Distribution of counterions and interaction between two similarly charged dielectric slabs: Roles of charge discreteness and dielectric inhomogeneity

TL;DR

This study investigates how charge discreteness and dielectric inhomogeneity influence counterion distribution and electrostatic interactions between similarly charged dielectric slabs, revealing complex behaviors including attraction, equilibrium states, and the effects of dielectric differences.

Contribution

It provides a detailed analysis of counterion distribution and slab interactions considering both charge discreteness and dielectric inhomogeneity in the strong coupling limit.

Findings

Dielectric inhomogeneity increases counterion tendency toward the middle at small separations.

Charge discreteness pushes counterions toward the slab surfaces.

Slab interactions can be attractive with multiple equilibrium states depending on parameters.

Abstract

The distribution of counterions and the electrostatic interaction between two similarly charged dielectric slabs is studied in the strong coupling limit. Dielectric inhomogeneities and discreteness of charge on the slabs have been taken into account. It is found that the amount of dielectric constant difference between the slabs and the environment, and the discreteness of charge on the slabs have opposing effects on the equilibrium distribution of the counterions. At small inter-slab separations, increasing the amount of dielectric constant difference increases the tendency of the counterions toward the middle of the intersurface space between the slabs and the discreteness of charge pushes them to the surfaces of the slabs. In the limit of point charges, independent of the strength of dielectric inhomogeneity, counterions distribute near the surfaces of the slabs. The interaction between the slabs is attractive at low temperatures and its strength increases with the dielectric constant difference. At room temperature, the slabs may completely attract each other, reach to an equilibrium separation or have two equilibrium separations with a barrier in between, depending on the system parameters.