arXiv:0903.3914v1 [cond-mat.soft] 23 Mar 2009
Effect of concentration on the thermodynamics of sodium chloride aqueous solutions
in the supercooled regime
D. Corradini, P. Gallo∗and M. Rovere
Dipartimento di Fisica, Universit` a “Roma Tre”
Via della Vasca Navale 84, I-00146 Roma, Italy
Molecular Dynamics simulations are performed on two sodium chloride solutions in TIP4P water
with concentrations c = 1.36mol/kg and c = 2.10mol/kg upon supercooling. The isotherms and
isochores planes are calculated. The temperature of maximum density line and the limit of mechani-
cal stability line are obtained from the analysis of the thermodynamic planes. The comparison of the
results shows that for densities well above the limit of mechanical stability, the isotherms and iso-
chores of the sodium chloride aqueous solution shift to lower pressures upon increasing concentration
while the limit of mechanical stability is very similar to that of bulk water for both concentrations.
We also find that the temperature of maximum density line shifts to lower pressures and temper-
atures upon increasing concentration. Indications of the presence of a liquid-liquid coexistence are
found for both concentrations.
PACS numbers: 65.20.Jk,De,64.60.My
The properties of aqueous ionic solutions besides being
of undoubtful importance in chemical physics1and elec-
trochemistry2, are relevant in many other fields of science
including biology and biophysics3, geophysics4, and even
atmospheric modeling.5In the supercooled region, ther-
modynamic properties of solutions are also of interest for
the cryopreservation of organs and food.6,7,8From a more
fundamental point of view an improved understanding of
the thermodynamics of these systems upon supercooling,
can help to shed light on the open questions on bulk liq-
It is well known that water presents, in the supercooled
region, peculiar thermodynamic behavior.10,11,12,13,14In
particular, the most striking effects are the existence of
a temperature of maximum density (TMD) line and the
divergence of the isothermal compressibility KT, of the
isobaric specific heat cP and of the coefficient of thermal
expansion αP. The origin of this anomalous behavior is
still a matter of large interest and debate in the liter-
ature.11Several theoretical15,16,17,18,19,20,21,22and com-
puter simulation23,24,25,26,27,28,29,30,31papers have shown
the presence in the supercooled region of water of a
liquid-liquid (LL) critical point. Experimental signatures
of this critical point have been also found.32The sec-
ond critical point of water would be the end point of
the coexistence line between a low density liquid (LDL)
and a high density liquid (HDL). In this framework, the
anomalous properties of water arise as a consequence of
the presence of the LL critical point. Furthermore in this
picture, the limit of mechanical stability (LMS) is non-
reentrant and the TMD line is knee-shaped and avoids
∗Author to whom correspondence should be addressed; e-mail: gal-
to cross the LMS line.
Aqueous ionic solutions have been extensively stud-
with particular emphasis on the hydration struc-
ture.33,34,35,36,37,38,39,40,41,42,43,44,45Many studies in the
supercooled regime deal with the glass transition phe-
nomenon (see Ref. 1 and references therein) while the
detailed comparison of the thermodynamic behavior of
the aqueous solutions with respect to bulk water in the
mild supercooled regime still lacks a thorough investi-
gation. Calorimetric experiments have shown that from
low to moderate concentration of ions several thermody-
namic properties of aqueous solutions are dominated by
In this paper, we present a Molecular Dynamics (MD)
simulation study of the thermodynamics of two sodium
chloride aqueous solutions, in the following denoted also
as NaCl(aq), in the supercooled regime. This work is an
extension of a previous study performed on bulk water
and on a NaCl(aq) solution with low salt concentration.47
The concentrations of salt in the solutions studied
in the present work are c = 1.36mol/kg and c =
2.10mol/kg. For both systems we study the isotherms
in the P −ρ plane and the isochores in the P −T plane.
The analysis of those thermodynamic planes leads to the
determination of the LMS and TMD lines. Moreover we
present the trend of the potential energy as a function
of density, at a low temperature. We will compare the
results of the present simulations with results on bulk
water and c = 0.67mol/kg NaCl(aq) studied in our pre-
vious work.47We also perform a comparison of the results
with what found for water confined in a hydrophobic en-
vironment of soft spheres.48
The paper is organized as follows. In Sec. II we explain
the details of the model and the computer simulation
setup. In Sec. III we show and discuss the thermody-
namic behavior. Conclusions are drawn in Sec. IV.
Pettitt-Rossky c = 0.67
Jensen-Jorgensen c = 0.67
Pettitt-Rossky c = 1.36
Jensen-Jorgensen c = 1.36
ρ = 1.025
FIG. 1: Isochores for c = 0.67mol/kg NaCl(aq)47and for c =
1.36mol/kg NaCl(aq) for ρ = 1.025 g/cm3for two different
force fields50,57(color online).
II.MODEL AND SIMULATION DETAILS
Two aqueous sodium chloride solutions with concen-
trations, given in moles of solute per mass of solvent, c =
1.36mol/kg and c = 2.10mol/kg are simulated by means
of MD technique. In the case of the c = 1.36mol/kg so-
lution the system is composed by 244 water molecules,
6 Na+ions and 6 Cl−ions, while in the case of the
c = 2.10mol/kg solution, it is composed by 238 water
molecules, 9 Na+ions and 9 Cl−ions.
The particles interact via the sum of coulombic and
Lennard-Jones (LJ) potentials. The analytical expres-
sion of the interaction potential is given by
where q is the electric charge and ǫijand σij are LJ pa-
rameters. Water molecules are modeled employing the
TIP4P potential.49Ion-ion and ion-water LJ parame-
ters are derived from Pettit and Rossky50parameters for
the Huggins-Mayer potential, via the reparametrization
made by Koneshan and Rasaiah35for LJ potential. The
ion-water and ion-ion LJ interaction parameters are sum-
marized in Table I.
Periodic boundary conditions are applied. The cutoff
radius is fixed at 9.0˚ A. Usually cutoff radius is fixed in
simulations between 8 and 10˚ A51. Long range electro-
static interactions are taken into account by the Ewald
summation method with convergence parameter α set to
6.4/L, where L is the edge of the cubic simulation box.
Ntot = 256
Ntot = 512
Ntot = 1024
c = 2.10
c = 1.36
FIG. 2: Isochores for c = 1.36mol/kg NaCl(aq) and for c =
2.10mol/kg NaCl(aq) for ρ = 0.98 g/cm3for three different
sistem sizes (color online).
TABLE I: Ion-water and ion-ion LJ interaction parameters.
The systems are equilibrated by controlling the tem-
perature with the Berendsen thermostat.52Production
runs are done in the NV E ensemble. The integration
timestep used is 1 fs.
For both systems we studied the densities ρ
For each density, a starting configuration is produced
distributing the particles on a face centered cubic lattice,
with random orientation of water molecules. The crystal
is then melted at T = 500 K and the temperature is
stepwise reduced during the equilibration runs.
lowest temperature investigated is T = 190 K. Equilibra-
tion runs become very long for the lowest temperatures
investigated.Each equilibration run is followed by a
production run in which the thermodynamic averages
are calculated. Production runs are always done with
T = 300 K
T = 280 K
T = 260 K
T = 250 K
T = 240 K
T = 230 K
T = 220 K
T = 210 K
c = 1.36 mol/kg
FIG. 3: Isotherms in the range 210K ≤ T ≤ 300K and LMS
line of c = 1.36mol/kg NaCl(aq) in the P − ρ plane (color
the same length of the equilibration runs. The longest
equilibration and production runs last up to 10 ns each.
The simulations are carried out using the DL POLY
package.53The pressures extracted are calculated with
the virial equation54.
The choice of the force field is very important in the
case of ionic aqueous solutions41,55since for example in
KCl recent studies have evidenciated possible problems
that are water model independent56. However the NaCl
behavior seems to show an weaker dependence on the
specific force field since it shows a lower tendency to form
clusters56. For the c = 2.10mol/kg solution and ρ = 1.1
g/cm3at T = 300 K we have an internal energy value
of −62.81 kJ/mol. This value can be compared with
a simular value of −69.57 kJ/mol obtained for a c =
2.35mol/kg solution and ρ = 1.093g/cm3at T = 300 K
for a ionic potential with SPC flexible water potential58.
In order to stringently test the robustness of our potential
we have run simulations along a isochore with a recent
ionic potential by Jensen and Jorgensen57tailored for
TIP4P water. In Fig. 1 we show, for the two different
concentrations, the isochore ρ = 1.025 g/cm3calculated
with both potentials. We can see that the two potentials
produce similar results.
We have also conducted a test to verify that our data
do not depend significatively on the size of the box. Re-
sults are reported in Fig. 2. For c = 1.36mol/kg we
compare the ρ = 0.98 g/cm3isochore calculated for
244 water molecules and 6 ion pairs, and for 488 wa-
ter molecules and 12 ion pairs. The simulation box of
these systems is L = 20.037, 25.2468˚ Arespectively. For
T = 400 K
T = 350 K
T = 300 K
T = 280 K
T = 260 K
T = 250 K
T = 240 K
T = 230 K
T = 220 K
T = 210 K
c = 2.10 mol/kg
FIG. 4: Isotherms in the range 210K ≤ T ≤ 400K and LMS
line of c = 2.10mol/kg NaCl(aq) in the P − ρ plane (color
c = 2.10mol/kg we compare the ρ = 0.98 g/cm3isochore
calculated for 238 water molecules and 9 ion pairs, for
476 water molecules and 18 ion pairs and for 952 water
molecules and 36 ion pairs. The simulation box of these
systems is L = 20.132, 25.365, 31.958˚ Arespectively. We
note that the curves corresponding to the same concen-
trations are very similar and that their minimum does
not show any significant shift.
The simulated thermodynamic state points have been
reported in the P −ρ (isotherms) plane and in the P −T
(isochores) plane. The analysis of those planes allows the
determination of the LMS line and TMD line, respec-
tively. Both curves can be derived using thermodynamic
By considering the isothermal compressibility
the LMS line is defined by the locus of the points for
which KTdiverges. The line that joins the minima of the
isotherms corresponds to the LMS line. The TMD line
is defined as the locus of the points where the coefficient
of thermal expansion αP is zero.
450 500 550
c = 1.36 mol/kg
ρ = 1.125
ρ = 1.1
ρ = 1.05
ρ = 1.025
ρ = 0.98
ρ = 0.95
ρ = 0.90
FIG. 5: Isochores in the range 0.90g/cm3≤ ρ ≤ 1.125g/cm3,
TMD and LMS lines of c = 1.36mol/kg NaCl(aq) in the P−T
plane (color online).
Therefore the line joining the minima of the isochores
yields the TMD line.
In Fig. 3 and Fig. 4 we report the isotherms of the two
solutions in the P −ρ plane as given by our simulations.
In both cases we display only the curves that show min-
ima and thus contribute to the calculation of the LMS
Fig. 3 refers to the c = 1.36mol/kg solution.
show the isotherms in the range 210K ≤ T ≤ 300K
and the corresponding LMS line.
highest temperature isotherm which shows a minimum.
The LMS line starts at ρ = 0.87g/cm3at T = 300 K
and shifts to ρ = 0.90g/cm3for all the lower temper-
ature curves. The lowest temperature isotherms, T =
220 K and T = 210 K, show inflections that cross the
higher temperature isotherms for densities in the range
0.98g/cm3≤ ρ ≤ 1.05g/cm3.
Fig. 4 refers to the c = 2.10mol/kg solution.
report the isotherms in the range 210K ≤ T ≤ 400K
and the corresponding LMS line.
tion, minima of the isotherms can be found up to the
T = 400 K isotherm. The LMS line gradually shifts to-
ward higher densities upon decreasing the temperature.
In this case the only isotherm showing an inflection is
the one at T = 210 K. This inflection spans the density
range 1.025g/cm3≤ ρ ≤ 1.05g/cm3.
T = 300 K is the
At this concentra-
c = 2.10 mol/kg
FIG. 6: Isochores in the range 0.90g/cm3≤ ρ ≤ 1.125g/cm3,
TMD and LMS lines of c = 2.10mol/kg NaCl(aq) in the P−T
plane (color online).
Upon comparing the isotherms planes of the two so-
lutions we note that, at high densities, the isotherms of
the higher concentration solution are shifted by about
50 MPa toward lower pressures, with respect to the
isotherms of the lower concentration solution.
shift decreases at densities close to the minima of the
isotherms and it almost disappears for very low densi-
ties. This behavior of the isotherms is analogous to what
found in the comparison between bulk water and the
c = 0.67mol/kg solution.47A similar pressure shift can
be seen also when comparing the c = 1.36mol/kg and the
c = 0.67mol/kg solutions (not shown). Therefore upon
increasing ions concentration the isotherms progressively
shift toward lower pressures.
For the c = 1.36mol/kg solution the LMS line in the
isotherms plane (Fig. 3) is monotonic as already found for
bulk water23,30,59, confined water48and c = 0.67mol/kg
NaCl(aq).47In the c = 2.10mol/kg solution (Fig. 4) it
does not decrease on going from the T = 230 K to the
T = 220 K isotherm.
An important feature of the isotherms planes of the two
solutions is the presence of inflections of the low tempera-
ture isotherms. It has been previously shown for bulk wa-
ter that those inflections in the isotherms are a signature
of the approach of the systems to liquid-liquid (LL) coex-
istence.23,30,59As already noted for the c = 0.67mol/kg
solution47, this behavior is maintained in the NaCl(aq).
Therefore we can infer that the HDL/LDL coexistence,
possibly terminating in a second critical point, is present
in the NaCl(aq) solutions, at least up to c = 2.10mol/kg
concentration. Nonetheless the shrinkage of the density
FIG. 7: Isochores in the temperature range 210K ≤ T ≤
300K, starting from the top, for bulk water (diamonds),
c = 0.67mol/kg (circles), c = 1.36mol/kg (squares) and
c = 2.10mol/kg (triangles) solutions at densities ρ = 1.05
(filled symbols) and 0.90 (unfilled symbols) g/cm3(color on-
range of inflections in the isotherms seems to indicate a
gradual disappearance of the coexistence upon increasing
These findings are consistent with what found by
Archer and Carter5in their experimental paper. They
found that the anomalous behavior of supercooled wa-
ter, and in particular the divergence of isobaric specific
heat and the existence of a TMD line are maintained in
NaCl(aq) up to concentrations of about 2mol/kg. Thus,
in the framework of the second critical point scenario,
it could be proposed that those anomalies are a conse-
quence of a second critical point in the NaCl(aq) system,
shifted toward lower pressures with respect to bulk water.
In Fig. 5 and Fig. 6 the isochores planes of the two
solutions are reported. The isochores are presented along
with the LMS lines and the TMD lines. For both systems
the isochores lying below the LMS line are not reported.
The minima are obtained by fitting the isochores with
fourth degree polynomial functions.
In Fig. 5 we show the isochores in the range
0.90g/cm3≤ ρ ≤ 1.125g/cm3, the LMS line and the
TMD line for the c = 1.36mol/kg solution. The range of
temperatures spanned is 210K ≤ T ≤ 500K. All the iso-
chores above ρ = 0.90g/cm3display a minimum, while
the ρ = 0.90g/cm3isochore is almost completely coinci-
dent with the LMS line. Such LMS line is entirely in the
region of negative pressure and it is nonre-entrant down
to the lowest temperature we simulated. This behavior
Bulkc = 0.67 mol/kg
c = 1.36 mol/kgc = 2.10 mol/kg
P − T
0.67mol/kg NaCl(aq)47(top right panel), c = 1.36mol/kg
NaCl(aq) (bottom left panel) and c = 2.10mol/kg NaCl(aq)
(bottom right panel), in the temperature range 210K ≤
300K and, starting from the top, for densities
ρ = 1.05,1.00,0.98.0.95, 0.90,0.87,0.85g/cm3for bulk wa-
ter, and for densities ρ = 1.05,1.025,0.98.0.95, 0.90g/cm3
for NaCl(aq) solutions (also ρ = 0.87g/cm3only for the
c = 0.67mol/kg solution), (color online).
Isochores and LMS lines (open circles) in the
plane for bulk water47
(top left panel), c=
has been already found in bulk water23,24,30,59,60,61, con-
fined water48and c = 0.67mol/kg NaCl(aq).47
In Fig. 6 the isochores in the range 0.90g/cm3≤
ρ ≤ 1.125g/cm3, the LMS line and the TMD line for
the c = 2.10mol/kg solution are displayed.
this case the range of temperatures spanned is 210K ≤
T ≤ 500K. The isochores above the ρ = 0.95g/cm3
show a minimum. At this concentration some oscilla-
tions can be found in the LMS line at low temperatures.
This line approximately follows the trend found for the
ρ = 0.90g/cm3isochore.
The comparison of the two isochores planes shows that
also the isochores of the c = 2.10mol/kg solution are
shifted toward lower pressures by roughly 50 MPa, with
respect to the c = 1.36mol/kg solution, as already noted
for the isotherms of the systems. This pressure shift de-
creases at low densities and at ρ = 0.90g/cm3it almost
In order to have a direct comparison of the two aqueous
solutions studied here with both bulk water and the c =
0.67mol/kg solution, we report in Fig. 7 the isochores for
bulk water, c = 0.67mol/kg, c = 1.36mol/kg and c =
2.10mol/kg solutions in the temperature range 210K ≤
T ≤ 300K and for densities ρ = 0.90g/cm3and ρ =
1.05g/cm3. In this picture it is more evident that the
increase in concentration leads to a downward pressure
shift of the corresponding isochores. This shift is quite
consistent at high densities while it tends to reduce at low
densities, close to the LMS line. To best show the overall
packing of the isochores upon increasing salt content in
Fig. 8 we show the blow-up of the P − T plane in the
temperature range 210K ≤ T ≤ 300K for all systems in
the same density range. On going from bulk water to the
c = 2.10mol/kg solution we observe a decrease by about
50% of the spanned range of pressures.
It has been previously observed in the literature that
at constant pressure, ions have an effect on the structure
of liquid water equivalent to the application of an ex-
ternal pressure.33,42,44,62,63This effect is consistent with
our findings since we see that the bulk isochores at a cer-
tain density coincide with higher density isochores of the
In Fig. 9 we show the comparison of TMD and LMS
lines in the P − T plane among different systems: the
two solutions studied in the present paper, the c =
0.67mol/kg NaCl(aq) and bulk water47and TIP4P water
confined in a hydrophobic environment of soft spheres.48
The temperature range spanned here is 210K ≤ T ≤
300K. We note that the LMS line appears not to be
significantly affected by the presence of ions. For the
c = 0.67mol/kg and the c = 1.36mol/kg solutions the
LMS line is almost identical to the bulk LMS. Only at the
highest concentration, c = 2.10mol/kg, it shows minor
differences. In the case of water in hydrophobic matrix,
which behaves similarly to a solution of small apolar so-
lutes48, the LMS line is similar in shape to that of bulk
water and NaCl(aq) solutions but presents a significant
shift, circa 200 MPa, in the direction of higher pressures
due to excluded volume effects caused by the strong so-
lute solvent repulsive strength.
At variance with the LMS line, the TMD line is
markedly influenced by the presence of ions. Upon in-
creasing concentration, in fact, it shifts to lower tem-
peratures and pressures. Moreover in all our solutions
the TMD line extends to lower densities with respect
to bulk water. Also the shape is modified by the ions
and this effect appears to be influenced by concentration.
For the c = 0.67mol/kg solution the TMD line is much
broader than for bulk water. For the c = 1.36mol/kg
and the c = 2.10mol/kg solutions, the TMD narrows,
remaining broader than that of bulk water. In the case
of the hydrophobic solute, the TMD line is broadened
with respect to bulk water in a way similar to the case
of c = 0.67mol/kg NaCl(aq), but it is shifted by roughly
200 MPa (upwards) in pressure and 40 K (to the left) in
temperature with respect to the bulk. A similar shift in
temperature was found also by Kumar et al. in TIP5P
water confined between hydrophobic plates.64
Now we further inquire on the possibility of a LL co-
existence in our solutions. In Fig. 10 we show the poten-
tial (or configurational) energy per molecule of the two
solutions, U, at T = 210 K, as a function of the den-
c = 0.67 TMD
c = 1.36 TMD
c = 2.10 TMD
c = 0.67 LMS
c =1.36 LMS
c = 2.1 LMS
FIG. 9: TMD and LMS lines in the P − T plane for the
c = 1.36mol/kg and the c = 2.10mol/kg solutions, the c =
0.67mol/kg solution and bulk water studied in 47 and the
hydrophobic confinement system studied in 48 (color online).
sity. For both solutions, U shows two minima. For the
c = 1.36mol/kg solution, these minima are in correspon-
dence with densities ρ = 0.95g/cm3and ρ = 1.05g/cm3.
For the c = 2.10mol/kg solution, minima can be found
in correspondence with densities ρ = 0.87g/cm3and
ρ = 0.98g/cm3. The existence of minima in the potential
energy as a function of the density, at low temperatures,
can be related to the presence of LDL/HDL coexistence,
as shown by Kumar et al.64for water in hydrophobic
confinement at T = 220 K. Therefore the presence of
two minima in the potential energy, at low temperature,
in our solutions confirms the indication of the existence
of a LL coexistence inferred from the inflections of low
temperatures isotherms that we observed.
We can thus infer that, up to the highest concentra-
tion we studied, the anomalous behavior of supercooled
water is maintained in the NaCl(aq) solutions. The pres-
ence of the ions does not seem to hinder the mechanism
of emergence of this anomalous behavior. On the other
hand the shift and the packing in the thermodynamic
plane and the gradual weakening of the inflection in the
isotherms, upon increasing salt content, are signatures of
a progressive disappearance of the anomalies for higher
concentrations of ions.
We performed MD simulations on two sodium chlo-
ride aqueous solutions in TIP4P water, with concentra-
c = 1.36 mol/kgc = 2.10 mol/kg
FIG. 10: Potential energy per molecule at T = 210 K, as
a function of density for the c = 1.36mol/kg solution (left
panel) and for the c = 2.10mol/kg solution (right panel).
tions c = 1.36mol/kg and c = 2.10mol/kg, extending
our previous work on bulk water and c = 0.67mol/kg
NaCl(aq).47Using the simulated state points, we drew
the isotherms and the isochores planes of the systems.
The analysis of those planes allowed the determination
of the LMS line and of the TMD line, respectively.
By comparing the results obtained for the solutions
studied here and in previous work, we can observe that
the presence of minima in the isotherms, determining the
presence of a LMS line, is preserved in all the NaCl(aq)
solutions analyzed. Importantly, also the inflections for
low temperatures isotherms, at high densities, are main-
tained in the solutions. Nonetheless, they become less
pronounced upon increasing concentration.
ously shown for bulk water23,30,59, those inflections sig-
nal the presence of phase coexistence between LDL and
HDL in the systems. Being the LL coexistence still
present up to the highest concentration we studied, we
can hypothesize that whether a second critical point ex-
ists for bulk water, it is preserved in the NaCl(aq) solu-
tion. Also the existence of a TMD line, determined by
the presence of minima in the isochores plane, is main-
tained in the NaCl(aq) solutions. Experimental results
have shown that the TMD at ambient pressure is still
present for a c = 1.49mol/kg solution and disappears
for c = 2.33mol/kg.5In our results we note that the
minima of the isochores become less pronounced for the
c = 2.10mol/kg solution and correspondingly the TMD
Although the overall thermodynamic behavior of the
NaCl(aq) solution is similar to that of bulk water, some
differences can be noted. In fact, for densities high with
respect to the LMS line, both the isotherms and the iso-
chores shift to lower pressures upon increasing concen-
tration. This behavior results in a significant packing of
the curves, as it is particularly evident in the isochores
plane. The difference of pressure between the highest
density isochore and the LMS line is in fact much broader
in bulk water than in solutions and it is reduced upon in-
creasing concentration. The LMS line is not influenced
by the presence of ions. In fact both the position in the
P − T plane and the shape remains similar to bulk wa-
ter, with some minor differences appearing for the highest
concentration studied. The TMD line is instead modified
in shape and shifted toward lower pressures and temper-
atures upon increasing concentration.
The results for the LMS line and TMD line were also
compared to those for water confined in a hydrophobic
environment of soft spheres.48For this system the LMS
line is similar in shape to that of bulk water but it is
shifted to higher pressures. The TMD line is instead
similar to that of c = 0.67mol/kg NaCl(aq) in shape but
it is shifted to higher pressures and lower temperatures.
The existence of two minima in the curves of the po-
tential energy as function of density indicates that LL co-
existence is present in the the NaCl(aq) solutions studied
here, in analogy with what found for water confined be-
tween two hydrophobic plates.64This result strengthen
the hypothesis of a LL coexistence deduced from the ob-
servation of inflections in the low temperature isotherms.
We note on passing that signatures of LL coexistence
have been experimentally found in LiCl(aq) solutions.65
We have shown that various anomalous features of su-
percooled water are preserved in aqueous solutions of
sodium chloride up to the highest concentration investi-
gated. Interestingly the TMD can be even followed down
to lower densities with respect to bulk. From the ther-
modynamic features investigated we hypothesize that the
LL critical point would be slightly shifted in tempera-
ture and more markedly shifted in pressure with respect
to bulk water. Therefore an experimental observation of
the LL critical point in aqueous solutions, for which crys-
tallization is more easily avoided than in the bulk phase9,
could be possible.
The authors gratefully acknowledge the computational
support of the Democritos National Simulation Center,
at SISSA, Trieste and of the Roma Tre INFN-GRID.
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