Counterion-controlled phase equilibria in a charge-regulated polymer solution

TL;DR

This paper investigates how charge regulation and counterions influence phase behavior in polymer solutions, revealing complex effects like re-entrant phase transitions and coexistence of diverse charge states.

Contribution

It introduces a minimal model that explicitly accounts for variable polymer charge states and analyzes their impact on phase equilibria and charge distribution regimes.

Findings

Charge regulation significantly affects polymer solubility.

Re-entrant phase behavior occurs with increasing acidity.

Phase separation can lead to coexistence of different charge states.

Abstract

We study phase equilibria in a minimal model of charge-regulated polymer solutions. Our model consists of a single polymer species whose charge state arises from protonation-deprotonation processes in the presence of a dissolved acid, whose anions serve as screening counterions. We explicitly account for variability in the polymers' charge states. Homogeneous equilibria in this model system are characterised by the total concentration of polymers, the concentration of counter-ions and the charge distributions of polymers which can be computed with the help of analytical approximations. We use these analytical results to characterise how parameter values and solution acidity influence equilibrium charge distributions and identify for which regimes uni-modal and multi-modal charge distributions arise. We then study the interplay between charge regulation, solution acidity and phase separation. We find that charge regulation has a significant impact on polymer solubility and allows for non-linear responses to the solution acidity: re-entrant phase behaviour is possible in response to increasing solution acidity. Moreover, we show that phase separation can yield to the coexistence of local environments characterised by different charge distributions and mixture compositions.