Françoise Brochard. Université Paris 6, Inst. Curie. March 13,

Transcription

1 Polymers in confined geometries Françoise Brochard Université Paris 6, Inst. Curie March 13,

2 Three classes of polymers Flexible Rigid: proteins, colloids Semi-flexible: DNA Transfer of T5 genome into proteoliposomes O. Lambert et al, PNAS 2000, 97 March 13, 2008 F. Brochard 2

3 d=1 Rigid tubes Nuclepore membrane filters (pioneered by GE 1976) 10 nm < D < 1 µm Agar sci. Radiation-etching of polycarbonate films (Guillot et al, J. Appl. Phys. 52, 1981) Filters used in fabrication of cheese and low fat milk Porous rocks Oil recovery Xanthans (Saffman Taylor) Low fat milk producing cow?! March 13, 2008 F. Brochard 3

4 d=1 Soft lipidic tubes N. Borghi, K. Guevorkian, S. Kremer A. Karlsson, et al, Nature 409, 2001 QuickTime?and a Microsoft Video 1 decompressor are needed to see this picture. Hydrodynamic tether extrusion Vesicle networks Flows in soft lipidic tubes P. G. Dommersnes, et al., EPL, 70 (2005) QuickTime?and a decompressor are needed to see this picture. March 13, 2008 F. Brochard 4

5 d=2 confinement Rigid: slits Soft: soap films D. Langevin, A.C.I.S, 89 (1989 Stabilizing Polymers in foams P. G. de Gennes, C. R. Acad. Sc. 289 (1979) Spreading (fluorinated foams) March 13, 2008 F. Brochard 5

6 d=0, nano holes Holes: Protein pores: α-hemolysin Nano fabricated pores Translocation of polymer through a narrow hole under an electric field. QuickTime?and a YUV420 codec decompressor are needed to see this picture. March 13, 2008 F. Brochard 6

7 Flexible polymers in confined geometry: Statics Flory: Swollen chain R=N ν a Ideal chain R 0 =N 1/2 a F ch kt =R2 R 0 2 +NvC F ch R = 0 R =N 3 d +2 a vn R where v =a d C = N R d 2 d d 0 c = 4 N d 2 2, d ν 3/5 3/4 1 d ν Excluded volume effects increases in confined geometries PGG: Blobs g monomers R = N g D =Na a D 2/3 D =g 3 5 a d= 3 d= 1 F conf N kt kt R g D f = kt c D March 13, 2008 F. Brochard 7

8 f = C pore C =e N /g March 13, 2008 F. Brochard 8

9 Forced penetration Hydrodynamic analysis S. Daoudi and F. Brochard, Macromolecules, (11) & γ > J r = R τ z kt / η J r kt3 3 ηr 3 1/3 Affine deformation R R = r r R =r=d r =R J C = kt η March 13, 2008 F. Brochard 9

10 Forced penetration Role of fluctuations = suction model P. G. de Gennes, 1984 Force on a blob: ηvd = ηj /D Aspiration energy: F A = n g ηj D L F = F c + F a =kt n g η J kt n g 2 J c = kt η Penetration of first blob J c does not depend on chain length, N March 13, 2008 F. Brochard 10

11 Role of topology Stars F. Brochard & P.G. de Gennes, CRAS Paris 323 (1996) Symmetric J c =J c f 2 Asymmetric J c1 =J c * D Naf 1/2 March 13, 2008 F. Brochard 11

12 γ = 1 4 M Branched Polymers ξ = D4 / 3 a 1/ 3 M 1/ 6 C. Gay et al, Macromolecules, (29) 1996 J =J c D 4 ξ 4 f = D2 ξ 2 T. Sakaue, et al., EPL, (72) 2005 J c = kt η! f V f c f V increased faster than f c Penetration of first blob (ξ=d) limits the penetration March 13, 2008 F. Brochard 12

13 DNA: semi-rigid polymers v B l a 2 p F. Brochard, et al, Langmuir (21) 2005 R 0 =N D 1/ 2 l p = Nal p g = l p a F ch kt =R2 R +F ve 2 0 kt d=3 F ve kt l < = a p 6 1 if N < Nc3 10! 3 d= /3 4/3 p * p D 3 Fv e N l a l = < 1 if N < N = 10 2 kt g R D a a Long DNA is ideal in 3d but swollen in nanotubes March 13, 2008 F. Brochard 13

14 D >l p D <l p Reisner, et al., PRL L = N N *L* F conf = N * * F F * N kt =N al p D 2 Forced penetration N Electric field f E: =qen = f c E * =E *N * 1 N qe > al 1/ 2 p kt passage N * D 2 Flow: ideal blobs f v = N * R Sponge ξ=d 2 /R * N * ηvr* D passage f * v = f c J SR c = kt D η R * f c = F conf L = F * L N * al p D 2 March 13, 2008 F. Brochard = N N f * * v D =J c l p 2 / 3 a l p 2 / 3 1/ 2 kt Barrier 1st blob

15 Soft tubes Snake vs Globule D > l p F snake = Nal p D 2 kt F Globule = σr 2 + N 2 a 3 kt R 3 F snake =F Globule N c = ad4 l p 5 F. Brochard, et al., LANGMUIR 21 (2005) M. Tokarz, et al, PNAS 102 (2006) κ kt 3 snake saturation March 13, 2008 F. Brochard 15

16 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 Charged polymers: (DNA - Polyelectrolytes) Force: Electric field i (pa) Observation: Blockade of the pore M. Bates et al, Biophys. J. 84, 2003 J. Storm et al, Nanoletters, 5, 2005 V=100 mv τ=20 µs time March 13, 2008 F. Brochard 16

17 Problems of DNA entering a cell ηlv τ E p µ = a r p = V 4 10 s R : N ν a η RR& = f ( ev / a) τ p η R f 2 PGG Physica A 274 (1999) PGG PNAS 96 (1999) τp N DNA 1.2 τp N swollen polymer τe C 3 τ transfection =, n = rp hours! n N Fast DNA translocation τ p R 2 N 1.27 QuickTime?and a decompressor are needed to see this picture. J. Storm et al, Nanoletters, 5, 2005 March 13, 2008 F. Brochard 17

18 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 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 18

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20 Former students Acknowledgments Axel Buguin Pierre Nassoy - Biology J.-P. Thiery M. Bornens Y.-S. Chu M. Théry March 13, 2008 F. Brochard 20

21 Thanks Pierre Gilles for sharing with us your insatiable love for science 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 March 13, 2008 F. Brochard 21