Patchy Colloids, Proteins and Network Forming Liquids: Analogies and new insights from computer simulations

Lyon - CECAM - June 26-28

Dynamics in patchy colloidsand network forming liquids: gels and strong glass-forming liquids

Francesco Sciortino

Motivations• The fate of the liquid state…. Gels and phase separation:

essential features (Sticky colloids - Proteins, network-forming liquids)

Models of patchy particles. Why to revisit them ?

• Thermodynamic and dynamic behavior of new patchy colloids .

• Clues in understanding dynamics in network forming liquids (Silica, water….)

• Essential ingredients of “strong behavior” (A. Angell scheme) in glass-forming liquids.

Glass line (D->0)

Liquid-Gas Spinodal

Binary Mixture LJ particles

“Equilibrium” “homogeoues” arrested states only for large packing fraction

BMLJ

The general (spherical) case(for hard core complemented by attraction)

Nmax=4 phase diagram - Isodiffusivity lines

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

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

Equilibrium phase diagram (PMW)

Pagan and GuntonJCP (2005)

Equilibrium Phase Diagram PSM

Critical Point of PMWGC simulationBOX SIZE=TC=0.1095C=0.153

Critical Point of PMSGC simulationBOX SIZE=TC=0.075C=0.0445 s=0.45

Potential Energy for the PMW

Optimal density !

Potential Energy -- Approaching the ground state

Progressive increase in packing prevents approach to the GS

E-Egs vs. 1/T

Potential Energy along isotherms

Optimal densityHints of a LL CP

S(q) in the phase-separation region

S(q) in the network region

PMS -Potential Energy

PMS E vs 1/T

PMSStructure (r-space)

Structure (q-space)

E vs n

Summary of static data

OptimalNetworkRegion

-Arrhenius

Approach toGround State

Regionof

phaseseparation

Packing Region

Phase Separation RegionPackingRegion

Diffusion Coefficient

D along isotherms

Diffusion Anomalies

Isodiffusivities ….Isodiffusivities (PMW) ….

Si dynamic in PSM

Comparing different potentials

Bonded-triples angle

How to compare these (and other) models for tetra-coordinated liquids ?

Focus ONLY on the # of 4-coordinated particles (other particles are “bond-mediators”) (#)

Length scale ---- nn-distance among 4-coordinated particles (l44)

Scaled Density = # (l44 )3/V

Energy scale ---- Tc

Comparing E(n) at low T

Comparing isodiffusivity lines

Analogies with other network-forming potentials

SPC/E ST2 (Poole)

BKS silica(Saika-Voivod)

Faster on compression

Slower on compression

Water Phase Diagram

~ 0.34

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. Directional bonding is essential for being strong.

• Gels and strong liquids are two faces of the same medal.

Graphic SummaryTwo glass lines ?

Strong liquids - Gels Arrest line

Fragile Liquids - Colloidal Glasses

Coworkers:

Cristiano De Michele (PMW,PMS)Simone Gabrielli (PMW)

Piero TartagliaEmanuela Zaccarelli

http://www.socobim.de/

Gelation as a result of phase separation

(interrupted by the glass transition)

T T

Density Anomalies…(and possible 2’nd CP)

D vs (1-pb)

D vs (1-pb) --- (MC)

D ~ f04

~(Stanley-Teixeira)

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