Cluster Phases, Gels and Yukawa Glasses in charged colloid-polymer mixtures. Francesco Sciortino titolo

Motivations Dynamic Arrest in Colloidal Systems: Glasses and Gels Excluded Volume Short Range Attraction (SRA) SRA+ Longer Range Repulsion Investigate the competing effects of short range attraction and longer-range repulsion in colloidal systems Dynamics close to arrested states of matter: Cluster Phases, Glasses and/or Gels Outline

Hard Spheres Potential (No temperature, only density) V(r) r s Hard spheres present a a fluid–solid phase separation due to entropic effects Experimentally, at h=0.58, the system freezes forming disordered aggregates. MCT transition =51.6% W. van Megen and P.N. Pusey Phys. Rev. A 43, 5429 (1991) U. Bengtzelius et al. J. Phys. C 17, 5915 (1984) W. van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993) HS

Explanation of the cage and analysis of correlation function .The Cage Effect (in HS). Rattling in the cage F(t) Cage changes log(t) Explanation of the cage and analysis of correlation function

Colloids: Possibility to control the Interparticle interactions Hard Sphere Chemistry (surface) r s Asakura- Oosawa Physic Processes (solvent modulation, polydispersity, Depletions) s Yukawa r - + + + + - - r Design Potenziale

Depletion Interactions A (C. Likos) Cartoon V(r ) s D r D<<s Depletion Interactions

Adding attraction (phase diagram) The presence of attraction modifies the behaviour of the system: New phases and their coexistence emerge. With narrow interactions the appeareance of metastable liquid-liquid critical point is typical for colloids. V.J. Anderson and H.N.W. Lekkerkerker Nature 416, 811 (2002) Adding attraction (phase diagram)

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

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

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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 ? Long Bond Lifetime LowTemperature Condensation The quest The quest

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

Cluster Ground State Energy : Only Attraction

Routes to Arrest at low packing fractions (in the absence of a “liquid-gas” phase separation) Competition between short range attraction and long-range repulsion (this talk) Limited Valency (see E. Zaccarelli et al PRL xxx

Cluster Ground State: Attraction and Repulsion (Yukawa)

Cluster Ground State: Attraction and Repulsion (Yukawa) Vanishing of the “surface tension” !

Competition Between Short Range Attraction and Longer Range Repulsion: Role in the clustering --dominant in small clusters Longer Range Repulsion Importance of the short-range attraction: Only nn interactions

Typical Shapes in the ground state x =0.5 s A=0.05 x=2 s

Size dependence of the cluster shape “Linear” Growth is an “attractor”

From isolated to interacting clusters Role of T and f: On cooling (or on increasing attraction), monomers tend to cluster…. In the region of the phase diagram where the attractive potential would generate a phase separation….repulsion slows down (or stop) aggregation. The range of the attractive interactions plays a role. How do clusters interact ?

How do cluster interact How do “spherical” clusters interact ? How do cluster interact

Yukawa Phase Diagram

Description of the flow in the Yukawa model

N=2

N=4

N=8

N=16

N=32

N=64

Yukawa Phase Diagram

Figure gel yukawa Tc=0.23 n=100 lowering T Increasing packing fraction Figure gel yukawa Tc=0.23 n=100

Brief Intermediate Summary Equilibrium Cluster-phases result from the competition between aggregation and repulsion. Arrest at low packing fraction generated by a glass transition of the clusters. Aggregation progressively cool the system down till the repulsive cages become dominant

Interacting cluster linear case Interacting Clusters - Linear case The Bernal Spiral Campbell, Anderson, van Dujneveldt, Bartlett PRL June (2005) Interacting cluster linear case

Pictures of the clusters at f=0.08 Aggshape c=0.08

T=0.07

Pictures of the aggregation at f=0.125 T=0.12

Cluster shape c=0.125 T=0.07 A gel !

Cluster size distribution n ~ s s  = 2.2 (random percolation)

Fractal Dimension T=0.1 size

Bond Correlation funtions stretched exponential ~0.7 (a.u.)

Density fluctuations

bartlett

Shurtemberger

Conclusions…… Several morphologies can be generated by the competition of short-range attraction (fixing the T-scale) and the strength and length of the interaction. A new route to gelation. Continuous change from a Wigner-like glass to a gel While equilibrium would probably suggest a first order transition to a lamellar phase, arrested metastable states appear to be kinetically favored Possibility of exporting ideas developed in colloidal systems to protein systems (Schurtenberger, Chen) and, more in general to biological systems in which often one dimensional growth followed by gelation is observed.

Upper Limit Optimal Size Groenewold and Kegel Yukawa

No density dependence in prepeak No strong density dependence in peak position No density dependence in prepeak

Mean square displacement

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

Barsh PRL (phi effect)

Science Pham et al Fig 1

Diffusion Coefficient  ~ 2.1-2.3 power law fits D~ (T-Tc ) 

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Hard Spheres Potential Mean squared displacement repulsive attractive Hard Sphere (repulsive) glass s (0.1 s)2 Square-Well short range attractive Potential D2 Log(t) Attractive Glass s + D Figure 1 di Natmat

increasing colloid density Bartlet data increasing colloid density Campbell, Anderson, van Dujneveldt, Bartlett PRL (June 2005)

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

T=0.15 T=0.10 MD simulation