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Introduzione

Introduzione. Francesco Sciortino Universita’ di Roma La Sapienza. “Self-Assembly of patchy particles and DNA-functionalized dendrimers”. Motivations and outline of the talk. Self-Assembly requires interaction energies larger than kT ( b u<<1). Long lifetime of the assembly

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Introduzione

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  1. Introduzione Francesco Sciortino Universita’ di Roma La Sapienza “Self-Assembly of patchy particles and DNA-functionalized dendrimers”

  2. Motivations and outline of the talk Self-Assembly requires interaction energies larger than kT (bu<<1). Long lifetime of the assembly Need to study the phase behavior at low T (crystal formation, phase separation, dynamic arrest, gelation) Spherical interacting potentials Limited valence potentials (patchy) DNA-functionalized particles Reversible and Irreversible aggregation

  3. Main Messages (and outline of the talk) • Strongly interacting particles (bu<<1)---with simple spherical potentials -- at small and intermediate densities ---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 (equilibrium gels, network forming liquids). Models for self-assemblyEmpty liquids • For (small valence) patchy particles, a parameter free description of self-assembly (both equilibrium and equilibration !) can be formulated joining Wertheim and Flory-Stockmayer theories. Connections to chemical gels (and supramolecular chemistry) • Valence controlled universality (DNA-dendrimers)

  4. Phase diagram of spherical potentials* 0.13<fc<0.27 *One component, “Hard-Core” plus attraction (Foffi et al PRL 94, 078301, 2005)

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

  6. Two possibilities, on reducing the range of interaction (depletion interactions, proteins) Contradictory exp results MCT (Fuchs, Bergenholtz) Simulations Supported (Foffi et al PRL 94, 078301, 2005)

  7. For depletion interactions, arrest at low f (gelation) is the result of a phase separation process interrupted by the glass transition CONFOCAL IMAGES First Order Transition But.. Where are we ?

  8. How to estimate the position of the system in the phase diagram ? Use connectivity information (cluster size distributions) Which potential ? Use B2* scaling (Noro-Frenkel)

  9. Cp <---> B2*

  10. Spinodal Decomposition Behavior before Arrest (S(q) from confocal)

  11. Spinodal Decomposition Behavior before Arrest ! q1 =dq S(q) q

  12. Non-equilibrium route to gelation Gels resulting from arrested phase separation (interrupted by the glass transition) quench arrested dense phase From Zaccarelli, Topical Review JPCM 19, 323101 (2007)

  13. How to go to low T at low f (in metastable equilibrium) How to suppress phase separation ? reducing “valence”

  14. Patchy particles maximum number of “bonds”, (different from fraction of bonding surface) It enforces the one bond per patch condition Hard-Core (gray spheres) Short-range Square-Well (gold patchy sites) Energy= Number of bonds = bond probability No dispersion forces The essence of bonding !!!

  15. 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 15968 - 15975; Pine Pine

  16. Mohwald

  17. DNA functionalized particles

  18. Wertheim TPT for associated liquids(particles with M identical sticky sites ) Wertheim in a nut-shell Appendix A: Bianchi et al J. Chem. Phys. 128, 144504 (2008)

  19. Wertheim TPT for associated liquids(particles with M identical sticky sites ) At low densities and low T (for SW)….. Vb Wertheim in a nut-shell Appendix A: Bianchi et al J. Chem. Phys. 128, 144504 (2008)

  20. Wertheim TPT for associated liquids(particles with M identical sticky sites ) At low densities and low T (for SW)….. Vb Wertheim in a nut-shell Appendix A: Bianchi et al J. Chem. Phys. 128, 144504 (2008)

  21. Equilibrium Polymerization (no bond rings) FS et al J. Chem.Phys.126, 194903, 2007 M=2

  22. M=2 EQUILIBRIUM (Chains) FS et al J. Chem.Phys.126, 194903, 2007 Symbols = Simulation Lines = Wertheim Theory <L> Chain length distributions Average chain length L

  23. M=2 EQUILIBRATION (Growth of the Chains) ` Low T limit: FS, C. De Michele and J. Douglas Growth of equilibrium polymers under non-equilibrium conditions J. Phys. Condensed Matter 20, 155101 (2008)

  24. M=2 EQUILIBRATION (Growth of the Chains) FS, C. De Michele and J. Douglas Growth of equilibrium polymers under non-equilibrium conditions J. Phys. Condensed Matter 20, 155101 (2008)

  25. M=2 EQUILIBRATION (Growth of the Chains) Same l Same f Low T limit: FS, C. De Michele and J. Douglas Growth of equilibrium polymers under non-equilibrium conditions J. Phys. Condensed Matter 20, 155101 (2008)

  26. What happens with (rear) branching ?

  27. A snapshot of <M>=2.025 N2=5670 N3=330 T=0.05, f=0.01

  28. Wertheim theory predicts pbextremely well (in this model)! (ground state accessed in equilibrium !!!!!) <M>=2.055 Emanuela Bianchi, Piero Tartaglia, Emilia La Nave and FS, Fully Solvable Equilibrium Self-Assembly Process: Fine-Tuning the Clusters Size and the Connectivity in Patchy Particle Systems, J. Phys. Chem. B 111, 11765 (2007).

  29. Generic features of the phase diagram Branching introduces percolation and phase-separation! Cvmax line Percolation line unstable

  30. Connectivity properties and cluster size distributions: Flory and Wertheim Flory-Stockmayer cluster size distributions observed

  31. Wertheim Mixtures of particles with 2 and 3 bonds Cooling the liquids without phase separating! Empty liquids !

  32. Phase Diagram - Theory and Simulations E. Bianchi, J. Largo, P. Tartaglia, E. Zaccarelli, FS Phase diagram of patchy colloids: towards empty liquids Phys. Rev. Lett. 97, 168301, 2006

  33. First Summary • Directional interaction and limited valency are essential ingredients for offering a DIFFERENT final fate to the liquid state and in particular to arrested states at low f. • Possibility to reach (in homogeneous conditions) states where bu>>1 and the bond lifetime is large • In the newly available density region (whose with is controlled by the valence), at low T the system forms a “equilibrium” gel

  34. DNA functionalized particles: modulating the interaction

  35. DNA Gels 1 DNA-dendrimers Four Arm Ologonucleotide Complexes as precursors for the generation of supramolecular periodic assemblies JACS 126, 2050 2004

  36. Our minimal model: Selectivity of the bonding “DNA” : chain of WAC-LJ (purely repulsive) particles, chained by a FENE potential. Three-body bending potential to model chain rigidity Bases modeled as labeled sites (A,T,G,C), constrained (FENE) to stay at a fixed distance from the monomer center. Site-site interactions are WAC-LJ (purely repulsive) between non-complementary bases and LJ for (A-T) and (G-C) pairs. Base-sites F.W. Starr and FS Model for assembly and gelation of four-armed DNA dendrimers J. Phys. Cond. Matt. 18, L347-L353, 2006

  37. Selectivity of the bonding (single bond per arm !) A T G C G C T A A T G C C G A T Double Strand Single strand

  38. “DNA”-pairing (ss-ds) transition Small T-range where transition takes place

  39. “DNA”-Tetramers (kinetic)phase diagram (“homogeneous”gel !!!) Largo, J.; Starr, F. W and FS. Self-Assembling DNA Dendrimers: A Numerical Study Langmuir, 23, 5896-5905. 2007

  40. 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

  41. A collection of phase diagrams of four-coordinated models F. Sciortino Gel-forming patchy colloids and network glass formers: thermodynamic and dynamic analogies Eur. Phys. J. B e2008-00034-0 (2008)

  42. A collection of phase diagrams of four-coordinated liquids F. Sciortino Gel-forming patchy colloids and network glass formers: thermodynamic and dynamic analogies Eur. Phys. J. B e2008-00034-0 (2008) Physical Gels <===> Network forming liquids

  43. Message: Valence “fixes” the phase diagram type Opening of a region of intermediate densities where the system can be cooled down without the intervention of phase separation Arrest driven by “bonding” more than by “packing” Possibility of interpreting the behavior of functionalized particles in the same “spirit” as patchy colloids Analogies between “patchy particles” and “network liquids” Physical gels <---> network forming liquids

  44. Il primo amore non si scorda mai…… (P. H. Poole, FS, U. Essmann, H. E. Stanley Phase behavior of metastable water Nature 360, 324-328, 1992) Liquid-liquid critical point in one-component systems (water!)

  45. P.H. Poole, I. Saika-Voivod and FS Density minimum and liquid-liquid phase transition J. Phys. Cond. Matt.17, L431-L437, 2005 Compressibility Liquid-gas spinodal density Specific heat Liquid-liquid spinodal

  46. Can tetrahedral DNA-functionalized particles display the phenomenology which has been proposed for supercooled water ? Can this teach us something on the mechanism behind the existence of a liquid-liquid phase transition in network forming systems ? Four “tetrahedral” bonds in both cases: but hard and soft cores….

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