CPE analysis by local electrochemical impedance spectroscopy

Constant-phase elements (CPE) are used extensively in equivalent electrical circuits for fitting of experimental impedance data. The CPE behavior is generally attributed to distributed surface reactivity, surface inhomogeneity, roughness or fractal geometry, electrode porosity, and to current and potential distributions associated with electrode geometry. In this work, different electrochemical systems showing the CPE dependence in the high-frequency range for the overall impedance were considered. Local electrochemical impedance spectroscopy was found to provide a good means for assessing the influence of local variations on the CPE behavior seen in global impedance measurements. A separation between 2D and 3D distributions could be easily observed. In the case of a 2D distribution (AZ91 Mg alloy), the origin of the CPE behavior was the distribution of high-frequency resistance associated with the geometry of the disk electrode; whereas, the capacitance was independent of position. In the case of the aluminium electrode, the CPE behavior could be attributed to a combination of 3D and 2D distributions. Geometric distributions can play a significant role in the impedance response of electrochemical systems, and these distributions can lead to CPE behavior

Constant-Phase-Element Behavior Caused by Coupled Resistivity and Permittivity Distributions in Films

A recent proposed model showed that the impedance of a film with a uniform permittivity and a resistivity that varies along its thickness according to a power-law is in the form of a constant phase element (CPE). This model is further considered in order to assess the effect of non-uniform permittivity profiles. It is shown that a power-law permittivity profile is also compatible with a CPE behavior when resistivity and permittivity vary in opposite ways along the film thickness. This work shows that, for important classes of materials which show CPE behavior, relaxation of the assumption of a uniform permittivity does not alter the conclusions developed in the earlier work, and the formula relating film properties to CPE parameters is shown to apply

The Apparent Constant-Phase-Element Behavior of an Ideally Polarized Blocking Electrode

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 CPE but can be considered to be only an apparent CPE because the CPE exponent is a function of frequency

The Apparent Constant-Phase-Element Behavior of a Disk Electrode with Faradaic Reactions

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 (CPE) character, but with a CPE coefficient alpha that is a function of both dimensionless frequency K and dimensionless current density J. For small values of J, alpha approached unity, whereas, for larger values of J, alpha reached values near 0.78. The calculated values of alpha 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 alpha 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

The origin of the complex character of the ohmic impedance

The local and global Ohmic response for an electrode exhibiting geometry-induced potential and/or current distributions has recently been shown to be represented by a frequency-dependent complex impedance. A physical explanation for this result is provided in terms of the radial contribution to local current density and the decrease in current density along the current lines. Experiments performed with Cu/Al and Mg/Al galvanic couples show that, in regions where a radial current density does not exist, the local Ohmic impedance is independent of position; whereas, in regions where the radial current density cannot be neglected, the local Ohmic impedance is a function of position. Simulations performed on recessed electrodes show that, even in the absence of a radial current, an axial variation of current density gives rise to a complex Ohmic impedance. The complex character of the Ohmic impedance shows that an equivalent circuit, using the usual two-terminal resistor to represent the Ohmic contribution of the electrolyte, provides an inadequate representation of an electrode with geometry-induced current and potential distributions

Local electrochemical impedance spectroscopy: A review and some recent developments

Local 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

Impedance analysis of the distributed resistivity of coatings in dry and wet conditions

A commercial coating (epoxy-polyaminoamide waterborne paint) deposited on a 2024 aluminium alloy was characterized by impedance measurements, first in dry conditions and then as a function of the immersion time in NaCl solutions (wet conditions). The behaviour of the dry coating was close to that of an ideal capacitor and could be accurately modelled with the power-law model corresponding to a constant phase element (CPE) behaviour. Upon immersion in NaCl solutions, the behaviour of the wet coating became progressively less ideal, i.e. farther from a capacitive behaviour. This result provided support to the hypothesis that an inhomogeneous uptake of the electrolyte solution was the cause of the often observed non-ideal responses of wet coatings. The experimental EIS data recorded for immersion times up to 504 hours were compared with models assuming either a power-law or an exponential variation of the coating resistivity along its thickness, respectively implying a phase angle independent of frequency or slightly dependent on it

Local electrochemical impedance spectroscopy: Considerations about the cell geometry

Local electrochemical impedance spectroscopy provides a powerful tool for the investigation of surface heterogeneities on electrode surfaces. However, measurements are greatly influenced by geometry-induced frequency dispersion. In order to account for this frequency dispersion, both simulations and experiments were performed to explore the influence of a recessed electrode on the local and global impedance response. The calculations presented here demonstrated that the depth of the recessed electrode required to achieve a uniform primary current distribution was twice the electrode radius. The calculations provide guidelines for design of LEIS measurements, and were in good agreement with results obtained for a stainless steel disk electrode in a Na2SO4 electrolyte

Determination of water uptake in organic coatings deposited on 2024 aluminium alloy: Comparison between impedance measurements and gravimetry

Electrochemical impedance spectroscopy (EIS) and gravimetric measurements on two water-based coatings, containing either SrCrO4 or a mixture of Cr(VI)-free pigments and deposited on 2024 aluminium alloy, were performed to follow the water uptake in a 0.5 M NaCl solution as a function of exposure time. To account for the observed non-ideal capacitive behaviour, the coating capacitance and dielectric constant values were extracted from the EIS data in two ways: (i) by using a complex-capacitance representation and (ii) by fitting to the EIS data a model that assumed an exponential distribution of coating resistivity. The agreement of values obtained by these independent methods served to validate the model used to account for the observed pseudo constant-phase-element (CPE) behaviour of the coatings. The water uptake calculated from dielectric constant values, employing a linear combination formula, was in good agreement with that directly measured by gravimetry, using supported-films

Identification of Resistivity Distributions in Dielectric Layers by Measurement Model Analysis of Impedance Spectroscopy

The Voigt measurement model, developed in the 1990s for identification of the error structure of impedance measurements, is shown here to have utility in identifying resistivity distributions that give rise to frequency dispersion. The analysis was validated by application to synthetic data derived from a constant–phase–element model, a power–law distribution of resistivity, and an exponential distribution corresponding to a Young impedance. The application to experimental data obtained from coated aluminum demonstrates its utility for interpretation of impedance measurements