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Dynamic arrest in colloidal systems:
from glasses to gels
Francesco Sciortino
Email: [email protected]
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Outline
Routes to gelation in colloidal systems.
Hard-Sphere Glasses Attractive Glasses
Phase-separation driven gels (D. Weitz)Competing Interactions arrested states
Equilibrium Gels
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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)
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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 !
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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)
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Signatures of the slowing down of the dynamics (with packing…. or with T) - The log-scale
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van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993)
(t) HS (slow) dynamics
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.Two time scales: The Cage Effect
(in HS).
Rattling in thecage
Cagechanges
log(t)
(t) Non ergodicity parameter fq
Order parameterof the transition
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Mean square displacement (in the glass)
log(t)
(0.1 )2
MSD
Localizzationlength
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Equazioni MCT !
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van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993)
(t) HS (slow) dynamics
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MCT --- Comparison “simulation” and “theory” for Binary HS
Foffi et al Phys. Rev. E 69, 011505, 2004
A=1B=0.6
1/l
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The effect of short-range attraction on the Phase Diagram
hard spheres large range short range
Anderson and Lekkerkerker, Nature 2001
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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
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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 ?
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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)
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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)
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Comparing simulation and theory in the A4-region
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Tem
pera
ture
Glass samplesFluid samples
MCT fluid-glass
line
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Temperature
Colloidal-Polymer Mixture with Re-entrant Glass Transition in a Depletion Interactions
T. Eckert and E. Bartsch
Phys.Rev. Lett. 89 125701 (2002)
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Arrest phenomena in short-range potentials
Competition betweenexcluded volume caging andbond caging
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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
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How to go to low T at low (in metastable equilibrium)
reducing “valence”
How to suppress phase separation ?
Competing interactions
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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
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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)?
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Attraction and Repulsion (Yukawa)
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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
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Cluster Ground State: Attraction and Repulsion
Vanishing of !
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A=8 =0.5
A=0.05=2
Typical shapes in the ground state
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Size dependence of the cluster shape
“Linear” shape is an “attractor”
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T=0.15 T=0.10
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Shurtemberger
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Proteins as colloids…
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Scenario 2): equilibrium route to gelationwith long-range repulsion
equilibrium gelation
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How to go to low T at low (in metastable equilibrium)
reducing “valence”
How to suppress phase separation ?
Competing interactions
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DNA functionalized particles: modulating the interaction
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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
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Phase- Diagram -- valence depencence
Empty liquids !Cooling the liquids without phase separating!
Bianchi et al, PRL 2006
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Phase Diagram - Theory and Simulations
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Phase diagram of a small valence system (exact description)
Flory-Stockmayercluster size distributionsobserved
arrest line
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A snapshot of <M>=2.025
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N3=330
N2=5670
T=0.05, =0.01
An “empty liquid” configuration
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Scenario 3): equilibrium route to gelation
with patches
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One last connection… atomic and molecular networks….
Physical Gels <===> Network forming liquids
Silica
Water
Water
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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)
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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)
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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)
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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 ?
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How do “spherical” clusters interact ?
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Yukawa Phase Diagram
bcc
fcc
bcc
3/6 n
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N=1
3/6 n
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N=2
3/6 n
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N=43/6 n
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N=8
3/6 n
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N=16
3/6 n
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N=32
3/6 n
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N=64
3/6 n
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Yukawa Phase Diagram
3/6 n
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lowering T
Increasing packing fraction