Gelation Routes in
Colloidal Systems
Emanuela Zaccarelli
Dipartimento di Fisica &
SOFT Complex Dynamics in Structured Systems
Università La Sapienza, Roma Italy
Bangalore,
30/06/2004
Outline of the Talk
•
Simple Model of attractive colloids
to describe asymmetric colloid-polymer mixtures
Introduce “Gelation problem”
•
Necessity of model for “reversible
gelation”
•
Two different approaches:
• Take into account Charge Effects
• Introduce a geometrical constraint on
Bond Formation
Simple model of Attractive Colloids
(eg Square Well potential)
at high densities….
Phase Diagram
MCT predictions
Dawson et al. PRE 2001
confirmed by experiments
Mallamace et al. PRL (2000)
Pham et al. Science (2002)
Eckert and Bartsch PRL (2002)
and simulations
Puertas et al PRL (2002)
F. Sciortino, Nat. Mat. 1, 145 (2002).
Zaccarelli et al PRE (2002)
… simulations at low densities…
A phase separation occurs
Gels can be only obtained via spinodal
decomposition
EZ, F.Sciortino, S. Buldyrev and P. Tartaglia condmat/0310765
Necessity of new models
for thermo-reversible GELS
incorporating:
•
No phase Separation
•
Long-Lived Bonds
1. Additional charge
2. Maximum Number of Bonds
1. Competition between short-range
attraction and long-range repulsion
2n-n potential (n=100)
Yukawa potential
(screened electrostatic interactions)
Ground State Clusters
Energy per particle
Ground State Clusters
gyration radius
Ground State Clusters
Structures for A=0.05, =2.0
“Structural Phase Diagram” at T=0
S. Mossa, F. Sciortino, P. Tartaglia, EZ, condmat/0406263.
Effect of Cluster-Cluster Interactions
Renormalize Yukawa form
Flow in the phase diagram
N=1
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=1
N=2
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=1
N=2
N=4
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=1
N=2
N=4
N=8
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=1
N=2
N=4
N=8
N=16
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=1
N=2
N=4
N=8
N=16
N=32
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=1
N=2
N=4
N=8
N=16
N=32
N=64
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Snapshots from simulations
Cluster glass transition
Static structure Factor
Dynamical density correlators (q~2.7)
Main Results
Evidence of an equilibrium cluster phase
experimentally observed in weakly charged
colloid/polymer mixtures
Segre et al. PRL (2001), Sedgwick et al. (to be
published)
and protein solutions Stradner&Schurtenberger,
Chen et al. (to be published)
Gel interpreted in terms of
glass transition of clusters
2. Maximum Number of Bonds NMAX
per particle
• Model for particles with fixed number of
sticky points
(eg. Manoharan, Elsesser and Pine, Science 2003)
• Simple modification of square well potential,
weakening phase separation,
enhancing more ramified structure
formation
NMAX-modified Phase Diagram
Diffusivity along special isochores
Bond Lifetime (NMAX=3, =0.20)
Energy per Particle
Viscosity
(preliminary results)
Static structure factor
NMAX=3
reminder: at the Glass Transition
(BMSW =0.58, T=2.0)
… while for the NMAX model
(NMAX=3, =0.20, T=0.1)
… looking in more
details…
… gel transition
Conclusions
Moreover,a model with
We have introduced
ideal gel features:
the model appears to be a
• increase
of relaxation
byLiquid,
orders
GOOD candidate
of atimes
strong
ofi.e.
magnitude
highly degenerate ground state
• density autocorrelation
and functions with
non-glassy
behaviour.
absence(but
of apercolative)
(finite) Kauzmann
temperature
Many Thanks to my Collaborators
Francesco Sciortino and Piero Tartaglia
Stefano Mossa ESRF Grenoble
Sergey Buldyrev Boston
Ivan Saika-Voivod, Emilia LaNave,
Angel Moreno
Roma
Configurational Entropy
(preliminary results)