3rd lecture: confined polymers

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3rd lecture confined polymers
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D
Ideal chains
DFconf kBT(R0/D)2
R0
R0 Nna, N monomers each of size a, and n 0.5
for ideal chains, and (3/5) for real chains in a
good solvent (excluded volume dominates)
D
For sticking energy dkBT/monomer, easy to show
that in equilibrium a single chain forms thick,
tenacious layer D (a/d), DFbinding -NkBTd2
For many-chain adsorption the picture is
different, but thick, tenacious idea holds
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lt r gt
L0
f
f
lt r gt R02/3kBT.f
Ideal chain spring constant
s
Polymer brushes do not adsorb, but are attached
by one end to a surface. Can show readily that
in a good solvent the chains stretch out, L0
Na(a/s)2/3
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Mean field models of interactions across confined
neutral adsorbed polymers are well developed
(e.g. de Gennes Macromolecules 1981, JK Pincus
Macromolecules 1982 Jones and Richards, Polymers
at surfaces and interfaces, CUP 1999) Some
puzzles remain e.g. cyclic polymers (see e.g.
Macromolecules 23, 2984) Issue of confined
charged chains - still largely open
Poor solvent, PS/C6H12 JK, Nature 288, 248 (1980)
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0.1M KNO3
vdW Double -layer
PEO added
30 mins
F/R, mN/m
Increasing adsorbance
90 mins
12 - 24 hrs
JK Luckham Nature 1984 Faraday Trans. 86,
1363 (1990))
200 D, nm
100
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Polymer brushes in a good solvent (Taunton, JK et
al. Nature 332, 712 (1988)
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Surface
separation
Bridging
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Brushes can reduce friction 1000-fold
(JK et al., Nature 370, 634 (1994))
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Polystyrene brushes in toluene
Toluene (14Å, 2 layers)
P
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Sharp increase in Fs due to onset of glassy regime
(JK et al., Nature 370, 634 (1994))
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For compressed, overlapping brushes
J.K., Annual Rev. Material Sci 26, 581 (1996)
eqs. (17) - (22)
Repulsive potential of existing brush
Witten et al, 1990 Wijmans et al, 1994 Grest, 1999
s
d interpenetration
D
d
Witten, et al 1990 Wijmans, Zhulina, Fleer
1994 Grest, Adv. Pol. Sci., 138, 149 (1999)
a
a
a
a
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Tadmor, JK et al, Phys. Rev. Lett., 91, 115503
(2003)
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Force spectroscopy
a -gt b part chain extension, part spring
bending at (b) Fs(max), chain ca. 20
extended (D). Force well accounted for by
elastic tension f 3D.kBT/R02 per chain
Tadmor, JK et al, Phys. Rev. Lett., 91, 115503
(2003)
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Tadmor, JK et al, Phys. Rev. Lett., 91, 115503
(2003)
Relaxation time of chain moiety in
interpenetration zone is t(d)
Then expect zone to be self-regulating
according to
(Relaxation rate)
, (shear rate within zone)
since chains will pull out from zone until this
condition fulfilled. This results in very weak
dependence of frictional drag on vs
(some analogy with friction of networks past
grafted chains H. Brown, L. Leger, F. Brochard,
P.G. de Gennes, A. Ajdari)
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From arm-retraction mechanism (as for
star-branched chains) t(lr) t1exp(alr/le),
where a 0.6, le is (concentration-dependent)
entanglement length, t1 varies weakly with
lr. This gives tension in unrelaxed portion of
chain fs(t) µ L0 - lr(t), and finally, for
overall shear force FS(t),
Tadmor, JK et al, Phys. Rev. Lett., 91, 115503
(2003) see also Macromolecules 40, 2539 (2007)
0.04
(Note
for D 7nm)
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Tadmor, JK et al, Phys. Rev. Lett., 91, 115503
(2003)
Variation of shear force following cessation of
applied lateral motion (predicted slope 0.04)
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Modes of polymer/polymer shear
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Thus far dealt with neutral polymers. What
about charged chains (polyelectrolytes)?
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Confined charged polymers of great biological
relevance
JK, Science 323 47 (2009) (2 January 2009)
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Polyelectrolyte brushes

• Theory
• P. Pincus, Macromolecules 24, 2912 (1991) ( many
  others)
• To create
• 1) Need strong anchor/tether to overcome strong
  repulsion between charged tails
• (cells do this naturally)
• 2) Create diblock
• 3) Self-assemble on hydrophobic surface.

(L/s) 3 - 4
L
Hydrophobized surface
s
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Poly(metylmethacrylate) poly(glycidylmethacrylat
e sodium sulfonate)
(PMMA-PGMAS)
Mw 28,800 Mw/Mn 1.1 (anionically
polymerised)
Hydrophobic block
Hydrophilic block
Hydrophilic block FECL a N 29 nm RF
a N3/5 4.5 nm (freely-linked chain)
C
H
C
H
3
3
C
H
C
H
C
C
2
2
115
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C
C
O
O
O
O
Hydrophobic block, collapsed 2R (vol)1/3
1.93 nm pR2 2.9 nm2
C
H
2
C
H
3
O
H
C
H
PMMA
C
H
Raviv, JK et al., Nature 425, 163 (2003)
Langmuir 24, 8678 (2008)
2
-

S
O
N
a
3
PGMAS
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Hydrophobic attraction
Raviv, JK et al., Nature 425, 163 (2003)
Langmuir 24, 8678 (2008)
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meff 0.0006
Raviv, JK et al., Nature, 425, 163-165, (2003)
Langmuir, 24, 8678 (2008)
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Nature, 425, 163-165, (2003) Langmuir, 24,
8678-8687 (2008)
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JK et al., J. Physics Cond. Mat. 16 S5437 (2004)

• Excluded volume (configurational entropy)
• Counter-ion osmotic pressure
• Hydration layers surrounding charges (at
  highest compressions)

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meff 0.0006
meff 0.0006 (P 0.3 MPa)
Raviv, JK et al., Nature, 425, 163-165, (2003)
Langmuir, 24, 8678-8687 (2008)
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2-Methacryloyloxyethyl phosphorylcholine
Meng Chen, Hagai Cohen Wuge Briscoe Steven Armes
(Sheffield)
Very highly hydrated - ca. 17 - 21 water
molecules/ monomer (Ishihara)
Very high brush density
(L/s) 25
Chen, JK et al, ChemPhysChem, 8, 1303-1306 (2007)
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This suggestion was implemented a year later, as
in next slide
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Summary

• Polymers, whether adsorbed or brush-like, form
  thick, tenacious layers on substrates, which
  strongly modify interactions between confining
  surfaces
• In shear brush-like (but NOT adsorbed) polymers
  provide excellent lubrication properties due to
  entropic suppression of interpenetration
• This effect is enhanced for charged/hydrated
  polymers but the molecular ball-bearing-like
  effect of tenacious but labile hydration layers