Gelation Routes in Colloidal Systems Emanuela Zaccarelli Dipartimento di Fisica & SOFT Complex...

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)