A Monatomic System with a Liquid-Liquid Critical Point and

Two Distinct Glassy States

Sergey BuldyrevDepartment of Physics

Yeshiva UniversityCollaborators:

L. Xu, N. Giovambattista, C. A. Angel, H. E. Stanley, S.-H. Chen, P. G. Debenedetti, I. Ehrenberg, P. Kumar, P. Poole, P.J. Rossky,

F. Starr, F. Sciortino, Z. Yan

L.Xu, S.V.Buldyrev,N.Giovambattista, C.A.Angell, H.E.Stanley,JCP, in press (2008)L. Xu et al., Proc. Natl. Acad. Sci. (2005); L. Xu et al., Phys. Rev. E (2006); L. Xu et al., J. Phys.: Condensed Matter (2006), S. V. Buldyrev et al.,  Proc. Natl. Acad. Sci. 104: 20177 (2007).Z. Yan et al., PRE 77, 042201 (2008).

What makes Water Water?

Anomalous thermodynamic properties of supercooled waterAnomalous thermodynamic properties of supercooled 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)

Anomalous region: KT < 319K CP < 308K

Phases of liquid waterPhases of liquid water

Courtesy of Dr. O. Mishima

HypothesisHypothesis

Poole et al., Nature (1992))

Traditional MD computer water models (ST2,SPC,TIP3P,TIP4P,TIP5P)

replace 3 nuclei and 18 electrons interacting via quantum mechanics by a few point charges and 3

point masses interacting via classical mechanics. Integrate equations of motion:ri(t+Δt)=ri(t)+Δt vi(t+Δt/2);vi(t+Δt/2)= vi(t-Δt/2)+Δt fi[r(t)]/mi

Δt=10-15 sec.

Why not to do further simplifications?

Effective potential of water at T=280K

Jagla potential

F.H..Stillinger and T. Head-Gordon, Phys. Rev. E 47,2484 (1993)

Spherically symmetric potential for water?

How to relate the ramp potential to water?Hard core= water 1st coordiantion shellSoft core = water 2nd coordination shell

1ramp particle = 2 water molecules (1+4/4)

Discrete Molecular Dynamics: D.C. Rapaport, Art of MD,A.Yu. Grosberg and A.R. Khohklov, Giant Molecules (AP, 1997)

Educational site : http://polymer.bu.edu/vmdl

Discrete Version of Jagla Potential

c=3a

b=1.72a,

Equation of state of the Jagla liquid

Phase Segregationat coexistence line

HDL LDL

Changes in response functions

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

CPmax

KTmax

Changes in response functions

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

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

Comparison with water

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?

Comparison of Jagla model with water

Similarities with water: JM has a liquid-liquid critical point. JM has regions of density, structural, and diffusivity anomalies

embedded into one another as in water. Response functions has maxima upon crossing the Widom lines

emanating from the critical point. Solubility of nonpolar compounds decrease with temperature Hydrophobic polymers swell upon cooling. These similarities are caused by the huge empty space between

molecules in JM and water.

Differences with water:■The liquid-liquid coexistence line and the Widom lines have positive slopes.■HDL is more ordered than LDL.■HDL is strong, LDL is fragile.

Probing Jagla Model with DSC

Path α

Path α’

Path β

Path β’

Jagla Model has two glassy states: HDA and LDA

α’

β’

LDA-HDA-VHDA transformations

HDL-HDA glass transition andWidom Line Crossover

TW

α

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

α

q1≈7∙108K/s

HDL-HAD glass transition and Widom line crossover (thermal expansion coefficient)

P(V/T)P / V

LDL-LDA glass transition

Heating rate dependence of LDA-LDL glass transition and crystallization

β

LDA-LDL glass transition and density anomaly

Density minimum and glass transition

Temperature

Den

sity

0.1 0.2 0.3 0.4 0.5

Widom line,compressibility maximum, and density anomaly

Davies and Jones:

Comparison of LDL and HDLglass transitions far away from CP

cooling

Entropy behavior

Conclusions• Jagla model tells us how to distinguish glass transition

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

• CP peak near Widom line is less sensitive to heatig rate

than the glass transition peak.

• CP peak near Widom line is more sensitive to pressure

than the glass transition peak.• Abrupt change in Glass transition temperature at certain

pressure indicates liquid-liquid phase transition. • Density minimum can be a property of the equilibrium

liquid but can be also caused by the glass transition.• Density minimum is not necessarily related to Widom

Line, however it is related with compressibility maxima.