Electrostatic image effects for counter-ions between charged planar walls

TL;DR

This paper investigates how dielectric inhomogeneities and electrostatic image effects influence interactions between charged surfaces with mobile counter-ions, revealing their significance especially in the strong coupling regime.

Contribution

It provides a detailed analysis of image charge effects on charged surfaces, highlighting their importance in strong coupling conditions and offering insights where simulations are challenging.

Findings

Image effects are negligible at weak coupling, affecting only second-order fluctuations.

In strong coupling, image effects significantly alter surface interactions.

The study offers analytical insights into complex electrostatic interactions.

Abstract

We study the effect of dielectric inhomogeneities on the interaction between two planparallel charged surfaces with oppositely charged mobile charges in between. The dielectric constant between the surfaces is assumed to be different from the dielectric constant of the two semiinfinite regions bounded by the surfaces, giving rise to electrostatic image interactions. We show that on the weak coupling level the image charge effects are generally small, making their mark only in the second order fluctuation term. However, in the strong coupling limit, the image effects are large and fundamental. They modify the interactions between the two surfaces in an essential way. Our calculations are particularly useful in the regime of parameters where computer simulations would be difficult and extremely time consuming due to the complicated nature of the long range image potentials.