1. 6th Liquid Matter Conference titolo Cluster Phases, Gels and Yukawa Glasses in charged colloid-polymer mixtures. Francesco Sciortino In collaboration with S. Mossa, P. Tartaglia, E. Zaccarelli MRTN-CT-2003-504712

2. Motivations Outline Investigate the competing effects of short range attraction and longer-range repulsion in colloidal systems Focus: Dynamics close to arrested states of matter: Cluster Phases, Glasses and/or Gels

3. Cluster Ground State: Only Attraction Cluster Ground State: Only Repulsion ---> No clusters !

4. Cluster Ground State: Attraction and Repulsion (Yukawa) Vanishing of the “surface tension” !

5. 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

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

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

8. 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 ?

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

10. Yukawa Phase Diagram

11. Yukawa Phase Diagram

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

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

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

15. T=0.07

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

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

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

19. Fractal Dimension T=0.1 size

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

21. Diffusion Coefficient  ~ 2.1-2.3 power law fits D~ (T-Tc ) 

22. Density fluctuations

23. 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……

24. Bartlet data increasing colloid density Campbell, Anderson, van Dujneveldt, Bartlett PRL in press (2005)

25. Yukawa Upper Limit Optimal Size Groenewold and Kegel

26. MD simulation T=0.15 T=0.10

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

28. Mean square displacement