1. Cluster Phases, Gels and Yukawa Glasses in charged colloid-polymer mixtures.
Francesco Sciortino
titolo

2. 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
Outline

3. Hard Spheres Potential (No temperature, only density) V(r) r s
Hard spheres present a a fluid–solid phase separation due to entropic effects
Experimentally, at h=0.58, the system freezes forming disordered aggregates.
MCT transition
=51.6%
W. van Megen and P.N. Pusey Phys. Rev. A 43, 5429 (1991)
U. Bengtzelius et al. J. Phys. C 17, (1984)
W. van Megen and S.M. Underwood Phys. Rev. Lett. 70, 2766 (1993) HS

4. Explanation of the cage and analysis of correlation function
.The Cage Effect (in HS).
Rattling
in the
cage
F(t)
Cage
changes
log(t)
Explanation of the cage and analysis of correlation function

5. 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
Design Potenziale

6. Depletion Interactions
A (C. Likos) Cartoon
V(r ) s D r
D<<s
Depletion Interactions

7. 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)
Adding attraction (phase diagram)

8. Nat Mat 2

9. Phase Diagram for Square Well (3%)
Iso-
diffusivity
lines
Percolation
Line
Repulsive
Glass A3
Spinodal (and Baxter)
Attractive
Glass
Liquid+Gas Coexistence
Spinodal AHS
(Miller&Frenkel)
Square Well 3% width

10. Gelation as a result of phase separation (interrupted by the glass transition)

11. Nat Nat

12. 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
The quest

13. The quest 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)?
Surface Tension
The quest

14. Cluster Ground State Energy : Only Attraction

15. 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)
Limited Valency (see E. Zaccarelli et al
PRL xxx

16. Cluster Ground State: Attraction and Repulsion (Yukawa)

17. Cluster Ground State: Attraction and Repulsion (Yukawa)
Vanishing of the
“surface tension” !

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

19. Typical Shapes in the ground state
x =0.5 s
A=0.05
x=2 s

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

21. 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 ?

22. How do cluster interact
How do “spherical” clusters interact ?
How do cluster interact

23. Yukawa Phase Diagram

24. Description of the flow in the Yukawa model

25. N=2

26. N=4

27. N=8

28. N=16

29. N=32

30. N=64

31. Yukawa Phase Diagram

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

33. 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

34. Interacting cluster linear case
Interacting Clusters - Linear case
The Bernal Spiral
Campbell, Anderson,
van Dujneveldt,
Bartlett PRL June (2005)
Interacting cluster linear case

35. Pictures of the clusters at f=0.08
Aggshape c=0.08

36. T=0.07

37. Pictures of the aggregation
at f=0.125
T=0.12

38. Cluster shape c=0.125
T=0.07
A gel !

39. Cluster size distribution
n ~ s s 
= 2.2
(random
percolation)

40. Fractal Dimension
T=0.1
size

41. Bond Correlation funtions
stretched
exponential
~0.7
(a.u.)

42. Density fluctuations

45. bartlett

46. Shurtemberger

47. 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.

48. Upper Limit
Optimal Size
Groenewold
and Kegel
Yukawa

49. No density dependence in prepeak
No strong density dependence in peak position
No density dependence in prepeak

50. Mean square displacement

52. F. Sciortino, Nat. Mat. 1, 145 (2002).
Nat Mat

53. Barsh PRL (phi effect)

54. Science Pham et al Fig 1

55. Diffusion Coefficient
 ~
power law fits
D~ (T-Tc ) 

56. foffi

57. 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
Figure 1 di Natmat

58. increasing colloid density
Bartlet data
increasing colloid density
Campbell, Anderson, van Dujneveldt, Bartlett PRL (June 2005)

59. Phase Diagram for Square Well (3%)
Iso-diffusivity
lines
Spinodal AHS
(Miller&Frenkel)
Percolation
Line
Repulsive
Glass
Percolation
Line A3
Attractive
Glass
Spinodal
Liquid+Gas

60. T=0.15
T=0.10
MD simulation