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

2. Outline Motivations 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. 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

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

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

8. 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 ?

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

10. Yukawa Phase Diagram

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

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

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

15. T=0.07

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

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

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

19. Fractal Dimension size T=0.1

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

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

22. Density fluctuations

23. 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.

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

25. Groenewold and Kegel Upper Limit Optimal Size Yukawa

26. T=0.15T=0.10 MD simulation

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

28. Mean square displacement