Dimensional Description of Cyclic Macromolecules

Cyclic structures are often used to model and simulate long chain molecules due to the simplification of no chain-end effects. Many technically important and biologically relevant molecules are cyclics. Further, ring polymers display dramatic viscosity enhancement when blended with linear polymers in the melt. It has been proposed that cyclic melts may display a topologically driven coil collapse at high molecular weights reminiscent of cyclic DNA. Despite the structural simplicity and importance of cyclics a quantitative analytic distinction between cyclics and linear chains in the melt or in solution has been elusive since both linear and cyclic macromolecules display similar disordered, fractal structures. A dimensional analysis of cyclic polymers and its use to describe scattering data from cyclic macromolecules is presented. The validity of the new approach to describe cyclic structures is demonstrated using experimental data, and the Casassa form factor, previously used for cyclic polymers, is critically revisited. The scaling model is also used to quantify cyclic coil collapse in simulations from the literature.