Mark E. Orazem

Enhanced Graphical Representation of Electrochemical Impedance Data

Bode plots, corrected for Ohmic resistance, logarithmic plots of the imaginary component of the impedance, and effective capacitance plots are shown to be useful complements to the more traditionally used complex-plane and Bode representations for electrochemical impedance data. The graphical methods are illustrated by synthetic data and by experimental data associated with corrosion in saline environments. Bode plots are shown, in particular, to be confounded by the influence of electrolyte resistance. The plots proposed here provide useful guides to model development for both reactive and blocking systems. The logarithmic plots of the imaginary component of the impedance and effective capacitance plots are useful for all impedance data, and the correction for Ohmic resistance in Bode plots is useful when the solution resistance is not negligible.

Measurement Models for Electrochemical Impedance Spectroscopy I . Demonstration of Applicability

Use of measurement models is suggested as an intermediate step in the analysis of impedance data. In a manner analogous to the routine use of measurement models in the deconvolution of optical spectra, the measurement model could be used to guide development of physicoelectrochemical models by determining whether a data set is consistent with the Kramers‐Kronig relations, by suggesting a form for the error structure of the data, and by providing an indication of the number and type of physical processes that can be resolved from the data. In this paper, a general measurement model is shown to apply for a wide variety of typical electrochemical impedance spectra. The application of the measurement models as a data filter will be addressed in subsequent papers.

Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films I. Theory

I. Theory Bryan Hirschorn,* Mark E. Orazem,** Bernard Tribollet,** Vincent Vivier,*** Isabelle Frateur, and Marco Musiani*** Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, USA Laboratoire Interfaces et Systemes Electrochimiques, UPR 15 du CNRS, Université Pierre et Marie Curie, 75252 Paris cedex 05, France Laboratoire de Physico-Chimie des Surfaces, UMR CNRS-ENSCP 7045, Ecole Nationale Supérieure de Chimie de Paris, Chimie ParisTech, 75005 Paris, France Istituto per l’Energetica e le Interfasi, Consiglio Nazionale delle Ricerche, 35127 Padova, Italy

Constant-Phase-Element Behavior Caused by Resistivity Distributions in Films II. Applications

II. Applications Bryan Hirschorn,* Mark E. Orazem,** Bernard Tribollet,** Vincent Vivier,*** Isabelle Frateur, and Marco Musiani*** Department of Chemical Engineering, University of Florida, Gainesville, Florida 32611, USA Laboratoire Interfaces et Systemes Electrochimiques, UPR 15 du CNRS, Université Pierre et Marie Curie, 75252 Paris cedex 05, France Laboratoire de Physico-Chimie des Surfaces, UMR CNRS-ENSCP 7045, Ecole Nationale Supérieure de Chimie de Paris, Chimie ParisTech, 75005 Paris, France Istituto per l’Energetica e le Interfasi, Consiglio Nazionale delle Ricerche, 35127 Padova, Italy

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.

Application of Measurement Models to Impedance Spectroscopy II . Determination of the Stochastic Contribution to the Error Structure

Development of appropriate models for the interpretation of impedance spectra in terms of physical properties requires, in addition to insight into the chemistry and physics of the system, an understanding of the measurement error structure. The time-varying character of electrochemical systems has prevented experimental determination of the stochastic contribution to the error structure. A method is presented by which the stochastic contribution to the error structure can be determined, even for systems for which successive measurements are not replicate. Although impedance measurements are known to be heteroskedastic in frequency (i.e., have standard deviations that are functions of frequency) and time varying over the duration of the experiment, the analysis conducted in the impedance plane suggests that the standard deviations for the real and imaginary parts of the impedance have the same magnitude, even at frequencies at which the imaginary part of the impedance asymptotically approaches zero. On this basis, a general model for the error structure was developed which shows good agreement for a broad variety of experimental measurements.

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

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 NaCI + 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.

Extension of the measurement model approach for deconvolution of underlying distributions for impedance measurements

Electrochemical impedance spectra frequently reveal the influence of distributions of activation or relaxation processes, but methods for extracting information concerning these distributions are not well developed. Complex non-linear weighted regression of Voigt elements was applied to synthetic impedance data to identify the influence of stochastic noise and incomplete frequency ranges on the ability to resolve the expected distribution. The method was also applied to analysis of impedance data for heat-separated human stratum corneum. Regression of a Voigt series was found to provide a convenient way to identify a distribution of relaxation time constants corresponding to a given experimental spectrum. While the presence of stochastic noise reduces the number of Voigt elements that can be resolved, the parameters trace the same profile for the distribution of time constants. The technique should be particularly useful for experimental systems for which no deterministic model is available.

Corrosion of Tungsten Microelectrodes used in Neural Recording Applications

In neuroprosthetic applications, long-term electrode viability is necessary for robust recording of the activity of neural populations used for generating communication and control signals. The corrosion of tungsten microwire electrodes used for intracortical recording applications was analyzed in a controlled bench-top study and compared to the corrosion of tungsten microwires used in an in vivo study. Two electrolytes were investigated for the bench-top electrochemical analysis: 0.9% phosphate buffered saline (PBS) and 0.9% PBS containing 30 mM of hydrogen peroxide. The oxidation and reduction reactions responsible for corrosion were found by measurement of the open circuit potential and analysis of Pourbaix diagrams. Dissolution of tungsten to form the tungstic ion was found to be the corrosion mechanism. The corrosion rate was estimated from the polarization resistance, which was extrapolated from the electrochemical impedance spectroscopy data. The results show that tungsten microwires in an electrolyte of PBS have a corrosion rate of 300-700 μm/yr. The corrosion rate for tungsten microwires in an electrolyte containing PBS and 30 mM H₂O₂ is accelerated to 10,000-20,000 μm/yr. The corrosion rate was found to be controlled by the concentration of the reacting species in the cathodic reaction (e.g. O₂ and H₂O₂). The in vivo corrosion rate, averaged over the duration of implantation, was estimated to be 100 μm/yr. The reduced in vivo corrosion rate as compared to the bench-top rate is attributed to decreased rate of oxygen diffusion caused by the presence of a biological film and a reduced concentration of available oxygen in the brain.