Transcript Multi-faceted nature of equilibrium self

Multi-faceted nature of equilibrium
self-association phenomena
Karl F. Freed & Jacek Dudowicz
James Franck Inst., U. Chicago
Jack F. Douglas
Polymers Div., NIST
Self-assembly Phenomena
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Occurs in diverse systems:
Polymerization (chem., vdW, H-bond,…)
Actin, microtubules, platelets, blood
Polymer coated colloids
Gels (electrochm. E storage; asphaltine)
Dipolar & ionic fluids
Irreversible: kT << Esticking
Covalent: kinetically controlled
Non-covalent: reversible: kT ~ Esticking
Categories of Equilibrium Clustering
Dynamic Equilibrium
kf
+
kd
k2 = kf/kd , k2 = exp (-fp / kBT)
fp = hp - T sp
+
enthalpy hp, entropy sp of associati
Polymerization Universality Classes
1) Linear chains
2) Branched Chains
3) Compact Clusters
Lattice Model of Equilibrium,
reversible Self-association:
Flory-Huggins Type Model
• Formulate in terms of free energy  all
thermodynamic properties
• Include polymer-solvent interaction ( = FH/T)
• omon = initial monomer concentration
• Aim: distinguish between various mechanisms
• Competition: assembly vs. phase separation
F/kBT = fFH + fAssoc
Models: Free association (F), activated (A,
low, high, med), initiated (I)
Average Chain Length
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Low T L: diverges for Alow
Saturates for I model
Diverges for T  0 in F
 1.2 as T  0 for Ahigh
cpc  0 for I & Alow models
cpc = 0 for other models
Literature: only 01/2 scaling
Extent of Polymerization 
•  is fraction of monomers
converted into polymers
•  = 1  complete
polymerization
• Sharp change of  for I, Alow,
& Aint models
• Gradual change for F model
• Very limited polymerization
in Ahigh at low T (where L  1)
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Specific heat & multiple critical points
• Sharp transition: I & Alow
High Tc: monomer/solvent Tc
• Limiting 2nd order transition Other T on polymerization
c
• Very broad for F & Ahigh
line
Appears for sharp transitions
• Maximum in C  T
v
p
Fit to experiment for G-actin
polymerization
G-actin monomer: PDB ID2HMP
Treat a single multi-lattice site “bead”
in FH model, but include volume
Theory (lines) and experiment (points)
changes on assembly.
Greer et al., JCP 123,194906 (2005).
Recent studies: equilibrium self-assembly
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Hierarchical self-assembly
Assembly in polymer matrix
Influence of crowding
Assembly on surface vs. in bulk
Mutual A+B (ApBq)  (ApBq)n assembly
Cooperativity in self-assembly
Entropy-enthalpy compensation
Monomer structure & “sticky interactions
Hierarchical self-assembly
• Self-assembly is cascade of
ordering transitions increasing mM1  Mm ,
mMm(j)  Mm(j+1)
structural complexity.
Example for m = 6
• Roundedness  different
generations coexist at
equilibrium
• Can tune properties by varying
thermodynamic conditions.
• Self-assembly sharpens with
increasing m.
• Sublinear concentration
dependence of < M >, any m.
Sierpinski gasket
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Mutual association
Hierarchical assembly
pA + qB  ApBq
nApBq  (ApBq)n
Clustering in lipid
membranes, peaked
for specific
compositions
Appears in liquid
mixtures, polymers
that form charge
transfer complexes
Mutual association
x10 p
x103 p
• composition at various
temperatures
allylthiocarbimide-diethylamine
and allylthiocarbimidemethylaniline binary mixtures
Jaeger F. M. Second Report on Plasticity;
Nordemann Publ.: New York, 1938; pp 8182, Chapter II
Shear viscosity vs.  at
various T
Self-assembly in polymer matrix
•Polymer matrix can affect viscoelastic, optical,
glass, etc., properties
•Self-assembly transforms phase boundary:
dilute solution  blend as Nmatrix increases
•Figures: self-assembly on heating
Crowding & self-assembly:
Entropy-enthalpy compensation
•Relative solubility of self-assembly in presence of
crowding by polymers
•Balance attractive & repulsive interactions
(Minton)
•Balance entropy vs. enthalpy
Self-assembly in bulk vs. on surface
• Surface adsorption promoted by cooling
• Assembly (bulk, surface) promoted by heating
• Control surface activity (∆hp on surface)
 surface vs. bulk assembly
Lattice Cluster Theory & Monomer Structure
Self-association Phenomena: Summary
• Diverse systems:
pico nano  micro
• Bio  materials & technology
• Several categories of universal
behavior
• Simple Flory-Huggins theory
•  geometric details secondary
• Control of assembly, competition
• Extension to “sticky” interactions
and molecular details (LCT)