Electrode polarization in the presence of a first order ionic trapping reaction

The electric response of a system formed by an electrolyte in contact with porous electrode is investigated. The simple case in which only the positive ions are mobile is considered. The first scenario is the one in which the mobile ions can be immobilized by means of an irreversible reaction. We show that the existing model, based on this assumption, is not suitable to describe in a proper manner the electric response of the cell to an external electric excitation, because in a one dimensional problem the electric current density, usually defined as the sum of the conduction and displacement currents, is not position independent. Consequently, it cannot be used to analyze the current-voltage characteristics, or the electrical impedance of the cell. A generalization of the model, in which the mobile ions are instead immobilized by a reversible reaction, allows the impedance of the cell to be determined in such a way to be meaningful for the investigations carried out with the impedance spectroscopy technique. Special attention is devoted to the problem of a cell limited by one blocking electrode and one transparent electrode, which corresponds to a porous electrode of immersed in an electrolytic solution. The model is subsequently generalized in such a way that the ionic diffusion is regulated by a time fractional equation to take into account the porous nature of the medium. In order to validate the theoretical model, we select a case of study that well represent the modeled system in which the working electrode is made up of lithium titanate () nanotubes in contact with an organic electrolyte. The theoretical predictions of the resulting model are in good agreement with the experimental data on the full frequency range explored.