The Marie Curie ResearchTraining Network on Dynamical Arrest

The Marie Curie Research/Training Network on Dynamical Arrest Workshop Le Mans, November 19 -22, 2005 Francesco Sciortino Slow dynamics in the presence of attractive patchy interactions

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).

Liquid-Gas Spinodal Glass line (D->0) Binary Mixture LJ particles “Equilibrium” “homogeoues” arrested states only for large packing fraction

Gelation as a result of phase separation (interrupted by the glass transition) T T f f

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

Geometric Constraint: Maximum Valency V(r ) (E. Zaccarelli et al, PRL, 2005) SW if # of bonded particles <= Nmax HS if # of bonded particles > Nmax r

Phase Diagram

Nmax=4 phase diagram - Isodiffusivity lines

The model J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987) V(r) Hard-Sphere + Tetrahedral coordinated SW (bond geometry) r u 0 (energy scale) s (length scale) (HS repulsive geometry) Bonding is properly defined --- Lowest energy state is well defined

Pagan and Gunton JCP (2005)

Critical Point of PMW GC simulation BOX SIZE=6 s TC=0. 1095 m. C=0. 0388 f. C=0. 153

Water Phase Diagram F ~ 0. 34

Potential Energy for the PMW Optimal density !

Potential Energy -- Approaching the ground state Progressive increase in packing prevents approach to the GS

Potential Energy along isotherms Optimal density Hints 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 ST 2 (Poole) SPC/E Faster on compression BKS silica (Saika-Voivod) 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 f • 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 assemblies JACS 126, 2050 2004 Palindroms in complementary space

The DNA gel model

Optimal density Percolation close to dynamic arrest ! Bonding equilibrium involves a significant change in entropy (zip-model)

D vs (1 -pb)

D vs (1 -pb) --- (MC) D ~ f 04 ~(Stanley-Teixeira)

Hard Sphere Colloids: model for fragile liquids

It is possible to calculate exactly the vibrational entropy of one single bonding pattern (basin free energy) (Ladd and Frenkel)

Thermodynamics in the Stillinger-Weber formalism F(T)=-T Sconf(E(T))+fbasin(E, T) with Fbasin (E) Sampled Space with E bonds and Sconf(E)=k. Bln[W(E)] Number of configurations with E bonds

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

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