Phase diagram of dilute polyelectrolytes: Collapse and redissolution by association of counterions and coions

TL;DR

This paper develops a theoretical phase diagram for dilute polyelectrolyte solutions, revealing how multivalent salt induces collapse and redissolution through counterion and coion association, with implications for understanding electrolyte behavior.

Contribution

It introduces a mean free energy model that explicitly accounts for counterion and coion association, providing new insights into the phase transitions of polyelectrolyte solutions.

Findings

Redissolution occurs when coions and counterions reassociate in the bulk.

Electrolytes can be overcharged and have variable effective charge signs.

The phase diagram predicts the coexistence and transition boundaries.

Abstract

Dilute solutions of strongly charged polymer electrolytes undergo, upon addition of multivaltent salt to the solutions, a phase transition from extended conformations to collapsed or bundled ones. Upon further addition of salt they experience a second transition, a redissolution back into extended conformations. This paper presents a theoretical study of the structure and properties of the phase diagram of these solutions. On the basis of simple phenomenological observations a schematic phase diagram is constructed that allows a simple and explicit determination of the direction of the tie lines within the coexistence region. The actual shape of the coexistence boundary is determined by means of a model mean free energy functional that explicitly includes the possibility of association of both counterions and coions to the electrolyte. It is found that it is possible to redissolve the electrolytes into conformations where the bare charge of the electrolyte is overcompensated by the counterions but, due to the associated coions, can have either sign of total effective charge. When coion association is possible, the redissolution approximately coincides with the reassociation of the coions and counterions in the bulk of the solution.