Electric energies of a charged sphere surrounded by electrolyte

Abstract

By using the recently generalized version of Newton's Shell Theorem [6] analytical equations are derived to calculate the electric potential energy needed to build up a charged sphere, and the field and polarization energy of the electrolyte inside and around the sphere. These electric energies are calculated as a function of the electrolyte's ion concentration and the radius of the charged sphere. The work needed to build up the charged sphere, ECC (i.e. the total charge-charge interaction energy) decreases with increasing ion concentration of the electrolyte because of the electrolyte ions' increasing screening effect on the charge-charge interaction. The work needed to build up the charged sphere appears as a sum of the field and polarization energy of the electrolyte. At zero ion concentration the electrolyte's field energy is equal with ECC while the polarization energy is zero. At high electrolyte ion concentrations (C > 10mol/m3) 50% of ECC appears as the polarization energy of the electrolyte, 25% as the electrolyte's field energy inside the sphere and 25% as the electrolyte's field energy around the sphere.

Keywords

• debye length
• screened potential
• electrolyte's field energy
• charge-charge interaction energy