- Access by Xinjiang University
Stretching of buckled filaments by thermal fluctuations
Phys. Rev. E 76, 061914 – Published 21 December, 2007
DOI: https://doi.org/10.1103/PhysRevE.76.061914
Abstract
We study the buckling instability of filaments or elastic rods in two spatial dimensions in the presence of thermal fluctuations. We present an analytical solution based on a renormalizationlike procedure where we integrate out short wavelength fluctuations in order to obtain an effective theory governing the buckling instability. We calculate the resulting shift of the critical force by fluctuation effects and the average projected filament length parallel to the force direction as a function of the applied force and of the contour length of the filament. We find that, in the buckled state, thermal fluctuations lead to an increase in the mean projected length of the filament in the force direction. As a function of the contour length, the mean projected length exhibits a cusp at the buckling instability, which becomes rounded by thermal fluctuations. Our analytic results are confirmed by Monte Carlo simulations.
Article Text
References (16)
- L. Landau and E. M. Lifshitz, Theory of Elasticity (Pergamon, New York, 1986).
- J. Howard, Mechanics of Motor Proteins and the Cytoskeleton (Sinauer Associates, Inc., Sunderland, 2001).
- J. Kierfeld, P. Gutjahr, T. Kühne, P. Kraikivski, and R. Lipowsky, J. Comput. Theor. Nanosci. 3, 898 (2006).
- M. Dogterom and B. Yurke, Science 278, 856 (1997).
- F. Gittes, E. Meyhöfer, S. Baek, and J. Howard, Biophys. J. 70, 418 (1996).
- M. Elbaum, D. Kuchnir Fygenson, and A. Libchaber, Phys. Rev. Lett. 76, 4078 (1996).
- R. E. Goldstein and A. Goriely, Phys. Rev. E 74, 010901(R) (2006).
- P. L. Hansen, D. Svensek, V. A. Parsegian, and R. Podgornik, Phys. Rev. E 60, 1956 (1999).
- L. Golubovic, D. Moldovan, and A. Peredera, Phys. Rev. Lett. 81, 3387 (1998).
- P. Ranjith and P. B. Sunil Kumar, Phys. Rev. Lett. 89, 018302 (2002).
- P. Gutjahr, R. Lipowsky, and J. Kierfeld, Europhys. Lett. 76, 994 (2006).
- T. Odijk, J. Chem. Phys. 108, 6923 (1998).
- S. M. Carr, W. E. Lawrence, and M. N. Wybourne, Phys. Rev. B 64, 220101(R) (2001).
- A. M. Polyakov, Gauge Fields and Strings (Harwood Academic Publishers, Chur, Switzerland, 1987); P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics (Cambridge University Press, Cambridge, England, 1995).
- M. Abramowitz and A. I. Stegun, Handbook of Mathematical Functions (National Bureau of Standards, Washington, DC, 1965).
- L. R. G. Treloar, The Physics of Rubber Elasticity (Clarendon Press, Oxford, 1975).