Charge regulation and local dielectric function in planar polyelectrolyte brushes

TL;DR

This paper develops a field-theory to analyze how inhomogeneity affects charge regulation and dielectric properties in planar polyelectrolyte brushes, revealing the roles of ion-pair dipoles, salt concentration, and pH.

Contribution

A novel field-theory approach to study charge regulation and dielectric function in polyelectrolyte brushes considering inhomogeneity and ion-pair effects.

Findings

Dielectric decrement occurs with low dipole moment monomers.

Ion-pair formation can increase dielectric function locally.

Higher salt concentration enhances local charge within the brush.

Abstract

Understanding the effect of inhomogeneity on the charge regulation and dielectric properties, and how it depends on the conformational characteristics of the macromolecules is a long-standing problem. In order to address this problem, we have developed a field-theory to study charge regulation and local dielectric function in planar polyelectrolyte brushes. The theory is used to study a polyacid brush, which is comprised of chains end-grafted at the solid-fluid interface, in equilibrium with a bulk solution containing monovalent salt ions, solvent molecules and pH controlling acid. In particular, we focus on the effects of the concentration of added salt and pH of the bulk in determining the local charge and dielectric function. Our theoretical investigations reveal that the dipole moment of the ion-pairs formed as a result of counterion adsorption on the chain backbones play a key role in affecting the local dielectric function. For polyelectrolytes made of monomers having dipole moments lower than the solvent molecules, dielectric decrement is predicted inside the brush region. However, the formation of ion-pairs (due to adsorption of counterions coming from the dissociation of added salt) more polar than the solvent molecules is shown to increase the magnitude of the dielectric function with respect to its bulk value. Furthermore, an increase in the bulk salt concentration is shown to increase the local charge inside the brush region.