Fluctuations of a long, semiflexible polymer in a narrow channel

Abstract

We consider an inextensible, semiflexible polymer or worm-like chain, with persistence length $P$ and contour length $L$, fluctuating in a cylindrical channel of diameter $D$. In the regime $D\ll P\ll L$, corresponding to a long, tightly confined polymer, the average length of the channel $<R_{\parallel }>$ occupied by the polymer and the mean square deviation from the average vary as $<R_{\parallel }>=[1-{\alpha }_{\circ }(D/P{)}^{2/3}]L$ and $<\Delta R_{\parallel }^2>={\beta }_{\circ }(D^2/P)L$, respectively, where ${\alpha }_{\circ }$ and ${\beta }_{\circ }$ are dimensionless amplitudes. In earlier work we determined ${\alpha }_{\circ }$ and the analogous amplitude ${\alpha }_{\square }$ for a channel with a rectangular cross section from simulations of very long chains. In this paper we estimate ${\beta }_{\circ }$ and ${\beta }_{\square }$ from the simulations. The estimates are compared with exact analytical results for a semiflexible polymer confined in the transverse direction by a parabolic potential instead of a channel and with a recent experiment. For the parabolic confining potential we also obtain a simple analytic result for the distribution of $R_{\parallel }$ or radial distribution function, which is asymptotically exact for large $L$ and has the skewed shape seen experimentally.

21 pages, including 4 figures

References in corpus (4)

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• Helical polymer in cylindrical confining geometries
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