Two numerical methods were used to calculate the influence of geometry-induced current and potential distributions on the impedance response of an ideally polarized disk electrode. A coherent notation is proposed for local and global impedance which accounts for global, local, local interfacial, and both global and local ohmic impedances. The local and ohmic impedances are shown to provide insight into the frequency dispersion associated with the geometry of disk electrodes. The high-frequency global impedance response has the appearance of a constant-phase element ͑CPE͒ but can be considered to be only an apparent CPE because the CPE exponent ␣ is a function of frequency.

OATAO is an open access repository that collects the work of Toulouse researchers and makes it freely available over the web where possible. This is an author-deposited version published in: http://oatao.univ-toulouse.fr/ Eprints ID : 2418To link to this article : URL : http://dx.Geometry-induced current and potential distributions modify the global impedance response of a disk electrode subject to faradaic reactions. The problem was treated for both linear and Tafel kinetic regimes. The apparent capacity of a disk electrode embedded in an insulating plane was shown to vary considerably with frequency. At frequencies above the characteristic frequency for the faradaic reaction, the global impedance response has a quasi-constant-phase element ͑CPE͒ character, but with a CPE coefficient ␣ that is a function of both dimensionless frequency K and dimensionless current density J. For small values of J, ␣ approached unity, whereas, for larger values of J, ␣ reached values near 0.78. The calculated values of ␣ are typical of those obtained in impedance measurements on disk electrodes. For determining the interfacial capacitance, the influence of current and potential distributions on the impedance response cannot be neglected, even if the apparent CPE exponent ␣ has values close to unity. Several methods taken from the literature were tested to determine their suitability for extracting interfacial capacitance values from impedance data on disk electrodes. The best results were obtained using a formula which accounted for both ohmic and charge-transfer resistances.

Numerical methods were used to calculate the influence of geometry-induced current and potential distributions on the impedance response of a blocking disk electrode with a local constant-phase element behavior. While the calculated global impedance is purely capacitive, the local impedance has high-frequency inductive loops that were observed in experiments conducted on a stainless steel electrode in 0.05 M NaCl + 0.005 M Na 2 SO 4 electrolyte. The calculated global impedance responses are in good agreement with experimental results obtained using both the steel electrode and a glassy-carbon disk in KCl electrolytes of differing concentrations. The computed local and both local and global ohmic impedances are shown to provide insight into the frequency dispersion associated with the geometry of disk electrodes.The term constant-phase element ͑CPE͒ is used in impedance spectroscopy to describe the impedance that, for a blocking circuit, follows a form such as 1-3where the parameters ␣ and Q are constant with respect to frequency. When ␣ = 1, Q has units of a capacitance, i.e., F/cm 2 , and represents the capacity of the interface. When ␣ 1, the system shows behavior that has been attributed to surface heterogeneity 4,5 or to continuously distributed time constants for charge-transfer reactions. 6-10 Independent of the origin of the behavior, the phase angle associated with a CPE is independent of frequency. CPE behavior may arise from a variation of properties in the direction that is normal to the electrode surface. Such variability may arise, for example, from changes in the conductivity of oxide layers 11-18 or from porosity or surface roughness. 19,20 This CPE behavior is said to arise from a 3D distribution, with the third direction being the direction normal to the plane of the electrode. 21,22 For a blocking electrode, a 3D distribution should yield a local impedance that shows CPE behavior at low frequencies. As discussed by Huang et al., 22 local impedance measurements can be easily used to distinguish CPE behavior that has an origin with a 3D distribution from one that arises from a 2D distribution of properties along the surface of the electrode.Using both global and local impedance measurements on a disk made of AZ91 magnesium alloy, Jorcin et al. 21 found CPE behavior that was attributed to a 2D distribution, which yielded locally a pure capacitive response coupled with a radial distribution of local resistance. Jorcin et al. 21 have also found CPE behavior on a pure aluminum disk in which the local impedance response showed a CPE which was modified only slightly by an apparent 2D distribution.The disk geometry is well-defined and amenable to numerical calculation of the impedance response. Newman developed both numerical and analytic treatments for the impedance response of a faradaic reaction on a nonpolarizable disk electrode. 23 A similar approach was taken by Nisancioglu. 24,25 Their work is closely related to numerical solutions for the transient response of a disk electrode to current and/or p...

a b s t r a c tLocal electrochemical impedance spectroscopy (LEIS), which provides a powerful tool for exploration of electrode heterogeneity, has its roots in the development of electrochemical techniques employing scanning of microelectrodes. The historical development of local impedance spectroscopy measurements is reviewed, and guidelines are presented for implementation of LEIS. The factors which control the limiting spatial resolution of the technique are identified. The mathematical foundation for the technique is reviewed, including definitions of interfacial and local Ohmic impedances on both local and global scales. Experimental results for the reduction of ferricyanide show the correspondence between local and global impedances. Simulations for a single Faradaic reaction on a disk electrode embedded in an insulator are used to show that the Ohmic contribution, traditionally considered to be a real value, can have complex character in certain frequency ranges.

A detailed analysis from both numerical calculations and experimental results is presented for the local electrochemical impedance spectroscopy ͑LEIS͒ measurements of a disk electrode, which accounted for the placement of the LEIS probe above the electrode surface. The calculations for an electrode with a local constant phase element behavior were in excellent agreement with experimental observations for a stainless steel electrode in a Na 2 SO 4 /NaCl ͑pH 4͒ electrolyte. Measurement of the local impedance at two positions above the electrode surface allowed estimations of the local interfacial impedance and the local ohmic impedance, which were in excellent agreement with the simulations. The results demonstrate that the local impedance measurement itself cannot be used to estimate the surface area sampled by the LEIS probe. The area sampled must be determined instead by the probe geometry.