Critical adsorption of polyelectrolytes onto planar and convex highly charged surfaces: the nonlinear Poisson-Boltzmann approach

TL;DR

This study investigates how highly charged surfaces influence polyelectrolyte adsorption using nonlinear Poisson-Boltzmann theory and Monte Carlo simulations, revealing significant deviations from classical scaling laws at high charge densities.

Contribution

It introduces a nonlinear Poisson-Boltzmann approach to analyze polyelectrolyte adsorption on highly charged surfaces, extending understanding beyond weak charge regimes.

Findings

Critical surface charge density increases with ionic strength.

Nonlinear electrostatics significantly alter adsorption thresholds.

Adsorption is suppressed above a critical salt concentration.

Abstract

We study the adsorption-desorption transition of polyelectrolyte chains onto planar, cylindrical and spherical surfaces with arbitrarily high surface charge densities by massive Monte Carlo computer simulations. We examine in detail how the well known scaling relations for the threshold transition-demarcating the adsorbed and desorbed domains of a polyelectrolyte near weakly charged surfaces-are altered for highly charged interfaces. In virtue of high surface potentials and large surface charge densities, the Debye-Hueckel approximation is often not feasible and the nonlinear Poisson-Boltzmann approach should be implemented. At low salt conditions, for instance, the electrostatic potential from the nonlinear Poisson--Boltzmann equation is smaller than the Debye-Hueckel result, such that the required critical surface charge density for polyelectrolyte adsorption $\sigma_c$ increases. The nonlinear relation between the surface charge density and electrostatic potential leads to a sharply increasing critical surface charge density with growing ionic strength, imposing an additional limit to the critical salt concentration above which no polyelectrolyte adsorption occurs at all. We contrast our simulations findings with the known scaling results for weak critical polyelectrolyte adsorption onto oppositely charged surfaces for the three standard geometries. Finally, we discuss some applications of our results for some physical-chemical and biophysical systems.