Electric energies of a charged sphere surrounded by electrolyte

TL;DR

This paper derives analytical equations to calculate the electric energy of a charged sphere in an electrolyte, showing how ion concentration influences energy components due to screening effects.

Contribution

It introduces a generalized Shell Theorem approach to quantify electric and polarization energies in electrolytes surrounding a charged sphere, considering ion concentration effects.

Findings

Electric energy decreases with increasing ion concentration due to screening.

At zero ion concentration, the electrolyte's field energy equals the charge interaction energy.

At high ion concentrations, energy is distributed as 50% polarization, 25% inside, and 25% outside the sphere.

Abstract

By using the generalized version of the Shell Theorem analytical equations are derived to calculate the electric energy of a charged sphere and the field energy of the electrolyte inside and around the sphere. These electric energies are calculated as a function of the ion concentration of the electrolyte. The work needed to build up the charged sphere (i.e. the total charge-charge interaction energy) decreases with increasing ion concentration of the electrolyte because of the screening effect of the electrolyte on the charge-charge interaction. The energy needed to build up the charged sphere appears as sum of the field energy of the electrolyte and the polarization energy of the electrolyte ions. At zero ion concentration the field energy of the electrolyte is equal with the charge-charge interaction energy, while the polarization energy is zero. At high ion concentrations 50% of the charge-charge interaction energy appears as the polarization energy of ions, 25% as the field energy of the electrolyte inside the sphere and 25% as the field energy of the electrolyte around the sphere.