Gouy-Chapman theory nonlinear

Since the potential verifies the Poisson equation the nonlinear Gouy-Chapman theory is recovered. In what follows we summarize some results of the nonlinear Gouy-Chapman (NLGC) theory that are useful for the subsequent part of this work. 

Poisson-Boltzmann equation — The Poisson-Boltz-mann equation is a nonlinear, elliptic, second-order, partial differential equation which plays a central role, e.g., in the Gouy-Chapman (- Gouy, - Chapman) electrical -> double layer model and in the - Debye-Huckel theory of electrolyte solutions. It is derived from the classical -> Poisson equation for the electrostatic potential... 

The publication in 1948 of a monograph by Verwey and Overbeek detailing work done by them and others during World War II on the application of the PB equation, and, in particular, the Gouy-Chapman version of it, to the study of colloids has proved to be as important as the initial publications by Gouy and Chapman and Debye and Hiickel. This study laid the foundation for the modern study of colloids and has served as the primary guidepost for most of the work described here. Today, the PB equation, and in particular the Debye-Hiickel (DH) linearized approximation, forms the foundation for modern descriptions of electrolyte and colloid theory. New theories are compared with and often derived from the nonlinear Poisson-Boltzmann equation and in the appropriate limits reduce to the DH result. As has been shown by modern statistical methods, the Debye-Hiickel theory of electrolyte solutions is analogous to the lowest-order harmonic approximation in potential theory. ... 

GC Gouy-Chapman PB, Poisson-Boltzmann DH, Debye-Huckel ADH, apparent Debye-Hflckel NLDH, nonlinear Debye-Huckel PGC, perturbed Gouy-Chapman DIT, dressed-ion theory... 

Gouy [29] and Chapman [30] independently proposed an alternative treatment. It is based on an analytical solution of the nonlinear Poisson-Boltzmann equation for the electric potential created by a system of mobile point charges near a charged wall imitating an electrode surface. However, in the original form of this theory, most of its predictions were at variance with experimental data. 

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