Current-Voltage Characteristics and Impedance Spectroscopy: Surface Conduction and Adsorption-Desorption Effects in Electrolytic Cells

We present a theoretical analysis of the current-voltage characteristics of electrolytic cells using their electrical impedance response to a simple periodic external voltage of small amplitude. The examined cell is a thin-film electrolyte (solid, liquid, or gel) sandwiched between flat electrodes at which Ohmic conduction or adsorption-desorption phenomena occur. The basic equations of the Poisson-Nernst-Planck (PNP) model are analytically solved for the case of two diffusing mobile ions (ambipolar diffusion), yielding the charge densities in thermal equilibrium and the profile of the electric potential across the sample. Proper boundary conditions permit us to explore the influence of blocking, Ohmic and adsorbing-desorbing electrodes on the final I(V) curves. Remarkable, it is possible to establish an equivalence between the Ohmic and adsorption-desorption boundary conditions for a general set of physically relevant values of the parameters characterizing the electrodes. This equivalence is a natural way to further incorporate a frequency dispersion caused by the surfaces on the whole response of the cell. This makes the approach well-tailored to investigate the role of the different diffusion coefficients for cations and anions as well as the surface effects on the voltammetry measurements in insulators containing ionic impurities.