Structural and electrostatic properties between pH-responsive polyelectrolyte brushes studied by augmented strong stretching theory

TL;DR

This study uses an augmented strong stretching theory to analyze electrostatic and structural behaviors of pH-responsive polyelectrolyte brushes, revealing how charge density, excluded volume, and pH influence brush interactions and properties.

Contribution

It introduces a comprehensive theoretical framework accounting for excluded volume, chargeable site density, and Born energy to predict polyelectrolyte brush behaviors.

Findings

Electrostatic potential and osmotic pressure increase with chargeable site density.

Brush thickness decreases as two pH-responsive brushes approach each other.

Born energy difference affects brush thickness and osmotic pressure.

Abstract

In this paper, we study electrostatic and structural properties between pH-responsive polyelectrolyte brushes by using a strong stretching theory accounting for excluded volume interactions, the density of polyelectrolyte chargeable sites and the Born energy difference between the inside and outside of the brush layer. In a free energy framework, we obtain self-consistent field equations to determine electrostatic properties between two pH-responsive polyelectrolyte brushes. We elucidate that in the region between two pH-responsive polyelectrolyte brushes, electrostatic potential at the centerline and osmotic pressure increase not only with excluded volume interaction, but also with density of chargeable sites on a polyelectrolyte molecule. Importantly, we clarify that when two pH-responsive polyelectrolyte brushes approach each other, the brush thickness becomes short and that a large excluded volume interaction and a large density of chargeable sites yield the enhanced contract of polyelectrolyte brushes. In addition, we also demonstrate how the influence of such quantities as pH, the number of Kuhn monomers, the density of charged sites, the lateral separation between adjacent polyelectrolyte brushes, Kuhn length on the electrostatic and structural properties between the two polyelectrolyte brushes is affected by the exclusion volume interaction. Finally, we investigate the influence of Born energy difference on the thickness of polyelectrolyte brushes and the osmotic pressure between two pH-responsive polyelectrolyte brushes.