Chapter 3 Diffuse double layer equations for use in surface complexation models: approximations and limits

Abstract

This chapter presents a discussion on the diffuse double layer formed near a solid–liquid interface, which plays the important role in surface complexation models. On the basis of the Poisson–Boltzmann equation for the diffuse double layer potential, analytic expressions are first derived for the relationship between the diffuse double layer charge and potential for a planar surface in contact with various types of electrolytes. The chapter presents the corresponding approximate analytic expressions for a spherical or cylindrical surface together with the limits of approximations as compared with exact numerical calculations. The chapter also discusses the fluctuation potential of electrolyte ions, which is neglected in the usual Poisson–Boltzmann equation. The chapter presents the most widely used surface complexation model is the triple layer model. The spherical or cylindrical Poisson–Boltzmann equation has not been solved analytically except when the Debye–Hiickel linearization for small potentials is allowed and approximate analytic solutions are available, which are presented. The Laplace equation for the inner region can always be solved not only for the planar case but also for the spherical and cylindrical cases.