ABSTRACT

The description of a system, consisting of an equilibrium, inhomogeneous, ionic distribution in the vicinity of charged surface(s), is done addopting the mean field approximation. The solutions of  the resulting non linear elliptic equation (Poisson-Boltzmann Equation) are derived for systems allowing the solution to be written using a finite  number of elementary exponential, logarithimic and polynomial functions. An integral equation for the mean electrostatic potential, equivalent to the Poisson-Boltzmann Equation, is written for systhems showing planar, cylindrical or spherical symmetry. An iterative numerical method for the solution of the integral equation is presented. The implications of the assumptions taken in formulating the model, in a way to have it as a well defined mathematical problem, are analized