Structural Order for One-Scale and Structural Order for One-Scale and Two-Scale PotentialsTwo-Scale Potentials

Zhenyu YanZhenyu Yan

Advisor: Advisor: H. Eugene StanleyH. Eugene Stanley

Collaborators:Collaborators:Sergey V. Buldyrev, Sergey V. Buldyrev,

NicolasNicolas Giovambattista, Giovambattista,

Center for Polymer Studies and Department of Physics, Boston University

For details see: Phys. Rev. Lett. 95, 130604 (Sep, 2005)

Motivation: aMotivation: anomalies nomalies of waterof water

TMD

DM

TMD: Temperature of Maximum Density

Density anomaly of waterDensity anomaly of water Diffusion anomaly of waterDiffusion anomaly of water

DM: Diffusion Maximum/Minimum

Recent Finding in water: structural anomaly coupled with density and diffusion anomaly

J. R.. Errington and P. G. Debenedetti, Nature 409, 318 (2001).

T=350k

T=220k

Questions ?Questions ?

1. Are the strong orientational tetrahedral interactions necessary for water anomalies ?

2. Can we find water-like anomalies in simple liquids(monatomic model with simple potential)? If YES, then what features should be present in the potential in order to get water-like anomalies ?

The models: one-scale and two-scale The models: one-scale and two-scale ramp potentialsramp potentials

σ0/ σ1=0

r

U(r)

σ1 r

U(r)

σ1σ0

one-scale two-scale

TMD, DM TMD, DM

E. A. Jagla, J. Chem. Phys. 111, 8980 (1999)

Result: phase diagramsResult: phase diagrams

isochores isochores

DMTMD

TMDDM

One-Scale Two-Scale

Region of DM encloses the region of TMD

What about the structural anomaly?What about the structural anomaly?

How to quantify structural orderHow to quantify structural order

Ramp potential: FCC

Two basic types of order:

. Orientational order: degree to adopt specific local structure (space angle)

Translational order t: degree to adopt preferential separationsseparations (distance)

Water: tetrahedrality,tetrahedrality,

The value increases with increasing order

drrgtcr

0

1)(

Result: structural order for ramp potentialsResult: structural order for ramp potentials

isotherms

tmax

tmin

Qmax

isotherms tmin

Qmax

tmax

tmax and tmin for both one-scale and two-scale, Qmax only for two-scale ramp

Result: order mapsResult: order maps

Two-scale ramp order map is similar to water

T=260k

isotherms

water

T=350k

T=220k

T=0.03

two-scale ramp

water

Inaccessible region

Q

t

isotherm

Q

t

q

q

t

T=260k

T=0.03

T=0.1

Result: anomalous regions of density, Result: anomalous regions of density, diffusion and structurediffusion and structure

tmax tmin

tmax tmin Qmax

water

Two-scale ramp is similar to water

TMD

DM

Qmax tmin

TMD

DM

TMD

DM

Summary and ConclusionSummary and Conclusion

1. Are the strong orientational tetrahedral interactions necessary for water anomalies ?

Not necessaryNot necessary

2. Can we find water-like anomalies in simple liquids with simple potentials ? yes If YES, then what features should be present in the potential in order to get water-like anomalies ? It suggests that the water-like behavior is It suggests that the water-like behavior is related to two characteristic repulsive length scales related to two characteristic repulsive length scales in potentials.in potentials.

Thank you !Thank you !