Water and anomalous liquids · 2019-07-31 · Water and anomalous liquids Valentino Bianco1, Romina...

Water and anomalous liquids

Valentino Bianco1 Romina Ruberto2 Sergiy Ancherbak3

Giancarlo Franzese1

1Departament de Fısica Fonamental Universitat de BarcelonaDiagonal 647 08028 Barcelona Spain2 Dipartimento di Fisica Universita di Messina Italy3 Dipartimento di Fisica Universita di Pisa Italy

AbstractWater 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 thanwhat so far supposed Here we review what is anomalous about water which are theother liquids that are as well anomalous and which are those that could be anomalousWe ask questions such as Why water is anomalous Are the other liquids anomalousfor the same reason as water How can we define models that capture the complexityof water and other anomalous liquids but are tractable for theory and simulationsCan we make predictions with these models that can be tested in experiments Wediscuss 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 argon-

like 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) [1ndash3] silicon (Si) [4 5]

selenium (Se) [6] phosphorus (P) [7ndash9] and water [10]

11 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 sim 4 C at atmospheric pressure For this reason the thermal expansivity

αP equiv minus(1V )(partVpartT )P where V is the volume vanishes at T sim 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 equiv minus(1V )(partVpartP )T [12] and the specific heat CP equiv (partHpartT )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 sim 46 C for KT and T sim35 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 [20ndash22] 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

12 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 sim11 kbar at 283 K [23]


13 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 [25ndash30] 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 [7ndash9] triphenyl

phosphite [31ndash33] 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

14 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


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 Coulombrsquos law while other attractive and repulsive forces are modeled

by using the Lennard-Jones potential (eg 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


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 [45ndash50] 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 [46ndash51] 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

U equiv minussumij

ε

[(r0

rij

)12

minus(

r0

rij

)6]

(1)

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 = 1q [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 = 18030 = 6 states where only 16 corresponds to the formation of a HB The

covalent HB interaction is represented by the Hamiltonian term

HHB equiv minusJsumltijgt

ninjδσijδσji

(2)

where J gt 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

HCoop equiv minusJσ

sumi

sum(kl)i

δσikσil (3)


Figure 1 Schematic representation of the model Each cell can be empty or occupatedby a water molecule with oxigen (in red) hydrogens (in blue) and lone electrons pairrepresented by gray sticks To each hydrogen and lone pair we associate a bondingvariable σij

where Jσ gt 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 equiv V0 + NHBvHB (4)

where vHB is the increment due to the HB and V0 equiv Nv0 for N water molecules

The total enthalpy for the water is

H equiv U + HHB + HCoop + PV = U minus (J minus PvHB)NHB minus JNσ + PV0 (5)

where the total number of HB and is

NHB equivsumltijgt

ninjδσijδσji

(6)

and

Nσ equivsum

i

sum(kl)i

δσikσil (7)

is the total number of HBs optimizing the cooperative interaction [46ndash525556]

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 [46ndash525556] (Figure 2) At fixed temperature for increasing


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 εv0 (a) Athigh temperature the discontinuity in ρ marks the liquid-gas phase transition endingin a critical point The black line represents the locus of maximum density (b) Atlow T another discontinuity in ρ marks the phase transition between HDL and LDLDashed 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 PndashT 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 high-

density 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 minus T plane because the entropy is higher in the

HDL phase


Figure 3 By mapping the system in the space of parameters J and Jσ Stokelyet al [56] recover all the scenarios proposed to explain the anomalous behavior ofsupercooled water (i) If Jσ = 0 (red line along x-axis) independently of J we recoverthe singularity-free scenario (ii) For large enough Jσ (yellow region in top left) waterexhibits a first-order liquid-liquid phase transition line terminating at the LiquidGasspinodal as predicted in the critical-point-free scenario (iii) For other combinations ofJ and Jσ water would be described by the LLCP scenario For larger Jσ the LLCP isat negative pressure (brown region between dashed lines) For smaller Jσ the LLCPis at positive pressure (orange region in bottom right)

The singularity-free scenario [53] predicts lines of maximum in the P minus 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 freestability 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 sim 1

kJmol ε sim 55 kJmol and J sim 6minus 12 kJmol With this set of parameters the model

predicts the LLCP scenario with a liquid-liquid critical point C prime 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


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

C(t) = C0eminus( t

τ )β

(8)

where C0 τ and β le 1 are fitting constant (β = 1 correspond to exponential decay)

For pressure close to the critical pressure PCprime the time correlation function has an

exponential decay for high temperature far from the LLCP temperature TCprime As we

approach TCprime the time correlation function is well described by a stretched exponential

(β lt 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 TCprime 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 [5859]

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 [6162] Simulations

and mean field calculations show how the network of HBs percolates in the system as

we approach to the critical point C prime (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) [4951] The large fluctuations of the number

of HBs indicate the occurrence of a macroscopic structural change from HDL-like liquid

to LDL-like liquid


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 Thevertices are situated at the center of the square partion used to represent the systemEach site of a molecule represents a bonding variable σij Sites with the same colorare 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 1T as

τ = τ0eEAkBT (9)

The quantity EA is the activation energy kB is the Boltzmann constant and τ0 the

characteristic relaxation time for T rarr infin 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 ie occurs when the system reaches a characteristic correlation time that is

independent of the pressure The predictions are in agreement with the experiments on


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 Y2O3-Al2O3

(Yttrium OxideAluminum Oxide Melts) [34] and molecular liquids [31] Molecular

dynamics simulations of specific models for supercooled water [2 39 43 67ndash69] liquid

carbon [70] and supercooled silica [3 4 7172] 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 Paulirsquos 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 [1974ndash78]

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 hard-

core repulsion at short distance can describe a single component system with a first-

order 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


-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆

Figure 5 Potentials with two characteristic lengths the continuous shouldered wellpotential (continuous lines) and the discontinuous shouldered well potential (dottedblack line) The parameter ∆ estabilishes the slope of the shoulder between r = a andr = 2a

and density [80] This behavior can be qualitatively reproduced by a modified van der

Waals equation [81]

P =ρkBT

1minus ρB(ρ T )minus Aρ2 (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


(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 (eg 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 eg 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 [7ndash9]

(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-Martınez P Kumar G Malescio F Mallamace M I Marques

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 Innovacion

Grants FIS2009-10210 (co-financed FEDER) and V B thanks the Generalitat de

Catalunya Grant 2010 FI-DGR for support


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[4] Saika-Voivod I Sciortino F Poole PH (2000) Computer simulations of liquid silica Equation ofstate and liquidndashliquid phase transition Physical Review E 63 011202

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[15] P L S S W K (1976) Structure of molten bi-sb-alloys by means of neutron diffraction ZeitschriftNaturforschung Teil A 31 90

[16] Thurn H Ruska J (1976) Change of bonding system in liquid sexte1-1 alloys as shown by densitymeasurements Journal of Non-Crystalline Solids 22 331-343

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[21] Sharma R Chakraborty SN Chakravarty C (2006) Entropy diffusivity and structural order inliquids with waterlike anomalies The Journal of Chemical Physics 125 204501

[22] Shell MS Debenedetti PG Panagiotopoulos AZ (2004) Saddles in the energy landscapeExtensivity and thermodynamic formalism Physical Review Letters 92 035506

[23] Angell CA Finch ED Bach P (1976) Spinndashecho diffusion coefficients of water to 2380 bar and -20

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phases of ice induced by pressure Nature 314 76-78


[26] Mishima O (1994) Reversible first-order transition between two H2O amorphs at sim 02 GPa andsim 135 K The Journal of Chemical Physics 100 5910-5912

[27] Mishima O (1996) Relationship between melting and amorphization of ice Nature 384 546-549[28] Mishima SY Osamu (2002) Propagation of the polyamorphic transition of ice and the liquid-liquid

critical point Nature 419 599-603[29] Mishima O Stanley HE (1998) The relationship between liquid supercooled and glassy water

Nature 396 329ndash335[30] Franzese G Stanley HE (2010) Understanding the unusual properties of water In Lynden-Bell

RM Conway Morris S Barrow JD Finney JL Harper C editors Water and Life The UniqueProperties of H20 CRC Press URL httpdxdoiorg101201EBK1439803561-c7

[31] Kurita R Tanaka H (2004) Critical-like phenomena associated with liquid-liquid transition in amolecular liquid Science 306 845-848

[32] Tanaka H Kurita R Mataki H (2004) Liquid-liquid transition in the molecular liquid triphenylphosphite Physical Review Letters 92 025701

[33] Kurita R Tanaka H (2005) On the abundance and general nature of the liquid-liquid phasetransition in molecular systems Journal of Physics Condensed Matter 17 L293

[34] Greaves GN Wilding MC Fearn S Langstaff D Kargl F et al (2008) Detection of first-orderliquidliquid phase transitions in yttrium oxide-aluminum oxide melts Science 322 566-570

[35] Bruggeller P Mayer E (1980) Complete vitrification in pure liquid water and dilute aqueoussolutions Nature 288 569-571

[36] Finney JL Bowron DT Soper AK Loerting T Mayer E et al (2002) Structure of a new denseamorphous ice Physical Review Letters 89 205503

[37] Kanno H Speedy RJ Angell CA (1975) Supercooling of water to -92 C under pressure Science189 880-881

[38] Soper A Ricci M (2000) Structures of high-density and low-density water Physical Review Letters84 2881-2884

[39] Poole P Sciortino F Essmann U Stanley H (1992) Phase-behavior of metastable water Nature360 324-328

[40] Stanley HE Teixeira J (1980) Interpretation of the unusual behavior of H2O and D2O at lowtemperatures Tests of a percolation model The Journal of Chemical Physics 73 3404ndash3422

[41] Angell CA (2008) Insights into phases of liquid water from study of its unusual glass-formingproperties Science 319 582ndash587

[42] Brovchenko I Geiger A Oleinikova A (2005) Liquid-liquid phase transitions in supercooled waterstudied by computer simulations of various water models The Journal of Chemical Physics 123044515

[43] Liu Y Panagiotopoulos AZ Debenedetti PG (2009) Low-temperature fluid-phase behavior of ST2water The Journal of Chemical Physics 131 104508

[44] Vilaseca P Franzese G (2011) Isotropic soft-core potentials with two characteristic length scalesand anomalous behaviour Journal of Non-Crystalline Solids 357 419-426

[45] Molinero V Moore EB (2009) Water modeled as an intermediate element between carbon andsilicon The Journal of Physical Chemistry B 113 4008ndash4016

[46] Franzese G Stanley HE (2002) A theory for discriminating the mechanism responsible for thewater density anomaly Physica A Statistical Mechanics And Its Applications 314 508ndash513

[47] Franzese G Stanley HE (2002) Liquid-liquid critical point in a hamiltonian model for wateranalytic solution Journal of Physics Condensed Matter 14 2201ndash2209

[48] Franzese G Marques MI Stanley HE (2003) Intramolecular coupling as a mechanism for a liquid-liquid phase transition Physical Review E 67 011103

[49] Franzese G Stanley HE (2007) The widom line of supercooled water Journal of PhysicsCondensed Matter 19 205126

[50] Kumar P Franzese G Stanley HE (2008) Predictions of dynamic behavior under pressure for twoscenarios to explain water anomalies Physical Review Letters 100 105701


[51] Franzese G Hernando-Martınez A Kumar P Mazza MG Stokely K et al (2010) Phase transitionsand dynamics of bulk and interfacial water Journal of Physics Condensed Matter 22 284103

[52] Franzese G de los Santos F (2009) Dynamically slow processes in supercooled water confinedbetween hydrophobic plates Journal of Physics Condensed Matter 21 504107

[53] Sastry S Debenedetti PG Sciortino F Stanley HE (1996) Singularity-free interpretation of thethermodynamics of supercooled water Physical Review E 53 6144ndash6154

[54] Ricci MA Bruni F Giuliani A (2009) Similarities between confined and supercooled waterFaraday Discussions 141 347-358

[55] Mazza MG Stokely K Strekalova EG Stanley HE Franzese G (2009) Cluster monte carlo andnumerical mean field analysis for the water liquid-liquid phase transition Computer PhysicsCommunications 180 497-502

[56] Stokely K Mazza MG Stanley HE Franzese G (2010) Effect of hydrogen bond cooperativity onthe behavior of water Proceedings of the National Academy of Sciences of the United Statesof America 107 1301ndash1306

[57] Speedy RJ (1982) Limiting forms of the thermodynamic divergences at the conjectured stabilitylimits in superheated and supercooled water The Journal of Physical Chemistry 86 3002ndash3005

[58] Settles M Doster W (1996) Anomalous diffusion of adsorbed water A neutron scattering studyof hydrated myoglobin Faraday Discussions 103 269-279

[59] Doster W (2010) The protein-solvent glass transition Biochimica et Biophysica Acta 1804 3-14[60] Bianco V Iskrov S Franzese G (2011) Understanding the role of hydrogen bonds on water dynamics

and protein stability Accepted on Journal of Biological Physics [61] Coniglio A Klein W (1980) Clusters and ising critical droplets a renormalisation group approach

Journal of Physics A Mathematical and General 13 2775[62] Fortuin CM Kasteleyn PW (1972) On the random-cluster model i introduction and relation to

other models Physica 57 536-564[63] Franzese G Bianco V Iskrov S (2011) Water at interface with proteins Food Biophysics 6

186-198[64] qiang Chu X Faraone A Kim C Fratini E Baglioni P et al Pressure dependence of the dynamic

crossover temperatures in protein and its hydration water URL httparXiv08101228v1[65] Mazza MG Stokely K Pagnotta SE Bruni F Stanley HE et al (2009) Two dynamic

crossovers in protein hydration water and their thermodynamic interpretation URL http

arxivorgabs09071810[66] Mazza MG Stokely K Stanley HE Franzese G (2008) Anomalous specific heat of supercooled

water URL httparxivorgabsarXiv08074267[67] Mishima O (2000) Liquid-liquid critical point in heavy water Physical Review Letters 85 334ndash

336[68] Peter H Poole ISV Sciortino F (2005) Density minimum and liquidliquid phase transition

Journal of Physics Condensed Matter 17[69] Abascal JLF Vega C (2010) Widom line and the liquidndashliquid critical point for the tip4p2005

water model The Journal of Chemical Physics 133 234502[70] Glosli JN Ree FH (1999) Liquid-liquid phase transformation in carbon Physical Review Letters

82 4659-4662[71] Vasisht VV Saw S Sastry S (2011) Liquid-liquid critical point in supercooled silicon Nature

Physics 7 549-553[72] Sciortino F (2011) Liquid-liquid transitions Silicon in silico Nature Physics 7 523-524[73] Lennard-Jones JE (1931) Wave functions of many-electron atoms Mathematical Proceedings of

the Cambridge Philosophical Society 27 469-480[74] Stillinger FH Head-Gordon T (1993) Perturbational view of inherent structures in water Physical

Review E 47 2484ndash2490[75] Quesada-Perez M Moncho-Jorda A Martinez-Lopez F Hidalgo-Alvarez R (2001) Probing

interaction forces in colloidal monolayers Inversion of structural data The Journal of Chemical


Physics 115 10897-10902[76] Franzese G Malescio G Skibinsky A Buldyrev SV Stanley HE (2001) Generic mechanism for

generating a liquid-liquid phase transition Nature 409 692ndash695[77] Jagla EA (1999) Core-softened potentials and the anomalous properties of water The Journal of

Chemical Physics 111 8980-8986[78] Jagla EA (2002) Boundary lubrication properties of materials with expansive freezing Physical

Review Letters 88 245504[79] Franzese G Malescio G Skibinsky A Buldyrev SV Stanley HE (2002) Metastable liquid-liquid

phase transition in a single-component system with only one crystal phase and no densityanomaly Physical Review E 66 051206

[80] Malescio G Franzese G Skibinsky A Buldyrev SV Stanley HE (2005) Liquid-liquid phasetransition for an attractive isotropic potential with wide repulsive range Physical Review E 71061504

[81] Skibinsky A Buldyrev SV Franzese G Malescio G Stanley HE (2004) Liquid-liquid phasetransitions for soft-core attractive potentials Physical Review E 69 061206

[82] Franzese G (2007) Differences between discontinuous and continuous soft-core attractive potentialsThe appearance of density anomaly Journal on Molecular Liquids 136 267

[83] de Oliveira AB Franzese G Netz PA Barbosa MC (2008) Waterlike hierarchy of anomalies in acontinuous spherical shouldered potential The Journal of Chemical Physics 128 064901

[84] Vilaseca P Franzese G (2010) Softness dependence of the anomalies for the continuous shoulderedwell potential The Journal of Chemical Physics 133 084507

[85] Strekalova EG Mazza MG Stanley HE Franzese G (2011) Large decrease of fluctuations forsupercooled water in hydrophobic nanoconfinement Phys Rev Lett 106 145701

[86] Franzese G Stokely K Chu XQ Kumar P Mazza MG et al (2008) Pressure effects in supercooledwater comparison between a 2d model of water and experiments for surface water on a proteinJournal of Physics Condensed Matter 20 494210

An overview on anomalous liquids and water

Thermodynamic anomalies

Dynamic anomalies

Structural anomalies and polymorphism

A few questions

An Hamiltonian model for water

Phase diagram and supercooled water

Water confined between hydrophobic surfaces

Percolating approach

Dynamical crossover

Liquid-liquid phase transitions

Conclusions


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 argon-

like 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) [1ndash3] silicon (Si) [4 5]

selenium (Se) [6] phosphorus (P) [7ndash9] and water [10]

11 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 sim 4 C at atmospheric pressure For this reason the thermal expansivity

αP equiv minus(1V )(partVpartT )P where V is the volume vanishes at T sim 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 equiv minus(1V )(partVpartP )T [12] and the specific heat CP equiv (partHpartT )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 sim 46 C for KT and T sim35 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 [20ndash22] 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

12 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 sim11 kbar at 283 K [23]













for silica [22]













14 A few questions










































nanotechnology



















with experiments









U equiv minussumij

ε

[(r0

rij

)12

minus(

r0

rij

)6]

(1)




interaction













ninjδσijδσji

(2)









sumi

sum(kl)i

δσikσil (3)







change is






NHB equivsumltijgt

ninjδσijδσji

(6)

and

Nσ equivsum

i

sum(kl)i

δσikσil (7)
























HDL phase
































decay In general

C(t) = C0eminus( t

τ )β

(8)























to LDL-like liquid









τ = τ0eEAkBT (9)



























































-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆



Waals equation [81]

P =ρkBT












potential [84]

8 Conclusions



































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions













for silica [22]













14 A few questions










































nanotechnology



















with experiments









U equiv minussumij

ε

[(r0

rij

)12

minus(

r0

rij

)6]

(1)




interaction













ninjδσijδσji

(2)









sumi

sum(kl)i

δσikσil (3)







change is






NHB equivsumltijgt

ninjδσijδσji

(6)

and

Nσ equivsum

i

sum(kl)i

δσikσil (7)
























HDL phase
































decay In general

C(t) = C0eminus( t

τ )β

(8)























to LDL-like liquid









τ = τ0eEAkBT (9)



























































-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆



Waals equation [81]

P =ρkBT












potential [84]

8 Conclusions



































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions



























nanotechnology



















with experiments









U equiv minussumij

ε

[(r0

rij

)12

minus(

r0

rij

)6]

(1)




interaction













ninjδσijδσji

(2)









sumi

sum(kl)i

δσikσil (3)







change is






NHB equivsumltijgt

ninjδσijδσji

(6)

and

Nσ equivsum

i

sum(kl)i

δσikσil (7)
























HDL phase
































decay In general

C(t) = C0eminus( t

τ )β

(8)























to LDL-like liquid









τ = τ0eEAkBT (9)



























































-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆



Waals equation [81]

P =ρkBT












potential [84]

8 Conclusions



































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions






with experiments









U equiv minussumij

ε

[(r0

rij

)12

minus(

r0

rij

)6]

(1)




interaction













ninjδσijδσji

(2)









sumi

sum(kl)i

δσikσil (3)







change is






NHB equivsumltijgt

ninjδσijδσji

(6)

and

Nσ equivsum

i

sum(kl)i

δσikσil (7)
























HDL phase
































decay In general

C(t) = C0eminus( t

τ )β

(8)























to LDL-like liquid









τ = τ0eEAkBT (9)



























































-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆



Waals equation [81]

P =ρkBT












potential [84]

8 Conclusions



































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions







change is






NHB equivsumltijgt

ninjδσijδσji

(6)

and

Nσ equivsum

i

sum(kl)i

δσikσil (7)
























HDL phase
































decay In general

C(t) = C0eminus( t

τ )β

(8)























to LDL-like liquid









τ = τ0eEAkBT (9)



























































-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆



Waals equation [81]

P =ρkBT












potential [84]

8 Conclusions



































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions



















HDL phase
































decay In general

C(t) = C0eminus( t

τ )β

(8)























to LDL-like liquid









τ = τ0eEAkBT (9)



























































-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆



Waals equation [81]

P =ρkBT












potential [84]

8 Conclusions



































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions
































decay In general

C(t) = C0eminus( t

τ )β

(8)























to LDL-like liquid









τ = τ0eEAkBT (9)



























































-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆



Waals equation [81]

P =ρkBT












potential [84]

8 Conclusions



































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions









τ = τ0eEAkBT (9)



























































-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆



Waals equation [81]

P =ρkBT












potential [84]

8 Conclusions



































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions











































-1

0

1

2

3

4

UU

A

0 05 1 15 2 25 3

ra

1530100300500

RRa

URU

A (RA-R

R)a

∆



Waals equation [81]

P =ρkBT












potential [84]

8 Conclusions



































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions

































nanomedicine

Acknowledgments





































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions































































































Dynamic anomalies


A few questions





Dynamical crossover


Conclusions

Water and anomalous liquids · 2019-07-31 · Water and anomalous liquids Valentino Bianco1, Romina...

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Transcript of Water and anomalous liquids · 2019-07-31 · Water and anomalous liquids Valentino Bianco1, Romina...