A functional theoretical approach to the electrical double layer of a spherical colloid particle Original Research Article

By employing the iterative method in functional analysis, the governing Poisson–Boltzmann equation of a spherical colloid particle that is based on the so-called Gouy–Chapman–Stern model has been solved under general potential condition. The solution of the potential in the second iteration is a function of the distance from the center of the particle with the concentration of ions, the temperature of system and the particle charge as parameters. From this solution the radius and the surface potential of a particle have been defined and the corresponding values have been estimated with the help of the Newtonʹs iterative method. Based on the equivalent condenser model with the same center of the particle, the correlation among the electric double layer thickness, the radius and the surface potential has been established. The analysis of the quartic equation of the thickness shows that it has a sole positive real root which is much more reasonable than the Debye reciprocal length from the Debye–Hüchel approximation to represent the thickness. The calculation of the thickness can be much simplified in case of a higher concentration of ions or a higher particle charge.