iv workshop on non equilibrium phenomena in supercooled fluids, glasses and amorphous materials...
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![Page 1: IV Workshop on Non Equilibrium Phenomena in Supercooled Fluids, Glasses and Amorphous Materials Pisa, September 2006 Francesco Sciortino Gel-forming patchy](https://reader036.vdocuments.us/reader036/viewer/2022062407/56649d3a5503460f94a14df9/html5/thumbnails/1.jpg)
IV Workshop on Non Equilibrium Phenomenain Supercooled Fluids,
Glasses and Amorphous Materials
Pisa, September 2006
Francesco Sciortino
Gel-forming patchy colloids and network glass formers: Thermodynamic and Dynamic analogies
Imtroduzione
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Motivations
• The fate of the liquid state (assuming crystallization can
be prevented)…. 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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Glass line (D->0)
Liquid-Gas Spinodal
Binary Mixture LJ particles
“Equilibrium” “homogeneous” arrested states only for large packing fraction
BMLJ (Sastry)
(see also Debenedetti/Stillinger)
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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%)]
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Gelation (arrest at low ) as a result of
phase separation (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 ?
-controlling valency (Hard core complemented by attractions)-l.r. repulsion (Hard core complemented by both attraction and repulsions
How to suppress phase separation ?
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Geometric Constraint: Maximum Valency(E. Zaccarelli et al, PRL, 2005)
SW if # of bonded particles <= Nmax
HS if # of bonded particles > Nmax
V(r)
r
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Nmax phase diagram
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Patchy particles
Hard-Core (gray spheres) Short-range Square-Well (gold patchy sites)
No dispersion forces The essence of bonding !!!
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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 YangJ. Am. Chem. Soc.; 2005; 127(45) pp 15968 - 15975;
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Steric incompatibilities satisfied if SW width <0.11
No double bonding
Single bond per bond site
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Wertheim Theory
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Wertheim Theory (TPT): predictions
E. Bianchi et al, PRL, in press
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Mixtures of particles with 2 and 3 bonds
Empty liquids !
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Patchy particles (critical fluctuations)
E. Bianchi et al, PRL, in press
(N.B. Wilding)
~N+sE
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Patchy particles - Critical Parameters
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Lattice-gas calculation forreduced valence (Sastry/La Nave) cond-mat
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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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Del Gado …..
Del Gado/Kob EPL 2005
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MESSAGE (so far…):
REDUCTION OF THE MAXIMUM VALENCYOPENS A WINDOW IN DENSITIES WHERE THELIQUID CAN BE COOLED TO VERY LOW T WITHOUTENCOUNTERING PHASE SEPARATION
THE LIFETIME OF THE BONDS INCREASES ON COOLINGTHE LIFETIME OF THE STRUCTURE INCREASESARREST A LOW CAN BE APPROACHED CONTINUOUSLY ON COOLING (MODEL FOR GELS)
HOW ABOUT MOLECULAR NETWORKS ? IS THE SAME MECHANISM ACTIVE ? HOW ABOUT DYNAMICS ?
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The PMW modelJ. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987)
Hard-Sphere + 4 sites (2H, 2LP)Tetrahedral arrangement
H-LP interact via a SWPotential, of range 0.15 .
V(r)
r
(length scale)
(energy scale)
u0
Bonding is properly defined --- Lowest energy state is well defined
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Equilibrium phase diagram (PMW)
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Critical Point of PMW GC simulationBOX SIZE=TC=0.1095C=0.153
(Flavio Romano Laurea Thesis)
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Pagan and GuntonJCP (2005)
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The PMS ModelFord, Auerbach, Monson, J.Chem.Phys, 8415,121
(2004)
Silicon
Four sites
(tetrahedral)
OxygenTwo sites
145.8 o
OO=1.6
SW interaction betweenSi sites and O sites
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Equilibrium Phase Diagram PSM
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Critical Point of PMSGC simulationBOX SIZE=TC=0.075C=0.0445 s=0.45
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Potential Energy (# of bonds) 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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E-Egs vs. 1/T
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Potential Energy along isotherms
Optimal densityHints of a LL CP
Phase-separation
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S(q) in the network region
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PMS -Potential Energy
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PMS E vs 1/T
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PMSStructure (r-space)
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Structure (q-space)
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E vs n
Phase-separation
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Summary of static data
OptimalNetworkRegion
-Arrhenius
Approach toGround State
Regionof
phaseseparation
Packing Region
Phase Separation RegionPackingRegion
SphericalInteractions
PatchyInteractions
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How About Dynamics (in the new network region) ?
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Dynamics in the Nmax=4 model(no angular constraints)
Strong Liquid Dynamics !
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Nmax=4 phase diagram - Isodiffusivity lines
Zaccarelli et al JCP 2006
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PMW
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PMW -- Diffusion Coefficient
Cross-over tostrong behavior
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D along isotherms
Diffusion Anomalies
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Isodiffusivities ….Isodiffusivities (PMW) ….
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Diffusion PMS
De Michele et al, cond mat
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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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Spinodals and isodiffusivity lines: PMW, PMS, Nmax
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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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Water Phase Diagram
~ 0.34
Do we need do invoke disperison forces for LL ?
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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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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
• The resulting low T liquid state is (along isochores) a strong liquid. The bond energy scale: is bonding essential for being strong ?.
• Gels and strong liquids are two faces of the same medal.
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Graphic SummaryTwo glass lines ?
Strong liquids - Gels Arrest line
Fragile Liquids - Colloidal Glasses
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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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Thermodynamics in the Stillinger-Weber formalism
F(T)=-T Sconf(E(T))+E(T)+fbasin(E,T)
with
fbasin (E,T)
and
Sconf(E)=kBln[(E)]
Sampled Space with E bonds
Number of configurations with E bonds
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It is possible to calculate exactly the vibrational entropy of one single bonding pattern
(basin free energy)
(Ladd andFrenkel)
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•Comment:In models for fragile liquids, the number of configurations with energy E has been found to be gaussian distributed
Non zero ground state entropy
ex
ex
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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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Colloidal Gels, Molecular Gels, …. and DNA gels
Four Arm Ologonucleotide Complexes as precursors for the generation of supramolecular periodic assembliesJACS 126, 2050 2004
Palindroms in complementary space
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The DNA gel model (F. Starr and FS, JPCM, 2006)
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Optimaldensity
Bonding equilibriuminvolves a significantchange in entropy(zip-model)
Percolation close (in T) to dynamicarrest !
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Final Message: Universality Class ofvalence controlled particles
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Coworkers:Emanuela Bianchi (Patchy)Cristiano De Michele (PMW,PMS)Simone Gabrielli (PMW)Julio Largo (DNA,Patchy)Emilia La Nave, Srikanth Sastry (Bethe)Angel Moreno (Landscape)Flavio Romano (PMW)Francis Starr (DNA)Piero TartagliaEmanuela Zaccarelli
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http://www.socobim.de/
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Density Anomalies…(and possible 2’nd CP)
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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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G. Foffi, E. Zaccarelli, S. V. Buldyrev, F. Sciortino, P. TartagliaAging in short range attractive colloids: A numerical studyJ. Chem. Phys. 120, 1824, 2004
Foffi aging
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Hard SphereColloids: model for fragile liquids
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S(q) in the phase-separation region
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