Water and anomalous liquids
Valentino Bianco1 , Romina Ruberto2 , Sergiy Ancherbak3 ,
Giancarlo Franzese1
1
Departament de Fı́sica Fonamental, Universitat de Barcelona
Diagonal 647, 08028 Barcelona, Spain
2
Dipartimento di Fisica, Università di Messina, Italy
3
Dipartimento di Fisica, Università di Pisa, Italy
Abstract.
Water is an anomalous liquid because its properties are different from those of the
majority of liquids. However, the category of anomalous liquids could be greater than
what so far supposed. Here, we review what is anomalous about water, which are the
other liquids that are as well anomalous, and which are those that could be anomalous.
We ask questions such as: Why water is anomalous? Are the other liquids anomalous
for the same reason as water? How can we define models that capture the complexity
of water and other anomalous liquids, but are tractable for theory and simulations?
Can we make predictions with these models that can be tested in experiments? We
discuss here possible answers to these questions.
Water and anomalous liquids
2
1. An overview on anomalous liquids and water
What is an anomalous liquid? We define as anomalous liquid as a mono-component
substance that, in the liquid phase, behaves generally different in respect to the argonlike liquids. We will describe here thermodynamic anomalies, dynamic anomalies
and structural anomalies that are related, respectively, to non-monotonic trends of
thermodynamics functions, dynamics functions and structural functions upon changing
the temperature T or the pressure P of the system. Among the substances showing
anomalous properties in the liquid phase we find silica (SIO2 ) [1–3], silicon (Si) [4, 5],
selenium (Se) [6], phosphorus (P) [7–9] and water [10].
1.1. Thermodynamic anomalies
Water and other anomalous liquids display a maximum density in the liquid phase,
related to negative thermal expansion coefficient, and implying that the liquid expands
upon cooling or shrinks upon heating. The presence of a temperature of maximum
density (TMD) for water is known since centuries: the maximum density of water
is at ∼ 4 ◦ C at atmospheric pressure. For this reason the thermal expansivity
αP ≡ −(1/V )(∂V /∂T )P , where V is the volume, vanishes at T ∼ 4 ◦ C and its absolute
value increases as a power law below 4 ◦ C [11].
Other anomalous thermodynamic functions of water are the isothermal
compressibility KT ≡ −(1/V )(∂V /∂P )T [12] and the specific heat CP ≡ (∂H/∂T )P [13],
where H is the enthalpy of the system, respectively related to fluctuations in volume
and entropy. For normal liquid KT and CP tend to 0 upon cooling, while in the case of
water they reach a minimum value at certain temperature (T ∼ 46 ◦ C for KT and T ∼
35 ◦ C for CP ) and than increase for decreasing T .
Experiments for Ga [14], Bi [15], Te [16], S [17, 18], Be, Mg, Ca, Sr, Ba [19],
SiO2 , P, Se, Ce, Cs, Rb, Co, Ge [10] and simulations on SiO2 [20–22], S [5], BeF2 [20]
reveal the presence of TMD at constant pressure also for these substances in the liquid
phase. As for the case of water, also for these substances the TMD implies anomalies
in thermodynamic response functions.
1.2. Dynamic anomalies
An example of dynamic anomaly is the non-monotonic behavior of diffusion constant
D as function of P . In a normal liquid D decreases when density or pressure are
increased. Anomalous liquids, instead, are characterized by a region of phase diagram
where D increases upon increasing the pressure at constant temperature. In the case of
water, for example, experiments show that the normal behavior of D is restored only at
pressures higher than P ∼1.1 kbar at 283 K [23].
Water and anomalous liquids
3
1.3. Structural anomalies and polymorphism
A typical structural anomaly is the non-monotonic behavior of structural order
parameters of the system as a function of T and P . Normal liquids tend to become
more structured when compressed. The molecules adopt preferential separation and a
certain orientational order. This ordering can be described by two order parameters:
a translational order parameter and an orientational order parameter. The higher is
the value of these parameters, the higher is the order of the system. Therefore, for
normal liquids these parameters increase with increasing pressure or density at constant
temperature. Anomalous liquids, instead, show a region where the system becomes
more disordered as the pressure increases, leading to lower values of the structural order
parameters. This is emphasized in molecular dynamics simulations for water [24] and
for silica [22].
The presence of different solid structures is often related to anomalous properties of
the substance. By definition a substance is polymorphic if has several crystalline phases,
and is polyamorphic if has several glassy or liquid phases. An example of polymorph
is water, with at least 17 crystalline phases [25–30], some of them stable only at high
pressure. Another example is carbon with graphite, graphene and diamond. Evidences
of polyamorphism in liquid state have been observed in phosphorous [7–9], triphenyl
phosphite [31–33] and in yttrium oxidealuminum oxide melts [34]. At low temperature
and low pressure water forms low-density amorphous (LDA) ice [35]. Upon increasing
the pressure it transforms from LDA to high-density amorphous (HDA) ice [25], and
upon further increasing of the pressure from HDA to very-high-density amorphous
(VHDA) [36]. As we discuss later, the presence of several amorphous states could
indicate the presence of a liquid-liquid phase transition.
1.4. A few questions
Water, the most common and possibly the most important liquid for life, is one of the
liquids with more anomalies. Despite its apparently simple structure, it displays more
than sixty anomalies. Water can exist as a supercooled liquid at temperatures far below
the melting temperature. The lowest measured temperature for supercooled liquid water
is about -92 ◦ C at 2 kbars [37].
A characteristic feature of water molecule is the formation of hydrogen bonds (HBs)
with nearby water molecules. The HBs form a dynamic network of water molecules with
a preferential tetrahedral structure. At ambient pressure and temperature a few degrees
below the melting, water forms a tetrahedral structure up to the second shell of each
molecule [38]. Upon increasing pressure, the second shell collapses on top of the first
giving rise to an increase of density of the system. This experimental observation, is
consistent with at least three possible scenarios suggested for supercooled water: the
liquid-liquid phase transition scenario [39], the singularity-free scenario [40] and the
critical point free scenario [41]. The difference among these hypothesis is related to
how the density changes from LDA to HDA. These interpretations suppose that LDA
Water and anomalous liquids
4
and HDA transform with continuity in a low-density liquid (LDL) and high-density
liquid (HDL), respectively, for temperatures above the temperature of spontaneous
crystallization. In the case of discontinuous change in density between LDL and HDL, a
first order phase transition occurs as hypothesized in the liquid-liquid phase transition
scenario. In this case the phase transition could end in a liquid-liquid critical point at
positive pressure [39, 42, 43], at negative pressures [?], or continues until the liquid-gas
limit of stability is reached at negative pressure [41]. In the singularity free scenario
LDL and HDL do not represent distinct phases and the sharp, but continuous, change
in density is due to local density fluctuations. We will discuss in the next sections these
scenarios with more details.
The physics of the HBs is the key to understand the properties of water.
Nevertheless, there are a few natural questions that are interesting to ask.
(i) Is bonding the only possible mechanism for the anomalies? The interest of this
question comes from the fact that other possible mechanisms could be relevant
for explaining anomalous behavior in liquids different from water and not forming
network. A simple observation is that two characteristic lengths can be associated
to water: a distance at which two water molecules form hydrogen bonds and a
shorter distance of maximum approach. Several potentials with two characteristic
interacting distances have been proposed to study the physics of anomalies. A
recent review on this subject is Ref. [44].
(ii) Can we understand if anomalies imply a liquid-liquid phase transition?
(iii) A liquid-liquid phase transition would imply an anomalous behavior?
(iv) How to write a microscopic theory for this phenomena?
(v) Can a model be predictive and help us in designing experiments and understand
the implications for fields such as biology, medicine, food technology, or
nanotechnology?
In the following we will discuss possible answers to these questions.
2. An Hamiltonian model for water
A variety of statistical models have been proposed in order to reproduce the main
features of liquid water, including the anomalies. From a general stand point, different
models can be classified as isotropic models or as models with directional interactions.
Commonly used models treat the water molecule as rigid and use isotropic interactions
due to a specific distribution of charges on the molecule. The electrostatic interaction is
modeled by using Coulomb’s law, while other attractive and repulsive forces are modeled
by using the Lennard-Jones potential (e.g. TIP3P, TIP4P and TIP5P water models).
These pair potentials reproduce water anomalies with fare agreement, but do not succeed
in reproducing all the properties. For example, many of them fails in reproducing the
crystal phases of water. However, the real problem with these models is that they are
computationally expensive due to the long range Coulomb interaction.
Water and anomalous liquids
5
This problem is particular relevant in simulations of biological processes where
macromolecules are surrounded by milions of water molecules. To overcome this problem
a possible way is to consider coarse-grained models for water [45–50]. In particular, these
models can be used to study nano-confined water in extreme conditions and to compare
with experiments.
Here, we will describe in detail the model proposed by Franzese and Stanley in
2002 [46–51]. The simplest approximation of nano-confined water is a monolayer of water
confined between two plates [52]. We divide the system into cells, each one occupied
by one water molecule. For each cell i we associate an occupation number ni = 1 if
in the cell there is a molecule, otherwise ni = 0. Each molecule has a minimum hard
core volume corresponding to the minimum volume v0 of a cell. Isotropic interactions
(van der Wall attraction and hard core repulsion) in the system are represented by the
Lennard-Jones potential
#
"
X r0 12 r0 6
,
(1)
−
U ≡−
rij
rij
ij
where rij is the distance between molecules i and j and the sum is performed over all
the molecules up to a cutoff distance at about three shells. This term depends only
on the relative distance between two molecule and represent the isotropic part of the
interaction.
In order to describe the HB interaction, that is a directional interaction, we
introduce variables σij = 1...q [53] for each occupied site i facing the cell j. The value
of q is discussed in the following. Assuming that a water molecule can form up to
four HBs, we fix to four the number of variables σij for each cell. Variables σij are
introduced to account for the number of bonding configurations accessible to a water
molecule. The state of a water molecule is completely determined by the values assumed
by the four variables σij . The condition for two first neighbor molecules to form a HB is
σij = σji . We adopt a geometrical definition of HB, assuming that the HB is broken if
the angle H-O-O deviates more than 30◦ from the linear bond. Therefore, we consider
q = 180◦ /30◦ = 6 states, where only 1/6 corresponds to the formation of a HB. The
covalent HB interaction is represented by the Hamiltonian term
X
HHB ≡ −J
ni nj δσij δσji ,
(2)
<ij>
where J > 0 represent the covalent energy gained per HB, the sum is over nearest
neighbors cells, and δab = 1 if a = b, 0 otherwise. Experimental evidences show
that the distribution of angles O-O-O is changing with T and becomes sharper and
sharper with decrease of T , approaching the distribution corresponding to tetrahedral
arrangement [54]. Therefore, there is a correlation among HBs formed by the same
molecule. Hence, we introduce a term representing the many-body interaction between
the HBs of a single molecule
XX
HCoop ≡ −Jσ
δσik σil ,
(3)
i
(k,l)i
Water and anomalous liquids
6
Figure 1. Schematic representation of the model. Each cell can be empty or occupated
by a water molecule with oxigen (in red), hydrogens (in blue) and lone electrons pair
represented by gray sticks. To each hydrogen and lone pair we associate a bonding
variable σij .
where Jσ > 0 is the characteristic energy of this cooperative component.
The formation of a HB leads to an open structure that induces a local increase
of volume per molecule. This effect is incorporated in the model by considering that
the total volume of the system depends linearly on the number of HBs. So the volume
change is
V ≡ V0 + NHB vHB ,
(4)
where vHB is the increment due to the HB, and V0 ≡ N v0 for N water molecules.
The total enthalpy for the water is
H ≡ U + HHB + HCoop + P V = U − (J − P vHB )NHB − JNσ + P V0 , (5)
where the total number of HB and is
X
NHB ≡
ni nj δσij δσji ,
(6)
<ij>
and
Nσ ≡
XX
i
δσik σil ,
(7)
(k,l)i
is the total number of HBs optimizing the cooperative interaction [46–52, 55, 56].
3. Phase diagram and supercooled water
By both mean field and simulations we calculate the properties of the model in Eq.
(5). It reproduces qualitatively the phase diagram of water. At high T it displays the
liquid-gas phase transition [46–52,55,56] (Figure 2). At fixed temperature, for increasing
Water and anomalous liquids
7
Figure 2. Density ρ as function of temperature T along isobars for the model in Eq.
(5). Labels near each isobar show the corrisponding pressure P in units of /v0 . (a) At
high temperature the discontinuity in ρ marks the liquid-gas phase transition ending
in a critical point. The black line represents the locus of maximum density. (b) At
low T , another discontinuity in ρ marks the phase transition between HDL and LDL.
Dashed lines approximate the coexistence regions [52].
pressure the diffusion constant increases up to a maximum, reproducing the anomalous
behavior of diffusion, a characteristic of water. By decreasing P at constant T , KT ,
αP and CP increase in a way that is not expected for normal liquids. These anomalies
become more evident approaching the supercooled region of the phase diagram. As a
rationale to this phenomena various scenarios have been proposed.
The stability limit scenario [57] hypothesizes that the locus of the limit of stability
of superheated liquid water in P –T plane have a positive slope at high T. Decreasing
T, this locus reaches a minimum pressure and for further decrease of T it acquires a
negative slope at low T. The reentrant behavior of this locus would be consistent with
the observed anomalies of water.
The liquid-liquid critical point (LLCP) scenario [39] supposes that the anomalies of
water are due to the large fluctuations of thermodynamics quantities as a consequence of
a first order phase transition in the supercooled region between two metastable liquids
at different densities: the low-density liquid (LDL) at low P and low T , and the highdensity liquid (HDL) at high P and high T . The phase transition line ends in a critical
point and has a negative slope in the P − T plane because the entropy is higher in the
HDL phase.
Water and anomalous liquids
8
Figure 3. By mapping the system in the space of parameters J and Jσ , Stokely
et al. [56] recover all the scenarios proposed to explain the anomalous behavior of
supercooled water. (i) If Jσ = 0 (red line along x-axis), independently of J, we recover
the singularity-free scenario. (ii) For large enough Jσ (yellow region in top left), water
exhibits a first-order liquid-liquid phase transition line terminating at the LiquidGas
spinodal, as predicted in the critical-point-free scenario; (iii) For other combinations of
J and Jσ , water would be described by the LLCP scenario. For larger Jσ , the LLCP is
at negative pressure (brown region between dashed lines). For smaller Jσ , the LLCP
is at positive pressure (orange region in bottom right).
The singularity-free scenario [53] predicts lines of maximum in the P − T for the
response functions, similar to those observed in the LLCP scenario, but shows that no
singularities are present for non-zero temperatures.
The critical-point-free scenario [41] hypothesizes an order-disorder transition
extending to negative pressure and reaching the supercooled limit of stability of liquid
water. This scenario predicts no critical point and a behavior for the limit of stability
of liquid water as in the stability limit scenario.
It is possible to map all these scenarios in the Hamiltonian model proposed by
Franzese and Stanley [Eq. (5)] tuning the coupling constants J (for the covalent
component of the HBs) and Jσ (for the many-body component of the HB interaction) [56]
(Figure 3). The absence of the many-body component leads to the singularity free
scenario, while a large value of the many-body component, with respect to the covalent
component, gives rise to the critical-point free/stability limit scenario. Intermediate
values of J and Jσ lead to the LLCP scenario. All scenarios are obtained from the same
mechanism. Estimating the parameters J and Jσ from the experiments, we get Jσ ∼ 1
kJ/mol, ∼ 5.5 kJ/mol and J ∼ 6 − 12 kJ/mol. With this set of parameters the model
predicts the LLCP scenario, with a liquid-liquid critical point C 0 at positive pressure.
Therefore, the cooperative behavior of HBs is the principal responsible for the
anomalous behavior of water. The model shows that the HB many-body component, as
Water and anomalous liquids
9
large as can be deduced from experiments, implies a LLCP.
4. Water confined between hydrophobic surfaces
Franzese and los Santos studied the dynamics of water confined between hydrophobic
plates at low temperature [52]. They observed different behaviors of water at different
pressures. At very high pressure, the formation of HBs is inhibited and the system
exhibits large cavities at low T due to the condensation of water molecules on the
hydrophobic surface. At higher T , the system is quite homogeneous in a wide range of
temperature. In this case, the time correlation function C(t), that quantifies the time
in which the HBs of two water molecules are statistically correlated, has an exponential
decay. In general
t
β
C(t) = C0 e−( τ ) ,
(8)
where C0 , τ and β ≤ 1 are fitting constant (β = 1 correspond to exponential decay).
For pressure close to the critical pressure PC0 the time correlation function has an
exponential decay for high temperature, far from the LLCP temperature TC0 . As we
approach TC0 , the time correlation function is well described by a stretched exponential
(β < 1). The study shows observe that the network of HBs is well developed already
in the high density phase but has no global order. Approaching TC0 , the effect of
cooperativity results in a strong heterogeneity in the system. The value predicted for the
stretched exponential β, that quantifies the degree of deviation from homogeneity of the
system, is in agreement with experimental results on water hydrating myoglobin [58,59].
Further decrease of pressure and temperature leads the system to a glassy state with
a strong HB network that traps the system in arrested configurations. As a consequence,
the time correlation function has a constant value close to one.
5. Percolating approach
The analysis of the system with a percolating approach allow us to understand better the
formation of the HB network [60]. We define a cluster as the region of the statistically
correlated water molecules connected by HBs in a tetrahedral state [61,62]. Simulations
and mean field calculations show how the network of HBs percolates in the system as
we approach to the critical point C 0 (Figure 4). As a consequence, the tetrahedral order
of the water molecules increases [55, 63]. Large fluctuations if the number of HBs are
observed in the region of the Widom line (the region of the phase diagram where the
system has a maximum correlation length) [49,51]. The large fluctuations of the number
of HBs indicate the occurrence of a macroscopic structural change from HDL-like liquid
to LDL-like liquid.
Water and anomalous liquids
10
Figure 4. Water monolayer between two hydrophobic slabs (not showed in the figure).
Each water molecule is represented by four sites at the vertices of a square lattice. The
vertices are situated at the center of the square partion used to represent the system.
Each site of a molecule represents a bonding variable σij . Sites with the same color
are in the same bonding state and, at the same time, are statistically correlated.
6. Dynamical crossover
As we already mentioned, at low T the model predicts an arrested state. This is
consistent with experiments for water, that glassifies rapidely if quenched at very low
T . By definition the relaxation time τ of the system changes greatly as we approach
the glassy temperature, reaching 100 sec at the glassy temperature. A liquid systems is
said to be Arrhenius if τ depends exponentially on 1/T as
EA
τ = τ0 e kB T
.
(9)
The quantity EA is the activation energy, kB is the Boltzmann constant and τ0 the
characteristic relaxation time for T → ∞. The liquids that deviate from this relation
are classified as non-Arrhenius.
Kumar et al. [50], using this model find a dynamic crossover for the correlation
time τ of the HBs from non-Arrhenius behavior at high T , to Arrhenius behavior at
low T . They show that this behavior is independent on the existence of a LLCP. This
crossover corresponds to a local rearrangement of the HBs for the formation of more
tetrahedral structure. From the low T Arrhenius behavior of the correlation time the
authors estimate the T -independent activation energy EA . Furthermore, by mean field
calculations, they are able to show that for T greater than the temperature of the Widom
line, a decrease of T leads to an increase of the number of HBs and to an increase of the
EA . For T lower that the temperature of the Widom line the number of HBs and EA
remains constant upon further decreasing of temperature. Therefore, they show that
the crossover occurs exactly at the Widom line. They find also that the crossover is
isochronic, i.e. occurs when the system reaches a characteristic correlation time that is
independent of the pressure. The predictions are in agreement with the experiments on
Water and anomalous liquids
11
the hydrated lysozyme [64].
Mazza et al. show that the model predicts also another crossover, at lower T , for
the HBs correlation time. This second crossover is experimentally observed in lysozyme
hydration water [65]. At low P two structural changes take place in the HB network of
the hydration shell. One at about 250 K is due to the building up of the HB network,
and another at about 180 K is consequence of the cooperative reorganization of the HBs.
Both crossovers are related to the two maxima found by the authors for the heat capacity
of the system [66] for low pressure. These two maxima are due to the fluctuations of
the tetrahedral order, and to the fluctuations in HB formation. For increasing pressure,
the two maxima merge and give rise to a single locus that approaches the Widom line.
7. Liquid-liquid phase transitions
In recent years, several experiments have shown the occurrence of a liquid-liquid phase
transition in different substances, such as phosphorus [7, 8], liquid metals Y2 O3 -Al2 O3
(Yttrium OxideAluminum Oxide Melts) [34] and molecular liquids [31]. Molecular
dynamics simulations of specific models for supercooled water [2, 39, 43, 67–69], liquid
carbon [70] and supercooled silica [3, 4, 71, 72] predict LDL-HDL critical point.
To describe simple atomic systems (like argon) an isotropic pair interaction
potential is commonly used. Probably the most famous potential is the one proposed
in 1931 [73] by John Edward Lennard-Jones (LJ) for real gases. The LJ potential
incorporates the van der Waals attraction, due to the instantaneous formation of dipoles,
between the electronic clouds; and the short range repulsion, due to the Pauli’s quantum
exclusion principle, among electron orbitals. The LJ potential reproduces a phase
diagram with gas, liquid and solid phases for simple atomic or molecular systems.
Moreover the dynamics and kinetics of these systems are correctly described.
Simple variation of LJ were used to describe more complex system like colloids
or protein solutions. However, with this kind of potential is not possible to reproduce
anomalous properties of systems like liquid metals or water.
All the system we talked about are network-forming substances with strongly
anisotropic interactions. However it is possible to describe the anomalous properties
of some substances considering a soft-core isotropic potential with two characteristic
lengths [19, 74–78].
Franzese et al. [79] show that a spherically symmetric potential, with an attractive
interaction at long distance, a repulsive soft-core at intermediate distance, and a hardcore repulsion at short distance, can describe a single component system with a firstorder liquid-liquid phase transitions. The simplest approximation for such kind of
potential is a square potential as showed in Figure 5.
In particular, they showed that a system with this potential has a gas-liquid critical
point and a liquid-liquid critical point, for a certain range of potential parameters.
They find that a balance between the attractive and repulsive part of the potential
leads to the existence of two fluid-fluuid critical points, well separated in temperature
Water and anomalous liquids
12
4
∆
15
30
100
300
500
2
1
UR/UA
U/UA
3
(RA-RR)/a
0
RR/a
-1
0
0.5
1
1.5
2
2.5
3
r/a
Figure 5. Potentials with two characteristic lengths: the continuous shouldered well
potential (continuous lines), and the discontinuous shouldered well potential (dotted
black line). The parameter ∆ estabilishes the slope of the shoulder between r = a and
r = 2a.
and density [80]. This behavior can be qualitatively reproduced by a modified van der
Waals equation [81]
P =
ρkB T
− Aρ2
1 − ρB(ρ, T )
,
(10)
where A represents the strength of attraction and B the excluded volume. This equation
has the same form of the van der Waals equation, but with an excluded volume B(ρ, T )
depending on density and temperature. B(ρ, T ) varies between the hard-core value for
high temperature and the soft-core value for low temperature.
They also show that with the discontinuous version of the potential the occurrence
of the the liquid-liquid phase transition does not imply the presence of density anomaly
[76]. Nevertheless, a continuous version of the soft-core potential exhibits water-like
anomalies. In particular, it has been shown that density anomaly [82], anomalous
diffusion and anomalous structures [83] occur in a water-like hierarchy. Furthermore,
the extension and accessibility of the anomalous region depends on the softness of the
potential [84].
8. Conclusions
The results shortly presented here allows us to formulate possible answers to the
questions asked at the beginning of this review.
Water and anomalous liquids
13
(i) We clarify that directional bonding is not the only possible mechanism for the
anomalies. The anomalies can be related both to bonding and to two competing
interaction distances.
(ii) We understand that anomalies imply a liquid-liquid phase transition, in the sense
that the mechanism responsible for the anomalies (e.g. hydrogen bonding for water,
or competing interaction distances for liquid metals) are enough to generate a
liquid-liquid phase separation. Nevertheless, if the iquid-liquid phase coexistence is
reachable or not in experiments is a question more complex to answer. In the case of
water it is evident from experiments that the phase separation cannot be observed
in the bulk, because it is predicted by models in a region where only solid water
(amorphous or crystal ice) exists. Confinement can reduce the tendency of water
to solidify, but can also change drastically the thermodynamics of water [85]. In
other cases, e.g. phosphorous, the liquid-liquid phase separation is experimentally
accessible, but experiments cannot be performed in the region where a possible
liquid-liquid critical point would be [7–9].
(iii) We clarify that a liquid-liquid phase transition would not necessarly imply an
anomalous behavior, because there is at least one case, for a theoretical model [76],
in which this has been shown.
(iv) We understand how to write a microscopic theory for this phenomena for both
possible mechanisms proposed here. For the case of directional bonding, as in
water, a Hamiltonian model allows us to make analytic calculations and perform
efficient numerical simulations, that amke possible to interpret in a clear way the
experimental results for supercooled water. For the case of competing interaction
distances, as in liquid metals or colloids, we can develop a theory and make
simulations for an isotropic model.
(v) With these models we can predict new phenomena, such as the occurrence of a
sequence of partial structural changes in protein hydration water, corresponding to
different maxima in the heat capacity and to different crossover in the relaxation
dynamics [65]. Or to predict how the pressure would affect the thermodynamics
of nanoconfined water [85] or the dynamics of protein hydration water [86]. These
results are potentially relevant in many applicative fields, such as criobiology or
nanomedicine.
Acknowledgments
We thank for discussions and collaboration M. C. Barbosa, S. V. Buldyrev, F. Bruni, S.H. Chen, A. Hernando-Martı́nez, P. Kumar, G. Malescio, F. Mallamace, M. I. Marqués,
M. G. Mazza, A. B. de Oliveira, S. Pagnotta, F. de los Santos, H. E. Stanley, K. Stokely,
E. G. Strekalova, P. Vilaseca. We thank the Spanish Ministerio de Ciencia e Innovación
Grants FIS2009-10210 (co-financed FEDER), and V. B. thanks the Generalitat de
Catalunya Grant 2010 FI-DGR for support.
Water and anomalous liquids
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