Dynamics of polymer rings: The Rouse ring chain with attractive harmonic potential of spherical symmetry

The static and dynamic properties of a cyclic Rouse chain modified by the introduction of an effective, spherically symmetric, attracting potential of entropic nature are studied. It is shown that a relatively weak potential can lead to a strong contraction of the polymer chain: the radius of gyration becomes much smaller compared to the size of the free cyclic chain. The pronounced decrease in the terminal relaxation time of cyclic macromolecules in the presence of a harmonic potential compared to the Rouse relaxation time leads to a lengthening of the time interval for the transition to the normal, i.e., the Fickian, diffusion regime, generating a quasi-plateau at increasing molecular mass for the time dependence of segmental mean squared displacement.