Self-Consistent Field study of Polyelectrolyte Brushes

TL;DR

This paper develops a self-consistent field theory to analyze polyelectrolyte brushes with counterions, examining density profiles, charge distributions, and scaling relations, revealing weak height dependence on grafting density and counterion saturation effects.

Contribution

It introduces a novel self-consistent field approach for polyelectrolyte brushes that incorporates counterion effects and compares scaling predictions with existing theories.

Findings

Brush height shows weak dependence on grafting density.

Counterion distribution outside the brush saturates with increasing charge.

The Gouy-Chapman solution effectively models counterion distribution outside the brush.

Abstract

We formulate a self-consistent field theory for polyelectrolyte brushes in the presence of counterions. We numerically solve the self-consistent field equations and study the monomer density profile, the distribution of counterions, and the total charge distribution. We study the scaling relations for the brush height and compare them to the prediction of other theories. We find a weak dependence of the brush height on the grafting density.We fit the counterion distribution outside the brush by the Gouy-Chapman solution for a virtual charged wall. We calculate the amount of counterions outside the brush and find that it saturates as the charge of the polyelectrolytes increases.