Post on 31-Mar-2015
Gelation Routes in Colloidal Systems
Emanuela Zaccarelli
Dipartimento di Fisica & SOFT Complex Dynamics in Structured
SystemsUniversità 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
at high densities….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)Zaccarelli et al PRE
(2002)
(eg Square Well potential)
Phase Diagram
Simple model of Attractive Colloids
F. Sciortino, Nat. Mat. 1, 145 (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 ClustersEnergy per particle
Ground State Clustersgyration radius
Ground State ClustersStructures 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
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
N=1
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=4
N=1
N=2
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=4
N=1
N=2
N=8
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=16
N=4
N=1
N=2
N=8
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=16
N=4
N=1
N=2
N=8
N=32
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
N=16
N=4
N=1
N=2
N=8
N=32
N=64
F. Sciortino, S. Mossa, EZ, P. Tartaglia, condmat/0312161; PRL in press.
Flow in the phase diagram
Snapshots from simulations
Cluster glass transition
Static structure Factor
Dynamical density correlators (q~2.7)
Main ResultsEvidence of an equilibrium cluster phaseexperimentally 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)
NMAX=3Static structure factor
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
We have introduced a model with ideal gel features:
• increase of relaxation times by orders of magnitude
• density autocorrelation functions with non-glassy (but percolative) behaviour.
Moreover,
the model appears to be a GOOD candidate of a strong
Liquid,i.e. highly degenerate ground
stateand
absence of a (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)