Physical Gels and strong liquids 5th International Discussion Meeting on Relaxations in Complex Systems New 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 Ivan HS gel Simple Model for Chemical Gels [with HS g(r)]  Irreversible Gelation

Behavior of the density autocorrelation functions  dependence

Irreversible Gelation f q Signatures of percolation at fixed q

Finite Lifetime…. V(r) r  See also Del Gado works

Square Well 3% width Generic Phase Diagram for Square Well (3%) What on cooling ?

The dream

The quest for the ideal (thermoreversible) gel….model 1) Long Living (but reversible) bonds 2)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 ? The quest Reasons for condensation (Frank, Hill, Coniglio) Physical Clusters at low T ifthe infinite cluster is the lowest (free)energy state How to make the surface as stable as the bulk (or more)?

E=0 E=-N max E=-1 E=-N max N max on a Bethe lattice S.Sastry and E. La Nave  max   max   max 

Geometric Constraint: Maximum Valency SW if # of bonded particles <= N max HS if # of bonded particles > N max V(r) r Maximum Valency

N MAX -modified Phase Diagram 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 R 2 vs t (along isochores)

Gel vs Glass - MSD

What is the gel dynamics (in this model) ? Bond lifetime R 2 vs t F q (t)

D along isochores… D along isoterms D vs isochores and isotherms

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 assemblies JACS 126, 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 fqfq

Fq gel vs glass

Bond Lifetime.. Several more decades..

Stoke