The Global and Local Impedance Response of a Blocking Disk Electrode with Local Constant-Phase-Element Behavior

Abstract

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...

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“…It first decreases by a few degrees than increases again (Figure 6 b). This behaviour is due to the geometry-induced current and potential distribution, as described in ref [30][31] for a disk electrode. The characteristic frequency f c corresponding to the geometric effect is equal to 1/8R e C [28], where C is the interfacial capacitance.…”

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“…The current density was thus calculated by integrating the local admittance of the system over the electrode disk surface. As previously observed for a planar embedded disk electrode [44][45][46], the results could be expressed in terms of a dimensionless frequency, K, which is defined by…”

“…All measurements were generally performed under potentiostatic regulation, with the amplitude of the applied sinusoidal voltage set to be as large as possible to improve the ratio signal/noise but sufficiently low that the linear approximation of the potential/current curve can be used. For instance, some experiments have been performed using a 100 mV peak-to-peak signal, 50 acquisition cycles, and 7 points per decade of frequency [45]. Home-made software developed for scanning electrochemical microscopy was used for data acquisition.…”

“…In a recent series of papers [44][45][46], our group revisited the basis of the LEIS technique. A key contribution was the definition of three local impedances.…”

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“…The size of admittance maps is influenced by the AC frequency because the potential distribution depends on this parameter in the case of nonuniform potential distribution induced by the cell geometry. This phenomenon was first predicted theoretically by Newman [19] for a disk electrode embedded in an isolating plane, then expanded and explained in details for other systems in more recent works [20][21][22][23][24][25].…”