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Francesco Sciortino Universita’ di Roma La Sapienza

October 4 2007 ISMC Aachen. Francesco Sciortino Universita’ di Roma La Sapienza. Patchy colloidal particles: the role of the valence in the formation of gels. Main Messages.

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Francesco Sciortino Universita’ di Roma La Sapienza

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  1. October 4 2007 ISMC Aachen Francesco Sciortino Universita’ di Roma La Sapienza Patchy colloidal particles: the role of the valence in the formation of gels

  2. Main Messages • Strongly interacting particles (bu<<1)---with simple spherical potentials -- at small and intermediate densities ALWAYS phase-separate (in a dense and dilute phase - (Zaccarelli talk)) • Strongly interacting particles with LIMITED valence ---patchy particles, highly directional interactions, dipolar, quadrupolar --- form equilibrium open structures (GELS, network forming liquids). Empty liquids • Self-assembly as an equilibrium liquid-state problem

  3. Outline • The fate of the liquid state (neglecting crystallization): phase diagram of 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. Analogies between network forming liquids (silica, water) and colloidal gels.

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

  5. For sperical potentials (including the depletion potential) arrest at low f (gelation) is the result of a phase separation process interrupted by the glass transition T T f f E. Zaccarelli, Talk and JPCM, Topical Review 2007

  6. How to go to low T at low f (in metastable equilibrium) How to suppress phase separation ? reducing “valence”

  7. 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 !!! (one bond per patch)

  8. 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

  9. Wertheim TPT for associated liquidsparticles with M identical sticky sites -( one bond per patch ) At low densities and low T (for SW)…..

  10. FS et al J. Chem.Phys.126, 194903, 2007 Self-assembly Equilibrium Polymerization M=2

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

  12. What happens with branching ?

  13. Binary Mixture of M=2 and 3 E. Bianchi et al JPCB (in press) N2=5670 N3=330 X3=0.055 <M>=2.055 Each color labels a different cluster

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

  15. Connectivity properties and cluster size distributions: Flory and Wertheim Percolation Line (theory) Non percolating state points Percolating state points Phase-separation

  16. Wertheim Theory works (for small M) Predictions for larger M

  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 Parameters

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

  21. Del Gado Dipolar Hard Spheres (Camp) Del Gado/Kob EPL 2005 Dipolar Hard Spheres (Blaak, Miller, Hansen)

  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. Is there some kind of universal behavior controlled by valence ?

  25. Noro-Frenkel Scaling for Kern-Frenkel particles G. Foffi and FS, JPCB 2007

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

  27. 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

  28. 4-coordinate “DNA” dendrimed model (F. Starr and FS, JPCM, 2006J. Largo et al Langmuir 2007 ) Limited Coordination (4) Bond Selectivity Steric Incompatibilities Limited Coordination (4) Bond Selectivity Steric Incompatibilities

  29. An example: the PMW phase diagram

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

  31. A collection of phase diagrams of four-coordinated liquids

  32. 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

  33. Conclusions • Directional interaction and limited valency are essential ingredients for offering a DIFFERENT final fate to the liquid state and in particular to arrested states at low f. • In the newly available density region, at low T the system forms a “equilibrium” gel (or a network glass). • Equilibrium Gels and network forming liquids: two faces of the same medal.

  34. Collaborators : Emanuela Bianchi (Patchy Colloids) Cristiano De Michele (PMW, PMS) Julio Largo (DNA, Patchy Colloids) Francis Starr (DNA) Jack Douglas (M=2) Emilia La Nave (Mixture M=2-M=3) Giuseppe Foffi (Kern particles) Piero Tartaglia Emanuela Zaccarelli

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

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

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

  38. One last four-coordinated model !

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

  40. “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 !

  41. Final Message: Universality Class ofvalence controlled particles

  42. Angoli modelli Tetrahedral Angle Distribution

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

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

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

  46. DNA-Tetramers phase diagram

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