March 25 2007ACS Chicago

Francesco Sciortino Universita’ di Roma La Sapienza

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

Introduzione

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• 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….)

Glass line (D->0)

Liquid-Gas Spinodal

Binary Mixture LJ particles

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

BMLJ (Sastry)

Debenedetti,Stillinger,Sastry

Phase diagram of spherical potentials*

* “Hard-Core” plus attraction* “Hard-Core” plus attraction

0.13<c<0.27

[if the attractive rangeis very small ( <10%)]

(Foffi et al PRL 94, 078301, 2005)

For this class of potentials arrest at low (gelation) is the result of a

phase separation process interrupted by the glass transition

T T

How to go to low T at low (in metastable equilibrium) ?

Is there something else beside Sastry’s scenario for a liquid to end ?

-The role of the “valence”

How to suppress phase separation ?

Valence-Controlled Patchy particles

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

No dispersion forces The essence of bonding !!!

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

Pine’s particles

Self-Organization of Bidisperse Colloids in Water DropletsYoung-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;

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

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

Steric incompatibilities satisfied if SW width <0.11

No double bonding

Single bond per bond site

No ring configurations !

M=2

Cond-mat/0701531, JCP in pressSelf-assembly

Equilibrium Polymerization

M=2 (Chains)

Symbols = Simulation

Lines = Wertheim Theory

<L>

Cond-mat/0701531, JCP in press

Average chain length Chain length distributions

Energy per particle

Binary Mixture of M=2 and 3 La Nave et al(in preparation)

X3=0.055<M>=2.055

N3=330

N2=5670

Each colorlabelsa differentcluster

<M>=2.055

Wertheim theory predicts pb extremely well (in this model) !

(ground state accessed in equilibrium)

Connectivity properties and cluster size distributions: Flory and Wertheim

Wertheim Theory (TPT): predictions

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

Mixtures of particles with valence 2 and 3A critical point at vanishing packing

Empty liquids !Cooling the liquids without phase separating!

Patchy particles (critical fluctuations)

E. Bianchi et al, PRL, 2006

(N.B. Wilding method)

~N+sE

Patchy particles - Critical Parameters

A snapshot of a <M>=2.025 (low T) case, =0.033

Ground State (almost)reached !

Bond Lifetime

~eu

Dipolar Hard Spheres…

Tlusty-Safram, Science (2000)

Camp et al PRL (2000)

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 CAN BE APPROACHED CONTINUOUSLY ON COOLING EQUILIBRIUM GELS !!!

Connecting colloidal particles with

network forming liquids

Colloidal Water and Colloidal Silica !

The Primitive Model for Water (PMW)J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987)

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

HLone Pair

SiliconFour Sites(tetrahedral)

OxygenTwo sites

145.8 o

S(q) in the network region (PMW)

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

Structure (q-space)

C. De Michele et alJ. Chem. Phys. 125, 204710, 2006

T-dependence of the Diffusion

Coefficient

Cross-over tostrong behavior !

Strong Liquids !!!

PMW phase diagram

Analogies with other network-forming potentials

SPC/E ST2 (Poole)

BKS silica(Saika-Voivod)

Faster on compression

Slower on compression

Spinodals and isodiffusivity lines: PMW, PMS, Nmax

E vs n

Phase-separation

Approaching the ground state (PMS)

Schematic Summary

NetworkRegion

-Approach toGround State

-Bond-Activated

Dynamics

Regionof

phaseseparation

Packing Region

Phase Separation RegionPackingRegion

SphericalInteractions

Patchy/directioalInteractions

LimitedCoordination(4)

BondSelectivity

StericIncompatibilities

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

LimitedCoordination(4)

BondSelectivity

StericIncompatibilities

DNA-Tetramers phase diagram

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

• The resulting low T liquid state is (along isochores) a strong liquid.

• Gels and strong liquids: two faces of the same medal.

Graphic SummaryTwo distinct arrest

lines ?

Strong liquids - Patchy colloids: Gels arrest line

Fragile Liquids - Colloidal Glasses:Glass arrest line

Fluid

Fluid

Coworkers:

Emanuela Bianchi (Patchy Colloids)Cristiano De Michele (PMW, PMS)Julio Largo (DNA, Patchy Colloids)Francis Starr (DNA)Jack Douglas (M=2)

Piero TartagliaEmanuela Zaccarelli

One last four-coordinated model !

Approaching the ground state (PMW)

Progressive increase in packing prevents approach to the GS

Optimaldensity

Bonding equilibriuminvolves a significantchange in entropy(zip-model)

Percolation close (in T) to dynamicarrest !

“Bond” is now a cooperative free-energy concept

Final Message: Universality Class ofvalence controlled particles

Tetrahedral Angle Distribution

Energie Modelli

Low T isotherms…..

Coupling between bonding (local geometry) and density

<M>=2.05

Slow Dynamics at low Mean squared displacement

=0.1

<M>=2.05 =0.1

Slow Dynamics at low Collective density fluctuations