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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
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)
Ground State Energy Known !(Liquid free energy known everywhere!)
It is possible to equilibrate at low T !
(Wertheim)
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
Entropies…
Svib increases linearly with the # of bonds
Sconf follows a x ln(x) law
Sconf does NOT extrapolate to zero
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
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 ……….