A kinetic derivation of a Butler-Volmer-like equation for the current-voltage characteristics in an adsorbing medium

The DC response of an electrochemical system submitted to an external difference of potential, is investigated by means of the Poisson-Nernst-Planck equations. We suppose that only positive ions are injected into the electrochemical cell by the electrodes. For the injection mechanism we assume that it is well described by Nernst model, where the injected bulk density of ions depends on the difference of electric potential between the electrode and the bulk. Our goal is the determination of the current-voltage characteristic. We show that the functional dependence of the current density on the applied difference of potential is similar to that predicted by the Butler-Volmer equation relevant to an electrolytic cell submitted to an external difference of electric potential.