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: (2007). Z. Yan et al., PRE 77, (2008).

What makes Water Water?

Anomalous thermodynamic properties of supercooled 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) Anomalous region: K T < 319K C P < 308K

Phases of liquid water Courtesy of Dr. O. Mishima Hypothesis 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: r i (t+Δt)=r i (t)+Δt v i (t+Δt/2); v i (t+Δt/2)= v i (t-Δt/2)+Δt f i [r(t)]/m i Δt= 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 1 st coordiantion shell Soft core = water 2 nd 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 :

Discrete Version of Jagla Potential c=3a b=1.72a,

Equation of state of the Jagla liquid

Phase Segregation at coexistence line HDL LDL

Changes in response functions 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

C P max K T max Changes in response functions 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!

Comparison with water

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?

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’α’ β’β’

LDA-HDA-VHDA transformations

HDL-HDA glass transition and Widom Line Crossover TWTW α

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

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. C P peak near Widom line is less sensitive to heatig rate than the glass transition peak. C P 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.