The surface charge density/surface potential relationship and the Poisson-Boltzmann equation

A procedure is described which provides an approximate analytic expression for the relationship between the surface charge density and the surface potential of a spherical or cylindrical colloidal particle in a general type of electrolyte. The first approximation is found and the approximation error is given. Also derived are the fourth approximation for a symmetric z-z type electrolyte and the second approximation for a symmetric z-z, 2z-2z type electrolyte.