Reentrant Condensation of Polyelectrolytes Induced by Diluted Multivalent Salts: The Role of Electrostatic Gluonic Effects

We explore the reentrant condensation of polyelectrolytes triggered by multivalent salts, whose phase-transition mechanism remains under debate. We propose a theory to study the reentrant condensation, which separates the electrostatic effect into two parts: a short-range electrostatic gluonic effect because of sharing of multivalent ions by ionic monomers and a long-range electrostatic correlation effect from all ions. The theory suggests that the electrostatic gluonic effect governs reentrant condensation, requiring a minimum coupling energy to initiate the phase transition. This explains why diluted salts with selective multivalency trigger a polyelectrolyte phase transition. The theory also uncovers that strong adsorption of multivalent ions onto ionic monomers causes low-salt concentrations to induce both collapse and reentry transitions. Additionally, we highlight how the incompatibility of uncharged polyelectrolyte moieties with water affects the polyelectrolyte phase behaviors. The obtained results will contribute to the understanding of biological phase separations if multivalent ions bound to biopolyelectrolytes play an essential role.