Solving the Poisson-Boltzmann Equation to Obtain Interaction Energies Between Confined, Like-charged Cylinders

TL;DR

This paper numerically solves the non-linear Poisson-Boltzmann equation to analyze how confinement between charged plates affects the electrostatic interaction energies between like-charged cylinders, revealing reduced repulsion due to confinement.

Contribution

It introduces a numerical approach to study confined cylinder interactions and demonstrates how confinement alters electrostatic screening and interaction energies.

Findings

Confinement reduces the repulsive interaction between cylinders.

Effective surface charge increases with confinement.

Screening length decreases due to confinement.

Abstract

We numerically solve the non-linear Poisson-Boltzmann equation for two cylinders confined by two parallel charged plates. The repulsive electrical double layer component of the cylinder pair potential is substantially reduced by confinement between like-charged plates. While the effective cylinder surface charge is increased by the confinement, the effective interaction screening length is reduced, this effect being dominant so that the repulsive confined cylinder-cylinder interaction potential is reduced.