Physical Gels and strong liquids

5th International Discussion Meeting on Relaxations in Complex SystemsNew results, Directions and Opportunities

Francesco Sciortino

Wednesday … last talk

Outline

• Irreversible (Chemical) Gelation in a simple model

• Thermoreversible (Physical) Gelation

• Gels (strong liquids) and Glasses

• Other gels…..(water, DNA-gels)

V(r)

r

Simple Model for Chemical Gels [with HS g(r)]

Irreversible Gelation

Behavior of the density autocorrelation functions

dependence

Irreversible Gelation fq

Signatures of percolation at fixed q

Finite Lifetime….V(r)

r

See also Del Gado works

Generic Phase Diagram for Square Well (3%)

What on cooling ?

The dream

The quest for the ideal (thermoreversible) gel….model1) Long Living (but reversible)

bonds2)No Phase Separation

Are 1 and 2 mutually exclusive ?

LowTemperature

Condensation

Long Bond Lifetime

The quest

Surface Tension

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)?

E=0 E=-NmaxE=-1 E=-Nmax

Nmax on a Bethe lattice

S.Sastry and E. La Nave

max

max

max

Geometric Constraint: Maximum Valency

SW if # of bonded particles <= Nmax

HS if # of bonded particles > Nmax

V(r)

r

Phase Diagram

et al

It is possible to equilibrate at low T !

The structure of the gel

What is the gel dynamics (in this model) ?

• Bond lifetime (Arrhenius along isochores)

What is the gel dynamics (in this model) ?

• Bond lifetime

• R2 vs t (along isochores)

Gel vs Glass - MSD

What is the gel dynamics (in this model) ?• Bond lifetime

• R2 vs t

• Fq(t)

D along isochores… D along isoterms

Dynamic Arrest Lines

The possibility of observing strong-liquid behavior intimately connected to reduction of bonding

Pair-wise model (geometric correlation between bonds) (PMW, I. Nezbeda)

Colloidal Gels, Molecular Gels, …. and DNA gels

Four Arm Ologonucleotide Complexes as precursors for the generation of supramolecular periodic assembliesJACS 126, 2050 2004

Palindroms in complementary space

Conclusions…..

• Gel propensity: Initial understanding of the ingredients requested to generate an “ideal” gel

• Gels and Glasses (two different faces of the arrest dynamics). Percolation not seen…

• Molecular and Atomic gels - Strong ! • Interesting questions…. Where is the MCT

line ?

C. De Michele, E. La Nave, P. Tartaglia, E. Zaccarelli (U. La Sapienza, Roma, Italy)

I. Saika-Voivod (U. Saskatchewan, Canada)

A. Moreno (Donostia International Center, Spain)

S. Bulderyev (DMD code) (Yeshiva U., USA)

S. Sastry (Bethe) (JNCASR, India)

F. Starr (DNA-Gels) (Wesleyan U., USA)

Gel vs Glass: Density Autocorrelation Functions

fq

Fq gel vs glass

Bond Lifetime.. Several more decades..