titolo

1
titolo
Amsterdam, November 2005, AMOLF
Cluster Phases, Gels and Yukawa Glasses in
charged colloid-polymer mixtures.
Francesco Sciortino
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Outline
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
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HS
Hard Spheres
Potential
(No temperature, only density)
V(r)
r
s

• Hard spheres present a a fluidsolid phase
  separation due to entropic effects
• Experimentally, at h0.58, the system freezes
  forming disordered aggregates.

MCT transition ?51.6-54

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)

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Explanation of the cage and analysis of
correlation function
.The Cage Effect (in HS).
Rattling in the cage
F(t)
Cage changes
log(t)
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Design Potenziale
Colloids Possibility to control
the Interparticle interactions
Hard Sphere
Chemistry (surface)
r
s
Asakura- Oosawa
Physic Processes (solvent modulation,
polydispersity, Depletions)
s
Yukawa
r
-




-
-
r
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Depletion Interactions
Depletion Interactions A (C. Likos) Cartoon
V(r
)
s
D
r
Dltlts
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Adding attraction (phase diagram)
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)
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Arrest phenomena in short-range potentials
Competition between excluded volume caging
and bond caging
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T. Eckert and E. Bartsch, Phys. Rev. Lett. 89
125701-1 (2002)PRL (phi effect)
T. Eckert and E. Bartsch, Phys. Rev. Lett. 89
125701-1 (2002)
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Square Well 3 width
Joining thermodynamics and dynamics information
Iso- diffusivity lines
Percolation Line
Repulsive Glass
A3
Spinodal (and Baxter
Miller-Frenkel)
Attractive Glass
LiquidGas Coexistence
SW 3
Spinodal AHS (MillerFrenkel)
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Gelation as a result of phase separation
(interrupted by the glass transition)
(generic for spherical potentials composed by
repulsive core attraction)
T
T
f
f
(Foffi et al PRL 2005)
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Nat Nat
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The quest
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 Lifetime
LowTemperature
Condensation
The quest
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Surface Tension
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)?
The quest
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Cluster Ground State Energy Only Attraction
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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)
• (inspired by Groenewold and Kegel work)
• Limited Valency E. Zaccarelli et al.
• Model for reversible colloidal gelation
• Phys. Rev. Lett. 94, 218301, 2005

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Cluster Ground State Attraction and Repulsion
(Yukawa)
Warning Use of Effective Potential
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Cluster Ground State Attraction and Repulsion
(Yukawa)
Vanishing of g !
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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
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Typical Shapes in the ground state
A8 x 0.5 s
A0.05 x2 s
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Size dependence of the cluster shape
Linear shape is an attractor
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From isolated to interacting clusters
Role of T and f 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 ?
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How do cluster interact
How do spherical clusters interact ?
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Yukawa Phase Diagram
bcc
bcc
fcc
ps3/6 n
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Description of the flow in the Yukawa model
N1
ps3/6 n
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N2
ps3/6 n
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N4
ps3/6 n
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N8
ps3/6 n
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N16
ps3/6 n
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N32
ps3/6 n
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N64
ps3/6 n
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Yukawa Phase Diagram
ps3/6 n
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Figure gel yukawa Tc0.23 n100
lowering T
Increasing packing fraction
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MD simulation
T0.15
T0.10
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• 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

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Interacting cluster linear case
Interacting Clusters - Linear case The Bernal
Spiral
Campbell, Anderson, van Dujneveldt, Bartlett
PRL June (2005)
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Pictures of the clusters at f0.08
T0.15
Aggshape ?c0.08
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T0.07
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Pictures of the aggregation
T0.15
at f0.125
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A gel !
Cluster shape ?c0.125
T0.07
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Cluster size distribution
? 2.2
(random percolation)
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Fractal Dimension
T0.1
size
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Bond Correlation funtions
stretched exponential ?0.7
(a.u.)
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Density fluctuations
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bartlett
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Shurtemberger
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Conclusions

• Several morphologies can be generated by the
  competition of short-range attraction (fixing the
  T-scale) 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.

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Collaborators

• Stefano Mossa (ESRF)
• Emanuela Zaccarelli (Roma)
• Piero Tartaglia (Roma)

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Yukawa
Upper Limit Optimal Size
Groenewold and Kegel
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No density dependence in prepeak
No strong density dependence in peak position
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Mean square displacement
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Nat Mat
F. Sciortino, Nat. Mat. 1, 145 (2002).
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Science Pham et al Fig 1
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Diffusion Coefficient
? 2.1-2.3
power law fits D (T-Tc ) ?
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foffi
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Figure 1 di Natmat
Hard Spheres Potential
Mean squared displacement
repulsive
attractive
Hard Sphere (repulsive) glass
s
(0.1 s)2
Square-Well short range attractive Potential
D2
Log(t)
Attractive Glass
s D
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Bartlet data
increasing colloid density
Campbell, Anderson, van Dujneveldt, Bartlett PRL
(June 2005)
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Phase Diagram for Square Well (3)
Iso-diffusivity lines
Spinodal AHS (MillerFrenkel)
Repulsive Glass
Percolation Line
Percolation Line
A3
Attractive Glass
Spinodal
LiquidGas