Cluster Phases Gels and Yukawa Glasses in charged

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

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

Hard Spheres Potential (No temperature, only density) V(r) s r • 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% 1. W. van Megen and P. N. Pusey Phys. Rev. A 43, 5429 (1991) 2. U. Bengtzelius et al. J. Phys. C 17, 5915 (1984) 3. W. van Megen and S. M. Underwood Phys. Rev. Lett. 70, 2766 (1993)

The Cage Effect (in HS). . Rattling in the cage F(t) Cage changes log(t)

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

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

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)

Phase Diagram for Square Well (3%) Percolation Line Isodiffusivity Repulsive Glass lines A 3 Spinodal (and Baxter) Attractive Glass Liquid+Gas Coexistence

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 ? Long Bond Low. Temperature Lifetime Condensation

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)?

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 Short Range Attraction, --dominant in small clusters Longer Range Repulsion Importance of the short-range attraction: Only nn interactions

Typical Shapes in the ground state A=8 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 : 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 “spherical” clusters interact ?

Yukawa Phase Diagram

N=1

N=2

N=4

N=8

N=16

N=32

N=64

Yukawa Phase Diagram

lowering T Increasing packing fraction

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

Pictures of the clusters at f=0. 08 T=0. 15 T=0. 12 T=0. 10

T=0. 07

T=0. 15 Pictures of the aggregation at f=0. 125 T=0. 10 T=0. 12

T=0. 07 Cluster shape c=0. 125 A gel !

Cluster size distribution ns~ s = 2. 2 (random percolation)

Fractal Dimension T=0. 1 size

Bond Correlation funtions stretched exponential ~0. 7 (a. u. )

Density fluctuations

Conclusions…… Several morphologies can be generated by the competition of short-range attraction (fixing the Tscale) 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

No strong density dependence in peak position

Mean square displacement

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

Barsh PRL (phi effect)

Science Pham et al Fig 1

Diffusion Coefficient ~ 2. 1 -2. 3 power law fits D~ (T-Tc )

Hard Spheres Potential Mean squared displacement Hard Sphere (repulsive) glass s 2 (0. 1 s) Square-Well short range attractive D 2 Potential repulsive attractive Log(t) Attractive Glass s+D

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

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

T=0. 15 T=0. 10