titolo

1. Genova, September 1 2004 titolo CCP2004 Routes to Colloidal Gel Formation In collaboration with S. Bulderyev, E. La Nave, A. Moreno, S. Mossa, I. Saika-Voivod, P. Tartaglia, E. Zaccarelli Thanks to the organizers and to Carlo Pierleone

2. Outline Outline and Motivations • Brief Review of Short-Range Attractive Colloidal Glass (asymmetric colloid-polymer mixtures) • How to model disordered arrested states at low packing fraction (gels) • Routes: • Interrupted phase separation (irreversible gels) • Long Range Repulsive interactions (reversible) • Geometrical constraints (reversible) • Differences between gel and glasses

3. Depletion Interactions: A (C. Likos) Cartoon Depletion Interactions V(r ) s D r D<<s

4. MCT IDEAL GLASS LINES (PY) - SQUARE WELL MODEL - CHANGING D The role of delta V(r) D Large D Small D A3 A4 PRE-63-011401-2001 Role of the width Vari delta

5. Nat Mat F. Sciortino, Nat. Mat. 1, 145 (2002).

6. Citazioni confirmed by experiments Mallamace et al. PRL (2000) Pham et al. Science (2002) Eckert and Bartsch PRL (2002) and simulations Puertas et al PRL (2002) Zaccarelli et al PRE (2002)

7. Pham et al 2004

8. Square Well 3% width Phase Diagram for Square Well (3%) Iso- diffusivity lines Percolation Line Repulsive Glass A3 Spinodal (and Baxter) Attractive Glass Liquid+Gas Coexistence Spinodal AHS (Miller&Frenkel)

9. Virial Scaling in the dynamics:Toward the Baxter Limit G. Foffi and C. De Michele,preprint

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

11. The quest The quest for the ideal (thermoreversible) gel….model 1) Long Living reversible bonds 2)No Phase Separation 3) No Crystallization Are 1 and 2 mutually exclusive ? Long Bond Lifetime LowTemperature Condensation The quest

12. Surface Tension How to stay at low T without condensation ? Reasons for condensation (Frank, Hill, Coniglio) Physical Clusters at low T if the infinite cluster is the lowest (free)energy state How to make the surface as stable as the bulk (or more)? The quest

13. Competition Between Short Range Attraction and Long Range Repulsion Short Range Attraction Long Range Repulsion FS et al, PRL 2004

14. Yukawa How to make negative ? Upper Limit Optimal Size Groenewold and Kegel

15. Figure gel yukawa lowering T Increasing packing fraction

16. Maximum Valency Geometric Constraint: Maximum Valency V(r ) SW if # of bonded particles <= Nmax HS if # of bonded particles > Nmax r

17. Phase Diagram NMAX-modifiedPhase Diagram

18. Bond Lifetime.. Several more decades..

19. Gel vs Glass - MSD T=0.1 Typical Glass Value

20. Gel vs Glass: Density Autocorrelation Functions fq

21. Fq gel vs glass

22. Summary…. • Designig Thermoreversible Gels: • Models with small surface tension (charged colloids, sticky points) • A simple model for thermoreversible gel • Gels and Glasses: • Differences in localization length • Differences in experimental observables

24. Stoke

26. Ground State Energy Known ! It is possible to equilibrate at low T ! Energy per Particle

31. How to stay at low T without condensation ? Reasons for condensation (Frank, Hill, Coniglio) Physical Clusters at low T if the infinite cluster is the lowest energy state How to make the surface more stable than the bulk ? The quest

32. Thermodynamics in the IS formalism Free energy Stillinger-Weber F(T)=-T Sconf(<eIS>, T) +fbasin(<eIS>,T) with Basin depth and shape fbasin(eIS,T)= eIS+fvib(eIS,T) and Number of explored basins Sconf(T)=kBln[W(<eIS>)]

33. It is possible to calculate exactly the basin free energy ! Basin Free energy

34. Viscosity and Diffusivity: Arrhenius

35. Stoke-Einstein Relation