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Imtroduzione

Imtroduzione. Conference on "Nucleation, Aggregation and Growth”, Bangalore January 29-31 2007. Francesco Sciortino. Gel-forming patchy colloids and network glass formers: Thermodynamic and dynamic analogies. Motivations.

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Imtroduzione

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  1. Imtroduzione Conference on "Nucleation, Aggregation and Growth”, Bangalore January 29-31 2007 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)…. Equilibrium Aggregation, 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 Debenedetti,Stillinger, Sastry

  4. Phase diagram of spherical potentials* 0.13<fc<0.27 [if the attractive range is very small ( <10%)] * “Hard-Core” plus attraction (Foffi et al PRL 94, 078301, 2005)

  5. For this class of potentials arrest at low f (gelation) is the result of a phase separation process 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) - Zaccarelli et al PRL 94, 218301, 2005 - Sastry et al JSTAT 2006

  7. Patchy particles (maximum number of “bonds”, (different from fraction of bonding surface Hard-Core (gray spheres) Short-range Square-Well (gold patchy sites) No dispersion forces The essence of bonding !!!

  8. Pine Pine’s particle

  9. 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;

  10. Wertheim TPT for associated liquids(particles with M identical sticky sites ) At low densities and low T (for SW)…..

  11. Steric Incompatibilities Steric incompatibilities satisfied if SW width d<0.11 No double bonding Single bond per bond site No ring configurations !

  12. Cond-mat/0701531 GC simulations (particles and chain insertions) M=2

  13. M=2 (Chains) Energy per particle Cond-mat/0701531 Symbols = Simulation Lines = Wertheim Theory Chain length distributions Average chain length <L>

  14. N2=5670 Binary Mixture of M=2 and 3 La Nave et al (in preparation) X3=0.055 <M>=2.055 N3=330

  15. Wertehim theory predicts pbextremely well (in this model)! <M>=2.055 (ground state accessed in equilibrium)

  16. Connectivity properties and cluster size distributions: Flory and Wertheim

  17. Wertheim Wertheim Theory (TPT): predictions E. Bianchi et al, PRL 97, 168301, 2006

  18. Wertheim Mixtures of particles with 2 and 3 bonds Cooling the liquids without phase separating! Empty liquids !

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

  20. Patchy particles - Critical Parameters

  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. 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)

  24. Connecting colloidal particles with network forming liquids

  25. The Primitive Model for Water (PMW) J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987) Lone Pair H The Primitive Model for Silica (PMS)Ford, Auerbach, Monson, J.Chem.Phys, 8415,121 (2004) Silicon Four Sites (tetrahedral) Oxygen Two sites 145.8 o

  26. S(q) in the network region (PMW) C. De Michele et al, J. Phys. Chem. B 110, 8064-8079, 2006

  27. Structure (q-space) C. De Michele et al J. Chem. Phys. 125, 204710, 2006

  28. Approaching the ground state (PMW) PMW energy Progressive increase in packing prevents approach to the GS

  29. Approaching the ground state (PMS) E vs n Phase- separation

  30. T-dependence of the Diffusion Coefficient Cross-over to strong behavior ! Strong Liquids !!!

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

  32. DNA gel model (F. Starr and FS, JPCM, 2006 J. Largo et al Langmuir 2007 ) Limited Coordination (4) Bond Selectivity Steric Incompatibilities

  33. DNA-Tetramers phase diagram

  34. Final Message: Universality Class ofvalence controlled particles

  35. Schematic Summary Phase Separation Region Packing Region Spherical Interactions Region of phase separation Optimal Network Region - Arrhenius Approach to Ground State Packing Region Patchy/ directioal Interactions

  36. Verbal Summary • 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. Are directional interactions (i.e. suppression of phase-separation) essential for being strong? • Gels and strong liquids: two faces of the same medal.

  37. Graphic SummaryTwo distinct arrest lines ? Fluid Fluid Fragile Liquids - Colloidal Glasses: Glass arrest line Strong liquids - Patchy colloids: Gels arrest line

  38. Coworkers: Emanuela Bianchi (Patchy Colloids) Cristiano De Michele (PMW, PMS) Simone Gabrielli (PMW) Julio Largo (DNA, Patchy Colloids) Emilia La Nave, Srikanth Sastry (Bethe) Flavio Romano (PMW) Francis Starr (DNA) Jack Douglas (M=2) Piero Tartaglia Emanuela Zaccarelli

  39. http://www.socobim.de/

  40. Unifying aspects of Dynamics (in the new network region)

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

  42. Nmax=4 phase diagram - Isodiffusivity lines T=0 ! Zaccarelli et al JCP 2006

  43. Isodiffusivities …. Isodiffusivities (PMW) ….

  44. 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

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

  46. Angoli modelli Tetrahedral Angle Distribution

  47. Energie Modelli Low T isotherms….. Coupling between bonding (local geometry) and density

  48. One last four-coordinated model !

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

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