Conformations and Thermodynamics of Mechanically Linked Polyelectrolyte Rings

By means of Langevin dynamics simulations and a primitive model of electrolytes, we study the conformations and thermodynamics of the simplest mechanically linked polyelectrolyte: two identical, unknotted rings concatenated by a Hopf-link (2catenane). We consider both quenched (strong) and charge-regulating (weak) rings; for the latter, ionization is pH-dependent and implemented via a stochastic constant pH scheme. We find that the link acts as a topological hotspot, where screening and correlations become highly nonuniform. In weak chains, ionization is locally suppressed at the tangle, yet the same region remains a preferred site for counterion accumulation. Increasing ionization swells and reorients the complex toward nearly orthogonal ring planes. Importantly, the rings keep a persistent contact at the link, rather than separating into a threaded interpenetrating geometry. We further show that the quenched charge patterning provides an additional control knob: homogeneous quenched charge distributions reproduce the charge-regulating behavior at matched ionization, whereas diblock patterns stabilize contact-rich states via neutral-block localization at the link and concomitant counterion depletion from the tangle. For fully ionized chains, added salt induces a marked reorganization of the 2catenane, with ring separation showing nontrivial trends as ionic conditions vary.