A generalized model of the equivalent circuits in the electrochemical impedance spectroscopy

The electrochemical impedance spectroscopy (EIS) is widely used in electrochemical research in spite of some ambiguous issues concerning the data evaluation and interpretation. The quantitative evaluation of EIS data takes place via the application of equivalent electrical circuits (EECs), which describe the transfer function of the electrochemical process in terms of electrical circuit elements: resistance, capacitance and other, more specific elements, e.g. the Warburg impedance and the Constant Phase Element (CPE). There is a general agreement among electrochemists that the CPE is inherently related to the dispersion of the parameters (time constants) of the EEC. The measured impedance data contains the effects of the EEC, determined by the kinetics of the electrochemical reaction and by the structure of the electrode surface and, superimposed to it, the effect of the parameter dispersion (“distributed elements”), which spreads the characteristic shapes of the ideal EEC elements. One of the main difficulties in evaluation of EIS data is to differentiate between the effects of the EECs and the distributed elements (CPE). Instead of separation, this paper proposes a model incorporating both the EEC and the CPE in the same mathematical formulation, also proposing a method to identify the time constants of complex EECs combined with the dispersion of time constants. The final equations are linear, in contrast to the general trends in impedance data analysis, therefore the advantages of the linear transformations of originally nonlinear problems is also discussed. The theory is checked on the quinhydrone redox system and also on simulated impedance data.