The Marie Curie ResearchTraining Network on Dynamical Arrest

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The Marie Curie Research/Training Network on
Dynamical Arrest Workshop Le Mans, November
19-22, 2005
Francesco Sciortino
Slow dynamics in the presence of attractive
patchy interactions
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Motivations

• The fate of the liquid state. Gels and phase
  separation essential features (Sticky colloids
  - Proteins)
• Revisiting network forming liquids (Silica,
  water.)
• Essential ingredients of strong behavior (A.
  Angell scheme).

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BMLJ
Liquid-Gas Spinodal
Glass line (D-gt0)
Binary Mixture LJ particles Equilibrium
homogeoues arrested states only for large
packing fraction
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Gelation as a result of phase separation
(interrupted by the glass transition)
T
T
f
f
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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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Maximum Valency
Geometric Constraint Maximum Valency (E.
Zaccarelli et al, PRL, 2005)
V(r
)
SW if of bonded particles lt Nmax HS if of
bonded particles gt Nmax
r
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Phase Diagram
NMAX-modified Phase Diagram
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Nmax4 phase diagram - Isodiffusivity lines
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The model
J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987)
V(r
)
Hard-Sphere Tetrahedral coordinated SW
r
(bond geometry)
u0
(energy scale)
s
(length scale)
(HS repulsive geometry)
Bonding is properly defined --- Lowest energy
state is well defined
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Pagan and Gunton JCP (2005)
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Critical Point of PMW
GC simulation BOX SIZE6s TC0.1095 mC0.0388 fC0
.153
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Water Phase Diagram
F 0.34
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Potential Energy for the PMW
Optimal density !
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Potential Energy -- Approaching the ground state
Progressive increase in packing prevents approach
to the GS
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Potential Energy along isotherms
Optimal density Hints of a LL CP
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S(q) in the network region
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Diffusion Coefficient
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D along isotherms
Diffusion Anomalies
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Isodiffusivities (PWM).
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Nmax4 phase diagram - Isodiffusivity lines
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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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Density anomalies
Density Anomalies (and possible 2nd CP)
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Comments

• 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. Directional bonding
  is essential for being strong.
• Gels and strong liquids are two faces of the same
  medal.
• Percolation and arrest-lines are well separated

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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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The DNA gel model
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Bonding equilibrium involves a significant change
in entropy (zip-model)
Optimal density
Percolation close to dynamic arrest !
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D vs (1-pb)
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D vs (1-pb) --- (MC)
D f04 (Stanley-Teixeira)
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Strong-fragile Dire Stretched, Delta Cp
Hard Sphere Colloids model for fragile liquids
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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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Stillinger-Weber
Thermodynamics in the Stillinger-Weber formalism
F(T)-T Sconf(E(T))fbasin(E,T)
with
Fbasin (E)
Sampled Space with E bonds
and
Number of configurations with E bonds
Sconf(E)kBlnW(E)
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• Comment
• In models for fragile liquids, the number of
  configurations with energy E has been found to be
  gaussian distribute d

Non zero ground state entropy
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Coworkers
Cristiano De Michele (Event driven code for
PMW) Simone Gabrielli (PMW) Emanuela Zaccarelli
Piero Tartaglia Angel Moreno
(Landscape) Francis Starr (DNA-gels)
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E vs. 1/T
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