Cyclic polymers display unique physical behaviors in comparison to 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 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 non-monotonic
behaviors for cyclic PEs. This stands in contrast to linear PEs, where these
shape characteristics exhibit a monotonic trend with increasing Bjerrum length.
A feasible analytical theory, developed to account for ionic distributions
around cyclic PE chains, suggests that the fundamental difference between
linear and cyclic chain conformations may be attributed to topological effects
influencing long-range electrostatic interactions