An Approximate Analytic Expression for the Surface Charge Density/Surface Potential Relationship for a Spherical...

An approximate analytic expression for the surface charge density/surface potential relationship (final sigma/psi0) for a spherical colloidal particle in a solution of mixed and nonsymmetrical electrolytes is obtained by solving a nonlinear Poisson-Boltzmann equation using a linearization approximation. The approximate analytic expression is fit for the case of large kappaa(kappa = Debye-Hückel inverse parameter, a = colloidal particle radius), but for the case of small kappaa, the approximate analytic expression is applicable only when kappaa >/= 0.03, with a maximal percent relative error of 5.0, even for surface potentials up to 334 mV (25 degreesC). The approximate analytic expressions reported in the literature have a low limit of kappaa, 0.5 or even 2.0. The present approximate analytic expression has a simple structure and is characterized by the ease with which it is adapted for analysis. Copyright 1998 Academic Press.