1. Francesco Sciortino Dynamical Arrest of Soft Matter and Colloids Lugano April 6-9 2006 (MRTN-CT-2003-504712) Tutorial: Recent developments in understanding gelation in colloidal systems

2. coherent mass consisting of a liquid in which particles are either dispersed or arranged in a fine network throughout the mass. A gel may be notably elastic and jellylike (as gelatin or fruit jelly), or quite solid and rigid (as silica gel). (Britannica) What is a gel ?

3. Recent reviews Cipelletti, Luca; Ramos, Laurence, Slow dynamics in glassy soft matter Journal of Physics: Condensed Matter, 17, R253-R285 (2005); Slow dynamics in glasses,gels and foams, Current Opinion in Colloid and Interface Science 7 (2002) 228-234. F. Sciortino and P. Tartaglia Glassy colloidal systems Advances in Physics 54, 2005 471-524 Future reviews K.A. Dawson The glass paradigm for colloidal glasses, gels, and other arrested states driven by attractive interactions, Coll. Int. Sci 7, 2002 218-227 V. Trappe, Colloidal gels -- low-density disordered solid-like states lassy colloidal systems Current Opinion in Colloid and Interface Science 8 (2004) 494.

4. --- Low packing fraction of the dispersed phase --- (visco) elastic properties (ability to sustain stress): The need of a “spanning” network (attraction between particles is requested) Two main conditions

5. Chemical Gels System with a fixed number of bonds (with infinite lifetime) connecting the dispersed particles rubberepoxy-resins Richard A.L. Jones, Condened Matter. Oxford

6. Percolation theory! Cluster Size distribution (cluster shape) Infinite Cluster (d.c. conductivity, elasticity) Bond percolation in a two-dimension square lattice

7. C 1 =z p Bond probability=p C 2 = (z-1) p C 1 C 3 = (z-1) p C 2 C N = [(z-1) p] N-1 C 1 (z-1) p c =1 ……………… Critical Value !!! A Caley-Tree with connectivity z=4 Flory-Stockmayer (mean field solution )

8. Predictions (close to p c ) : suscettibility magnetization (order parameter) Bethe:  =2.5,  =0.5, d f =4 3d (approx):  2.18,  =0.45, d f =2.53 Stauffer Phys. Rep. 1979

9. Colloids (Lu’s Talk) Polymers-Biopolymers Proteins (Cardineaux and Zaccarelli’s Talk) Dna-coated colloids (Largo’s Talk) Reversible Bonding ---- Bond Lifetime ---- ---- Persistence of the spanning network ---- ---- Equilibrium Thermodynamics ---- Physical Gels

10. Gels resulting from irreversible processes (kinetic pathways are important) (phase separation) “Ideal” gels. Gels in which dynamic arrest is progressively approached (and the system is (as close as possible) to thermodynamic equilibrium). [ Experimental timescales < Bond lifetime < equilibration time at geometric percolation]. Routes to Physical Gelation

11. Phase diagram of spherical potentials * Hard-Core plus attraction 0.13<  c <0.27

12. Coniglio-Klein Bond Lifetime Static Percolation -- Gelation ???

13. Two (times 2 !) ways to go to low T (at low  ) Suppress phase separation -valency -l.r. repulsion -DLCA -Glass Arrest

14. Diffusion Limited Cluster Aggregation (a T->0 phase separation) Particles (and clusters) performing brownian motion and sticking with probability one. Diffusion coefficient of the cluster proportional to M -  (DLVO potential without and with salt).

15. “monodisperse” fractal objects (d f = 1.9) Gels as space-filling of sticking clusters M~M 1 (R/R 1 ) df The cluster average density decreases with R df-d V occ /V=  (R/R 1 ) d-df R=R 1   df-d) Basic DLCA findings

16. Structure of DLCA gels

17. The dynamical rules defining DLCA are the T->0 limit of the lattice gas dynamics. M. Carpineti and M. Giglio, Phys. Rev. Lett. 68 3327 (1992) F. Sciortino and P. Tartaglia, Phys. Rev. Lett. 74 282 (1995) P. Pouline, J. Bibette and D. A. Weitz, Eur. Phys. J. B 277 (1999) C. Gimel, T. Nicolai, D. Durand, Phys. Rev. E 061405 (2002). MC (Lattice Gas) e -  u Gimel-Nicolai 1 if not bonded 0 if bonded { -  u= ln(1-p b ) DLCA and Spinodal Decomposition

18. Gels as arrested phase separation F. Sciortino et al, Phys. Rev. E 47, 4615 (1993). D. Sappelt and J. Jackle, Europhys. Lett. 37, 13(1997). M. Solomon and P. Varadan, Phys. Rev. E. 63 (2001) 051402 E. Zaccarelli et al, Unifying concepts in Granular Matter and Gels, Elsevier 2004 S. Manley et al, Phys. Rev. Lett. 95 (2005) 238302 E. Witman amd Z-G Wang, J.Phys. Chem B 110 6312 2006

19. Foffi aging G. Foffi et al, J. Chem. Phys. 122, 224903-224915, 2005 Arrested phase separation in a short-ranged attractive colloidal system: A numerical study

20. How to suppress phase separation ? Sticky patchy colloids ! Maximum Valency* --- Bond Selectivity * three-body interactions (Del Gado-Kob) E. Bianchi, Poster

21. Even more.. With mixtures of two and three sticky spots….

22. Del-Gado Kob Gel

23. N max =4 phase diagram - Isodiffusivity lines E.Zaccarelli et al, Phys. Rev. Lett. 94, 218301, 2005 ; J. Chem. Phys. 124, 124908 (2006). C. De Michele et al, J. Phys. Chem. B, jp056380y (2006).

24. Analogies with other network-forming potentials SPC/E ST2 (Poole) BKS silica (Saika-Voivod)

25. Short-Range Attraction and Long-Range Repulsion (Yukawa) Vanishing of the “surface tension” ! Clusters as microphase

26. 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

27. Gels in charged colloids FS,PT,EZ J. Phys. Chem. B 109, 21942-21953, 2005

28. proteins

29. What is the lowest  at which it is possible to form a gel In the absence of gravity Thermal stresses (DLCA, R c =100  m) On the earth Gravitational stresses (DLCA, R c =50  m) Interesting question Manley et al, PRL, 93 108302 (2004).

30. Viscosity Density autocorrelation functions Chemical Gels….. What is known Martin Libro Kon Physical Gels…. Cipelletti - Others Gel Dynamics

31. Cipelletti

32. Krall

33. Density Fluctuations (chemical gels) Below percolationAbove percolation Tagged particle properties: D finite at the transition and above I. Saika-Voivod et al, Phys. Rev. E 70, 041401, 2004 Kurt Broderix et al, Phys. Rev. Lett. 79, 3688–3691 (1997),

34. Non ergodicity factors in chemical gelation pbpb

35. Connection Between Gels and Glasses