Weak polyelectrolytes in the presence of counterion condensation with ions of variable size and polarizability

TL;DR

This paper develops a self-consistent variational theory for weak polyelectrolytes considering counterion polarizability, explaining experimental phenomena like size variation and collapse transitions influenced by ion properties.

Contribution

It introduces a novel theoretical model that incorporates counterion polarizability effects, advancing understanding of polyelectrolyte conformations and collapse behavior.

Findings

Reproduces non-monotonic size variation with electrostatic strength.

Predicts transition from continuous to discontinuous collapse with increasing dipole strength.

Shows size remains globular at high dipole strength regardless of solvent quality.

Abstract

Light scattering and viscometric measurements on weak polyelectrolytes show two important aspects of counterion condensation, namely, non-monotonic variation in the polyelectrolyte size with the increase in the electrostatic strength, and, monovalent counterion selectivity in determining the nature of collapse transition at high electrostatic strengths. Here, we present a self-consistent variational theory for weak polyelectrolytes which includes the effects of the polarizability of monovalent counterions. Our theory reproduces several experimental findings including non-monotonic conformational size with the variation in the electrostatic strength and a shift from a continuous to a discontinuous collapse transition with the increase in the dipole strength of condensed ions. At low dipole strength and high electrostatic strength, our theory predicts a series of solvent quality driven size transitions spanning the re-entrant poor, theta and good solvent regimes. At high dipole strength, the size remains that of a compact globule independent of solvent quality. The dipole strength of the ion-pair formed due to counterion condensation, which depends on the size and polarizability of the monovalent counterions, is found to be an important molecular parameter in determining the nature of collapse transition, and the size of the collapsed state at high electrostatic strength.