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Outline

Outline. Part I Part II. Thermodynamics in the IS formalism. Free energy. Stillinger-Weber. F(T)=-T S conf (<e IS >, T) +f basin (<e IS >,T). with. Basin depth and shape. f basin (e IS ,T)= e IS +f vib (e IS ,T). and. Number of explored basins. S conf (T)=k B ln[ W (<e IS >)].

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Outline

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  1. Outline Part I Part II

  2. Thermodynamics in the IS formalism Free energy Stillinger-Weber 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>)]

  3. 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

  4. Predictions of Gaussian Landscape

  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

  8. Density Minima P.Poole Density minimum and CV maximum in ST2 water inflection in energy inflection = CV max

  9. Sconf Silica Non-Gaussian Behavior in SiO2 Eis e S conf for silica… Esempio di forte 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 !!!

  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. It is possible to calculate exactly the basin free energy ! Basin Free energy

  19. S vib Svib increases linearly with the number of bonds Sconf follows a x ln(x) law Sconfdoes NOT extrepolate to zero

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

  21. Take home message: 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 Network liquids are intrinsically different from non-networks, since the approach to the ground state is hampered by phase separation

  22. Frenkel-Ladd (Einstein Crystal)

  23. Thermodyanmics Excess Entropy A vanishing of the entropy difference at a finite T ?

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