A Monatomic System with a Liquid-Liquid Critical Point and Two Distinct Glassy States

1
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).
2
What makes Water Water?
3
Anomalous thermodynamic properties of supercooled
water
Anomalous region KT lt 319K
CP lt 308K
4
(No Transcript)
5
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?t)ri(t)?t
vi(t?t/2) vi(t?t/2) vi(t-?t/2)?t
fir(t)/mi ?t10-15 sec.
Why not to do further simplifications?
6
Spherically symmetric potential for water?
F.H..Stillinger and T. Head-Gordon, Phys. Rev. E
47,2484 (1993)
7
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 (14/4)
8
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
9
(No Transcript)
10
Discrete Version of Jagla Potential
b1.72a,
c3a
11
Equation of state of the Jagla liquid
12
Phase Segregation at coexistence line
HDL LDL
13
Changes in response functions
HDL
Pc 0.24
PgtPc CP has maxima Anomaly occurs upon
crossing the Widom line ( Cpmax ) PltPc CP
increase monotonically, No anomalous behaviour!
14
Changes in response functions
PgtPc KT has maxima Anomaly occurs upon
crossing the Widom line ( KTmax ) PltPc KT
increase monotonically, No anomalous behaviour!
15
Comparison with water
16
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
17
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.

18
Probing Jagla Model with DSC
Path a
Path a
Path ß
Path ß
19
Jagla Model has two glassy states HDA and LDA
ß
a
20
LDA-HDA-VHDA transformations
21
HDL-HDA glass transition andWidom Line Crossover
a
TW
22
Heating rate dependence of HDA-HDL glass
transition and Widom line crossover
a
q17108K/s
23
HDL-HAD glass transition and Widom line crossover
(thermal expansion coefficient)
?
?P?(?V/?T)P / V
24
LDL-LDA glass transition
25
Heating rate dependence of LDA-LDL glass
transition and crystallization
ß
26
LDA-LDL glass transition and density anomaly
?
27
Density minimum and glass transition
Density
0.1 0.2 0.3 0.4
0.5
Temperature
28
Widom line,compressibility maximum, and density
anomaly
Davies and Jones
29
Comparison of LDL and HDLglass transitions far
away from CP
cooling
30
Entropy behavior
31
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.