Conformational properties of cyclic polyelectrolytes in dilute solution

Cyclic polymers represent a challenging and unresolved problem within the field of polymer physics. The introduction of electric charge to cyclic architectures has the potential to compound the complexity, as it introduces the influence of long-range electrostatic interactions. Despite their intriguing nature, studies on cyclic polyelectrolytes (PEs) are still in their early stages, with many aspects requiring further quantitative analysis. This leaves a gap in both theoretical and experimental approaches to comprehensively understand these systems.

We investigate the equilibrium conformations and structure of cyclic PE chains for a wide range of electrostatic strengths and polymerization degrees by using coarse-grained molecular dynamics and scaling arguments. Our analysis demonstrates significant distinctions between ring-shaped PEs and their linear counterparts. As the ionic strength of the solution increases, we observe remarkable shape transitions in PE rings, transitioning from flat to oblate to globular shapes, and these transitions are characterized by singular points. Additionally, simulations reveal that cyclic PEs display a pearl-necklace regime akin to linear PEs. Nonetheless, substantial conformational fluctuations impede the stability of this regime, promoting weakly collapsed polymer configurations irrespective of the degree of polymerization.