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Gelation Routes in Colloidal Systems Emanuela Zaccarelli Dipartimento di Fisica & SOFT Complex Dynamics in Structured Systems Università La Sapienza, Roma Italy Bangalore, 30/06/2004

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Outline of the Talk Simple Model of attractive colloids to describe asymmetric colloid-polymer mixtures Introduce “Gelation problem” Necessity of model for “reversible gelation” Two different approaches: Take into account Charge Effects Introduce a geometrical constraint on Bond Formation

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at high densities…. MCT predictions Dawson et al. PRE 2001 confirmed by experiments Mallamace et al. PRL (2000) Pham et al. Science (2002) Eckert and Bartsch PRL (2002) and simulations Puertas et al PRL (2002) Zaccarelli et al PRE (2002) (eg Square Well potential) Phase Diagram Simple model of Attractive Colloids F. Sciortino, Nat. Mat. 1, 145 (2002).

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… simulations at low densities… A phase separation occurs Gels can be only obtained via spinodal decomposition EZ, F.Sciortino, S. Buldyrev and P. Tartaglia condmat/0310765

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Necessity of new models for thermo-reversible GELS incorporating: No phase Separation Long-Lived Bonds 1.Additional charge 2. Maximum Number of Bonds

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1. Competition between short-range attraction and long-range repulsion 2n-n potential (n=100) Yukawa potential (screened electrostatic interactions)

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Ground State Clusters Energy per particle

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Ground State Clusters gyration radius

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Ground State Clusters Structures for A=0.05, =2.0

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Ground State Clusters Structures for N=38

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“Structural Phase Diagram” at T=0 S. Mossa, F. Sciortino, P. Tartaglia, EZ, condmat/0406263.

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Effect of Cluster-Cluster Interactions Renormalize Yukawa form

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Flow in the phase diagram

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F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press. N=1 Flow in the phase diagram

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N=1 N=2 F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press. Flow in the phase diagram

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N=4 N=1 N=2 F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press. Flow in the phase diagram

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N=4 N=1 N=2 N=8 F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press. Flow in the phase diagram

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N=16 N=4 N=1 N=2 N=8 F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press. Flow in the phase diagram

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N=16 N=4 N=1 N=2 N=8 N=32 F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press. Flow in the phase diagram

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N=16 N=4 N=1 N=2 N=8 N=32 N=64 F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press. Flow in the phase diagram

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Snapshots from simulations

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Cluster glass transition

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Static structure Factor

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Dynamical density correlators (q ~2.7)

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Main Results Evidence of an equilibrium cluster phase experimentally observed in weakly charged colloid/polymer mixtures Segre et al. PRL (2001), Sedgwick et al. (to be published) and protein solutions Stradner&Schurtenberger, Chen et al. (to be published) Gel interpreted in terms of glass transition of clusters

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2. Maximum Number of Bonds N MAX per particle Model for particles with fixed number of sticky points (eg. Manoharan, Elsesser and Pine, Science 2003 ) Simple modification of square well potential, weakening phase separation, enhancing more ramified structure formation

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N MAX -modified Phase Diagram

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Diffusivity along special isochores

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Bond Lifetime ( N MAX =3, =0.20)

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Energy per Particle

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Viscosity (preliminary results)

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N MAX =3 Static structure factor

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reminder: at the Glass Transition (BMSW =0.58, T=2.0)

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… while for the N MAX model (N MAX =3, =0.20, T=0.1)

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… looking in more details… … gel transition

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Conclusions We have introduced a model with ideal gel features: increase of relaxation times by orders of magnitude density autocorrelation functions with non-glassy (but percolative) behaviour. Moreover, the model appears to be a GOOD candidate of a strong Liquid, i.e. highly degenerate ground state and absence of a (finite) Kauzmann temperature

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Many Thanks to my Collaborators Francesco Sciortino and Piero Tartaglia Stefano Mossa ESRF Grenoble Sergey Buldyrev Boston Ivan Saika-Voivod, Emilia LaNave, Angel Moreno Roma

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Configurational Entropy (preliminary results)

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