Abstract
A variational principle associated with the free energy is used to determine an accurate yet simple analytical form for the electrostatic potential surrounding a spherical colloid particle. A simple analytical approximation is presented to the solution of the nonlinearized Poisson-Boltzmann equation which yields the Debye-Huckel results in the limit of dilute solutions or small surface potentials and is of comparable accuracy to the numerical solutions even for large surface potentials and concentrated solutions, wherein the region where the Goyu-Chapman theory becomes applicable. Included in the region where this approximation is essentially exact are those surface potentials and colloid sizes which are of particular interest in the study of micelles. It is anticipated that this solution will be useful in investigations of colloid stability and micelle-micelle interactions. (19 refs.)
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