Outline
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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 ?