Free energy and extension of a semiflexible polymer in cylindrical confining geometries

We consider a long, semiflexible polymer with persistence length P and contour length L fluctuating in a narrow cylindrical channel of diameter D. In the regime $D⪡P⪡L$ the free energy of confinement ΔF and the length of the channel R_ occupied by the polymer are given by Odijk's relations ΔF∕R_=A_∘kBTP^-1∕3D^-2∕3 and R_=L[1-α_∘(D∕P)2∕3], where A_∘ and α_∘ are dimensionless amplitudes. Using a simulation algorithm inspired by the pruned enriched Rosenbluth method, which yields results for very long polymers, we determine A_∘ and α_∘ and the analogous amplitudes for a channel with a rectangular cross section. For a semiflexible polymer confined to the surface of a cylinder, the corresponding amplitudes are derived with an exact analytic approach. The results are relevant for interpreting experiments on biopolymers in microchannels or microfluidic devices.