sion solved analytically for some simple geometries (1). The electrostatic potential distribution for a charged spheroidal Gouy and Chapman were able to solve the PBE exactly for a surface immersed in a symmetric electrolyte solution is derived. planar surface of arbitrary potential immersed in a symmetric Such surfaces simulate a wide class of dispersed entities. Two electrolyte solution (2). The analysis was extended by Hsu types of boundary condition at the solid surface are considered, and Kuo (3) to asymmetric electrolytes through a semianaconstant surface potential and constant amount of surface charges; lytical approach. For a nonplanar surface of arbitrary potenboth conductive and nonconductive surfaces are examined for the tial, the difficulty of solving PBE was circumvented either latter. The present analysis extends the conventional one-dimenby adopting an approximate method (4-16) or by resorting sional treatment on simple geometries to a two-dimensional space.
to a numerical procedure (17)(18)(19). The former includes, for A perturbation method is adopted to solve the governing Poisson-Boltzmann equation for the case of thin to moderately thick double example, the results for cylindrical surfaces (7, 16,22,23) layers. The classic results for planar and spherical surfaces can and spherical surfaces (4-6, 8-14, 20-23).
be recovered as special cases of the present analysis. The basic
The relevant analytical results reported in the literature thermodynamic properties of the system under consideration, such for a charged surface in an electrolyte solution are almost as Helmholtz free energy, entropy, and surface excess, are derived. always limited to simple geometries such as infinite flat plate, We show that using an equivalent sphere to approximate a spherlong cylinder, and sphere. In other words, an essentially oneoid can lead to an appreciable deviation in the prediction of the dimensional problem is considered. A model based on this Helmholtz free energy. For a thin double layer, assuming a planar consideration, although simplifying the mathematical treatgeometry will underestimate the Helmholtz free energy. แญง 1997 ment, is an approximation, at best, and can be unrealistic in
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practice. The linear size of a colloidal particle is finite, and