Genova, September 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

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

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

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

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

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

Pham et al 2004

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)

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

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

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

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)?

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

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

lowering T Increasing packing fraction Figure gel yukawa

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

N MAX -modified Phase Diagram Phase Diagram

Bond Lifetime.. Several more decades..

Gel vs Glass - MSD T=0.1 Typical Glass Value

Gel vs Glass: Density Autocorrelation Functions fqfq

Fq gel vs glass

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

Stoke

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

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 ?

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

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

Viscosity and Diffusivity: Arrhenius

Stoke-Einstein Relation