On the theoretical description of weakly charged surfaces

TL;DR

This paper demonstrates that the classical Poisson-Boltzmann theory fails to account for image charge effects near weakly charged surfaces, revealing the importance of self-energy and dielectric discontinuities in accurately describing electrostatic double layers.

Contribution

It introduces a corrected weak-coupling theory that includes ion self-energy due to image charges, highlighting effects beyond traditional PB theory.

Findings

Image charge repulsion creates a depletion boundary layer.

Self-energy inclusion alters double layer structure.

PB theory is invalid with dielectric discontinuity.

Abstract

It is widely accepted that the Poisson-Boltzmann (PB) theory provides a valid description for charged surfaces in the so-called weak coupling limit. Here, we show that the image charge repulsion creates a depletion boundary layer that cannot be captured by a regular perturbation approach. The correct weak-coupling theory must include the self-energy of the ion due to the image charge interaction. The image force qualitatively alters the double layer structure and properties, and gives rise to many non-PB effects, such as nonmonotonic dependence of the surface energy on concentration and charge inversion. In the presence of dielectric discontinuity, there is no limiting condition for which the PB theory is valid.