Patchy Colloids, Proteins and Network Forming Liquids: Analogies and new insights from computer simulations Lyon - CECAM - June Dynamics in patchy colloids and 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)

N max =4 phase diagram - Isodiffusivity lines

The PMW model J. Kolafa and I. Nezbeda, Mol. Phys (1987) Hard-Sphere + 4 sites (2H, 2LP) Tetrahedral arrangement H-LP interact via a SW Potential, of range  0.15 . V(r) r  (length scale) (energy scale) u0u0 Bonding is properly defined --- Lowest energy state is well defined

The PMS Model Ford, Auerbach, Monson, J.Chem.Phys, 8415,121 (2004) Silicon Four sites (tetrahedral) Oxygen Two sites o  OO =1.6   SW interaction between Si sites and O sites 

Equilibrium phase diagram (PMW)

Pagan and Gunton JCP (2005) Pagan-Gunton

Equilibrium Phase Diagram PSM

Critical Point of PMW GC simulation BOX SIZE=  T C =  C =0.153

Critical Point of PMS GC simulation BOX SIZE=  T C =0.075  C = s=0.45 Critical point PSM

Potential Energy for the PMW Optimal density !

Potential Energy -- Approaching the ground state Progressive increase in packing prevents approach to the GS PMW energy

E-E gs vs. 1/T

Potential Energy along isotherms Optimal density Hints 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

PMS Structure (r-space)

Structure (q-space)

E vs n

Summary of static data Optimal Network Region - Arrhenius Approach to Ground State Region of phase separation Packing Region Phase Separation Region Packing Region

R2 vs t

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 (l 44 ) Scaled Density = # (l 44 ) 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 Summary Two glass lines ? Strong liquids - Gels Arrest line Fragile Liquids - Colloidal Glasses

Coworkers: Cristiano De Michele (PMW,PMS) Simone Gabrielli (PMW) Piero Tartaglia Emanuela Zaccarelli

Gelation as a result of phase separation (interrupted by the glass transition) T T  

Density Anomalies… (and possible 2’nd CP) Density anomalies

D vs (1-p b )

D vs (1-p b ) --- (MC) D ~ f 0 4 ~(Stanley-Teixeira)

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 Foffi aging