Dynamic arrest in colloidal systems: from glasses to gels Francesco Sciortino Email:...
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Transcript of Dynamic arrest in colloidal systems: from glasses to gels Francesco Sciortino Email:...
Dynamic arrest in colloidal systems:
from glasses to gels
Francesco Sciortino
Email: [email protected]
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