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

March 13, 2008 F. Brochard 3

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

March 13, 2008 F. Brochard 5

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

March 13, 2008 F. Brochard 6

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� �

March 13, 2008 F. Brochard 7

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

March 13, 2008 F. Brochard 8

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

March 13, 2008 F. Brochard 9

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:

March 13, 2008 F. Brochard 10

∆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

March 13, 2008 F. Brochard 11

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

March 13, 2008 F. Brochard 12

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 *

March 13, 2008 F. Brochard 14

• 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

March 13, 2008 F. Brochard 15

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

March 13, 2008 F. Brochard 16

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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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

March 13, 2008 F. Brochard 18

Holes (citations: 587, 2003<275<2008)

– Detection of polymer length

– Polymer length separation using minute amount of sample

Goal:• Sequencing of DNA, RNA• Transfection

March 13, 2008 F. Brochard 19

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

March 13, 2008 F. Brochard 21

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