Dynamics of stiff chain

In this paper, the bending and stretching elastic potential energies are considered in calculating Hamilton actuating quantity. In the meantime, the mass density of the filament and the friction force are also considered. The normal mode analysis yields eigenfunctions and eigenvalues. In the dynamical equation of polymer chains without a Brownian force, two cases of ζ2−4ρξn>0 and ζ2−4ρξn<0 are taken into account, where ρ is the linear mass density of the filament, ζ is the friction constant per unit length of the filament, and ξn is the eigenvalue. We discuss the dependence of the relaxation times on the persistence length. In the flexible limit, we obtain the relaxation times of the Rouse model. In the stiff-chain case, the relaxation times τn are proportional to [L/(2n−1)]4.