Conformational Properties of a Back-Folding Wormlike Chain Confined in a Cylindrical Tube

When a semiflexible chain is confined in a narrow cylindrical tube, the formation of a polymer hairpin is a geometrical conformation that accompanies an exponentially large local free energy and, hence, is a relatively rare event. Numerical solutions of the hairpin distribution functions for persistence-length-to-tube-radius ratios over a wide range are obtained in high precision, by using the Green's function approach for the wormlike-chain model. The crossover region between the narrow and moderately narrow tubes is critically investigated in terms of the hairpin free energy, global persistence length, mean hairpin-tip distance from the tube axis, and hairpin-plane orientational properties. Accurate representations of the solutions by simple interpolation formulae are suggested.