Analytical description of the ionic relaxation in the presence of surface adsorption

The temporal evolution of the surface electric field in a cell in the presence of ionic adsorption is investigated. The analysis is performed in the framework of the Poisson–Nernst–Planck model, based on the conservation of particles and the equation of Poisson for the actual electric potential across the cell, assuming that only the ions of a given sign are mobile. The adsorption is described using a kinetic equation of Langmuir’s type. The simple case of small adsorption is considered, in which the saturation effect can be neglected, and the fundamental equations of the model can be linearized. In this framework, the effective relaxation time describing the dynamics of the system is evaluated, as well as the profiles of the ions and the electric field. The case in which the sample is a half-space is first considered. A more realistic situation where the sample is a slab of thickness d, limited by two identical or different electrodes, is analyzed too. The difference in electric potential due to the adsorption phenomenon between the electrodes is determined. Our analysis shows that its time dependence, when the electrodes have different adsorption properties, is not monotonic.