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

2. Outline Motivations 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 Hard spheres present a a fluid–solid phase separation due to entropic effects Experimentally, at  =0.58, the system freezes forming disordered aggregates. MCT transition  =51.6-54% 1.W. van Megen and P.N. Pusey Phys. Rev. A 43, 5429 (1991) 2.U. Bengtzelius et al. J. Phys. C 17, 5915 (1984) 3.W. van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993) Potential  V(r) r (No temperature, only density)

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

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

6. Depletion Interactions Depletion Interactions: A (C. Likos) Cartoon V(r) r   

7. 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 Nature 416, 811 (2002) Adding attraction (phase diagram)

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 Repulsive Glass Attractive Glass Liquid+Gas Coexistence A3 Spinodal AHS (Miller&Frenkel) Iso- diffusivity lines Percolation Line Spinodal (and Baxter Miller-Frenkel) SW 3%

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

12. Nat

13. 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 ? The quest LowTemperature Condensation Long Bond Lifetime The quest

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

15. Cluster Ground State Energy : Only Attraction

16. Routes to Arrest at low packing fractions (in the absence of a “liquid-gas” phase separation) 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

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

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

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

20. A=8  =0.5  A=0.05  =2  Typical Shapes in the ground state

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

22. Role of T and  : On cooling (or on increasing attraction), monomers tend to cluster…. From isolated to interacting clusters 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 “spherical” clusters interact ? How do cluster interact

24. Yukawa Phase Diagram bcc fcc bcc  3 /6 n

25. N=1 Description of the flow in the Yukawa model  3 /6 n

26. N=2  3 /6 n

27. N=4  3 /6 n

28. N=8  3 /6 n

29. N=16  3 /6 n

30. N=32  3 /6 n

31. N=64  3 /6 n

32. Yukawa Phase Diagram  3 /6 n

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

34. T=0.15T=0.10 MD simulation

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

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

38. T=0.07

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

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

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

42. Fractal Dimension size T=0.1

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

44. Density fluctuations

47. bartlett

48. Shurtemberger

49. Conclusions…… 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.

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

51. Groenewold and Kegel Upper Limit Optimal Size Yukawa

52. No strong density dependence in peak position No density dependence in prepeak

53. Mean square displacement

55. F. Sciortino, Nat. Mat. 1, 145 (2002). Nat Mat

56. Science Pham et al Fig 1

57. power law fits D~ (T-T c )   ~ 2.1-2.3 Diffusion Coefficient

58. foffi

59. Hard Spheres Potential Square-Well short range attractive Potential   Log(t) Mean squared displacement repulsive attractive (0.1  ) 2  Hard Sphere (repulsive) glass Attractive Glass Figure 1 di Natmat

60. Campbell, Anderson, van Dujneveldt, Bartlett PRL (June 2005) increasing colloid density Bartlet data

61. Phase Diagram for Square Well (3%) Percolation Line Spinodal AHS (Miller&Frenkel) Spinodal Repulsive Glass Attractive Glass Iso-diffusivity lines Percolation Line A3 Liquid+Gas