The interpretation of the response of an electrochemical system is usually based on the assumption that the current flowing through the electrode is the sum of two independent processes: the faradic current corresponding to the electrochemical processes and the capacitive current corresponding to the response of the interfacial capacitance. However, the separation of faradaic and capacitive currents is questionable in many different cases such as experiments performed in low-concentrated supporting electrolyte or the specific adsorption of diluted reactants. It was also shown that a charge injection to an ideal polarizable electrode results in two relaxations of the double layer corresponding to the charge neutralization on the electrode in the higher frequency domain and the charge rearrangement in the diffuse layer in a lower frequency range[1-3].

Passive layer and thin oxide films formed at a metal surface usually provide a natural protection of the metal resulting in an additional capacitive response in series with the electrical double layer. In the case of the contribution of such superficial phase, 2D- or 3D-film growth, the dielectric-like response of the interface can no longer be neglected. When these phases are kinetically involved in charge transfers, the decoupling can become particularly arbitrary. The modulation of the interfacial capacitance transfer function (MICTF) which was devised by Antaño-Lopez et al. for studying the influence of the ac and dc current on the interface capacitance [4] provides a unique way to overcome this difficulty. The MICTF provides the capacitive response of the interface at a frequency Ω when it is simultaneously scanned at a second frequency ω with the impedance spectrum. That is performed by a proper signal processing of the system response to a two- frequency, ω and Ω, composite measuring signal. It was used to study the double layer relaxation and specific adsorption of halide ions on mercury electrode [5] or to gather information on electron dynamics in TiO₂ dye-sensitized solar-cells [6].

In this work, we report on the response of the oxide film formed on iron in phosphoric acid solution using this double modulation technique. A specific attention will be paid on the capacitive response of the electrode as a function of the potential so as to be able to provide a detailed analysis of both the EIS and the capacity responses with the MICTF technique compared with other data interpretation such as the Mott-Schottky theory.

[1] F.C. Anson, R.F. Martin, C. Yarnitzky, Creation of nonequilibrium diffuse double layers and studies of their relaxation, J. Phys. Chem., 73 (1969) 1835-1842.

[2] C. Yarnitzky, F.C. Anson, Mechanism of charging and discharging ionic double layers at electrodes, J. Phys. Chem., 74 (1970) 3123-3130.

[3] S.W. Feldberg, Theory of relaxation of the diffuse double layer following coulostatic charge injection, J. Phys. Chem., 74 (1970) 87-90.

[4] R. Antaño-Lopez, M. Keddam, H. Takenouti, A new experimental approach to the time-constants of electrochemical impedance: frequency response of the double layer capacitance, Electrochim. Acta, 46 (2001) 3611-3617.

[5] E.R. Larios-Duran, R. Antaño-Lopez, M. Keddam, Y. Meas, H. Takenouti, V. Vivier, Dynamics of double-layer by AC Modulation of the Interfacial Capacitance and Associated Transfer Functions, Electrochim. Acta, 55 (2010) 6292-6298.

[6] H. Cachet, M. Keddam, H. Takenouti, R. Antaño-Lopez, T. Stergiopoulos, P. Falaras, Capacitance probe of the electron displacement in a dye sensitized solar cell by an intermodulation technique: a quantitative model, Electrochim. Acta, 49 (2004) 2541-2549.