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Understanding Gel Formation in Patchy Colloids: Thermodynamic and Dynamic Analogies

This study explores the thermodynamic and dynamic behavior of patchy colloids, focusing on gel formation and network glass formers. Essential features of gels, phase separation, and strong behavioral patterns are examined. Various models and scenarios are discussed to understand the suppression of phase separation and the dynamics in network-forming liquids. The research delves into key parameters and mechanisms influencing the behavior and bonding of colloidal particles, offering insights into the gelation process and dynamic arrest phenomena.

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Understanding Gel Formation in Patchy Colloids: Thermodynamic and Dynamic Analogies

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  1. Imtroduzione Mainz, November 28 2006 Gel-forming patchy colloids and network glass formers: Thermodynamic and dynamic analogies Francesco Sciortino

  2. 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).

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

  4. Phase diagram of spherical potentials* 0.13<fc<0.27 [if the attractive range is very small ( <10%)] * “Hard-Core” plus attraction

  5. Gelation (arrest at low f) as a result of phase separation (interrupted by the glass transition) T T f f

  6. How to go to low T at low f(in metastable equilibrium) ?Is there something else beside Sastry’s scenario for a liquid to end ? How to suppress phase separation ? -controlling valency (Hard core complemented by attractions) -l.r. repulsion (Hard core complemented by both attraction and repulsions

  7. Maximum Valency Geometric Constraint: Maximum Valency (E. Zaccarelli et al, PRL, 2005) V(r ) SW if # of bonded particles <= Nmax HS if # of bonded particles > Nmax r

  8. Nmax phase diagram NMAX-modifiedPhase Diagram

  9. Patchy particles Hard-Core (gray spheres) Short-range Square-Well (gold patchy sites) No dispersion forces The essence of bonding !!!

  10. Mohwald

  11. Pine Pine’s particle

  12. Pine 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 15968 - 15975;

  13. Steric Incompatibilities Steric incompatibilities satisfied if SW width d<0.11 No double bonding Single bond per bond site

  14. Wertheim Theory

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

  16. Wertheim Mixtures of particles with 2 and 3 bonds Empty liquids !

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

  18. Patchy particles - Critical Parameters

  19. M=2 (Chains) T=0.07 Symbols = Simulation Lines = Wertheim Theory

  20. <M>=2.055

  21. A snapshot of a <M>=2.025 (low T) case, f=0.033 Ground State (almost) reached ! Bond Lifetime ~ebu

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

  23. Del Gado Del Gado ….. Del Gado/Kob EPL 2005

  24. Hansen

  25. Message 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 f CAN BE APPROACHED CONTINUOUSLY ON COOLING (MODEL FOR GELS) HOW ABOUT DYNAMICS ? HOW ABOUT MOLECULAR NETWORKS ? IS THE SAME MECHANISM ACTIVE ?

  26. Slow Dynamics at low F Mean squared displacement <M>=2.05 T=0.05 F=0.1

  27. Slow Dynamics at low F Collective density fluctuations <M>=2.05 F=0.1

  28. Message: Gel dynamics: dynamic arrest due to percolation (in the limit of long-living bonds).

  29. The PMW model J. Kolafa and I. Nezbeda, Mol. Phys. 161 87 (1987) V(r ) Hard-Sphere + 4 sites (2H, 2LP) Tetrahedral arrangement H-LP interact via a SW Potential, of range l=0.15 s. r u0 (energy scale) s (length scale) Bonding is properly defined --- Lowest energy state is well defined

  30. Equilibrium phase diagram (PMW)

  31. Pagan-Gunton Pagan and Gunton JCP (2005)

  32. The PMS ModelFord, Auerbach, Monson, J.Chem.Phys, 8415,121 (2004) Silicon Four sites (tetrahedral) SW interaction between Si sites and O sites Oxygen Two sites 145.8 o sOO=1.6 s l=[1-3 /2]s 1/2

  33. Equilibrium Phase Diagram PSM

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

  35. Potential Energy along isotherms Phase-separation Optimal density Hints of a LL CP

  36. S(q) in the network region

  37. PMSStructure (r-space)

  38. Structure (q-space)

  39. E vs n Phase-separation

  40. Summary of static data Phase Separation Region Packing Region Spherical Interactions Region of phase separation Optimal Network Region - Arrhenius Approach to Ground State Packing Region Patchy Interactions

  41. How About Dynamics (in the new network region) ?

  42. Dynamics in the Nmax=4 model (no angular constraints) Strong Liquid Dynamics !

  43. Nmax=4 phase diagram - Isodiffusivity lines Zaccarelli et al JCP 2006

  44. PMW -- Diffusion Coefficient Cross-over to strong behavior

  45. Isodiffusivities …. Isodiffusivities (PMW) ….

  46. Diffusion PMS De Michele et al, cond mat

  47. Question Compare ? 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

  48. Phase Diagram Compared Spinodals and isodiffusivity lines: PMW, PMS, Nmax

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

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