Adsorption and Depletion of Polyelectrolytes from Charged Surfaces

TL;DR

This paper models the adsorption and depletion behavior of polyelectrolytes on charged surfaces using mean-field theory and scaling laws, revealing conditions for adsorption and the influence of salt concentration.

Contribution

It introduces a combined mean-field and scaling approach to predict polyelectrolyte adsorption and depletion, including new scaling laws for the adsorption layer and crossover conditions.

Findings

Adsorption occurs only for highly charged polyelectrolytes in low salt solutions.

Scaling laws relate salt concentration at the crossover to charge fraction and surface potential.

Depletion dominates in other conditions, with specific scaling for fixed surface charge density.

Abstract

Mean-field theory and scaling arguments are presented to model polyelectrolyte adsorption from semi-dilute solutions onto charged surfaces. Using numerical solutions of the mean-field equations, we show that adsorption exists only for highly charged polyelectrolytes in low salt solutions. Simple scaling laws for the width of the adsorbed layer and the amount of adsorbed polyelectrolyte are obtained. In other situations the polyelectrolyte chains will deplete from the surface. For fixed surface potential conditions, the salt concentration at the adsorption--depletion crossover scales as the product of the charged fraction of the polyelectrolyte f and the surface potential, while for a fixed surface charge density, \sigma, it scales as \sigma^{2/3}f^{2/3}, in agreement with single-chain results.