Radius of Gyration, Mean Span, and Geometric Shrinking Factors of Bridged Polycyclic Ring Polymers

Abstract

This study concerns the equilibrium geometric properties of a family of cyclic chains, referred to as the “bridged polycyclic rings,” which have f flexible subchains bridging two common branch points. By increasing the number of bridges, f, this family encompasses the usual linear chain (f = 1), monocyclic ring (f = 2), bicyclic θ-shaped polymer (f = 3), and multicyclic rings with increasing topological complexity. Results of their radius of gyration, mean span, and, consequently, geometric shrinking factors (also known as the g-factors) are obtained by three approaches—the Gaussian chain theory, simulations based on the Kremer–Grest bead-spring model, and a Flory-type mean-field approach. Using the confinement analysis from bulk structures method, the equilibrium partition coefficients (K) of several of those cyclic excluded volume chains in a cylindrical pore with inert surfaces are obtained, and the results fall onto a common curve on a graph of K versus the polymer-to-pore size ratio, using the mean span as the representative polymer size, in the range of K relevant to polymer separation in size exclusion chromatography (SEC) experiments. Applications of the results in predicting the SEC retention volume of such bridged polycyclic ring polymers are discussed in the framework of the equilibrium partition theory.