Polymer Brushes

Polymer Brushes E.B. Zhulina Institute of Macromolecular Compounds, R i Academy Russian A d off Sciences, S i St. Petersburg, Russia

« Simple Views on Polymers at Surfaces and Interfaces: Simposium Honoring P.- G. de Gennes » APS meeting, March 13, 2008, New Orleans USA

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Outline

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What is a polymer brush ?

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Alexander – de Gennes polymer brush model

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Impact of Alexander Alexander- de Gennes model and its extensions

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Polymer brush in biology

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What is a polymer brush ? Brush: array of polymer molecules (synthetic, biopolymer,..) end-attached to substrate Brush thickness H

Degree of chain polymerization N>>1

Brush thickness H

Substrate: bio surface, solid-liquid, air-liquid, liquid-liquid interfaces, self-assembled surfaces, etc.

Solve nt D Grafting density σ = D-2

Attachment: chemical bond, specific ligand, physical adsorption, selfassembly, etc.

Free ends

Depending on geometry of substrate brushes are planar, cylindrical or spherical

Examples of brush applications Stabilization of colloids

Artificial joints, transplants

Drug delivery by biodegradable micelles

Diagnostics of mutations

Diffusion Drug

DNA microarrays

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Prior to Alexander - de Gennes brush model Before A-G brush model: single tethered polymer was treated mostly as the G Gaussian i (f (fantom) t ) chain h i

Scaling theory of semidilute polymer solution Average end-to-end end to end distance R = aN3/5

Overlap concentration 4/5 φΝ* = Na N 3/R3 ~ N−4/5

R

Semidilute solution (melt of blobs) Brush-like structures in microsegregated block copolymers

φΝ >> φΝ*

ξ

Blob size ξ/a ~ φΝ-3/4 Average end-to-end distance

R2 ~ ξ2NB Interaction free energy

Fint ~ kBT NB Block copolymers

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Chain end-tethering to a substrate ξ

R ~ aN3/5 Fint/kBT ~ NB R

Felastic/kBT ~ 1 (Gaussian chain of blobs)

Brush

“Mushrooms” H~R

Fint/kBT ~ NB Felastic/kBT ~ NB Η ∼ ξ NB

H

Inert (nonadsorbing) surface

(Stretched string of blobs or directed random walk)

H

ξ

ξ

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Brush in solvent (S. Alexander 1977 ) Free brush ξ = D ξ

D = ξ = ag3/5 number of monomers per blob

Number of blobs NB = N/g

H

ξ

Free energy (per chain)

F = kBTNB

Brush thickness H = NB ξ ∼ Ν

D

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Brush in contact with polymer solution (P.- G. de Gennes 1980) P>>1

Dilute solution of P chains

Semidilute solution of P chains

σ =D-2

N

To the left of blue line: brush dominated regimes, “mushroom” and Alexander brush. Here, ξP > ξN, P and N chains are demixed d i d

Grafting density σ

D

σ∗=N-6/5 mushrooms

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φ∗= P-4/5

Volume fraction of mobile polymer φ

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Mushroom in contact with solution of mobile P chains

φ