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

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

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

5. 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 Foffi aging

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

7. N MAX -modified Phase Diagram Phase Diagram

8. N max =4 phase diagram - Isodiffusivity lines

9. The model J. 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) u0u0 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=  T C =0.1095  C =0.0388  C =0.153

12. Water Phase Diagram  ~ 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. N max =4 phase diagram - Isodiffusivity lines

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

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

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  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. 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 DNA Gels 1

26. The DNA gel model

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

28. D vs (1-p b )

29. D vs (1-p b ) --- (MC) D ~ f 0 4 ~(Stanley-Teixeira)

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

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

33. Thermodynamics in the Stillinger-Weber formalism F(T)=-T S conf (E(T))+f basin (E,T) with F basin (E) and S conf (E)=k B ln[  (E)] Sampled Space with E bonds Number of configurations with E bonds Stillinger-Weber

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