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Part I Part II Outline. Thermodynamics in the IS formalism Stillinger- Weber F(T)=-T S conf (, T) +f basin (,T) with f basin (e IS,T)= e IS +f vib (e.

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Presentation on theme: "Part I Part II Outline. Thermodynamics in the IS formalism Stillinger- Weber F(T)=-T S conf (, T) +f basin (,T) with f basin (e IS,T)= e IS +f vib (e."— Presentation transcript:

1 Part I Part II Outline

2 Thermodynamics in the IS formalism Stillinger- Weber F(T)=-T S conf (, T) +f basin (,T) with f basin (e IS,T)= e IS +f vib (e IS,T) and S conf (T)=k B ln[  ( )] Basin depth and shape Number of explored basins Free energy

3 The Random Energy Model for e IS Hypothesis:  e IS )de IS = e  N de IS e -(e IS -E 0 ) 2 /2  2 2222 S conf (e IS )/N=  - (e IS -E 0 ) 2 /2  2 Gaussian Landscape

4 Predictions of Gaussian Landscape

5 T-dependence of SPC/ELW-OTP T -1 dependence observed in the studied T-range Support for the Gaussian Approximation

6 BMLJ Configurational Entropy BMLJ Sconf

7 Non Gaussian Behaviour in BKS silica

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

9 Eis e S conf for silica… Esempio di forte Non-Gaussian Behavior in SiO 2 Non gaussian silica Sconf Silica

10 Maximum Valency Model ( Speedy-Debenedetti ) A minimal model for network forming liquids SW if # of bonded particles <= Nmax HS if # of bonded particles > Nmax V(r) r Maximum Valency 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 N MAX Square Well (3%)

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

14 Specific Heat (Cv) Maxima Cv

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 S vib increases linearly with the number of bonds S conf follows a x ln(x) law S conf does NOT extrepolate to zero

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

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

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24 Frenkel-Ladd (Einstein Crystal)

25 Excess Entropy Thermodyan mics A vanishing of the entropy difference at a finite T ?


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