by 〈τ〉 = βτMCT, while in case of equation (4) it is simply equal to τ . Hereafter we will refer
to 〈τ〉 simply as relaxation time and we will indicate it as τ .
MCT foresees that: (i) β < 1, experimentally found to be ≈ 0.6, and (ii) τ follows a power law
divergence as a function of temperature [18]:
τ(T ) = (T − TMCT)−δ. (6)
MCT calculations and Molecular Dynamics simulations [22] have estimated the divergence tem-
perature TMCT of water to be of about 220 K and δ = 2.3 ± 0.2.
By fitting IUVS spectra with the model function obtained inserting the Fourier transform of
equation (5) into equation (3), we determined the temperature dependence of both the structural
relaxation time and the stretching parameter of liquid and supercooled water. The obtained values
are displayed in figure 3. Concerning the relaxation time, the comparison to IXS results of [6]
shows a good agreement between the two techniques above the room temperature, despite the
two different models used for the memory function. In fact IXS data were fitted using the simple
exponential time decay for the relaxation (equation (4)) instead of the stretched one (equation (5)).
The temperature dependence of τ , either determined by IXS or IUVS, can be empirically described
by an activation (Arrhenius) law:
τ(T ) = exp(Ea/kBT ), (7)
51
C.Masciovecchio, F.Bencivenga, A.Gessini
where Ea and kB are the activation energy of the relaxation and the Boltzmann constant, respec-
tively. One can derive the Ea value (23± 2 kJ/mol) by fitting IUVS data with equation (7) which
is about the activation energy of water hydrogen bonds: i.e. 23 kJ/mol [26]. Despite the quite dif-
ferent temperature range explored in previous IXS experiments [6], discrete agreement with these
results (Ea = 16 ± 3 kJ/mol) is found as well. It is then possible to conclude that the relaxation
process is related to the making and breaking of hydrogen bond network in water.
Figure 3. Structural relaxation time of water as a function of inverse temperature. Here we
compare our IUVS results (solid blue circles) with IXS measurement (open squares [6]). Both
IXS and IUVS data, separately, can be interpreted as an Arrhenius behavior (dotted lines). The
whole data sets (IXS + IUVS) can be also described by a power-law divergence of τ towards
220 K (solid line), in good agreement with MCT predictions. In the inset we also highlight the
temperature independence of β, as foreseen by MCT.
Inspecting figure 3 one can also appreciate that the whole data set of IXS and IUVS data can
be also described by the power law predicted by MCT (equation (6)). The power law diverges
at TMCT = 220 ± 10 K, and has an exponent δ = 2.3 ± 0.2, in good agreement with previous
determinations [22]. Moreover, the stretching parameter is temperature independent and close to
0.6, consistently with MCT predictions [19]. Therefore these results support the interpretation of a
purely dynamic origin for the divergence of τ , releasing the need of an underlying thermodynamic
singularity for its explanation. However, it has to be pointed out that IXS and IUVS experiments
were not performed in the same thermodynamics conditions. In particular IXS experiment was
performed at a constant density (1 g/cm3), while the IUVS one was performed at constant pressure
(1 bar). Consequently, eventual explicit pressure/density dependencies of τ could play a role in
explaining the experimental data reported in figure 3. With the aim of clarifying this point we
decided to employ IUVS in order to systematically investigate the pressure/density behavior of τ ;
highlights of the preliminary results are reported further below.
3.2. Water at 273 K vs. pressure
In order to study the relaxation phenomenology as a function of pressure, a high-pressure device
based on a hand pump pressure generator and a hydrostatic pressure cell have been employed.
Details about this setup can be found elsewhere [25]. We used this kind of sample environment in
order to collect IUVS spectra of water at 273 K as a function of pressure in the 1–4000 bar range.
In figure 4 a selection of IUVS spectra of liquid water at 273 K at different pressures are reported.
Analogously to the ones shown in figure 4, a broadening of Brillouin peaks larger than the resolution
52
Water dynamics at the nanoscale
function was always noticed. Moreover, differently from room pressure data, an intense quasi-elastic
spectral component was observed in the spectra (≈ 90% of the whole spectral intensity). This
strong central peak arises from spurious scattering by the optical windows of the pressure cell and
does not permit to perform a reliable fitting procedure, as the one we did in the case of room
pressure water. However, manipulating equations (3) and (4), after some straightforward algebra,
it is possible to relate the energy position, EMAX, of the maxima of longitudinal current spectra,
JL(Q,E) = (E/Q~)2S(Q,E), to the relaxation parameters, τ and ∆, or, alternatively, it is possible
to express τ as a function of EMAX and ∆:
τ =
√
1 − (cs~Q/EMAX)4
2∆2 − 2(~csQ)2 − 2E2
MAX
. (8)
Figure 4. Selection of IUVS spectra of liquid water at 273 K at the indicated pressures (dots).
Data were taken at 5.1 eV incident photon energy (Q ≈ 0.07 nm−1). The fit results are superim-
posed (blue lines: DHO function; green lines: Lorentian function accounting for the spurious
central peak; red lines: sum).
The values of EMAX can be determined by fitting IUVS spectra with an empirical model
consisting in a DHO function describing the Brillouin peaks plus a Lorentian function centered at
E = 0 accounting for the central spurious component:
S(Q,E) ∝
AL
E2 + W 2
+ ADHO
E2
MAXΓ
(E2 − E2
MAX)2 + (EΓ)2
, (9)
where Γ and W are the widths of Brillouin and central peaks, respectively, while AL and ADHO
are intensity factors. On the other hand, in the pressure and temperature ranges where IUVS
experiments were performed, the parameter ∆ can be quite accurately estimated by the numerous
IXS experiments performed so far [6,7,9,27]. This alternative strategy for the determination of τ
can be also applied for room pressure data. As one can appreciate from the inset of figure 5, the
values of τ determined with the two different procedures are fully consistent with each other, thus
providing an excellent consistency check of the employed procedure. It is worth stressing that the
data shown in the inset of figure 5 (open squares) correspond both to old spectra taken at 6.7 eV
53
C.Masciovecchio, F.Bencivenga, A.Gessini
incident photon energy, as the ones shown in figure 2 but analyzed using equations (8) and (9), as
well as to new spectra recently taken at 5.1 eV incident photon energy.
Figure 5. Structural relaxation time of water as a function of pressure (solid symbols). The
open circle is the only available IXS datum (from [6]). The full lines depict the expected trend,
according to equation (10) (the stepper line corresponds to γ = 1, while the other corresponds
to γ = 0.5, see text for further details). In the inset we show the data of room pressure water as
a function of temperature as obtained either by direct fitting IUVS spectra with equations (3)
and (5) (full squares) or by using equations 8 and 9 (open squares).
The pressure dependence of relaxation time is reported in the main panel of figure 5; different
symbols stand for different data sets, corresponding to different experiments roughly performed
3 months one after the other. We can immediately observe that IUVS data sets are in excellent
agreement between them and with the only available IXS datum. Even from a first inspection
of this figure, one can appreciate that τ decreases with increasing pressure. This trend is quite
surprising since density increases of about 14% from 1 to 4000 bar and, simply considering the
reduction of the free volume, a non-negligible increase of τ is expected with increasing pressure.
In fact, using general arguments it is possible to derive the following equation for the temperature
and volume (i.e. density) dependence of τ [28]:
τ = exp(Ea/kBT + αv0/(v − v0)), (10)
where v is the specific volume, v0 is the volume of water molecules and α is a positive numerical
factor (usually between 0.5 and 1) accounting for the possible overlapping of volumes associated to
different molecules. A comment is deserved: in principle, also in the case of room pressure data we
need to account for the reduction of the free volume (vf = v − v0) but, since the density changes
only of about 1% in the probed temperature range, it can be safely neglected.
The excellent consistency between these methods highlights the soundness of the procedure
used for deriving the values of τ in the case of water under high pressure.
In conclusion, according to equation (10), the data shown in figure 5 suggest that Ea presents
a remarkable density dependence or, alternatively, that a temperature/volume behavior as the
one reported in equation (10) cannot describe those experimental results. Nevertheless, further
investigations are needed in order to better clarify these preliminary experimental data and to cast
them in an assessed framework. We are currently performing systematic IUVS measurements in the
pressure and temperature ranges of 1–5000 bar and 250–350 K with the aim to fully characterize
the density and temperature dependencies of τ .
54
Water dynamics at the nanoscale
4. Conclusions
We have shown the capability of inelastic UV scattering to study collective dynamics of disor-
dered systems in a kinematic region not accessible before. In the case of water we determined the
temperature dependencies of the structural relaxation time and stretching parameter in the region
where the transport properties start to diverge (i.e. in the supercooled liquid phase). Our experi-
mental results agree with mode coupling theory predictions suggesting that, at ambient pressure,
the divergence in transport properties is of a dynamic origin. We have also shown the capabilities of
IUVS to be coupled with high-pressure hydrostatic devices and, therefore, to determine the values
of relaxation time as a function of pressure. We noticed that the density dependence τ cannot be
accounted for by a simple reduction of the free volume. One possible explanation of the observed
behavior is that the activation energy of the relaxation is volume dependent or, alternatively, that
other physical processes could effect the observed relaxation behavior.
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Динамiка води на наномасштабах
К.Машiовеккiо, Ф.Бенчiвенґа, А.Ґессiнi
Синхротрон Трiєсту, Трiєст, Iталiя
Отримано 12 листопада 2007 р.
Недавня побудова лiнiї непружнього розсiяння ультрафiолетових променiв (НРУП) у синхротрон-
нiй лабораторiї ELETTRA вiдкриває новi можливостi для дослiдження спектру флуктуацiй густини,
S(Q, E), у невпорядкованих системах у мезоскопiчнiй областi передачi iмпульсу (Q) та енергiї (E),
яка є недоступною для iнших спектроскопiчних методик. Як приклад можливого застосування ме-
тоду НРУП ми обговорюємо новi результати для випадку динамiки води. З аналiзу спектрiв НРУП
ми мали можливiсть вимiряти залежнiсть вiд температури та тиску для часу структурної релакса-
цiї (τ ) у водi. Для випадку нормального тиску значення τ , визначене з НРУП, добре узгоджується з
попереднiми розрахунками та, що є бiльш важливо, його температурна залежнiсть узгоджується з
передбаченнями теорiї взаємодiючих мод. Крiм того, ми знайшли, що τ зменшується зi зростанням
тиску при фiксованiй температурi. Спостережувана тенденцiя демонструє, що явище структурної
релаксацiї має сильну залежнiсть вiд прикладеного тиску. Однак, для того, щоб вияснити фiзичне
значення цих попереднiх експериментальних результатiв, необхiднi подальшi дослiдження.
Ключовi слова: вода, непружнє розсiяння, релаксацiя
PACS: 78.35.+c, 62.60.+v, 62.50.+p
56
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