Patchy Colloids Proteins and Network Forming Liquids Analogies

Patchy Colloids, Proteins and Network Forming Liquids: Analogies and new insights from computer simulations Lyon - CECAM - June 26 -28 Francesco Sciortino Dynamics in patchy colloids and network forming liquids: gels and strong glass-forming liquids

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.

Liquid-Gas Spinodal Glass line (D->0) Binary Mixture LJ particles “Equilibrium” “homogeoues” arrested states only for large packing fraction

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

Nmax=4 phase diagram - Isodiffusivity lines

The PMW model J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987) V(r) Hard-Sphere + 4 sites (2 H, 2 LP) Tetrahedral arrangement r u 0 (energy scale) H-LP interact via a SW Potential, of range l=0. 15 s. s (length scale) 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 145. 8 o SW interaction between Si sites and O sites s. OO=1. 6 s 1/2 l=[1 -3 /2]s

Equilibrium phase diagram (PMW)

Pagan and Gunton JCP (2005)

Equilibrium Phase Diagram PSM

Critical Point of PMW GC simulation BOX SIZE=6 s TC=0. 1095 f. C=0. 153

Critical Point of PMS GC simulation BOX SIZE=9 s TC=0. 075 f. C=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 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)

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

Diffusion Coefficient

D along isotherms Diffusion Anomalies

Isodiffusivities …. (PMW) …. Isodiffusivities

Si dynamic in PSM

Comparing different potentials Bonded-triples angle q

How to compare these (and other) models for tetracoordinated 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 ST 2 (Poole) SPC/E Faster on compression BKS silica (Saika-Voivod) Slower on compression

Water Phase Diagram F ~ 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 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.

Graphic Summary Two glass lines ? Fragile Liquids Colloidal Glasses Strong liquids - Gels Arrest line

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

http: //www. socobim. de/

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

Density Anomalies… (and possible 2’nd CP)

D vs (1 -pb)

D vs (1 -pb) --- (MC) D ~ f 04 ~(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