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Dynamical Arrest of Soft Matter and Colloids Lugano April 6-9 2006 (MRTN-CT-2003-504712)

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. Francesco Sciortino. What is a gel ?.

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Dynamical Arrest of Soft Matter and Colloids Lugano April 6-9 2006 (MRTN-CT-2003-504712)

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

  2. What is a gel ? 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)

  3. Recent 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 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. V. Trappe, Colloidal gels -- low-density disordered solid-like states lassy colloidal systems Current Opinion in Colloid and Interface Science 8 (2004) 494. F. Sciortino and P. Tartaglia Glassy colloidal systems Advances in Physics 54, 2005 471-524 Future reviews

  4. Two main conditions --- 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)

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

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

  7. A Caley-Tree with connectivity z=4 Flory-Stockmayer (mean field solution) Bond probability=p C1=z p C2= (z-1) p C1 C3= (z-1) p C2 ……………… CN= [(z-1) p]N-1C1 Critical Value !!! (z-1) pc=1

  8. Predictions (close to pc) : Bethe: t=2.5, s=0.5, df=4 3d (approx): t=2.18, s=0.45, df=2.53 suscettibility magnetization (order parameter) Stauffer Phys. Rep. 1979

  9. Physical Gels 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 ----

  10. Routes to Physical Gelation 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].

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

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

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

  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-g (DLVO potential without and with salt).

  15. Basic DLCA findings “monodisperse” fractal objects (df= 1.9) M~M1 (R/R1)df The cluster average density decreases with Rdf-d Vocc/V= f (R/R1)d-df R=R1f 1/(df-d) Gels as space-filling of sticking clusters

  16. Structure of DLCA gels

  17. DLCA and Spinodal Decomposition MC (Lattice Gas) e -bu { 1 if not bonded Gimel-Nicolai 0 if bonded -bu= ln(1-pb) 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).

  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) 051402E. 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. Nmax=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 ST2 (Poole) SPC/E BKS silica (Saika-Voivod)

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

  26. 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

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

  28. proteins

  29. Interesting questionManley et al, PRL, 93 108302 (2004). What is the lowest f at which it is possible to form a gel In the absence of gravity Thermal stresses (DLCA, Rc=100 mm) On the earth Gravitational stresses (DLCA, Rc=50 mm)

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

  31. Cipelletti

  32. Krall

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

  34. Non ergodicity factors in chemical gelation pb

  35. Connection Between Gels and Glasses

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