Unusual phase behavior in one-component system with isotropic interaction Limei Xu WPI-AIMR, Tohoku University, Japan WPI-AIMR, Tohoku University, Japan In collaboration with: C. A. Angell Arizona State University S. V. Buldyrev Yeshiva University S.-H. Chen MIT N. Giovambattista New York Brookline college F. Sciortino University of Rome H. 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

Outline U nderstand 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?

P. G. Debenedetti, J. Phys.: Condens. Matter 15, R1669 (2003) =Vk B T  T =N k B Cp Anomalous Properties of Water Density CompressibilitySpecific Heat

Anomalous thermodynamic properties of supercooled bulk water C. A. Angell et al., J. Phys. Chem. 77, 3092 (1973) T S =228K 319K 308K R. J. Speedy et al. J. Chem. Phys. 65, 851 (1976) C p and K T diverge upon approaching T=228K? Anomalous behavior is more pronounced in deep supercooled region

Phases of liquid water Courtesy of Dr. O. Mishima Hypothesis Hypothesis Poole et al., Nature (1992) Tc=215K, Pc=100MPa

Experimental results in confined nanopores at 1 bar Specific Heat S. Maruyama, K. Wakabayashi, M. Oguni, AIP conference proceedings 708, 675 (2004) T=227K C p shows a peak at 227K, instead of diverges upon approaching T=228K Self Diffusion Mallamace et al, J. Chem. Phys. 124, (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?

E. A. Jagla, J. Chem. Phys. 111, 8980 (1999) Xu et. al, PNAS (2005); PRE(2006) MD simulation Number of particles: N=1728 Two-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 diagram L. Xu, S. V. Buldyrev, C. A. Angell, H. E. Stanley, Phys. Rev. E (2006); JC(2009)

Changes in response functions: Specific heat P>P c : C P has maxima Anomaly occurs upon crossing the Widom line ( C p max ) P<P c : C P increase monotonically, No anomalous behaviour! C P max HDL P c =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 diffusivity C P max  How to trace LL critical point using dynamic properties? Appearance or disappearance of a kink in diffusivity P c =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 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 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?

Outline U nderstand 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 heat The 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: LLPT and polyamorphism LLPT and polyamorphism  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 polyamorphism. polyamorphism. Conclusion II

Outline U nderstand water anomalies with isotropic potential Liquid-liquid transition and polyamorphism (glass-glass) Fractional Stokes-Einstein Relation and its structural origin

Background: Stokes-Einstein Relation (SER) Breakdown of Stokes-Einstein relation has been related to slow dynamics --- glass transition SER ： Viscosity vs. relaxation time : Stokes-Einstein Relation breaks down if c is temperature dependent D: diffusivity η: is the Viscosity R: 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 Relation TWTW L. Liu et al., Phys. Rev. Lett. (2005) S.-H Chen et al, PNAS (2006)

Fractional Stokes-Einstein Relation (Simulation)  Appearance of Fractional Stokes-Einstein relation is at Tx >> Tw  No effect is observed at Tw!! 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 (Experiment)  Appearance of Fractional Stokes-Einstein relation is at Tx >> Tw  No effect is observed at Tw!!

Structural changes upon cooling (Simulation)  Tx occurs at the appearance of a new species  Tw is related to the maximal change of the structure

Structural information: IR F. Mallamace et.al, PNAS (2007 )

Structural changes upon cooling (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 (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 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 Structures

Mallamace et al, PNAS(2006)

What makes water water

Perfect Crystal: Q 6 =0.57; Random configuration: Q 6 =0.28 Orientational order parameter : Changes in structures upon crossing Widom line

compressibility T W (P) Pc=0.24 P<P c : No anomalous behaviour! (Metastability ) P>P c : Response functions show peaks. The location of the peaks decreases approaching to the critical pressure Changes in thermodynamics upon crossing widom line

Low THigh 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 Diagram

C P max K T max Changes in response functions: Compressibility P>P c : K T has maxima Anomaly occurs upon crossing the Widom line ( K T max ) P<P c : K T increase monotonically, No anomalous behaviour! P c =0.24

Polyamorphism: LDA-HDA-VHDA transformations

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

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

Heating rate dependence of HDA-HDL glass transition and Widom line crossover α q 1 ≈7∙10 8 K/s

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