Modeling the charge transfer at the electrode-ionic liquid interface in dielectric spectroscopy measurements

The phenomena occurring at the interface between the electrodes and a liquid with ionic conductivity is manifested specifically in the spectrum of the dielectric permittivity. The theoretical model of the electrode polarization (charge space polarization) is met in the dielectric spectroscopy measurements in which electrodes are conductors (allow transfer of electric charge) and the adsorption-desorption of ions occurs on their surface. A pair of ions with equal and opposite charge is considered. The ions are produced by the association-dissociation of neutral molecules. We propose general boundary conditions (BCs) with charge transfer current which contains the adsorption-desorption parameters. The BCs and the basic equations of the Poisson-Nernst-Planck model, i.e. transport equations of charge carriers and Poisson equation, are re-formulated through new variables. The mathematical problem is solved analytically. The results allow finding a criterion for choosing a general and simple admittance expression, thus using a unified approach for different cases. We show that the small signal approximation is no longer needed, at least for modern dielectric spectroscopy equipment. The ions can be point-like or may have finite dimensions. For the last case a model of Stern compact layer with charge transfer is proposed, which allows to calculate the compact layer impedance. Finally we obtain the equivalent admittance of the physical system composed from metal electrodes and ionic liquid in the presence of the Stern layer and the space charge polarization. The limitations of the model are given by the hypothesis of “flat band” and the non-selective adsorption of ions.