Unusual phase behavior in one-Unusual phase behavior in one-componentcomponent

system with isotropic interaction system with isotropic interactionLimei Xu Limei Xu

WPI-AIMR, Tohoku University, JapanWPI-AIMR, Tohoku University, Japan

In collaboration with: C. A. Angell Arizona State UniversityS. V. Buldyrev Yeshiva UniversityS.-H. Chen MITN. Giovambattista New York Brookline collegeF. Sciortino University of RomeH. E. Stanley Boston University

Similar phase behaviors shared by very different materials:

Liquid-liquid phase transition: Tetrahedrally structured systems: water, Si, Ge, SiO2, BeF2 Metallic system: such as Y3Al5O12

Polyamorphism (amorphous-amorphous transition under pressure)

Tetrahedrally structured systems: water, Ge Metallic system: Ce55Al45

Motivation

Common feature: involving two local structures, with one having larger open spaces between particles that collapse under pressure.

Question: Universal model that determine whether these features and phenomena are related or exist independently

OutlineOutline

Understand water anomalies with isotropic potential

Liquid-liquid transition and polyamorphism (glass-glass)

Fractional Stokes-Einstein Relation and its structural origin

has importance as a solvent of solutes, such as chemical reactants and bio-molecules (proteins)

prototype of anomalous liquids, relevance to other liquids, such as Silicon, Silica

Why do we care about water?Why do we care about water?

P. G. Debenedetti, J. Phys.: Condens. Matter 15, R1669 (2003)

<(V)2>=VkBTT <(S)2>=N kB Cp

Anomalous Properties of Water Anomalous Properties of Water

Density Compressibility Specific Heat

Anomalous thermodynamic properties of supercooled bulk waterAnomalous thermodynamic properties of supercooled bulk water

C. A. Angell et al., J. Phys. Chem. 77, 3092 (1973)

TS=228K

319K

308K

R. J. Speedy et al. J. Chem. Phys. 65, 851 (1976)

Cp and KT diverge upon approaching T=228K?

Anomalous behavior is more pronounced in deep supercooled region

Phases of liquid waterPhases of liquid water

Courtesy of Dr. O. Mishima HypothesisHypothesis

Poole et al., Nature (1992)Poole et al., Nature (1992)

Tc=215K , Pc=100MPa

Experimental results in confined nanopores at 1 barExperimental results in confined nanopores at 1 bar

Specific Heat

S. Maruyama, K. Wakabayashi, M. Oguni, AIP conference proceedings 708, 675 (2004)

T=227K

Cp shows a peak at 227K, instead of diverges upon approaching T=228K

Self Diffusion

Mallamace et al, J. Chem. Phys. 124, 161102 (2006)

Diffusion coefficient shows a kink

How to interpret the experimental results– dynamic crossover and response function maximum?

Related to a hypothesized liquid-liquid critical point?

If yes, how to locate this critical point in water?

What are the questions?What are the questions?

E. A. Jagla, J. Chem. Phys. 111, 8980 (1999)Xu et. al, PNAS (2005); PRE(2006)

MD simulationNumber of particles: N=1728

Two-scale ramp modelTwo-scale ramp model

Effective potential of water at T=280K

T. Head-Gordon and F. H. Stilinger. J. Chem. Phys. 98, 3313 (1993)

U( r ) ~ ln g ( r )

Stable liquid-liquid critical point (LLCP)

Density anomaly (TMD)

Phase diagramPhase diagram

L. Xu, S. V. Buldyrev, C. A. Angell, H. E. Stanley, Phys. Rev. E (2006); JC(2009)

Changes in response functions: Specific heat Changes in response functions: Specific heat

P>Pc : CP has maxima Anomaly occurs upon crossing the Widom line ( Cpmax )

P<Pc : CP increase monotonically, No anomalous behaviour!

CPmax

HDL

Pc =0.24

How to effectively trace liquid-liquid critical point: not upon crossing coexistence line, but the Widom line the Widom line terminates at the Liquid-liquid critical point

Changes in diffusivityChanges in diffusivity

CPmax

How to trace LL critical point using dynamic properties?

Appearance or disappearance of a kink in diffusivity

Pc =0.24

L. Xu, S. V. Buldyrev, C. A. Angell, H. E. Stanley, Phys. Rev. E (2006); PNAS(2005)

Experimentally locating the Liquid-liquid critical pointExperimentally locating the Liquid-liquid critical point

The Widom line terminates at the liquid-liquid critical point

Self Diffusion

Specific Heat

L. Liu et al., Phys. Rev. Lett. (2005)

Tw

Conclusion IConclusion I

The two-scale model can reproduce water-like anomalies

Thermodynamic and dynamic quantities shows changes upon crossing the Widom line, not upon crossing the coexistence line

Provide a way for experiments to locate the possible existence of liquid-liquid critical point

Maybe not hydrogen bond, not tetrahedral local structure, but the two-scale matters for water-like anomalies?

OutlineOutline

Understand water anomalies with isotropic potential

Liquid-liquid transition and polyamorphism (glass-glass)

Fractional Stokes-Einstein Relation and its structural origin

Two glass states obtained upon cooling LDL LDA HDL HDA

Two glass states upon cooling: HDA and LDA

L. Xu, S. V. Buldyrev, N. Giovambattista, C. A. Angell, H. E. Stanley, JCP (2009)

L. Xu, S. V. Buldyrev, N. Giovambattista, C. A. Angell H. E. Stanley, JCP (2009)

H=U+PV

Detection of glass transition: thermal expansion and specific heatThe second approach is more pronounced, indicating that: Glass transition is the onset of the kinetics, while liquid-liquid Phase transition is the onset of the volume/density change

HDL-HDA glass transition and liquid-liquid phase transition

L. Xu, S. V. Buldyrev, H. E. Stanley, M. Tokuyama (in preparition)

HDA is stable at low pressure upon decompression

Polyamorphism

Stability of liquid-liquid critical point and polyamorphism

LLCP unaccessible

Stable LLCP

Simple two-scale potential shows rich phase behavior: Simple two-scale potential shows rich phase behavior:

LLPT and polyamorphism LLPT and polyamorphism

The model tells us how to distinguish glass transition from the The model tells us how to distinguish glass transition from the

Widom line associated with the liquid-liquid phase transition.Widom line associated with the liquid-liquid phase transition.

Our study indicates an alternative way to make glasses via Our study indicates an alternative way to make glasses via

polyamorphism.polyamorphism.

Conclusion II

OutlineOutline

Understand water anomalies with isotropic potential

Liquid-liquid transition and polyamorphism (glass-glass)

Fractional Stokes-Einstein Relation and its structural origin

BBackground: Stokes-Einstein Relation ackground: Stokes-Einstein Relation (SER)(SER)

Breakdown of Stokes-Einstein relation has been related to slow dynamics --- glass transition

SER ：

€

Dτ /T ~ c

Viscosity vs. relaxation time:

€

η ~ τ

Stokes-Einstein Relation breaks down if c is temperature dependent

€

D =kBT

6πηR

D: diffusivityη: is the ViscosityR: hydrodynamic radius of the sphere

Characterization of the dynamic properties of Brownian particles

Not due to glass transition Tg~130K

Breakdown of Stokes-Einstein relation is due to the crossing the Widom line

Breakdown of Stokes-Einstein Breakdown of Stokes-Einstein RelationRelation

TW

L. Liu et al., Phys. Rev. Lett. (2005)S.-H Chen et al, PNAS (2006)

Fractional Stokes-Einstein Relation Fractional Stokes-Einstein Relation (Simulation)(Simulation)

Appearance of Fractional Stokes-Einstein relation is at Tx >> Tw

No effect is observed at Tw!!

€

D ~τ

T

⎛

⎝ ⎜

⎞

⎠ ⎟−1

€

Dτ /T ~ cStokes-Einstein Relation: Stokes-Einstein Relation:

L. Xu, F. Mallamce, Z. Yan, F. W. Starr, S. V. Buldyrev, H. E. Stanley, Nature Physics (2009)

Fractional Stokes-Einstein Relation Fractional Stokes-Einstein Relation (Experiment)(Experiment)

Appearance of Fractional Stokes-Einstein relation is at Tx >> Tw

No effect is observed at Tw!!

Structural changes upon cooling Structural changes upon cooling (Simulation)(Simulation)

Tx occurs at the appearance of a new species

Tw is related to the maximal change of the structure

Structural information: IRStructural information: IR

F. Mallamace et.al, PNAS (2007)

Structural changes upon cooling Structural changes upon cooling (Experiment)(Experiment)

Tx occurs at the appearance of a new species

Tw is related to the maximal change of the structure

L. Xu, F. Mallamce, Z. Yan, F. W. Starr, S. V. Buldyrev, H. E. Stanley, Nature Physics (2009)

Structural changes upon cooling Structural changes upon cooling (Simulation)(Simulation)

Tx occurs at the appearance of a new species

Tw is related to the maximal change of the structure

L. Xu, F. Mallamce, Z. Yan, F. W. Starr, S. V. Buldyrev, H. E. Stanley, Nature Physics (2009)

Conclusion IIIConclusion III

Fractional Stokes-Einstein Relation is correlated with the onset of a different structure

A structural origin for the failure of the SER can be understood by recognizing that the SE relation defines an effective hydrodynamic radius.

The different species have different hydrodynamic radii, so when their relative population changes, the classical SER breaks down.

Changes in StructuresChanges in Structures

Mallamace et al, PNAS(2006)

What makes water waterWhat makes water water

Perfect Crystal: Q6=0.57; Random configuration: Q6=0.28

Orientational order parameter:

Changes in structures upon crossing Widom Changes in structures upon crossing Widom lineline

compressibility

TW(P)

Pc=0.24

P<Pc : No anomalous behaviour! (Metastability)

P>Pc : Response functions show peaks. The location of the peaks decreases approaching to the critical pressure

Changes in thermodynamics upon crossing Changes in thermodynamics upon crossing widom linewidom line

Low T High T

As in water, solubility of non-polar solutes decreases in the Jagla model upon heating

Can Jagla model explain the decrease of methane solubility upon heating?

Stable liquid-liquid critical point (LLCP)

Negative sloped melting line

LDA and HDA

L. Xu, S. V. Buldyrev, C. A. Angell, H. E. Stanley, Phys. Rev. E (2006)L. Xu, P. Kumar, S. V. Buldyrev, P. H. Poole, F. Sciortino, S.-H Chen, H. E. Stanley, PNAS (2005)

Widom line

Phase DiagramPhase Diagram

CPmax

KTmax

Changes in response functions: Compressibility Changes in response functions: Compressibility

P>Pc : KT has maxima Anomaly occurs upon crossing the Widom line (KTmax)

P<Pc: KT increase monotonically, No anomalous behaviour!

Pc =0.24

Polyamorphism: LDA-HDA-VHDA transformationsPolyamorphism: LDA-HDA-VHDA transformations

Anomaly in melting curve as a function of pressure water, Si, Ge, Cs, Ba, Eu

Background: Quasi-elastic Neutron Scattering Background: Quasi-elastic Neutron Scattering (QENS)(QENS)

Sca

tter

ing

Inte

nsit

y

QENS spectrumQENS spectrum

Heating rate dependence of HDA-HDL glass Heating rate dependence of HDA-HDL glass transition and Widom line crossovertransition and Widom line crossover

α

q1≈7∙108K/s

S. R. Becker, P. H. Poole, F. W. Starr, PRL 97, 055901 (2006)F. Ferandez-Alonson, F. J. Bermejo, S. E. McLain, J. F. C. Turner, J. J. Molaison, K. W. Herwig. PRL 98, 077801 (2007)