The effect of adsorption on the electrostatic behavior of an electrolytic cell

Understanding the interplay between bulk electrostatics and surface adsorption is crucial for optimizing the performance of electrochemical devices, sensors, and soft materials such as hydrogels. The present study aims to determine how ionic adsorption, both in the absence and presence of an external bias voltage, affects equilibrium ion distributions and electrostatic properties, within the framework of the Poisson-Nernst-Planck model. The analysis is performed assuming that the kinetic equation, describing the adsorption-desorption phenomenon, is well approximated by a Langmuir isotherm, containing an adsorption term proportional to the bulk density of adsorbate ions just in front of the adsorbent surface, and a desorption term proportional to the adsorbed ions. The system is modeled as a slab with only ions of a given sign being mobile. We consider both symmetric and asymmetric electrolytic cells under open-circuit, short-circuit and externally applied bias conditions. We determine the equilibrium bulk ion distributions, electric field and potential profiles, as well as the surface density of the adsorbed ions and the surface fields and potentials. The limit of non-interacting surfaces was investigated. The results provide insight into the coupling between surface processes and bulk electrostatics in complex ionic systems.