The Marie Curie Research/Training Network on Dynamical Arrest Workshop Le Mans, November 19-22, 2005

1. 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

2. 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).

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

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

5. Foffi aging 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

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

7. Phase Diagram NMAX-modifiedPhase Diagram

8. Nmax=4 phase diagram - Isodiffusivity lines

9. The model J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987) V(r ) Hard-Sphere + Tetrahedral coordinated SW (bond geometry) r u0 (energy scale) s (length scale) (HS repulsive geometry) Bonding is properly defined --- Lowest energy state is well defined

10. Pagan and Gunton JCP (2005)

11. Critical Point of PMW GC simulation BOX SIZE=6s TC=0.1095 mC=0.0388 fC=0.153

12. Water Phase Diagram F ~ 0.34

13. Potential Energy for the PMW Optimal density !

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

15. Potential Energy along isotherms Optimal density Hints of a LL CP

16. S(q) in the network region

18. Diffusion Coefficient

19. D along isotherms Diffusion Anomalies

20. Isodiffusivities (PWM)….

21. Nmax=4 phase diagram - Isodiffusivity lines

22. Analogies with other network-forming potentials ST2 (Poole) SPC/E Slower on compression Faster on compression BKS silica (Saika-Voivod)

23. Density anomalies Density Anomalies… (and possible 2’nd CP)

24. 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

25. DNA Gels 1 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

26. The DNA gel model

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

28. D vs (1-pb)

29. D vs (1-pb) --- (MC) D ~ f04 ~(Stanley-Teixeira)

31. Strong-fragile: Dire Stretched, Delta Cp Hard Sphere Colloids: model for fragile liquids

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

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

34. 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

35. Coworkers: Cristiano De Michele (Event driven code for PMW) Simone Gabrielli (PMW) Emanuela Zaccarelli Piero Tartaglia Angel Moreno (Landscape) Francis Starr (DNA-gels)

36. E vs. 1/T