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

Abstract

An approximate analytic expression for the surface charge density/surface potential relationship (ς/ψ0) 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 κa(κ = Debye–Hückel inverse parameter,a= colloidal particle radius), but for the case of small κa,the approximate analytic expression is applicable only when κa≥ 0.03, with a maximal percent relative error of 5.0, even for surface potentials up to 334 mV (25°C). The approximate analytic expressions reported in the literature have a low limit of κa,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.