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Introduzione. March 25 2007 ACS Chicago. Francesco Sciortino Universita’ di Roma La Sapienza. Gel-forming patchy colloids, and network glass formers: Thermodynamic and dynamic analogies. Main Messages.

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introduzione
Introduzione

March 25 2007

ACS Chicago

Francesco Sciortino

Universita’ di Roma La Sapienza

Gel-forming patchy colloids, and network glass formers: Thermodynamic and dynamic analogies

main messages
Main Messages
  • Strongly interacting particles ---with simple spherical potentials -- always phase-separate (in a dense and dilute phase)
  • Strongly interacting particles -- with limited valence [patchy particles, highly directional interactions, dipolar, quadrupolar] --- form equilibrium open structures (network forming liquids/glasses or gels). Empty liquids
  • Self-assembly as an equilibrium liquid-state problem
outline
Outline
  • The fate of the liquid state (neglecting crystallization):spherical and patchy attractive potentials
  • A theory-of-liquid approach to self-assembly in equilibrium polymerization (linear and branched)
  • The role of valence: Universality classes for the liquid-gas transition
  • Thermodynamic and dynamic behavior of new patchy colloids
  • Revisiting dynamics in network forming liquids (Silica, water….)
bmlj sastry
BMLJ (Sastry)

Liquid-Gas Spinodal

Glass line (D->0)

Binary Mixture LJ particles

“Equilibrium” “homogeneous” arrested states only for large packing fraction

Debenedetti,Stillinger,

Sastry

phase diagram of spherical potentials
Phase diagram of spherical potentials*

0.13<fc<0.27

[if the attractive range

is very small ( <10%)]

* “Hard-Core” plus attraction

(Foffi et al PRL 94, 078301, 2005)

slide6

For this class of potentials arrest at low f (gelation) is the result of a phase separation process interrupted by the glass transition

T

T

f

f

slide7
How to go to low T at low f(in metastable equilibrium) ?Is there something else beside Sastry’s scenario for a liquid to end ?

How to suppress phase separation ?

-The role of the “valence”

valence controlled patchy particles
Valence-Controlled Patchy particles

maximum # of “bonds”, (as opposed to # patches, fraction of bonding surface)

Hard-Core (gray spheres) Short-range Square-Well (gold patchy sites)

No dispersion forces

The essence of bonding !!!

slide9
Pine

Pine’s particles

Self-Organization of Bidisperse Colloids in Water Droplets

Young-Sang Cho, Gi-Ra Yi, Jong-Min Lim, Shin-Hyun Kim, Vinothan N. Manoharan,, David J. Pine, and Seung-Man Yang J. Am. Chem. Soc.; 2005;127(45) pp 15968 - 15975;

Pine

wertheim tpt for associated liquids particles with m identical sticky sites
Wertheim TPT for associated liquids(particles with M identical sticky sites )

At low densities and low T (for SW)…..

steric incompatibilities
Steric Incompatibilities

Steric incompatibilities satisfied if SW width d<0.11

No double bonding

Single bond per bond site

No ring configurations !

slide12

Cond-mat/0701531,

JCP in press

Self-assembly

Equilibrium Polymerization

M=2

slide13

M=2 (Chains)

Energy per particle

Cond-mat/0701531, JCP in press

Symbols = Simulation

Lines = Wertheim Theory

Chain length distributions

Average chain length

<L>

slide14

Binary Mixture of M=2 and 3

La Nave et al

(in preparation)

N2=5670

N3=330

X3=0.055

<M>=2.055

Each color

labels

a different

cluster

slide15

Wertheim theory predicts pbextremely well (in this model)!

<M>=2.055

(ground state accessed in equilibrium)

wertheim
Wertheim

Wertheim Theory (TPT): predictions

E. Bianchi et al, PRL 97, 168301, 2006

wertheim1
Wertheim

Mixtures of particles with valence 2 and 3

A critical point at vanishing packing

Cooling the liquids without phase separating!

Empty liquids !

patchy particles critical fluctuations
Patchy particles (critical fluctuations)

(N.B. Wilding method)

~N+sE

E. Bianchi et al, PRL, 2006

a snapshot of a m 2 025 low t case f 0 033
A snapshot of a <M>=2.025 (low T) case, f=0.033

Ground

State

(almost)

reached !

Bond

Lifetime

~ebu

dipolar hard sphere
Dipolar Hard Sphere

Dipolar Hard Spheres…

Camp et al PRL (2000)

Tlusty-Safram,

Science (2000)

message
Message

MESSAGE(S) (so far…):

REDUCTION OF THE MAXIMUM VALENCY OPENS A WINDOW IN DENSITIES WHERE THE LIQUID CAN BE COOLED TO VERY LOW T WITHOUT ENCOUNTERING PHASE SEPARATION

THE LIFETIME OF THE BONDS INCREASES ON COOLING.

THE LIFETIME OF THE STRUCTURE INCREASES.

ARREST A LOW f CAN BE APPROACHED CONTINUOUSLY ON COOLING

EQUILIBRIUM GELS !!!

slide24

Connecting colloidal particles

with

network forming liquids

Colloidal Water and Colloidal Silica !

the primitive model for water pmw
The Primitive Model for Water (PMW)

J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987)

Lone Pair

H

The Primitive Model for Silica(PMS)Ford, Auerbach, Monson, J.Chem.Phys, 8415,121 (2004)

Silicon

Four Sites

(tetrahedral)

Oxygen

Two sites

145.8 o

s q in the network region pmw
S(q) in the network region (PMW)

C. De Michele et al, J. Phys. Chem. B 110, 8064-8079, 2006

structure q space
Structure (q-space)

C. De Michele et al

J. Chem. Phys. 125, 204710, 2006

t dependence of the diffusion coefficient
T-dependence of the Diffusion Coefficient

Cross-over to

strong behavior !

Strong Liquids !!!

analogies with other network forming potentials
Analogies with other network-forming potentials

ST2 (Poole)

SPC/E

Slower on

compression

Faster on

compression

BKS silica

(Saika-Voivod)

phase diagram compared
Phase Diagram Compared

Spinodals and isodiffusivity lines: PMW, PMS, Nmax

schematic summary

Schematic Summary

Phase Separation Region

Packing

Region

Spherical

Interactions

Region

of

phase

separation

Network

Region

-

Approach to

Ground State

-

Bond-Activated

Dynamics

Packing

Region

Patchy/

directioal

Interactions

slide34

DNA gel model (F. Starr and FS, JPCM, 2006 J. Largo et al Langmuir 2007 )

Limited

Coordination

(4)

Bond

Selectivity

Steric

Incompatibilities

Limited

Coordination

(4)

Bond

Selectivity

Steric

Incompatibilities

conclusions
Conclusions
  • Directional interaction and limited valency are essential ingredients for offering a new final fate to the liquid state and in particular to arrested states at low f.
  • The resulting low T liquid state is (along isochores) a strong liquid.
  • Gels and strong liquids: two faces of the same medal.
slide37

Graphic SummaryTwo distinct arrest lines ?

Fluid

Fluid

Fragile Liquids -

Colloidal Glasses:

Glass arrest line

Strong liquids - Patchy colloids:

Gels arrest line

coworkers
Coworkers:

Emanuela Bianchi (Patchy Colloids)

Cristiano De Michele (PMW, PMS)

Julio Largo (DNA, Patchy Colloids)

Francis Starr (DNA)

Jack Douglas (M=2)

Piero Tartaglia

Emanuela Zaccarelli

pmw energy

Approaching the ground state (PMW)

PMW energy

Progressive increase

in packing prevents approach to the GS

dna pmw

“Bond” is now a cooperative free-energy concept

Optimal

density

DNA-PMW

Bonding equilibrium

involves a significant

change in entropy

(zip-model)

Percolation close (in T) to dynamic

arrest !

angoli modelli
Angoli modelli

Tetrahedral Angle Distribution

energie modelli
Energie Modelli

Low T isotherms…..

Coupling between bonding (local geometry) and density

slide45

Slow Dynamics

at low F

Mean squared

displacement

<M>=2.05

T=0.05

F=0.1

slide46

Slow Dynamics at low F

Collective density fluctuations

<M>=2.05

F=0.1