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Introduzione

Introduzione. June 19 2007 Universite Montpellier II. Francesco Sciortino Universita’ di Roma La Sapienza. Aggregation, phase separation and arrest  in low valence patchy particles. Motivations. The fate of the liquid state (assuming crystallization can be prevented)….

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Introduzione

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  1. Introduzione June 19 2007 Universite Montpellier II Francesco Sciortino Universita’ di Roma La Sapienza Aggregation, phase separation and arrest  in low valence patchy particles

  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….) • A four-coordinated patchy particle model - DNA functionalized colloids

  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’s particles 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; Pine Pine

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

  10. Wertheim (in a nut-shell)(ideal gas of equilibriumloop-less clusters of independent bonds (Sear, PRL DHS)

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

  12. FS et al J. Chem.Phys.126, 194903, 2007 M=2

  13. M=2 (Chains) Energy per particle FS et al J. Chem.Phys.126, 194903, 2007 Symbols = Simulation Lines = Wertheim Theory Chain length distributions Average chain length <L>

  14. Branching points in the self-assembly process

  15. Binary Mixture of M=2 and 3 E. Bianche et al (submitted) N2=5670 N3=330 X3=0.055 <M>=2.055 Each color labels a different cluster

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

  17. “Time” dependence of the potential energy (~pb) around the predicted Wertheim value ground-state

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

  19. No bond-loops in finite clusters !

  20. Generic features of the phase diagram Cvmax line Percolation line unstable

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

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

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

  24. Patchy particles - Critical Parameters

  25. A snapshot of <M>=2.025 T=0.05, f=0.01 Ground State (almost) reached ! Bond Lifetime ~ebu

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

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

  28. Noro-Frenkel Scaling for Kern-Frenkel particles

  29. 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 ?

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

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

  32. Connecting colloidal particles with network forming liquids

  33. 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

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

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

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

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

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

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

  40. 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

  41. 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. Directional interactions (suppressing phase-separation) appear to be essential for strong liquids • Gels and strong liquids: two faces of the same medal.

  42. One last four-coordinated model !

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

  44. “Bond” is now a cooperative free-energy concept Optimal density DNA-PMW Bonding equilibrium involves a significant change in entropy (zip-model) Percolation close (in T) to dynamic arrest !

  45. DNA-Tetramers phase diagram

  46. Building an effective potential for particles with valence (cond-mat/0703383)

  47. Two “macromolecules” in a (periodic) box Histogram of center-to-center distances Histogram of the bonding angle

  48. A two-state model for the bonding process

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