Electrostatic Potential Distribution for Spheroidal Surfaces in Symmetric Electrolyte Solutions

Abstract

The electrostatic potential distribution for a charged spheroidal surface immersed in a symmetric electrolyte solution is derived. Such surfaces simulate a wide class of dispersed entities. Two types of boundary condition at the solid surface are considered, constant surface potential and constant amount of surface charges; both conductive and nonconductive surfaces are examined for the latter. The present analysis extends the conventional one-dimensional treatment on simple geometries to a two-dimensional space. A perturbation method is adopted to solve the governing Poisson–Boltzmann equation for the case of thin to moderately thick double layers. The classic results for planar and spherical surfaces can be recovered as special cases of the present analysis. The basic thermodynamic properties of the system under consideration, such as Helmholtz free energy, entropy, and surface excess, are derived. We show that using an equivalent sphere to approximate a spheroid can lead to an appreciable deviation in the prediction of the Helmholtz free energy. For a thin double layer, assuming a planar geometry will underestimate the Helmholtz free energy.