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 >)].
F(T)=-T Sconf(<eIS>, T) +fbasin(<eIS>,T)
Basin depth and shape
Number of explored basins
e-(eIS -E0)2/2s 2
T-1 dependence observed in the studied T-range
Support for the Gaussian Approximation
BMLJ Configurational Entropy
Density minimum and CV maximum in ST2 water
inflection in energy
inflection = CV max
Non-Gaussian Behavior in SiO2
Eis e S conf for silica…
Esempio di forte
Non gaussian silica
Maximum Valency Model (Speedy-Debenedetti)
SW if # of bonded particles <= Nmax
HS if # of bonded particles > Nmax
A minimal model for network forming liquids
The IS configurations coincide with the bonding pattern !!!
Generic Phase Diagram for Square Well (3%)
Generic Phase Diagram for NMAX Square Well (3%)
It is possible to equilibrate at low T !
Energy per Particle
Specific Heat (Cv) Maxima
It is possible to calculate exactly the basin free energy !Basin Free energy
Svib increases linearly with
the number of bonds
a x ln(x) law
Sconfdoes NOT extrepolate to zero
Self-consistent calculation ---> S(T)
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
Network liquids are intrinsically different from non-networks, since the approach to the ground state is hampered by phase separation
A vanishing of the entropy difference at a finite T ?