March ACS Chicago Francesco Sciortino Universita’ di Roma La Sapienza Gel-forming patchy colloids, and network glass formers: Thermodynamic and dynamic analogies Introduzione

Main Messages Strongly interacting particles ---with simple spherical potentials -- always phase-separate (in a dense and dilute phase) Strongly interacting particles -- with limited valence [patchy particles, highly directional interactions, dipolar, quadrupolar] --- form equilibrium open structures (network forming liquids/glasses or gels). Empty liquids Self-assembly as an equilibrium liquid-state problem

Outline The fate of the liquid state (neglecting crystallization): spherical and patchy attractive potentials A theory-of-liquid approach to self-assembly in equilibrium polymerization (linear and branched) The role of valence: Universality classes for the liquid-gas transition Thermodynamic and dynamic behavior of new patchy colloids Revisiting dynamics in network forming liquids (Silica, water….)

Glass line (D->0) Liquid-Gas Spinodal Binary Mixture LJ particles “Equilibrium” “homogeneous” arrested states only for large packing fraction BMLJ (Sastry) Debenedetti,Stillinger, Sastry

Phase diagram of spherical potentials* * “Hard-Core” plus attraction 0.13<  c <0.27 [if the attractive range is very small ( <10%)] (Foffi et al PRL 94, , 2005)

For this class of potentials arrest at low  (gelation) is the result of a phase separation process interrupted by the glass transition T T  

How to go to low T at low  (in metastable equilibrium) ? Is there something else beside Sastry’s scenario for a liquid to end ? - The role of the “valence” How to suppress phase separation ?

Valence-Controlled Patchy particles Hard-Core (gray spheres) Short-range Square-Well (gold patchy sites) No dispersion forces The essence of bonding !!! maximum # of “bonds”, (as opposed to # patches, fraction of bonding surface)

Pine Pine’s particles Self-Organization of Bidisperse Colloids in Water Droplets Young-Sang Cho, Gi-Ra Yi, Jong-Min Lim, Shin-Hyun Kim, Vinothan N. Manoharan,, David J. Pine, and Seung-Man Yang J. Am. Chem. Soc.; 2005; 127 (45) pp ; Pine

Wertheim TPT for associated liquids (particles with M identical sticky sites ) At low densities and low T (for SW)…..

Steric incompatibilities satisfied if SW width  <0.11 No double bonding Single bond per bond site Steric Incompatibilities No ring configurations !

M=2 Cond-mat/ , JCP in press Self-assembly Equilibrium Polymerization

M=2 (Chains) Symbols = Simulation Lines = Wertheim Theory Cond-mat/ , JCP in press Average chain length Chain length distributions Energy per particle

Binary Mixture of M=2 and 3 La Nave et al (in preparation) X 3 =0.055 =2.055 N 3 =330 N 2 =5670 Each color labels a different cluster

=2.055 Wertheim theory predicts p b extremely well (in this model) ! (ground state accessed in equilibrium)

Connectivity properties and cluster size distributions: Flory and Wertheim

Wertheim Theory (TPT): predictions Wertheim E. Bianchi et al, PRL 97, , 2006

Mixtures of particles with valence 2 and 3 A critical point at vanishing packing Wertheim Empty liquids ! Cooling the liquids without phase separating!

Patchy particles (critical fluctuations) E. Bianchi et al, PRL, 2006 (N.B. Wilding method) ~N+sE

Patchy particles - Critical Parameters

A snapshot of a =2.025 (low T) case,  =0.033 Ground State (almost) reached ! Bond Lifetime ~ e  u

Dipolar Hard Spheres… Tlusty-Safram, Science (2000) Camp et al PRL (2000) Dipolar Hard Sphere

MESSAGE(S) (so far…): REDUCTION OF THE MAXIMUM VALENCY OPENS A WINDOW IN DENSITIES WHERE THE LIQUID CAN BE COOLED TO VERY LOW T WITHOUT ENCOUNTERING PHASE SEPARATION THE LIFETIME OF THE BONDS INCREASES ON COOLING. THE LIFETIME OF THE STRUCTURE INCREASES. ARREST A LOW  CAN BE APPROACHED CONTINUOUSLY ON COOLING EQUILIBRIUM GELS !!! Message

Connecting colloidal particles with network forming liquids Colloidal Water and Colloidal Silica !

The Primitive Model for Water (PMW) J. Kolafa and I. Nezbeda, Mol. Phys (1987) The Primitive Model for Silica (PMS) Ford, Auerbach, Monson, J.Chem.Phys, 8415,121 (2004) H Lone Pair Silicon Four Sites (tetrahedral) Oxygen Two sites o

S(q) in the network region (PMW) C. De Michele et al, J. Phys. Chem. B 110, , 2006

Structure (q-space) C. De Michele et al J. Chem. Phys. 125, , 2006

T-dependence of the Diffusion Coefficient Cross-over to strong behavior ! Strong Liquids !!!

PMW phase diagram

Analogies with other network-forming potentials SPC/E ST2 (Poole) BKS silica (Saika-Voivod) Faster on compression Slower on compression

Phase Diagram Compared Spinodals and isodiffusivity lines: PMW, PMS, N max

E vs n Phase- separation Approaching the ground state (PMS)

Schematic Summary Network Region - Approach to Ground State - Bond-Activated Dynamics Region of phase separation Packing Region Phase Separation Region Packing Region Spherical Interactions Patchy/ directioal Interactions

Limited Coordination (4) Bond Selectivity Steric Incompatibilities DNA gel model (F. Starr and FS, JPCM, 2006 J. Largo et al Langmuir 2007 ) Limited Coordination (4) Bond Selectivity Steric Incompatibilities

DNA-Tetramers phase diagram

Conclusions 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. Gels and strong liquids: two faces of the same medal.

Graphic Summary Two distinct arrest lines ? Strong liquids - Patchy colloids: Gels arrest line Fragile Liquids - Colloidal Glasses: Glass arrest line Fluid

Coworkers: Emanuela Bianchi (Patchy Colloids) Cristiano De Michele (PMW, PMS) Julio Largo (DNA, Patchy Colloids) Francis Starr (DNA) Jack Douglas (M=2) Piero Tartaglia Emanuela Zaccarelli

One last four-coordinated model !

Approaching the ground state (PMW) Progressive increase in packing prevents approach to the GS PMW energy

Optimal density Bonding equilibrium involves a significant change in entropy (zip-model) Percolation close (in T) to dynamic arrest ! DNA-PMW “Bond” is now a cooperative free-energy concept

Final Message: Universality Class of valence controlled particles

Angoli modelli Tetrahedral Angle Distribution

Energie Modelli Low T isotherms….. Coupling between bonding (local geometry) and density

=2.05 Slow Dynamics at low  Mean squared displacement  =0.1 

=2.05  =0.1 Slow Dynamics at low  Collective density fluctuations