Charge accumulation and potential difference generation in ion adsorbing cells

We analyze charge and field equilibrium distributions in an insulating medium with ions confined by two flat adsorbing–desorbing electrodes without an external electric field. The equilibrium charge density profile of the sample is determined by considering the accumulation of mobile charges at the surface, which generates a surface electric potential. Charging dynamics are explored using a kinetic balance equation, resulting in a time-dependent net charge surface and an inhomogeneous Volterra integral equation of the second kind, and determining the surface electric potential in the half-space approximation. The results show a non-monotonic time dependence for the surface electric potential due to adsorption–desorption processes. The analysis is extended to a finite sample and reveals the presence of a maximum in the time behavior of difference of potential when only one type of ion is selectively adsorbed. The trend is instead monotonic when one electrode only adsorbs positive, and the other one adsorbs only negative ions. This approach may be used as a convenient theoretical tool for further investigation of charge accumulation on the surfaces of electrolytic cells.