Abstract.
We study the transverse and longitudinal linear response function of rigid chains subjected to an external force. Our main concern are stiff polymers confined in narrow pores with diameter less than their persistence length. We explicitly consider confinement in a transverse harmonic potential and generalize results by scaling arguments. Our results describe the drift of the filament under an external force, time evolution of the filament shape, and filament diffusion. Diffusion of a confined filament resembles the celebrated reptation process for flexible chains, albeit with distinct kinetic exponents. The limiting case of stiff free filaments is also mentioned.
Similar content being viewed by others
References
M.E. Jason, M. Dogterom, Biophys. J. 87, 2723 (2004)
T. Sanchez, I.M. Kulić, Z. Dogic, Phys. Rev. Lett. 104, 098103 (2010)
K.M. Tautel, F. Pampaloni, E. Frey, E.-L. Florin, Phys. Rev. Lett. 100, 028102 (2008)
R. Granek, J. Phys. II 7, 1761 (1997)
D. Morse, Macromolecules 31, 7030 (1998)
D. Morse, Macromolecules 31, 7044 (1998)
R. Evaraers, F. Jülicher, A. Ajdari, A.C. Maggs, Phys. Rev. Lett. 82, 3717 (1999)
U. Seifert, W. Wintz, P. Nelson, Phys. Rev. Lett. 77, 5389 (1996)
G. Nam, N.-K. Lee, J. Chem. Phys. 126, 164902 (2006)
O. Hallatschek, E. Frey, K. Kroy, Phys. Rev. Lett. 94, 077804 (2005)
C.P. Brangwynne, G.H. Koenderink, E. Barry, Z. Doric, F.C. MacKintosh, D.A. Weitz, Biophys. J. 93, 346 (2007)
M.C. Choi et al., Macromolecules 38, 9882 (2005)
Y.-L. Chen, M.D. Graham, J.J. de Pablo, G.C. Randall, M. Gupta, P.S. Doyle, Phys. Rev. E 70, 060901(R) (2004)
D.J. Bonthuis, C. Meyer, D. Stein, C. Dekker, Phys. Rev. Lett. 101, 108303 (2008)
T. Odijk, Phys. Rev. E 77, 060901(R) (2008)
E. Farge, A.C. Maggs, Macromolecules 26, 5041 (1993)
G. Nam, N.-K. Lee, A. Johner, to be published in J. Chem. Phys. (2010)
When hydrodynamic interactions are taken into account, the frictional coefficients per unit length, $\zeta_{\parallel}$ and $\zeta_{\perp}$, are similar to those for a rod and carry logarithmic corrections in free space, $\zeta_{\parallel} = 2\pi\eta_s/\log(S/b)$, $\zeta_{\perp} \approx 4\pi\eta_s/\log(S/b)$, with $\eta_s$ being the solvent viscosity and $b$ the chain thickness. In our case of fluctuating filaments, the upper cut-off length $S$ is replaced with the longitudinal/transverse dynamic correlation length, respectively. For confined filaments the details of hydrodynamic boundary conditions matter
B. Obermayer, O. Hallatschek, Phys. Rev. Lett. 99, 098302 (2007)
In principle, the expectation value can be always measured provided that enough statistics is accumulated
T.B. Liverpool, A.C. Maggs, Macromolecules 34, 6064 (2001)
I. Nyrkova, A.N. Semenov, Phys. Rev. E 76, 011802 (2007)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Nam, G., Johner, A. & Lee, N.K. Drift and diffusion of a confined semiflexible chain. Eur. Phys. J. E 32, 119–126 (2010). https://doi.org/10.1140/epje/i2010-10624-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epje/i2010-10624-1