Bimodality in the transverse fluctuations of a grafted semiflexible polymer and the diffusion-convection analogue: an effective-medium approach

Details Bimodality in the transverse fluctuations of a grafted semiflexible polymer and the diffusion-convection analogue: an effective-medium approach Bimodality in the transverse fluctuations of a grafted semiflexible polymer and the diffusion-convection analogue: an effective-medium approach

2005-01-22

arxiv.org/abs/cond-mat/0501546v1

Phys. Rev. E 72, 030801(R) (2005)

Physics

Condensed Matter

Soft Condensed Matter

5 pages, 4 figures

Scientific paper

10.1103/PhysRevE.72.030801

Recent Monte Carlo simulations of a grafted semiflexible polymer in 1+1 dimensions have revealed a pronounced bimodal structure in the probability distribution of the transverse (bending) fluctuations of the free end, when the total contour length is of the order of the persistence length [G. Lattanzi et al., Phys. Rev E 69, 021801 (2004)]. In this paper, we show that the emergence of bimodality is related to a similar behavior observed when a random walker is driven in the transverse direction by a certain type of shear flow. We adapt an effective-medium argument, which was first introduced in the context of the sheared random-walk problem [E. Ben-Naim et al., Phys. Rev. A 45, 7207 (1992)], in order to obtain a simple analytic approximation of the probability distribution of the free-end fluctuations. We show that this approximation captures the bimodality and most of the qualitative features of the free-end fluctuations. We also predict that relaxing the local inextensibility constraint of the wormlike chain could lead to the disappearence of bimodality.

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