Helical Wrapping of Cylindrical Tubes by Wormlike-Chain Polymers

When a semiflexible polymer wraps around a solid cylinder with a radius comparable to the persistence length, it displays a helical conformation. What is the confinement free energy of this particular conformation and what is the pitch, the basic geometric measure of the helix, as a function of the persistence length to cylinder radius ratio? Here we explore these on the basis of a standard wormlike-chain model, by using the Green's function approach in statistical physics and numerical computation of the resulting differential equation. In the asymptotic limits of small and large cylinder radius, a power-law scaling relationship is also established from a scaling argument and from the exact solution to the theoretical model. The results from the calculation agree well with experimental data, computer-simulation data, and a previous theoretical estimate. The work sheds light on recent developments in the area of single-walled carbon nanotubes wrapped by various types of long polymers.