introduzione
DESCRIPTION
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 uTRANSCRIPT
Francesco Sciortino Universita’ di Roma La Sapienza
“Self-Assembly of patchy particles and DNA-functionalized
dendrimers”
Introduzione
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Motivations and outline of the talk
Self-Assembly requires interaction energies larger than kT (u<<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
Main Messages (and outline of the talk)• Strongly interacting particles (u<<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-assembly Empty 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)
Phase diagram of spherical potentials*0.13<c<0.27
*One component, “Hard-Core” *One component, “Hard-Core” plus attractionplus attraction
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
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Two possibilities, on reducing the range of interaction (depletion interactions, proteins)
Simulations Supported(Foffi et al PRL 94, 078301, 2005)
Contradictory exp resultsMCT (Fuchs, Bergenholtz)
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
For depletion interactions, arrest at low (gelation) is the result of a phase separation process interrupted by the glass transition
CONFOCAL IMAGESFirst Order Transition But.. Where are we ?
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
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)
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Cp <---> B2*
QuickTime™ and aPNG decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Spinodal Decomposition Behavior before Arrest (S(q) from confocal)
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Spinodal Decomposition Behavior before Arrest !
q 1 =d
q S
(q)
q
Gels resulting from arrested phase separation (interrupted by the glass transition)
arrested dense phase
quench
Non-equilibrium route to gelation
From Zaccarelli, Topical Review JPCM 19, 323101 (2007)
How to go to low T at low (in metastable equilibrium)
reducing “valence”
How to suppress phase separation ?
Patchy particles
Hard-Core (gray spheres) Short-range Square-Well (gold patchy sites)
No dispersion forces The essence of bonding !!!
maximum number of “bonds”, (different from fraction of bonding surface)
It enforces the one bond per patch condition
Energy= Number of bonds = bond probability
Pine’s particles
Self-Organization of Bidisperse Colloids in Water DropletsYoung-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;
DNA functionalized particles
Wertheim TPT for associated liquids(particles with M identical sticky sites )
Wertheim in a nut-shellAppendix A: Bianchi et alJ. Chem. Phys. 128, 144504 (2008)
Wertheim TPT for associated liquids(particles with M identical sticky sites )
At low densities and low T (for SW)…..Vb
Wertheim in a nut-shellAppendix A: Bianchi et alJ. Chem. Phys. 128, 144504 (2008)
Wertheim TPT for associated liquids(particles with M identical sticky sites )
At low densities and low T (for SW)…..Vb
Wertheim in a nut-shellAppendix A: Bianchi et alJ. Chem. Phys. 128, 144504 (2008)
M=2
FS et al J. Chem.Phys.126, 194903, 2007
EquilibriumPolymerization(no bond rings)
M=2 EQUILIBRIUM (Chains)
Symbols = Simulation
Lines = Wertheim Theory
<L>
FS et al J. Chem.Phys.126, 194903, 2007
Average chain length L
Chain length distributions
M=2 EQUILIBRATION (Growth of the Chains)
Low T limit:
FS, C. De Michele and J. DouglasGrowth of equilibrium polymers under non-equilibrium conditionsJ. Phys. Condensed Matter 20, 155101 (2008)
`
M=2 EQUILIBRATION (Growth of the Chains)
FS, C. De Michele and J. DouglasGrowth of equilibrium polymers under non-equilibrium conditionsJ. Phys. Condensed Matter 20, 155101 (2008)
M=2 EQUILIBRATION (Growth of the Chains)
Low T limit:
FS, C. De Michele and J. DouglasGrowth of equilibrium polymers under non-equilibrium conditionsJ. Phys. Condensed Matter 20, 155101 (2008)
Same l
Same
What happens with (rear) branching ?
A snapshot of
<M>=2.025
QuickTime™ and aYUV420 codec decompressor
are needed to see this picture.
N3=330
N2=5670
T=0.05, =0.01
<M>=2.055
Wertheim theory predicts pb extremely well (in this model) !(ground state accessed in equilibrium !!!!!)
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).
Generic features of the phase diagramBranching introduces percolation and phase-separation!
Cvmax line
Percolation line
unstable
Connectivity properties and cluster size distributions: Flory and Wertheim
Flory-Stockmayercluster size distributionsobserved
Mixtures of particles with 2 and 3 bonds
Empty liquids !Cooling the liquids without phase separating!
Phase Diagram - Theory and Simulations
E. Bianchi, J. Largo, P. Tartaglia,E. Zaccarelli, FSPhase diagram of patchy colloids:towards empty liquidsPhys. Rev. Lett. 97, 168301, 2006
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
• Possibility to reach (in homogeneous conditions) states where u>>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
DNA functionalized particles: modulating the interaction
DNA-dendrimers
Four Arm Ologonucleotide Complexes as precursors for the generation of supramolecular periodic assembliesJACS 126, 2050 2004
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 andLJ for (A-T) and (G-C) pairs.
Base-sites
F.W. Starr and FSModel for assembly and gelation of four-armedDNA dendrimersJ. Phys. Cond. Matt. 18, L347-L353, 2006
Selectivity of the bonding (single bond per arm !)
A
T
C
C
C
A
A
A
C
T
T
T
G
G
G
G
Single strand Double Strand
“DNA”-pairing (ss-ds) transition
Small T-range where transition takes place
“DNA”-Tetramers (kinetic)phase diagram
Largo, J.; Starr, F. W and FS.Self-Assembling DNA Dendrimers: A Numerical StudyLangmuir, 23, 5896-5905. 2007
(“homogeneous”gel !!!)
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
A collection of phase diagramsof four-coordinated models
F. SciortinoGel-forming patchy colloids and network glass formers: thermodynamic and dynamic analogiesEur. Phys. J. B e2008-00034-0 (2008)
A collection of phase diagramsof four-coordinated liquids
Physical Gels <===> Network forming liquids
F. SciortinoGel-forming patchy colloids and network glass formers: thermodynamic and dynamic analogiesEur. Phys. J. B e2008-00034-0 (2008)
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 separationArrest driven by “bonding” more than by “packing”
Possibility of interpreting the behavior of functionalized particlesin the same “spirit” as patchy colloids
Analogies between “patchy particles” and “network liquids”Physical gels <---> network forming liquids
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Il primo amore non si scorda mai…… (P. H. Poole, FS, U. Essmann, H. E. StanleyPhase behavior of metastable water Nature 360, 324-328, 1992)
Liquid-liquid critical point in one-component systems (water!)
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
P.H. Poole, I. Saika-Voivod and FSDensity minimum and liquid-liquid phase transitionJ. Phys. Cond. Matt.17, L431-L437, 2005
Compressibility
Specific heat
density
Liquid-gas spinodal
Liquid-liquid spinodal
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….
Julio Largo, Piero Tartaglia, and FSEffective nonadditive pair potential for lock-and-key interacting particles: The role of the limited valencePhys. Rev. E 76, 011402 2007
Effective potential for DNA-functionalized nanoparticles
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Three Ising-like critical points in the effective potential !!!!
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Second Messages (summary)• A challenge for functionalized nanoparticles: bonding
selectivity can provide an effective route to generate new networked materials with polyamorphic behavior.
• The interpenetration of networks provides an alternative simple and generic mechanism to understand the generation of multiple liquid phases, such as expected in water, silicon, silica and several other network forming fluids.
• it is possible to expand the potential tool-box of building blocks so as to open the possibility of a hierarchy of amorphous networked phases. With a proper mixing of particles functionalized with distinct sequences of DNA it should also be possible to control the properties of the individual interpenetrating networks, realizing a nanoscopic canvass woven by differently ”colored” DNA wires.
Self assembly of branched structures…..
Connecting time in chemical (irreversible)aggregation and temperature in physical (reversible) one.
Equilibration (to a finite T) in the presence of branching (but no loops !)
(P. van Dongen and M. Ernst, J. Stat Phys 37, 301 (1984).)
At all times, the cluster size distribution is the same as the equilibriumone, but with p(t) instead of peq
Equilibration (to a finite T) in the presence of branching (but no loops !)
(P. van Dongen and M. Ernst, J. Stat Phys 37, 301 (1984).)
At low T (irreversible coagulation)
At all times, the cluster size distribution is the same as the equilibriumone, but with p(t) instead of peq
The resulting equation for p(t) CAN be solved analytically !!!
Comparing simulation and theory(for patchy spheres)
QuenchprotocolEvolution of the number of bonds
following a T-jump, starting fromhigh-T
Same densityDifferent T
Same TDifferent
Irreversible aggregation in the absence of bond loops
Chemical Gels….. Quenchprotocol
Irreversible aggregation in the absence of bond loops
Smoluchowski coagulation works !
Chemical Gels….. Quenchprotocol
Chemical and physical gelation (in the absence of loops)
t <---->TAt p(t) =p(T)
Chemical and physical gelation (in the absence of loops)
t <---->TAt p(t) =p(T)
A zero-th order model inspired by epoxy-resin step polymerization
Comparing Simulation and Theory for patchy ellipsoids: Cluster size distributions following a quench
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Comparing Simulation and Theory for patchy ellipsoids: Evolution of the bond probability
QuickTime™ and aTIFF (Uncompressed) decompressor
are needed to see this picture.
Final Message:
In the absence of bond-loops, chemical gelation proceeds via a sequence of “quasi-”equilibrium steps (longer t --> smaller T)
The phase-diagram information (gas-liquid instability) are thus of relevance to the process of chemical gelation.
Syneresis and swelling as a “echo” of the equilibrium phase separation.
Coworkers:Emanuela Bianchi, Cristiano De MicheleFabio Ciulla, Piero Tartaglia, Emanuela Zaccarelli (Roma !)
Silvia Corezzi (Perugia)
Francis Starr, Chia W. Hsu (Wesleyan) Julio Largo (U. Cantabria, Santander)
Jack Douglas (NIST)
Peter Lu, David Weitz (Harvard)
Summary: routes to gels
arrested phase separation: non-equilibrium route
Equilibrium routes to gelation:with long-range repulsion / with patches
Zaccarelli, JPCM 19, 323101 (2007)
Next: Depletion interactionsadd linear polystyrene in good solvent
Two sets of polymers: 1) Rg=33nm; 2) Rg=10nminvestigated size ratios =0.059 =0.018
Investigated packing fractions: =0.045, 0.13, 0.16
Experimental system
PMMA particles (A. Schofield) radius a=560 nm density-and-index-matched solvent mixture (DHN+CXB) dielectric constant 7added 4mM TBAC: Debye length 12nm
Peter J. Lu and D.A. Weitz
Confocal microscopy: for each fluid state 26 3d-stacks are collected @ 10 frame/s; for the gel states 3d-stacks are collected over time.
<M>=2.05
Slow Dynamics at low Mean squared displacement
=0.1
<M>=2.05 =0.1
Slow Dynamics at low Collective density fluctuations
“Time” dependence of the potential energy (~pb) around the predicted Wertheim value
ground-state
Conclusions (II)• 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
• In the newly available density region, at low T the system forms a “equilibrium” gel (or a network glass).
• Equilibrium Gels and network forming liquids: two faces of the same medal.
Structure: center-center radial distribution function
()
Low T
High T
Structure: center-center structure factor
Dynamics (MSD)
(a.u.) (a.u.)
2 )
Effective-potential based on center-to-center distance r and angular orientation of the two dendrimers
A two-state model: bonded and non-bonded configurations
Julio Largo, Piero Tartaglia, and FSEffective nonadditive pair potential for lock-and-key interacting particles: The role of the limited valencePhys. Rev. E 76, 011402 2007
Two-state model effective potential:
Non-Spherical effective potential:
Spherical effective potential:
A look at the resulting effective potential
Soft
Second Message:
Selectivity in the bonding at microscopic level MUST BEretained in any coarse graining procedure. This may be encoded in a many-body contribution to the potential.
DNA-functionalized particles are particularly suitable to realize limited valence systems.
Julio Largo, Piero Tartaglia, and Francesco SciortinoEffective nonadditive pair potential for lock-and-key interacting particles: The role of the limited valencePhys. Rev. E 76, 011402 2007
MESSAGE(S) (so far…):
REDUCTION OF THE MAXIMUM VALENCYOPENS A WINDOW IN DENSITIES WHERE THELIQUID CAN BE COOLED TO VERY LOW T WITHOUTENCOUNTERING PHASE SEPARATION
THE LIFETIME OF THE BONDS INCREASES ON COOLINGTHE LIFETIME OF THE STRUCTURE INCREASESARREST A LOW CAN BE APPROACHED CONTINUOUSLY ON COOLING. ARREST DRIVEN BY BONDING INSTEAD OF PACKING (equilibrium gels !)
THE WIDTH OF THE GAS-LIQUID UNSTABLE REGION IS STRONGLY CONTROLLED BY THE VALENCE (empty liquids)