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October 4 2007 ISMC Aachen. Francesco Sciortino Universita’ di Roma La Sapienza. Patchy colloidal particles: the role of the valence in the formation of gels. Main Messages. - PowerPoint PPT Presentation
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Francesco Sciortino Universita’ di Roma La Sapienza
October 4 2007ISMC Aachen
Patchy colloidal particles: the role of the valence in the formation of gels
Main Messages
• Strongly interacting particles (u<<1)---with simple spherical potentials -- at small and intermediate densities ALWAYS phase-separate (in a dense and dilute phase - (Zaccarelli talk))
• Strongly interacting particles with LIMITED valence ---patchy particles, highly directional interactions, dipolar, quadrupolar --- form equilibrium open structures (GELS, network forming liquids). Empty liquids
• Self-assembly as an equilibrium liquid-state problem
Outline• The fate of the liquid state (neglecting
crystallization): phase diagram of 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. Analogies between network forming liquids (silica, water) and colloidal gels.
Phase diagram of spherical potentials*
* “Hard-Core” plus attraction (e.g. LJ)* “Hard-Core” plus attraction (e.g. LJ)
0.13<c<0.27
[if the attractive rangeis very small ( <10%)]
(Foffi et al PRL 94, 078301, 2005)
For sperical potentials (including the depletion potential) arrest at low
(gelation) is the result of a phase separation process interrupted by the
glass transition
T T
E. Zaccarelli, Talk and JPCM, Topical Review 2007
How to go to low T at low (in metastable equilibrium)
reducing “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 !!!(one bond per patch)
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;
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Wertheim TPT for associated liquidsparticles with M identical sticky sites -( one bond per patch )
At low densities and low T (for SW)…..
M=2
FS et al J. Chem.Phys.126, 194903, 2007
Self-assembly
Equilibrium Polymerization
Symbols = SimulationLines = Wertheim TheoryFS et al JCP 126, 194903, 2007
<L>
Average chain length Chain length distributions
Energy per particleM=2 (Chains)
What happens with branching ?
Binary Mixture of M=2 and 3 E. Bianchi et alJPCB (in press)
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
Non percolating state points
Percolating state points
Percolation Line (theory)
Phase-separation
Wertheim Theory works (for small M)
Predictions for larger M
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 Parameters
A snapshot of
<M>=2.025
T=0.05, =0.01
Ground State (almost)reached !
Bond Lifetime
~eu
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Del Gado/Kob EPL 2005 Dipolar Hard Spheres (Camp)
Dipolar Hard Spheres (Blaak, Miller, Hansen)
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 !!!
Is there some kind of universal behavior controlled by valence ?
Noro-Frenkel Scaling for Kern-Frenkel particles
G. Foffi and FS, JPCB 2007
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
LimitedCoordination(4)
BondSelectivity
StericIncompatibilities
4-coordinate “DNA” dendrimed model (F. Starr and FS, JPCM, 2006J. Largo et al Langmuir 2007 )
LimitedCoordination(4)
BondSelectivity
StericIncompatibilities
An example: the PMW phase diagram
E vs n
Phase-separation
Approaching the ground state (PMS)
A collection of phase diagramsof four-coordinated liquids
Schematic Summary
NetworkRegion
-Approach toGround State
-Bond-Activated
Dynamics
Regionof
phaseseparation
Packing Region
Phase Separation RegionPackingRegion
SphericalInteractions
Patchy/directioalInteractions
Conclusions• Directional interaction and limited valency are essential ingredients for offering a DIFFERENT final fate to the liquid state and in particular to arrested states at low
• In the newly available density region, at low T the system forms a “equilibrium” gel (or a network glass).
• Equilibrium Gels and network forming liquids: two faces of the same medal.
Collaborators :Emanuela Bianchi (Patchy Colloids)Cristiano De Michele (PMW, PMS)Julio Largo (DNA, Patchy Colloids)Francis Starr (DNA)Jack Douglas (M=2)Emilia La Nave (Mixture M=2-M=3)Giuseppe Foffi (Kern particles)
Piero TartagliaEmanuela Zaccarelli
Patchy particles (critical fluctuations)
E. Bianchi et al, PRL, 2006
(N.B. Wilding method)
~N+sE
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 !!!
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
DNA-Tetramers phase diagram
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