Polymers in confined geometries - American Physical Society · 2008-08-27 · Polymers in confined...
Transcript of Polymers in confined geometries - American Physical Society · 2008-08-27 · Polymers in confined...
Polymers in confined geometriesPolymers in confined geometries
Françoise BrochardUniversité Paris 6, Inst. Curie
March 13, 2008 1
Three classes of polymers
Flexible
Rigid: proteins, colloids
March 13, 2008 F. Brochard 2
Semi-flexible: DNATransfer of T5 genome
into proteoliposomes
O. Lambert et al, PNAS 2000, 97
d=1
Rigid tubes
10 nm < D < 1 µm
Nuclepore membrane filters (pioneered by GE 1976)
Radiation-etching of polycarbonate films
(Guillot et al, J. Appl. Phys. 52, 1981)Agar sci.
Filters used in fabrication of
cheese and low fat milk
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Low fat milk producing cow?!
• Porous rocks
• Oil recovery
• Xanthans (Saffman Taylor)
d=1
Soft lipidic tubes
A. Karlsson, et al,
Nature 409, 2001
Hydrodynamic tether extrusion
N. Borghi, K. Guevorkian, S. Kremer
QuickTime?and aMicrosoft Video 1 decompressorare needed to see this picture.
March 13, 2008 F. Brochard 4
Hydrodynamic tether extrusion
Vesicle networksP. G. Dommersnes, et al., EPL, 70 (2005)
Flows in soft lipidic tubes
QuickTime?and a decompressor
are needed to see this picture.
d=2 confinement
Soft: soap films
Rigid: slits
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Polymers in foams
Stabilizing
Spreading (fluorinated foams)
D. Langevin, A.C.I.S, 89 (1989
P. G. de Gennes, C. R. Acad. Sc. 289 (1979)
d=0, “nano holes”
Translocation of polymer through a narrow hole under an electric
field.
Holes:
• Protein pores: α-Hemolysin
• Nano fabricated pores
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www.apmaths.uwo.ca/~mkarttu/
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Flexible polymers in confined geometry:
StaticsStaticsStaticsStatics
Flory: Swollen chain R=Nνa Ideal chain R0=N1/2a
Fch
kT=R2
R0
2+ NvC
∂Fch∂R
= 0 R = N3
d+2a
where v = ad C =N
Rd
22
2
0
v,
4
d
d
c
NN
R
d
−
=
�d 3 2 1
ν 3/5 3/4 1
d ν� �
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Excluded volume effects increases in confined geometries
PGG: “Blobs”
g monomers
D = g35a
d=
1d=
3
R =N
gD = Na
a
D
2/3
conf
N kTF kT R
g D� � fc =
kT
D
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f =Cpore
C= e−N /g
Forced penetration
Hydrodynamic analysis
1
z
γτ
>&
J
r3kT
ηR3
1/3
/
Jr R
kT η∗
=
S. Daoudi and F. Brochard, Macromolecules, (11) 1978
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Affine deformationR⊥
R=r
r∗
r3 ηR3
R⊥ = r = D→ r∗ = R→ JC =kT
η
Forced penetration
Role of fluctuations = suction model
Force on a blob: ηVD = ηJ /D
∆FA = −n
gηJ
DL
P. G. de Gennes, 1984
Aspiration energy:
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∆F = ∆Fc + ∆Fa = kTn
g−η
J
kT
n
g
2
→ Jc =kT
ηPenetration of first blob
Jc does not depend on chain length, N
Role of topology
Stars
Jc∗ = Jc f
2
F. Brochard & P.G. de Gennes, CRAS Paris 323 (1996)
Symmetric
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Jc1 = Jc* D
Naf 1/2
Asymmetric
Branched Polymers
γ =1
4
C. Gay et al, Macromolecules, (29) 1996
J = JcD4
ξ 4f =
D2
ξ 2
ξ =D4 / 3
a1/ 3M1/ 6
M
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T. Sakaue, et al., EPL, (72) 2005
Jc =kT
η !
fV increased faster than fc
Penetration of first blob (ξ=D) limits the penetration
V cf f�
DNA: semi-rigid polymers
F. Brochard, et al, Langmuir (21) 2005
R0 = ND
1/ 2lp = Nalp
2vB pl a�
Fch
kT=R2
R0
2+Fve
kT
3
g =lp
a
March 13, 2008 F. Brochard 13
Long DNA is ideal in 3d but swollen in nanotubes
d=3
3
6v31 if < 10 !
pec
lFN N
kT a
< =
�
1/32 4/32
* 3v
21 if < 10
p pel a lF N D
N NkT g R D a a
= < =
�d=1
D > lp D < lpReisner, et al., PRL 94 2005
L =N
N *L*
Fconf =N
N *∆F * ∆F *
kT=N∗alp
D2fc =
Fconf
L=
∆F *
L≈N *alp
D2
1/ 2
kT
Forced penetrationN *
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• Flow: ideal blobs
Sponge ξ=D2/R*fv =
N
N *ηVR* R
*
D
2
=N
N *f v*
fv* = fc ⇒ Jc
SR =kT
ηD
R*
2
= JcD
lp
2 / 3
a
lp
2 / 3
passage
• Electric field E:f = qEN = f c → E * = E1
* N*
N
qE >alp
N *
1/ 2
kT
D2 Barrier 1st blobpassage
Soft tubesSnake vs Globule
F. Brochard, et al., LANGMUIR 21 (2005)
M. Tokarz, et al, PNAS 102 (2006)
D > lp Fsnake =Nalp
D2kT
FGlobule = σR2 +N 2a3kT
R3
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R
Fsnake = FGlobule Nc =aD4
lp5
κkT
3
snake
saturation
Holes = passage of polymers
Neutral polymers: (POE)
Force: chemical potential ∆µ
A. Oukhaled, et al, PRL, 98, 2007
P. Merzylak, et al., Biophys. J., 77, 1999
L. Movleanu, et al.,Biophys. J., 84, 2003
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Charged polymers: (DNA - Polyelectrolytes)
Force: Electric field
Observation: Blockade of the pore V=100 mV
τ=20 µs
time
i (p
A)
M. Bates et al, Biophys. J. 84, 2003
J. Storm et al, Nanoletters, 5, 2005
Problems of DNA entering a cell
PGG Physica A 274 (1999)
PGG PNAS 96 (1999)
410 s
p
p
E
l Va
r
V
µη
τ −
∆=
= �
( / )RR f eV aη =& �
2
p Rf
ητ �
1.2
DNA
swollen polymer
p
p
N
N
τ
τ
�
�
R : N νa
Cτ
www.ks.uiuc.edu
March 13, 2008 F. Brochard 17
PGG PNAS 96 (1999)
Fast DNA translocation
τ p ∼ R2 ∼ N1.27
J. Storm et al, Nanoletters, 5, 2005
3 , hours!Etransfection p
Cn r
n N
ττ = = �
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are needed to see this picture.
Conclusions
Tubes and slits (citations: 3000, 2003<1200<2008)
– Solid:
• polymer characterization and separation, oil separation
– Soft:
• gene therapy, soap films stabilization
• lipidic tubes: transport, nanoreactors
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Holes (citations: 587, 2003<275<2008)
– Detection of polymer length
– Polymer length separation using minute amount of sample
Goal:• Sequencing of DNA, RNA• Transfection
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Axel Buguin
Pierre Nassoy
Former students
Acknowledgments
March 13, 2008 F. Brochard 20
- BiologyJ.-P. Thiery
Y.-S. Chu
M. Bornens
M. Théry
Thanks Pierre Gilles for sharing with us your insatiable love for science
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From glues and grains to rheology
Using notions of symmetry and analogy
He illuminates the messy
With math not so dressy
But with insights deep from figurology
Mahadevan, Boston 2006