Dynamical Arrest of Soft Matter and Colloids Lugano April 6-9 2006

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					Dynamical Arrest of Soft Matter and Colloids
          Lugano April 6-9 2006

Tutorial: Recent developments in
understanding gelation in colloidal
          Francesco Sciortino
               What is a gel ?                                           QuickTime™ and a
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coherent mass consisting of a liquid in which
particles are either dispersed or arranged in a
fine network throughout the mass. A gel may
be notably elastic and jellylike (as gelatin or
fruit jelly), or quite solid and rigid (as silica

                                                             QuickTime™ an d a
                                                    TIFF (Uncompressed) decompressor
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                         Recent reviews
K.A. Dawson The glass paradigm for colloidal glasses, gels, and other arrested
states driven by attractive interactions, Coll. Int. Sci 7, 2002 218-227

Cipelletti, Luca; Ramos, Laurence, Slow dynamics in glassy soft matter
Journal of Physics: Condensed Matter, 17, R253-R285 (2005);
Slow dynamics in glasses,gels and foams,
Current Opinion in Colloid and Interface Science 7 (2002) 228-234.

V. Trappe, Colloidal gels -- low-density disordered solid-like states
lassy colloidal systems
Current Opinion in Colloid and Interface Science 8 (2004) 494.
F. Sciortino and P. Tartaglia Glassy colloidal systems
Advances in Physics 54, 2005 471-524

                          Future reviews
           Two main conditions

--- Low packing fraction of the dispersed

--- (visco) elastic properties (ability to sustain
stress): The need of a “spanning” network
(attraction between particles is
epoxy-resins   Chemical                                 rubber
               System with
               a fixed
               number of
               (with infinite
               particles        Richard A.L. Jones, Condened Matter. Oxford
                 Percolation theory!

  Bond percolation in a two-dimension square lattice

Cluster Size distribution (cluster shape)

Infinite Cluster (d.c. conductivity, elasticity)
  Flory-Stockmayer (mean field solution)
A Caley-Tree with connectivity z=4    Bond probability=p

                                     C1=z p

                                     C2= (z-1) p C1

                                     C3= (z-1) p C2
                                     CN= [(z-1) p]N-1 C1

                                      Critical Value !!!

                                     (z-1) pc=1
Predictions (close to pc) :
              Bethe: t=2.5, s=0.5, df=4
              3d (approx): t=2.18, s=0.45, df=2.53


                         (order parameter)

      Stauffer Phys. Rep. 1979
             Physical Gels
   Colloids (Lu’s Talk)
   Proteins (Cardineaux and Zaccarelli’s Talk)
   Dna-coated colloids (Largo’s Talk)
Reversible Bonding ---- Bond Lifetime ----

---- Persistence of the spanning network ----

---- Equilibrium Thermodynamics ----
      Routes to Physical Gelation
Gels resulting from irreversible processes
(kinetic pathways are important)
(phase separation)

“Ideal” gels. Gels in which dynamic arrest is
progressively approached (and the system is
(as close as possible) to thermodynamic
[ Experimental timescales < Bond lifetime < equilibration time
at geometric percolation].
       Phase diagram of spherical

* Hard-Core plus attraction
           Static Percolation -- Gelation ???


 Two (times 2 !) ways to go to low T (at low f)

-DLCA                      Suppress phase separation
-Glass Arrest
                           -l.r. repulsion
Diffusion Limited Cluster Aggregation
       (a T->0 phase separation)
  Particles (and clusters) performing brownian motion and
  sticking with probability one.
  Diffusion coefficient of the cluster proportional to M-g
  (DLVO potential without and with salt).
    Basic DLCA findings
“monodisperse” fractal objects (df= 1.9)
M~M1 (R/R1)df

The cluster average density decreases with Rdf-d

Vocc/V= f (R/R1)d-df

 R=R1 f 1/(df-d)

 Gels as space-filling of sticking clusters
Structure of DLCA gels
               DLCA and Spinodal Decomposition
                                                                      MC (Lattice Gas) e -bu
                                                                     Gimel-Nicolai   {    1 if not bonded
                                                                                          0 if bonded

                                  -bu= ln(1-pb)
    The dynamical rules defining DLCA are the T->0 limit of the
    lattice gas dynamics.

                                                                                      QuickTime™ and a
                                                                                  TIFF (LZW) decompressor
                                                                               are neede d to see this picture.

M. Carpineti and M. Giglio, Phys. Rev. Lett. 68 3327 (1992)
F. Sciortino and P. Tartaglia, Phys. Rev. Lett. 74 282 (1995)
P. Pouline, J. Bibette and D. A. Weitz, Eur. Phys. J. B 277 (1999)
C. Gimel, T. Nicolai, D. Durand, Phys. Rev. E 061405 (2002).
         Gels as arrested phase separation

F. Sciortino et al, Phys. Rev. E 47, 4615 (1993).
D. Sappelt and J. Jackle, Europhys. Lett. 37, 13(1997).
M. Solomon and P. Varadan, Phys. Rev. E. 63 (2001) 051402
E. Zaccarelli et al, Unifying concepts in Granular Matter and Gels, Elsevier 2004
S. Manley et al, Phys. Rev. Lett. 95 (2005) 238302
E. Witman amd Z-G Wang, J.Phys. Chem B 110 6312 2006
G. Foffi et al, J. Chem. Phys. 122, 224903-224915, 2005 Arrested
phase separation in a short-ranged attractive colloidal system: 
numerical study
 How to suppress phase separation ?
      Sticky patchy colloids !
Maximum Valency* --- Bond Selectivity

 * three-body interactions (Del Gado-Kob)
                          E. Bianchi, Poster
Even more.. With mixtures of two and three
             sticky spots….
Del-Gado Kob Gel
 Nmax=4 phase diagram - Isodiffusivity lines

E.Zaccarelli et al, Phys. Rev. Lett. 94, 218301, 2005 ; J. Chem. Phys. 124, 124908 (2006).
C. De Michele et al, J. Phys. Chem. B, jp056380y (2006).
Analogies with other network-forming potentials

SPC/E                           ST2 (Poole)

               BKS silica
     Short-Range Attraction and
   Long-Range Repulsion (Yukawa)

Clusters as microphase

                         Vanishing of the
                         “surface tension” !
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
 Gels in charged colloids
FS,PT,EZ J. Phys. Chem. B 109, 21942-21953, 2005
        Interesting question
           Manley et al, PRL, 93 108302 (2004).

What is the lowest f at which it is possible
to form a gel

In the absence of gravity
Thermal stresses (DLCA, Rc=100 mm)

On the earth
Gravitational stresses (DLCA, Rc=50 mm)
       Gel Dynamics

Density autocorrelation functions

 Chemical Gels….. What is known Martin Libro Kon

 Physical Gels…. Cipelletti - Others
      Density Fluctuations
                  (chemical gels)
Kurt Broderix et al, Phys. Rev. Lett. 79, 3688–3691 (1997),
Tagged particle properties: D finite at the transition and above

      Below percolation                               Above percolation
    I. Saika-Voivod et al, Phys. Rev. E 70, 041401, 2004
Non ergodicity factors in
   chemical gelation

Connection Between Gels and

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