Debye–Hückel approximation for simplification of ions adsorption equilibrium model based on Poisson–Boltzmann equation

A phenomenological model to represent the ions adsorption equilibrium is proposed. The model is based on the Poisson–Boltzmann equation for electric field modeling, resulting from the charges present in the bulk. With this approach, in solving the Poisson–Boltzmann equation the Debye–Huckel approximation was applied. Solving the equations of the model involves a system of nonlinear equations where the unknowns are the chemical potential and the electric potential on the adsorbent surface. To solve these equations an iterative procedure is presented. The main advantages of the developed model, when applied to the Debye–Huckel approximation, are intuitiveness and the difficulty in drawing physical meaning of parameters, which is simpler, and in fact delivers similar results to those obtained with the Poisson–Boltzmann model, without the Debye–Huckel simplification, in the cases studied.