Interaction energy between two separated charged spheres surrounded inside and outside by electrolyte

TL;DR

This paper derives analytical equations to calculate the electric interaction energy between two charged spheres in electrolyte, considering various factors like ion concentration, temperature, and sphere size, and extends the model to multiple spheres.

Contribution

It introduces a generalized analytical model for interaction energy between charged spheres in electrolyte, extending Newton Shell Theorem and including electrolyte effects.

Findings

Interaction energy decreases with higher electrolyte ion concentration.

Interaction energy increases with higher temperature.

At zero electrolyte concentration, the model reduces to Coulomb's law.

Abstract

By using the recently generalized version of Newton Shell Theorem analytical equations are derived to calculate the electric interaction energy between two separated charged spheres surrounded outside and inside by electrolyte. This electric interaction energy is calculated as a function of the electrolyte ion concentration, temperature, distance between the spheres and size of the spheres. At the same distance between the spheres the absolute value of the interaction energy decreases with increasing electrolyte ion concentration and increases with increasing temperature. At zero electrolyte ion concentration the derived analytical equation transforms into the Coulomb equation. Finally, the analytical equation is generalized to calculate the electric interaction energy of N separated charged spheres surrounded by electrolyte.