A Monatomic System with a
Liquid-Liquid Critical Point and
Two Distinct Glassy States
Sergey Buldyrev
Department of Physics
Yeshiva University
Collaborators:
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 water
TS=228K
308K
319K
C. A. Angell et al., J. Phys. Chem. 77, 3092 (1973)
Anomalous region: KT < 319K
R. J. Speedy et al. J. Chem. Phys. 65, 851 (1976)
CP < 308K
Phases of liquid water
Courtesy of Dr. O. Mishima
Hypothesis
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?
Spherically symmetric potential for water?
F.H..Stillinger and T. Head-Gordon, Phys. Rev. E 47,2484 (1993)
Effective potential
of water at
T=280K
Jagla potential
How to relate the ramp potential to water?
Hard core= water 1st coordiantion shell
Soft 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
b=1.72a,
c=3a
Equation of state of the Jagla liquid
Phase Segregation
at coexistence line
HDL
LDL
Changes in response functions
CPmax
HDL
Pc =0.24
P>Pc : CP has maxima Anomaly occurs upon crossing the Widom line ( Cpmax )
P<Pc : CP increase monotonically, No anomalous behaviour!
Changes in response functions
CPmax
KTmax
P>Pc : KT has maxima Anomaly occurs upon crossing the Widom line ( KTmax )
P<Pc : KT increase monotonically, No anomalous behaviour!
Comparison with water
Can Jagla model explain the decrease of methane
solubility upon heating?
Low T
High T
As in water, solubility of non-polar solutes
decreases in the Jagla model 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
β’
α’
LDA-HDA-VHDA transformations
HDL-HDA glass transition and
Widom Line Crossover
α
TW
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
Density minimum and glass transition
0.1
0.2
0.3
0.4
Temperature
0.5
Widom line,compressibility
maximum, and density anomaly
Davies and Jones:
Comparison of LDL and HDL
glass 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.