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Introduzione

Introduzione. March 25 2007 ACS Chicago. Francesco Sciortino Universita’ di Roma La Sapienza. Gel-forming patchy colloids, and network glass formers: Thermodynamic and dynamic analogies. Main Messages.

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Introduzione

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  1. Introduzione March 25 2007 ACS Chicago Francesco Sciortino Universita’ di Roma La Sapienza Gel-forming patchy colloids, and network glass formers: Thermodynamic and dynamic analogies

  2. Main Messages • Strongly interacting particles ---with simple spherical potentials -- always phase-separate (in a dense and dilute phase) • Strongly interacting particles -- with limited valence [patchy particles, highly directional interactions, dipolar, quadrupolar] --- form equilibrium open structures (network forming liquids/glasses or gels). Empty liquids • Self-assembly as an equilibrium liquid-state problem

  3. Outline • The fate of the liquid state (neglecting crystallization):spherical and patchy attractive potentials • A theory-of-liquid approach to self-assembly in equilibrium polymerization (linear and branched) • The role of valence: Universality classes for the liquid-gas transition • Thermodynamic and dynamic behavior of new patchy colloids • Revisiting dynamics in network forming liquids (Silica, water….)

  4. 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

  5. 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)

  6. 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

  7. 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 ? -The role of the “valence”

  8. Valence-Controlled Patchy particles maximum # of “bonds”, (as opposed to # patches, fraction of bonding surface) Hard-Core (gray spheres) Short-range Square-Well (gold patchy sites) No dispersion forces The essence of bonding !!!

  9. Pine 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

  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, JCP in press Self-assembly Equilibrium Polymerization M=2

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

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

  15. Wertheim 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 valence 2 and 3 A critical point at vanishing packing 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 EQUILIBRIUM GELS !!!

  24. Connecting colloidal particles with network forming liquids Colloidal Water and Colloidal Silica !

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

  29. PMW phase diagram

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

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

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

  33. Schematic Summary Phase Separation Region Packing Region Spherical Interactions Region of phase separation Network Region - Approach to Ground State - Bond-Activated Dynamics Packing Region Patchy/ directioal Interactions

  34. 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

  35. DNA-Tetramers phase diagram

  36. Conclusions • 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. • 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) Julio Largo (DNA, Patchy Colloids) Francis Starr (DNA) Jack Douglas (M=2) Piero Tartaglia Emanuela Zaccarelli

  39. One last four-coordinated model !

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

  41. “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 !

  42. Final Message: Universality Class ofvalence controlled particles

  43. Angoli modelli Tetrahedral Angle Distribution

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

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

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

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