Reentrant Condensation\nof Polyelectrolytes Induced\nby Diluted Multivalent Salts: The Role of Electrostatic Gluonic Effects

We explore the reentrant condensation of polyelectrolytes\ntriggered\nby multivalent salts, whose phase-transition mechanism remains under\ndebate. We propose a theory to study the reentrant condensation, which\nseparates the electrostatic effect into two parts: a short-range electrostatic\ngluonic effect because of sharing of multivalent ions by ionic monomers\nand a long-range electrostatic correlation effect from all ions. The\ntheory suggests that the electrostatic gluonic effect governs reentrant\ncondensation, requiring a minimum coupling energy to initiate the\nphase transition. This explains why diluted salts with selective multivalency\ntrigger a polyelectrolyte phase transition. The theory also uncovers\nthat strong adsorption of multivalent ions onto ionic monomers causes\nlow-salt concentrations to induce both collapse and reentry transitions.\nAdditionally, we highlight how the incompatibility of uncharged polyelectrolyte\nmoieties with water affects the polyelectrolyte phase behaviors. The\nobtained results will contribute to the understanding of biological\nphase separations if multivalent ions bound to biopolyelectrolytes\nplay an essential role.