Dynamic arrest in colloidal systems:

from glasses to gels

Francesco Sciortino

Email: francesco.sciortino@phys.uniroma1.it

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 theInterparticle interactions

Chemistry (surface)

Physic Processes (solvent modulation, polydispersity,Depletions)

r

r

r

Hard Sphere

Asakura-Oosawa

Yukawa

+ ++

+

- -

-

In this talk !

The simplest colloids: hard spheres: Entropy at work

Single control parameter: packing fraction

0.49 0.54 0.58glasscrystal(FCC)

fluid+crystal

Pusey &Van MegenNature 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)

(t) HS (slow) dynamics

.Two time scales: The Cage Effect

(in HS).

Rattling in thecage

Cagechanges

log(t)

(t) Non ergodicity parameter fq

Order parameterof the transition

Mean square displacement (in the glass)

log(t)

(0.1 )2

MSD

Localizzationlength

Equazioni MCT !

van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993)

(t) HS (slow) dynamics

MCT --- Comparison “simulation” and “theory” for Binary HS

Foffi et al Phys. Rev. E 69, 011505, 2004

A=1B=0.6

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:

V(r )

r

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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 ?

lowering T

Log(t)

Mean squared displacement

repulsiveattractive

(0.1 )2

A model with two different localization lengths

How does the system change from one confinement to the other ?

MCT predictions for short range attractive square-well

hard-sphere glass

(repulsive)

Short-range attractive glass

fluid

Type B

A3

Fluid-Glass on cooling and heating !!

Controlled by

Fabbian et al PRE R1347 (1999)Bergenholtz and Fuchs, PRE 59 5708 (1999)

MCT Predictions:

Wavevector dependence of the non ergodicity parameter (plateau) along

the glass line

Fabbian et al PRE R1347 (1999)Bergenholtz and Fuchs, PRE 59 5708 (1999)

Comparing simulation and theory in the A4-region

Tem

pera

ture

Glass samplesFluid samples

MCT fluid-glass

line

Temperature

Colloidal-Polymer Mixture with Re-entrant Glass Transition in a Depletion Interactions

T. Eckert and E. Bartsch

Phys.Rev. Lett. 89 125701 (2002)

Arrest phenomena in short-range potentials

Competition betweenexcluded volume caging andbond caging

foffi

Adding “gels” in the picture:Joining thermodynamics and dynamics information

What are the possible scenarios ?

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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!)

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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….model1) Long Living reversible bonds

2)No Phase Separation(No Crystallization)

Are 1 and 2 mutually exclusive ?LowTemperatur

e

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 stateHow 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”

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T=0.15 T=0.10

Shurtemberger

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Proteins as colloids…

Scenario 2): equilibrium route to gelationwith 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. 2005 127, p. 15968

Phase- Diagram -- valence depencence

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-Stockmayercluster size distributionsobserved

arrest line

A snapshot of <M>=2.025

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N3=330

N2=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

Water

Summary: routes to gels

arrested phase separation: non-equilibrium route

Equilibrium routes to gelation:with long-range repulsion / with patches

Zaccarelli, JPCM 19, 323101 (2007)

In collaboration with……

Piero TartagliaEmanuela Zaccarelli

Ivan Saika-Voivod (now Canada)Emanuela BianchiJulio 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 ?

Yukawa Phase Diagram

bcc

fcc

bcc

3/6 n

N=1

3/6 n

N=2

3/6 n

N=43/6 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