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March 25 2007ACS Chicago
Francesco Sciortino Universita’ di Roma La Sapienza
Gel-forming patchy colloids, and network glass formers: Thermodynamic and dynamic analogies
Introduzione
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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
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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….)
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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
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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)
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For this class of potentials arrest at low (gelation) is the result of a
phase separation process interrupted by the glass transition
T T
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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 ?
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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)
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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;
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Wertheim TPT for associated liquids(particles with M identical sticky sites )
At low densities and low T (for SW)…..
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Steric incompatibilities satisfied if SW width <0.11
No double bonding
Single bond per bond site
No ring configurations !
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M=2
Cond-mat/0701531, JCP in pressSelf-assembly
Equilibrium Polymerization
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M=2 (Chains)
Symbols = Simulation
Lines = Wertheim Theory
<L>
Cond-mat/0701531, JCP in press
Average chain length Chain length distributions
Energy per particle
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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
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<M>=2.055
Wertheim theory predicts pb extremely well (in this model) !
(ground state accessed in equilibrium)
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Connectivity properties and cluster size distributions: Flory and Wertheim
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Wertheim Theory (TPT): predictions
E. Bianchi et al, PRL 97, 168301, 2006
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Mixtures of particles with valence 2 and 3A critical point at vanishing packing
Empty liquids !Cooling the liquids without phase separating!
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Patchy particles (critical fluctuations)
E. Bianchi et al, PRL, 2006
(N.B. Wilding method)
~N+sE
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Patchy particles - Critical Parameters
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A snapshot of a <M>=2.025 (low T) case, =0.033
Ground State (almost)reached !
Bond Lifetime
~eu
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Dipolar Hard Spheres…
Tlusty-Safram, Science (2000)
Camp et al PRL (2000)
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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 !!!
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Connecting colloidal particles with
network forming liquids
Colloidal Water and Colloidal Silica !
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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
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S(q) in the network region (PMW)
C. De Michele et al, J. Phys. Chem. B 110, 8064-8079, 2006
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Structure (q-space)
C. De Michele et alJ. Chem. Phys. 125, 204710, 2006
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T-dependence of the Diffusion
Coefficient
Cross-over tostrong behavior !
Strong Liquids !!!
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PMW phase diagram
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Analogies with other network-forming potentials
SPC/E ST2 (Poole)
BKS silica(Saika-Voivod)
Faster on compression
Slower on compression
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Spinodals and isodiffusivity lines: PMW, PMS, Nmax
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E vs n
Phase-separation
Approaching the ground state (PMS)
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Schematic Summary
NetworkRegion
-Approach toGround State
-Bond-Activated
Dynamics
Regionof
phaseseparation
Packing Region
Phase Separation RegionPackingRegion
SphericalInteractions
Patchy/directioalInteractions
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LimitedCoordination(4)
BondSelectivity
StericIncompatibilities
DNA gel model (F. Starr and FS, JPCM, 2006 J. Largo et al Langmuir 2007 )
LimitedCoordination(4)
BondSelectivity
StericIncompatibilities
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DNA-Tetramers phase diagram
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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.
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Graphic SummaryTwo distinct arrest
lines ?
Strong liquids - Patchy colloids: Gels arrest line
Fragile Liquids - Colloidal Glasses:Glass arrest line
Fluid
Fluid
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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
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One last four-coordinated model !
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Approaching the ground state (PMW)
Progressive increase in packing prevents approach to the GS
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Optimaldensity
Bonding equilibriuminvolves a significantchange in entropy(zip-model)
Percolation close (in T) to dynamicarrest !
“Bond” is now a cooperative free-energy concept
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Final Message: Universality Class ofvalence controlled particles
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Tetrahedral Angle Distribution
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Energie Modelli
Low T isotherms…..
Coupling between bonding (local geometry) and density
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<M>=2.05
Slow Dynamics at low Mean squared displacement
=0.1
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<M>=2.05 =0.1
Slow Dynamics at low Collective density fluctuations