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≪P≪L, corresponding to a long,
tightly confined polymer, the average length of the channel
occupied by the polymer and the mean square deviation from the average vary as
=[1−α∘(D/P)2/3]L and <ΔR∥2>=β∘(D2/P)L, respectively, where
α∘ and β∘ are dimensionless amplitudes. In earlier work
we determined α∘ and the analogous amplitude α□ for a
channel with a rectangular cross section from simulations of very long chains.
In this paper we estimate β∘ and β□ 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∥ or radial distribution function, which is asymptotically exact
for large L and has the skewed shape seen experimentally.Comment: 21 pages, including 4 figure