The Marie Curie Research/Training Network on Dynamical ArrestWorkshop

Le Mans, November 19-22, 2005

Slow dynamics in the presence of attractive patchy interactions

Francesco Sciortino

Motivations

• The fate of the liquid state…. Gels and phase separation: essential features (Sticky colloids - Proteins)

• Revisiting network forming liquids (Silica, water….)

• Essential ingredients of “strong behavior” (A. Angell scheme).

Glass line (D->0)

Liquid-Gas Spinodal

Binary Mixture LJ particles

“Equilibrium” “homogeoues” arrested states only for large packing fraction

BMLJ

Gelation as a result of phase separation

(interrupted by the glass transition)

T T

G. Foffi, E. Zaccarelli, S. V. Buldyrev, F. Sciortino, P. TartagliaAging in short range attractive colloids: A numerical studyJ. Chem. Phys. 120, 1824, 2004

Foffi aging

Geometric Constraint: Maximum Valency(E. Zaccarelli et al, PRL, 2005)

SW if # of bonded particles <= Nmax

HS if # of bonded particles > Nmax

V(r)

r

Phase Diagram

Nmax=4 phase diagram - Isodiffusivity lines

The modelJ. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987)

Hard-Sphere + Tetrahedral coordinated SW

V(r)

r(bond geometry)

(HS repulsive geometry)

(length scale)

(energy scale)

u0

Bonding is properly defined --- Lowest energy state is well defined

Pagan and GuntonJCP (2005)

Critical Point of PMWGC simulationBOX SIZE=TC=0.1095C=0.0388C=0.153

Water Phase Diagram

~ 0.34

Potential Energy for the PMW

Optimal density !

Potential Energy -- Approaching the ground state

Progressive increase inpacking prevents approach to the GS

Potential Energy along isotherms

Optimal densityHints of a LL CP

S(q) in the network region

Diffusion Coefficient

D along isotherms

Diffusion Anomalies

Isodiffusivities (PWM)….

Nmax=4 phase diagram - Isodiffusivity lines

Analogies with other network-forming potentials

SPC/E ST2 (Poole)

BKS silica(Saika-Voivod)

Faster on compression

Slower on compression

Density Anomalies…(and possible 2’nd CP)

Comments

• Directional interaction and limited valency are essential ingredients for offering a new final fate to the liquid state and in particular to arrested states at low

• The resulting low T liquid state is (along isochores) a strong liquid. Directional bonding is essential for being strong.

• Gels and strong liquids are two faces of the same medal.

• Percolation and arrest-lines are well separated

Colloidal Gels, Molecular Gels, …. and DNA gels

Four Arm Ologonucleotide Complexes as precursors for the generation of supramolecular periodic assembliesJACS 126, 2050 2004

Palindroms in complementary space

The DNA gel model

Optimaldensity

Bonding equilibriuminvolves a significantchange in entropy(zip-model)

Percolation close to dynamicarrest !

D vs (1-pb)

D vs (1-pb) --- (MC)

D ~ f04

~(Stanley-Teixeira)

Hard SphereColloids: model for fragile liquids

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

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

Non zero ground state entropy

Coworkers:

Cristiano De Michele (Event driven code for PMW)Simone Gabrielli (PMW)Emanuela Zaccarelli Piero Tartaglia

Angel Moreno (Landscape)Francis Starr (DNA-gels)

E vs. 1/T