Part I

Part II

Outline

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

The Random Energy Model for eIS

Hypothesis:eIS)deIS=eN -----------------deIS

e-(eIS

-E0)2/22

22

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

Gaussian Landscape

Predictions of Gaussian Landscape

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

Density minimum and CV maximum in ST2 water

inflection = CV max

inflection in energy

P.Poole

Eis e S conf for silica…

Esempio di forte

Non-Gaussian Behavior in SiO2

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 !!!

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

It is possible to calculate exactly the basin free

energy !

Svib increases linearly withthe number of bonds

Sconf follows a x ln(x) law

Sconf does NOT extrepolate to zero

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

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 ArrheniusDynamics

Network liquids are intrinsically different from non-networks, since the approach to the ground state is hampered by phase separation

Frenkel-Ladd (Einstein Crystal)

Excess Entropy

A vanishing of the entropy difference at a finite T ?