Structural properties of cyclic polyelectrolytes in a dilute good solvent

Cyclic polymers display unique physical behaviors in comparison to those of their linear counterparts. Theoretical, computational, and experimental studies have revealed that some of their distinctive properties are also observed in charged variants of cyclic polymers, known as cyclic polyelectrolytes (PEs), especially in terms of their structural responses to variations in the strength of electrostatic interactions. In this study, we investigate the impact of cyclic topology on the conformations of PE chains in a dilute good solvent using scaling analysis and coarse-grained bead-spring molecular dynamics simulations. Our observations indicate that, in contrast to linear PE chains, cyclic topology results in more compact conformations at low and intermediate Bjerrum lengths. Moreover, two structural metrics, asphericity and prolateness, which quantify deviations from spherical and flat molecular shapes, exhibit nonmonotonic behaviors for cyclic PEs. This stands in contrast to linear PEs, where these shape characteristics exhibit a monotonic trend with an increasing Bjerrum length. A feasible analytical theory, developed to account for the ionic distributions around cyclic PE chains, suggests that the fundamental difference between the linear and cyclic chain conformations may be attributed to the topological effects influencing long-range electrostatic interactions.