Imtroduzione

1. Imtroduzione Mainz, November 28 2006 Gel-forming patchy colloids and network glass formers: Thermodynamic and dynamic analogies Francesco Sciortino

2. Motivations • The fate of the liquid state (assuming crystallization can be prevented)…. Gels and phase separation: essential features (Sticky colloids - Proteins) • Thermodynamic and dynamic behavior of new patchy colloids • Revisiting dynamics in network forming liquids (Silica, water….) • Essential ingredients of “strong behavior” (A. Angell scheme).

3. BMLJ (Sastry) Liquid-Gas Spinodal Glass line (D->0) Binary Mixture LJ particles “Equilibrium” “homogeneous” arrested states only for large packing fraction (see also Debenedetti/Stillinger)

4. Phase diagram of spherical potentials* 0.13<fc<0.27 [if the attractive range is very small ( <10%)] * “Hard-Core” plus attraction

5. Gelation (arrest at low f) as a result of phase separation (interrupted by the glass transition) T T f f

6. How to go to low T at low f(in metastable equilibrium) ?Is there something else beside Sastry’s scenario for a liquid to end ? How to suppress phase separation ? -controlling valency (Hard core complemented by attractions) -l.r. repulsion (Hard core complemented by both attraction and repulsions

7. 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

8. Nmax phase diagram NMAX-modifiedPhase Diagram

9. Patchy particles Hard-Core (gray spheres) Short-range Square-Well (gold patchy sites) No dispersion forces The essence of bonding !!!

10. Mohwald

11. Pine Pine’s particle

12. Pine Self-Organization of Bidisperse Colloids in Water Droplets Young-Sang Cho, Gi-Ra Yi, Jong-Min Lim, Shin-Hyun Kim, Vinothan N. Manoharan,, David J. Pine, and Seung-Man Yang J. Am. Chem. Soc.; 2005;127(45) pp 15968 - 15975;

13. Steric Incompatibilities Steric incompatibilities satisfied if SW width d<0.11 No double bonding Single bond per bond site

14. Wertheim Theory

15. Wertheim Wertheim Theory (TPT): predictions E. Bianchi et al, PRL, 2006

16. Wertheim Mixtures of particles with 2 and 3 bonds Empty liquids !

17. Patchy particles (critical fluctuations) (N.B. Wilding) ~N+sE E. Bianchi et al, PRL, 2006

18. Patchy particles - Critical Parameters

19. M=2 (Chains) T=0.07 Symbols = Simulation Lines = Wertheim Theory

20. <M>=2.055

21. A snapshot of a <M>=2.025 (low T) case, f=0.033 Ground State (almost) reached ! Bond Lifetime ~ebu

22. Dipolar Hard Sphere Dipolar Hard Spheres… Camp et al PRL (2000) Tlusty-Safram, Science (2000)

23. Del Gado Del Gado ….. Del Gado/Kob EPL 2005

24. Hansen

25. Message MESSAGE(S) (so far…): REDUCTION OF THE MAXIMUM VALENCY OPENS A WINDOW IN DENSITIES WHERE THE LIQUID CAN BE COOLED TO VERY LOW T WITHOUT ENCOUNTERING PHASE SEPARATION THE LIFETIME OF THE BONDS INCREASES ON COOLING THE LIFETIME OF THE STRUCTURE INCREASES ARREST A LOW f CAN BE APPROACHED CONTINUOUSLY ON COOLING (MODEL FOR GELS) HOW ABOUT DYNAMICS ? HOW ABOUT MOLECULAR NETWORKS ? IS THE SAME MECHANISM ACTIVE ?

26. Slow Dynamics at low F Mean squared displacement <M>=2.05 T=0.05 F=0.1

27. Slow Dynamics at low F Collective density fluctuations <M>=2.05 F=0.1

28. Message: Gel dynamics: dynamic arrest due to percolation (in the limit of long-living bonds).

29. The PMW model J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987) V(r ) Hard-Sphere + 4 sites (2H, 2LP) Tetrahedral arrangement H-LP interact via a SW Potential, of range l=0.15 s. r u0 (energy scale) s (length scale) Bonding is properly defined --- Lowest energy state is well defined

30. Equilibrium phase diagram (PMW)

31. Pagan-Gunton Pagan and Gunton JCP (2005)

32. The PMS ModelFord, Auerbach, Monson, J.Chem.Phys, 8415,121 (2004) Silicon Four sites (tetrahedral) SW interaction between Si sites and O sites Oxygen Two sites 145.8 o sOO=1.6 s l=[1-3 /2]s 1/2

33. Equilibrium Phase Diagram PSM

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

35. Potential Energy along isotherms Phase-separation Optimal density Hints of a LL CP

36. S(q) in the network region

37. PMSStructure (r-space)

38. Structure (q-space)

39. E vs n Phase-separation

40. Summary of static data Phase Separation Region Packing Region Spherical Interactions Region of phase separation Optimal Network Region - Arrhenius Approach to Ground State Packing Region Patchy Interactions

41. How About Dynamics (in the new network region) ?

42. Dynamics in the Nmax=4 model (no angular constraints) Strong Liquid Dynamics !

43. Nmax=4 phase diagram - Isodiffusivity lines Zaccarelli et al JCP 2006

44. PMW -- Diffusion Coefficient Cross-over to strong behavior

45. Isodiffusivities …. Isodiffusivities (PMW) ….

46. Diffusion PMS De Michele et al, cond mat

48. Question Compare ? How to compare these (and other) models for tetra-coordinated liquids ? Focus on the 4-coordinated particles (other particles are “bond-mediators”) Energy scale ---- Tc Length scale --- nn-distance among 4-coordinated particles

49. Phase Diagram Compared Spinodals and isodiffusivity lines: PMW, PMS, Nmax

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