Bad Gastein, January 2005

Gels and Strong Liquids

In collaboration with S. Bulderyev,C. De Michele, E. La Nave, A. Moreno, I. Saika-Voivod, P. Tartaglia, E. Zaccarelli

Hard SphereColloids: model for fragile liquids

Geometric Constraint: Maximum Valency

SW if # of bonded particles <= Nmax

HS if # of bonded particles > Nmax

V(r)

r

Phase Diagram

Viscosity and Diffusivity: Arrhenius

• =1

• Cv small

• Stokes-Einstein Relation

Other strong properties:

percolating

Ground State Energy Known !

•It is possible to equilibrate at low T !

•E(T) is known and hence free energy can be calculated exactly down to T=0

It is possible to calculate exactly the vibrational entropy of one single bonding pattern

(basin free energy)

(Ladd andFrenkel)

Thermodynamics in the Stillinger-Weber formalism

F(T)=-T Sconf(E(T))+fbasin(E,T)

with

Fbasin (E)

and

Sconf(E)=kBln[(E)]

Sampled Space with E bonds

Number of configurations with E bonds

sconf

•Comment:In models for fragile liquids, the number of configurations with energy E has been found to be gaussian distributed

Non zero ground state entropy

Landscape of strong and fragile liquids

Realistic ModelNetwork

Primitive Model for Network

Fragile Liquid

From models for gels to models for network forming liquid

Si

O

Points for discussions….

• Sticky points colloids: •Candidates for Gel formations by suppression of the spinodal decomposition• Candidates for strong liquid behavior.

• Landscape differences between strong and fragile liquids.•Is the configurational entropy of strong liquids at low T (in the classical limit) non zero

• Proteins: • Sticky areas. Gel if favored. Role of the space correlation between the points. No crystals for special sticky points configurations ?

Phase Diagram