STATISTICAL PROPERTIES OF THE LANDSCAPE OF A SIMPLE STRONG LIQUID

MODEL …. AND SOMETHING ELSE.

• E. La Nave, P. Tartaglia, E. Zaccarelli (Roma )

• I. Saika-Voivod (Canada)

• A. Moreno (Spain)

• S. Bulderyev (N.Y. USA)

5th International Discussion Meeting on Relaxations in Complex SystemsNew results, Directions and Opportunities

Francesco Sciortino

Outline

* Peter Harrowell (UCGS

Bangalore)

Part I -- A (numerically exact) calculation of the statistical properties of the landscape of a strong liquid

1. Thermodynamic in the Stillinger-Weber formalism2. Gaussian Statistic3. Deviation from Gaussian4. The model

• Dynamics ---- STRONG LIQUID• Landscape ---- KNOWN !

Part II -- Dynamic and Static heterogeneities (the central dogma*)

Thermodynamics in the IS formalism Stillinger-Weber

F(T)=-T Sconf(<eIS>, T) +fbasin(<eIS>,T)

with

fbasin(eIS,T)= eIS+fvib(eIS,T)

and

Sconf(T)=kBln[(<eIS>)]

Basin depth and shape

Number of explored basins

Free energy [for a recent review see FS JSTAT 5, p.05015 (2005)]

The Random Energy Model for eIS

Hypothesis:

eIS)deIS=eN -----------------deISe-(e

IS -E

0)2/22

22

Sconf(eIS)/N=- (eIS-E0)2/22

Gaussian Landscape

Predictions of Gaussian Landscape (for identical basins)

Sconf(T)/N=- (<eIS(T)> -E0)2/22

<eIS(T)>=E0 - 2/kT

T-dependence of <eIS> SPC/E LW-OTP

T-1 dependence observed in the studied T-rangeSupport for the Gaussian Approximation

BMLJ Configurational Entropy

Non Gaussian behaviour in BKS silica (low )

Saika-Voivod et al Nature 412, 514-517, 2001

Heuer works Heuer

Density minimum and CV maximum in ST2 water (impossible in the gaussian landascape

Phys. Rev. Lett. 91, 155701, 2003)

inflection = CV max

inflection in energy

P.Poole

Eis e S conf for silica…

Esempio di forte

Non-Gaussian Behavior in SiO2

Saika-Voivod et al Nature 412, 514-517, 2001

Maximum Valency Model (Speedy-Debenedetti)

A minimal model for network forming liquids

SW if # of bonded particles <= NmaxHS if # of bonded particles > Nmax

V(r)

r

The IS configurations coincide with the bonding pattern !!!Zaccarelli et al PRL (2005)Moreno et al Cond Mat (2004)

Generic Phase Diagram for Square Well (3%)

Generic Phase Diagram for NMAX Square Well (3%)

Ground State Energy Known !(Liquid free energy known everywhere!)

It is possible to equilibrate at low T !

(Wertheim)

Specific Heat (Cv) Maxima

Viscosity and Diffusivity: Arrhenius

Stoke-Einstein Relation

Dynamics: Bond Lifetime

Pair-wise model (geometric correlation between bonds) (PMW, I. Nezbeda)

Connection between Dynamics and Structure !

An IS is a bonding pattern !!!!!

F(T)=-T Sconf(<eIS>, T) +fbasin(<eIS>,T)

with

fbasin(eIS,T)= eIS+fvib(eIS,T)

and

Sconf(T)=kBln[(<eIS>)]

Basin depth and shape

Number of explored basins

It is possible to calculate exactly the basin free energy !

Frenkel-Ladd

Entropies…

Svib increases linearly with the # of bonds

Sconf follows a x ln(x) law

Sconf does NOT extrapolate to zero

Self-consistent calculation ---> S(T)

Part 1 - Take home message(s):•Network forming liquids tend to reach their (bonding) ground state on cooling (eIS different from 1/T)

•The bonding ground state can be degenerate. Degeneracy related to the number of possible networks with full bonding.

•The discretines of the bonding energy (dominant as compared to the other interactions) favors an Arrhenius dynamics and a logarithmic IS entropy.

•Network liquids are intrinsically different from non-networks, The approach to the ground state is NOT hampered by phase separation

Part II -Dynamic HeterogeneitiesJ. Chem. Phys. B 108,19663,2004

(attempting to avoid any a priori definition) Look at differences between different realizations

SPC/E Water 100 realizations

nn distance =0.28 nm

Follow dyanmics for MSD = (2 x 0.28)2 nm2

2MSD - vs - MSD

Connections with the landscape ?

Memory of the landscape location…..

Which D(eIS,T) ? 155 BMLJ

Which D(eIS,T) ?

Which D(eIS,T) ?

Conclusions… Part II

•Clear Connection between Local Dynamics and Local Landscape

•Deeper basins statistically generate slower dynamics

•Connection with the NGP

•More work to do !

See you in ……….

Frenkel-Ladd (Einstein Crystal)