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Genova, September 1 2004 Routes to Colloidal Gel Formation CCP2004 In collaboration with S. Bulderyev, E. La Nave, A. Moreno, S. Mossa, I. Saika-Voivod, P. Tartaglia, E. Zaccarelli titolo Thanks to the organizers and to Carlo Pierleone

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Outline Outline and Motivations Brief Review of Short-Range Attractive Colloidal Glass ( asymmetric colloid-polymer mixtures) How to model disordered arrested states at low packing fraction (gels) Routes: Interrupted phase separation (irreversible gels) Long Range Repulsive interactions (reversible) Geometrical constraints (reversible) Differences between gel and glasses

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Depletion Interactions Depletion Interactions: A (C. Likos) Cartoon V(r) r

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MCT IDEAL GLASS LINES (PY) - SQUARE WELL MODEL - CHANGING PRE-63-011401-2001 Role of the width A4A4 V(r) Vari delta The role of delta A3A3 Large Small

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F. Sciortino, Nat. Mat. 1, 145 (2002). Nat Mat

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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) Citazioni

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Pham et al 2004

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Square Well 3% width Phase Diagram for Square Well (3%) Repulsive Glass Attractive Glass Liquid+Gas Coexistence A3 Spinodal AHS (Miller&Frenkel) Iso- diffusivity lines Percolation Line Spinodal (and Baxter)

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Virial Scaling in the dynamics: Toward the Baxter Limit G. Foffi and C. De Michele,preprint

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Gelation as a result of phase separation (interrupted by the glass transition) T T

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The quest for the ideal (thermoreversible) gel….model 1) Long Living reversible bonds 2)No Phase Separation 3) No Crystallization Are 1 and 2 mutually exclusive ? The quest LowTemperature Condensation Long Bond Lifetime The quest

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Surface Tension How to stay at low T without condensation ? The quest Reasons for condensation (Frank, Hill, Coniglio) Physical Clusters at low T ifthe infinite cluster is the lowest (free)energy state How to make the surface as stable as the bulk (or more)?

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Short Range Attraction Long Range Repulsion Competition Between Short Range Attraction and Long Range Repulsion FS et al, PRL 2004

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Groenewold and Kegel Upper Limit Optimal Size How to make negative ? Yukawa

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lowering T Increasing packing fraction Figure gel yukawa

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Geometric Constraint: Maximum Valency SW if # of bonded particles <= N max HS if # of bonded particles > N max V(r) r Maximum Valency

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N MAX -modified Phase Diagram Phase Diagram

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Bond Lifetime.. Several more decades..

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Gel vs Glass - MSD T=0.1 Typical Glass Value

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Gel vs Glass: Density Autocorrelation Functions fqfq

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Fq gel vs glass

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Summary…. Designig Thermoreversible Gels: Models with small surface tension (charged colloids, sticky points) A simple model for thermoreversible gel Gels and Glasses: Differences in localization length Differences in experimental observables

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Stoke

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Energy per Particle Ground State Energy Known ! It is possible to equilibrate at low T !

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How to stay at low T without condensation ? The quest Reasons for condensation (Frank, Hill, Coniglio) Physical Clusters at low T ifthe infinite cluster is the lowest energy state How to make the surface more stable than the bulk ?

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Thermodynamics in the IS formalism Stillinger- Weber F(T)=-T S conf (, T) +f basin (,T) with f basin (e IS,T)= e IS +f vib (e IS,T) and S conf (T)=k B ln[ ( )] Basin depth and shape Number of explored basins Free energy

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It is possible to calculate exactly the basin free energy ! Basin Free energy

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Viscosity and Diffusivity: Arrhenius

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Stoke-Einstein Relation

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