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STATISTICAL PROPERTIES OF THE LANDSCAPE OF A SIMPLE STRONG LIQUID MODEL …. AND SOMETHING ELSE.

5th International Discussion Meeting on Relaxations in Complex Systems New results, Directions and Opportunities. 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)

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STATISTICAL PROPERTIES OF THE LANDSCAPE OF A SIMPLE STRONG LIQUID MODEL …. AND SOMETHING ELSE.

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  1. 5th International Discussion Meeting on Relaxations in Complex Systems New results, Directions and Opportunities 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) Francesco Sciortino

  2. Outline • Part I -- A (numerically exact) calculation • of the statistical properties of the landscape • of a strong liquid • Thermodynamic in the Stillinger-Weber formalism • Gaussian Statistic • Deviation from Gaussian • The model • Dynamics ---- STRONG LIQUID • Landscape ---- KNOWN ! • Part II -- Dynamic and Static heterogeneities • (the central dogma*) * Peter Harrowell (UCGS Bangalore)

  3. Thermodynamics in the IS formalism Free energy Stillinger-Weber [for a recent review see FS JSTAT 5, p.05015 (2005)] F(T)=-T Sconf(<eIS>, T) +fbasin(<eIS>,T) with Basin depth and shape fbasin(eIS,T)= eIS+fvib(eIS,T) and Number of explored basins Sconf(T)=kBln[W(<eIS>)]

  4. The Random Energy Model for eIS Gaussian Landscape Hypothesis: e-(eIS -E0)2/2s 2 W(eIS)deIS=eaN -----------------deIS 2ps2 Sconf(eIS)/N=a-(eIS-E0)2/2s 2 Predictions of Gaussian Landscape (for identical basins) <eIS(T)>=E0 - s 2/kT Sconf(T)/N=a-(<eIS(T)>-E0)2/2s 2

  5. T-dependence of <eIS> SPC/E LW-OTP T-1 dependence observed in the studied T-range Support for the Gaussian Approximation

  6. BMLJ Sconf BMLJ Configurational Entropy

  7. Non Gaussian behaviour in BKS silica (low r) Saika-Voivod et al Nature 412, 514-517, 2001 Heuer works Heuer

  8. Density Minima P.Poole Density minimum and CV maximum in ST2 water (impossible in the gaussian landascapePhys. Rev. Lett. 91, 155701, 2003) inflection = CV max inflection in energy

  9. Sconf Silica Non-Gaussian Behavior in SiO2 Eis e S conf for silica… Esempio di forte Saika-Voivod et al Nature 412, 514-517, 2001 Non gaussian silica

  10. Maximum Valency Maximum Valency Model (Speedy-Debenedetti) SW if # of bonded particles <= Nmax HS if # of bonded particles > Nmax V(r ) r A minimal model for network forming liquids The IS configurations coincide with the bonding pattern !!! Zaccarelli et al PRL (2005) Moreno et al Cond Mat (2004)

  11. Square Well 3% width Generic Phase Diagram for Square Well (3%)

  12. Square Well 3% width Generic Phase Diagram for NMAX Square Well (3%)

  13. Ground State Energy Known !(Liquid free energy known everywhere!) (Wertheim) It is possible to equilibrate at low T ! Energy per Particle

  14. Cv Specific Heat (Cv) Maxima

  15. Viscosity and Diffusivity: Arrhenius

  16. Stoke-Einstein Relation

  17. Dynamics: Bond Lifetime

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

  19. Connection between Dynamics and Structure !

  20. An IS is a bonding pattern !!!!! F(T)=-T Sconf(<eIS>, T) +fbasin(<eIS>,T) with Basin depth and shape fbasin(eIS,T)= eIS+fvib(eIS,T) and Number of explored basins Sconf(T)=kBln[W(<eIS>)]

  21. It is possible to calculate exactly the basin free energy ! Basin Free energy Frenkel-Ladd

  22. Entropies… Svib increases linearly with the # of bonds Sconf follows a x ln(x) law Sconfdoes NOT extrapolate to zero

  23. Self consistence Self-consistent calculation ---> S(T)

  24. 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

  25. Dynamic Eterogeneities Part II -Dynamic Heterogeneities J. 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

  26. s2MSD - vs - MSD

  27. peis Connections with the landscape ?

  28. Connessione eis - D Memory of the landscape location…..

  29. Which D(eIS,T) ? 155 BMLJ

  30. Which D(eIS,T) ?

  31. Which D(eIS,T) ?

  32. 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 ……….

  33. Frenkel-Ladd (Einstein Crystal)

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