Dynamic arrest in colloidal systems: from glasses to gels Francesco Sciortino Titolo !

collaboratori Outline Routes to gelation in colloidal systems.  Hard-Sphere Glasses  Attractive Glasses Phase-separation driven gels (D. Weitz)  Competing Interactions arrested states  Equilibrium Gels

Colloids….. Greek for Glue…. Nano and micromiter sized particles dispersed in a solvent (proteins….. ) From a physicist point of view… Effective interactions ….. Super-atoms with designed interactions…. Realization of theoretical models (hard-spheres). Test for integral equations approaches. Size comparable to light wavelength… (confocal microscopy)

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

The simplest colloids: hard spheres: Entropy at work Single control parameter: packing fraction  glasscrystal (FCC) fluid+crystal Pusey & Van Megen Nature 1986 V(r)

Signatures of the slowing down of the dynamics (with packing…. or with T) - The log-scale

van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993) HS e MCT  (t) HS (slow) dynamics

. Two time scales: The Cage Effect (in HS). Explanation of the cage and analysis of correlation function Rattling in the cage Cage changes log(t)  (t) Non ergodicity parameter f q Order parameter of the transition

Mean square displacement (in the glass) The MSD in HS log(t) (0.1  ) 2 MSD Localizzation length

Equazioni MCT ! Equazioni base della MCT

van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993) HS e MCT  (t) HS (slow) dynamics

MCT --- Comparison “simulation” and “theory” for Binary HS Foffi et al Phys. Rev. E 69, , 2004  A =1  B =0.6 Giuseppe e Thomas 1/ l

The effect of short-range attraction on the Phase Diagram hard spheres large range short range Anderson and Lekkerkerker, Nature 2001

Depletion Interactions Depletion Interactions: V(r) r   

What if …. Hard Spheres Potential Square-Well short range attractive Potential   Can the localization length be controlled in a different way ? What if we add a short-range attraction ? Attractive Glass   lowering T

Log(t) Mean squared displacement repulsive attractive (0.1  ) 2  Figure 1 di Natmat A model with two different localization lengths How does the system change from one confinement to the other ?

The MCT predictions for short-range attractive square well MCT predictions for short range attractive square-well hard-sphere glass (repulsive) Short-range attractive glass fluid Type B A3A3  Fluid-Glass on cooling and heating !! Controlled by  Fabbian et al PRE R1347 (1999) Bergenholtz and Fuchs, PRE (1999)

Non ergodicity parameters for the two glasses MCT Predictions: Wavevector dependence of the non ergodicity parameter (plateau) along the glass line Fabbian et al PRE R1347 (1999) Bergenholtz and Fuchs, PRE (1999)

Funzioni di correlazione Comparing simulation and theory in the A4-region

Science Pham et al Fig 1 Temperature Glass samples Fluid samples MCT fluid- glass line

Barsh PRL (phi effect) Temperature Colloidal-Polymer Mixture with Re-entrant Glass Transition in a Depletion Interactions T. Eckert and E. Bartsch Phys.Rev. Lett (2002)

Arrest phenomena in short-range potentials Competition between excluded volume caging and bond caging

foffi Adding “gels” in the picture: Joining thermodynamics and dynamics information What are the possible scenarios ?

Nature, in press For HS+attraction, arrest at low  (gelation) is the result of a phase separation process interrupted by the glass transition CONFOCAL IMAGES (THE REAL STUFF!)

Gels resulting from arrested phase separation (interrupted by the glass transition) arrested dense phase quench Scenario 1): Non-equilibrium route to gelation

How to go to low T at low  (in metastable equilibrium) reducing “valence” How to suppress phase separation ? Competing interactions

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

How to stay at low T without phase-separating ? Reasons for separation: (Frank, Hill, Coniglio) Physical Clusters at low T if the infinite cluster (the liquid state !) is the lowest (free)energy state How to make the surface as stable as the bulk (or more)?

Attraction and Repulsion (Yukawa)

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

Cluster Ground State: Attraction and Repulsion Vanishing of  !

A=8  =0.5  A=0.05  =2  Typical shapes in the ground state

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

bartlett

ground state clusters: energy per particle the attractive case

T=0.15T=0.10 MD simulation

Shurtemberger Proteins as colloids…

Scenario 2): equilibrium route to gelation with long-range repulsion equilibrium gelation

How to go to low T at low  (in metastable equilibrium) reducing “valence” How to suppress phase separation ? Competing interactions

DNA functionalized particles: modulating the interaction

patchy colloids - colloidal molecules Hard-Core (gray spheres); Short-range Square-Well (gold patchy sites) Self-Organization of Bidisperse Colloids in Water Droplets Cho et al J. Am. Chem. Soc , p

Phase- Diagram -- valence depencence Wertheim Empty liquids ! Cooling the liquids without phase separating! Bianchi et al, PRL 2006

Phase Diagram - Theory and Simulations

Phase diagram of a small valence system (exact description) Flory-Stockmayer cluster size distributions observed arrest line

A snapshot of =2.025 N 3 =330 N 2 =5670 T=0.05,  =0.01 An “empty liquid” configuration

Scenario 3): equilibrium route to gelation with patches

One last connection… atomic and molecular networks…. Physical Gels Network forming liquids Silica Water

Summary: routes to gels arrested phase separation: non-equilibrium route Equilibrium routes to gelation: with long-range repulsion / with patches Zaccarelli, JPCM 19, (2007)

In collaboration with…… Piero Tartaglia Emanuela Zaccarelli Ivan Saika-Voivod (now Canada) Emanuela Bianchi Julio Largo (now Spain) Angel Moreno (now Spain) Stefano Mossa (now France ESRF) Sergey Buldyrev (New York)

Conclusions…. (open questions) Glass-glass transitions Empty liquids Competing interactions Network-forming liquids --- equilibrium gels (no Kauzmann) Self-assembly and network formation (loops) Surface geometry (Janus particles)

Role of T and  : On cooling (or on increasing attraction), monomers tend to cluster…. From isolated to interacting clusters 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 ? How do cluster interact

Yukawa Phase Diagram bcc fcc bcc  3 /6 n

N=1 Description of the flow in the Yukawa model  3 /6 n

N=2  3 /6 n

N=4  3 /6 n

N=8  3 /6 n

N=16  3 /6 n

N=32  3 /6 n

N=64  3 /6 n

Yukawa Phase Diagram  3 /6 n

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