Conformations of semiflexible ring polymers

Abstract

We investigate the conformational properties of semiflexible ring polymers theoretically within the principles of optimized Rouse–Zimm theory. Semiflexibility is implemented by imposing topological constraints on the directions and orientations of the constituent bond vectors. This work characterizes various structural features, i.e., the radius of gyration, static structure factor, scattering intensity, fractal dimensions, and shape factor of the semiflexible rings via a comparison of such properties relative to those of the Rouse rings and the rings with excluded volume interactions. Semiflexible rings are maximally expanded in size, while the Rouse rings are compact. Both semiflexible and Rouse rings display a pronounced Kratky peak, in sharp contrast to those of linear polymers and large rings with excluded volume interactions, indicating a more compact ring topology. Semiflexible rings span a wider range of conformations that vary from the expanded to the compact ones with different fractal dimensions, which is distinctly different from that of a Rouse ring and ring with excluded volume interactions. For Rouse rings, the shape factor is size independent and equals 1.25, while for small semiflexible rings it is 1.58 and increases with the size of the ring up to a limiting size. The shape factor of large rings approaches that of the ideal chains in good solvents, while in poor solvents it decreases with an increase in the ring size.