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titolo. Amsterdam, November 2005, AMOLF. Cluster Phases, Gels and Yukawa Glasses in charged colloid-polymer mixtures. Francesco Sciortino. Motivations. Outline. Dynamic Arrest in Colloidal Systems: Glasses and Gels Excluded Volume Short Range Attraction (SRA)

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  1. titolo Amsterdam, November 2005, AMOLF Cluster Phases, Gels and Yukawa Glasses in charged colloid-polymer mixtures. Francesco Sciortino

  2. Motivations Outline Dynamic Arrest in Colloidal Systems: Glasses and Gels Excluded Volume Short Range Attraction (SRA) SRA+ Longer Range Repulsion Investigate the competing effects of short range attraction and longer-range repulsion in colloidal systems Dynamics close to arrested states of matter: Cluster Phases, Glasses and/or Gels

  3. HS Hard Spheres Potential (No temperature, only density) V(r) r s • Hard spheres present a a fluid–solid phase separation due to entropic effects • Experimentally, at h=0.58, the system freezes forming disordered aggregates. MCT transition =51.6-54% • W. van Megen and P.N. Pusey Phys. Rev. A 43, 5429 (1991) • U. Bengtzelius et al. J. Phys. C 17, 5915 (1984) • W. van Megen and S.M. Underwood Phys. Rev. Lett.70, 2766 (1993)

  4. Explanation of the cage and analysis of correlation function .The Cage Effect (in HS). Rattling in the cage F(t) Cage changes log(t)

  5. Colloids: Possibility to control the Interparticle interactions Design Potenziale Hard Sphere Chemistry (surface) r s Asakura- Oosawa Physic Processes (solvent modulation, polydispersity, Depletions) s Yukawa r - + + + + - - r

  6. Depletion Interactions: A (C. Likos) Cartoon Depletion Interactions V(r ) s D r D<<s

  7. Adding attraction (phase diagram) Adding attraction (phase diagram) • The presence of attraction modifies the behaviour of the system: New phases and their coexistence emerge. • With narrow interactions the appeareance of metastable liquid-liquid critical point is typical for colloids. V.J. Anderson and H.N.W. Lekkerkerker Nature416, 811 (2002)

  8. Arrest phenomena in short-range potentials Competition between excluded volume caging and bond caging

  9. T. Eckert and E. Bartsch, Phys. Rev. Lett. 89 125701-1 (2002)PRL (phi effect) T. Eckert and E. Bartsch, Phys. Rev. Lett. 89 125701-1 (2002)

  10. Square Well 3% width Joining thermodynamics and dynamics information Iso- diffusivity lines Percolation Line Repulsive Glass A3 Spinodal (and Baxter Miller-Frenkel) Attractive Glass Liquid+Gas Coexistence SW 3% Spinodal AHS (Miller&Frenkel)

  11. Gelation as a result of phase separation (interrupted by the glass transition) (generic for spherical potentials composed by repulsive core + attraction) T T f f (Foffi et al PRL 2005)

  12. Nat Nat

  13. The quest The quest for the ideal (thermoreversible) gel….model 1) Long Living reversible bonds 2)No Phase Separation 3) No Crystallization Are 1 and 2 mutually exclusive ? Long Bond Lifetime LowTemperature Condensation The quest

  14. Surface Tension How to stay at low T without condensation ? Reasons for condensation (Frank, Hill, Coniglio) Physical Clusters at low T if the infinite cluster is the lowest (free)energy state How to make the surface as stable as the bulk (or more)? The quest

  15. Cluster Ground State Energy : Only Attraction

  16. Competition between short range attraction and long-range repulsion (this talk) (inspired by Groenewold and Kegel work) Limited Valency: E. Zaccarelli et al. Model for reversible colloidal gelation Phys. Rev. Lett. 94, 218301, 2005 Routes to Arrest at low packing fractions (in the absence of a “liquid-gas” phase separation)

  17. Cluster Ground State: Attraction and Repulsion (Yukawa) Warning: Use of Effective Potential

  18. Cluster Ground State: Attraction and Repulsion (Yukawa) Vanishing of g !

  19. Competition Between Short Range Attraction and Longer Range Repulsion: Role in the clustering Short Range Attraction, --dominant in small clusters Longer Range Repulsion Importance of the short-range attraction: Only nn interactions

  20. Typical Shapes in the ground state A=8 x =0.5 s A=0.05 x=2 s

  21. Size dependence of the cluster shape “Linear” shape is an “attractor”

  22. From isolated to interacting clusters Role of T and f: On cooling (or on increasing attraction), monomers tend to cluster…. In the region of the phase diagram where the attractive potential would generate a phase separation….repulsion slows down (or stop) aggregation.The range of the attractive interactions plays a role. How do clusters interact ?

  23. How do cluster interact How do “spherical” clusters interact ?

  24. Yukawa Phase Diagram bcc bcc fcc ps3/6 n

  25. Description of the flow in the Yukawa model N=1 ps3/6 n

  26. N=2 ps3/6 n

  27. N=4 ps3/6 n

  28. N=8 ps3/6 n

  29. N=16 ps3/6 n

  30. N=32 ps3/6 n

  31. N=64 ps3/6 n

  32. Yukawa Phase Diagram ps3/6 n

  33. Figure gel yukawa Tc=0.23 n=100 lowering T Increasing packing fraction

  34. MD simulation T=0.15 T=0.10

  35. Brief Intermediate Summary Equilibrium Cluster-phases result from the competition between aggregation and repulsion. Arrest at low packing fraction generated by a glass transition of the clusters. Aggregation progressively cool the system down till the repulsive cages become dominant

  36. Interacting cluster linear case Interacting Clusters - Linear case The Bernal Spiral Campbell, Anderson, van Dujneveldt, Bartlett PRL June (2005)

  37. Pictures of the clusters at f=0.08 T=0.12 T=0.10 T=0.15 Aggshapec=0.08

  38. T=0.07

  39. Pictures of the aggregation T=0.10 T=0.12 T=0.15 at f=0.125

  40. A gel ! Cluster shapec=0.125 T=0.07

  41. Cluster size distribution  n ~ s s = 2.2 (random percolation)

  42. Fractal Dimension T=0.1 size

  43. Bond Correlation funtions stretched exponential ~0.7 (a.u.)

  44. Density fluctuations

  45. bartlett

  46. Shurtemberger

  47. Several morphologies can be generated by the competition of short-range attraction (fixing the T-scale) and the strength and length of the interaction. A new route to gelation. Continuous change from a Wigner-like glass to a gel While equilibrium would probably suggest a first order transition to a lamellar phase, arrested metastable states appear to be kinetically favored Possibility of exporting ideas developed in colloidal systems to protein systems (Schurtenberger, Chen) and, more in general to biological systems in which often one dimensional growth followed by gelation is observed. Conclusions……

  48. Stefano Mossa (ESRF) Emanuela Zaccarelli (Roma) Piero Tartaglia (Roma) Collaborators

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