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Workshop on Non-Equilibrium Phenomena in Supercooled Fluids: Thermodynamic and Dynamic Analogies

Explore gel-forming patchy colloids and network glass formers in this workshop, discussing thermodynamic and dynamic behaviors using essential ingredients of "strong behavior." Discover how to control phase separation through valency and repulsion. Dive into molecular networks and the dynamics of Nmax=4 phase diagram.

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Workshop on Non-Equilibrium Phenomena in Supercooled Fluids: Thermodynamic and Dynamic Analogies

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  1. Imtroduzione IV Workshop on Non Equilibrium Phenomena in Supercooled Fluids, Glasses and Amorphous Materials Pisa, September 2006 Francesco Sciortino Gel-forming patchy colloids and network glass formers: Thermodynamic and Dynamic analogies

  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

  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, in press

  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, in press

  18. Patchy particles - Critical Parameters

  19. Lattice-gas calculation for reduced valence (Sastry/La Nave) cond-mat

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

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

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

  23. Message MESSAGE (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 MOLECULAR NETWORKS ? IS THE SAME MECHANISM ACTIVE ? HOW ABOUT DYNAMICS ?

  24. 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

  25. Equilibrium phase diagram (PMW)

  26. Critical Point of PMW GC simulation BOX SIZE=6s TC=0.1095 fC=0.153 (Flavio Romano Laurea Thesis)

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

  28. 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

  29. Equilibrium Phase Diagram PSM

  30. Critical point PSM Critical Point of PMS GC simulation BOX SIZE=9s TC=0.075 fC=0.0445 s=0.45

  31. Potential Energy (# of bonds) for the PMW Optimal density !

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

  33. E-Egs vs. 1/T

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

  35. S(q) in the network region

  36. PMS -Potential Energy

  37. PMS E vs 1/T

  38. PMSStructure (r-space)

  39. Structure (q-space)

  40. E vs n Phase-separation

  41. 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

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

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

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

  45. R2 vs t PMW

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

  47. D along isotherms Diffusion Anomalies

  48. Isodiffusivities …. Isodiffusivities (PMW) ….

  49. Diffusion PMS De Michele et al, cond mat

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