Imtroduzione

1
Imtroduzione
Conference on "Nucleation, Aggregation and
Growth, Bangalore January 29-31 2007
Francesco Sciortino
Gel-forming patchy colloids and network glass
formers Thermodynamic and dynamic analogies
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Motivations

• The fate of the liquid state (assuming
  crystallization can be prevented).
• Equilibrium Aggregation, Gels and Phase
  separation essential features (Sticky colloids
  - Proteins)
• Thermodynamic and dynamic behavior of new patchy
  colloids
• Revisiting dynamics in network forming liquids
  (Silica, water.)
• Essential ingredients of strong behavior (A.
  Angell scheme).

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BMLJ (Sastry)
Liquid-Gas Spinodal
Glass line (D-gt0)
Binary Mixture LJ particles Equilibrium
homogeneous arrested states only for large
packing fraction
Debenedetti,Stillinger, Sastry
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Phase diagram of spherical potentials
0.13ltfclt0.27
if the attractive range is very small ( lt10)
Hard-Core plus attraction
(Foffi et al PRL 94, 078301, 2005)
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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
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How to go to low T at low f (in metastable
equilibrium) ?Is there something else beside
Sastrys scenario for a liquid to end ?
How to suppress phase separation ?
-controlling valency (Hard core complemented by
attractions)
- Zaccarelli et al PRL 94, 218301, 2005 - Sastry
et al JSTAT 2006
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Patchy particles
(maximum number of bonds, (different from
fraction of bonding surface
Hard-Core (gray spheres) Short-range
Square-Well (gold patchy sites)
No dispersion forces The essence of bonding !!!
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Pine
Pines particle
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Pine
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
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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
Steric incompatibilities satisfied if SW width
dlt0.11 No double bonding Single bond per bond
site
No ring configurations !
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Cond-mat/0701531
GC simulations (particles and chain insertions)
M2
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M2 (Chains)
Energy per particle
Cond-mat/0701531
Symbols Simulation Lines Wertheim Theory
Chain length distributions
Average chain length
ltLgt
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N25670
Binary Mixture of M2 and 3
La Nave et al (in preparation)
X30.055 ltMgt2.055
N3330
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Wertehim theory predicts pb extremely well (in
this model) !
ltMgt2.055
(ground state accessed in equilibrium)
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Connectivity properties and cluster size
distributions Flory and Wertheim
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Wertheim
Wertheim Theory (TPT) predictions
E. Bianchi et al, PRL 97, 168301, 2006
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Wertheim
Mixtures of particles with 2 and 3 bonds
Cooling the liquids without phase separating!
Empty liquids !
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Patchy particles (critical fluctuations)
(N.B. Wilding method)
NsE
E. Bianchi et al, PRL, 2006
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Patchy particles - Critical Parameters
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A snapshot of a ltMgt2.025 (low T)
case, f0.033
Ground State (almost) reached !
Bond Lifetime ebu
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Dipolar Hard Sphere
Dipolar Hard Spheres

Camp et al PRL (2000)
Tlusty-Safram, Science (2000)
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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
(MODEL FOR GELS)
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Connecting colloidal particles with network
forming liquids
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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
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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 al J. Chem. Phys. 125, 204710,
2006
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PMW energy
Approaching the ground state (PMW)
Progressive increase in packing prevents
approach to the GS
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E vs n
Approaching the ground state (PMS)
Phase- separation
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T-dependence of the Diffusion Coefficient
Cross-over to strong behavior ! Strong Liquids
!!!
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Phase Diagram Compared
Spinodals and isodiffusivity lines PMW, PMS,
Nmax
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DNA gel model (F. Starr and FS, JPCM, 2006
J. Largo et al
Langmuir 2007 )
Limited Coordination (4) Bond Selectivity Steri
c Incompatibilities
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DNA-Tetramers phase diagram
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Final Message Universality Class ofvalence
controlled particles
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Schematic Summary
Phase Separation Region
Packing Region
Spherical Interactions
Optimal Network Region - Arrhenius Approach
to Ground State
Region of phase separation
Packing Region
Patchy/ directioal Interactions
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Verbal Summary

• 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. Are directional
  interactions (i.e. suppression of
  phase-separation) essential for being strong?
• Gels and strong liquids two faces of the same
  medal.

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Graphic SummaryTwo distinct arrest lines ?
Fluid
Fluid
Fragile Liquids - Colloidal Glasses Glass
arrest line
Strong liquids - Patchy colloids Gels arrest
line
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Coworkers
Emanuela Bianchi (Patchy Colloids) Cristiano De
Michele (PMW, PMS) Simone Gabrielli (PMW) Julio
Largo (DNA, Patchy Colloids) Emilia La Nave,
Srikanth Sastry (Bethe) Flavio Romano
(PMW) Francis Starr (DNA) Jack Douglas
(M2) Piero Tartaglia Emanuela Zaccarelli
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http//www.socobim.de/
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Unifying aspects of Dynamics (in the new
network region)
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Dynamics in the Nmax4 model
(no angular constraints)
Strong Liquid Dynamics !
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Nmax4 phase diagram - Isodiffusivity lines
T0 !
Zaccarelli et al JCP 2006
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Isodiffusivities .
Isodiffusivities (PMW) .
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(No Transcript)
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Question Compare ?
How to compare these (and other) models for
tetra-coordinated liquids ? Focus on the
4-coordinated particles (other particles are
bond-mediators) Energy scale ---- Tc Length
scale --- nn-distance among 4-coordinated
particles
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Analogies with other network-forming potentials
ST2 (Poole)
SPC/E
Slower on compression
Faster on compression
BKS silica (Saika-Voivod)
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Angoli modelli
Tetrahedral Angle Distribution
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Energie Modelli
Low T isotherms..
Coupling between bonding (local geometry) and
density
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One last four-coordinated model !
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DNA-PMW
Bonding equilibrium involves a significant change
in entropy (zip-model)
Optimal density
Percolation close (in T) to dynamic arrest !
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Slow Dynamics at low F Mean squared
displacement
ltMgt2.05
T0.05
F0.1
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Slow Dynamics at low F Collective density
fluctuations
ltMgt2.05
F0.1
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Appendix I

• Possibility to calculate exactly potential energy
  landscape properties for SW models (spherical and
  patcky)

Moreno et al PRL, 2005
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Stillinger-Weber
Thermodynamics in the Stillinger-Weber formalism
F(T)-T Sconf(E(T))E(T)fbasin(E,T)
with
fbasin (E,T)
Sampled Space with E bonds
and
Number of configurations with E bonds
Sconf(E)kBlnW(E)
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Basin Free energy
It is possible to calculate exactly the
vibrational entropy of one single bonding
pattern (basin free energy)
(Ladd and Frenkel)
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ex

• Comment
• In models for fragile liquids, the number of
  configurations with energy E has been found to be
  gaussian distributed

ex
Non zero ground state entropy
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Appendix II

• Percolation and Gelation
• How to arrest at (or close to) the percolation
  line ?

F. Starr and FS, JPCM, 2006
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DNA Gels 1
Colloidal Gels, Molecular Gels, . and DNA gels
Four Arm Ologonucleotide Complexes as precursors
for the generation of supramolecular periodic
assemblies JACS 126, 2050 2004
Palindroms in complementary space
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D vs (1-pb) --- (MC)
D f04 (Stanley-Teixeira)
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Foffi aging
G. Foffi, E. Zaccarelli, S. V. Buldyrev, F.
Sciortino, P. Tartaglia Aging in short range
attractive colloids A numerical study J. Chem.
Phys. 120, 1824, 2004
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Strong-fragile Dire Stretched, Delta Cp
Hard Sphere Colloids model for fragile liquids
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Critical point PSM
Critical Point of PMS
GC simulation BOX SIZE9s TC0.075 fC0.0445
s0.45
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Critical Point of PMW
GC simulation BOX SIZE6s TC0.1095 fC0.153
(Flavio Romano Laurea Thesis)
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D along isotherms
Diffusion Anomalies
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Hansen
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Water Phase Diagram
F 0.34
Do we need do invoke dispersion forces for LL ?
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Mohwald
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Del Gado
Del Gado ..
Del Gado/Kob EPL 2005
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Maximum Valency
Geometric Constraint Maximum Valency
Nmax Model (E.
Zaccarelli et al, PRL, 2005)
V(r
)
Speedy-Debenedetti
SW if of bonded particles lt Nmax HS if of
bonded particles gt Nmax
r
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Equilibrium Phase Diagram PSM
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Pagan-Gunton
Pagan and Gunton JCP (2005)
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Equilibrium phase diagram (PMW)
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Potential Energy along isotherms
Phase-separation
Optimal density Hints of a LL CP
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PMSStructure (r-space)