Theoretical Impedance Function Research Articles

An EIS based study of a Ni–MH battery prototype. Modeling and identification analysis

Modeling and simulation of the dynamics of batteries is a useful method to improve design and predict their performance. This paper outlines the development of a simple physicochemical model to simulate the impedance response of the Ni–MH battery system. The model describes the individual electrodes as porous flooded structures where the electrochemical processes take place at the active material/electrolyte interface. The physicochemical system parameters are grouped in such a way that the derived simple model can be experimentally identifiable. Experimental electrochemical impedance spectroscopy (EIS) data, recorded with a laboratory built prototype, are used to identify the model parameters by fitting the theoretical impedance function derived from the model. An analysis of the predicted dependence of the impedance function with the battery SOC and the identifiability of different system parameters are presented.

Why Electrochemical Impedance Spectroscopy is the Ultimate Tool in Mechanistic Analysis

The history of Electrochemical Impedance Spectroscopy (EIS) is briefly reviewed, starting with the foundations laid by Heaviside in the late nineteenth century in the form of Linear Systems Theory (LST). Extension of the impedance concept to electrochemical systems was apparently first made by Warburg at the turn of the nineteenth century, when he derived the impedance for a diffusional process. Impedance spectroscopy was next employed extensively using reactive bridges to measure the capacitance of ideally polarizable electrodes (mostly mercury), leading to the development of models for the electrified interface. However, it was the invention of the potentiostat by Hickling in the early 1960s that led to the use of EIS in exploring electrochemical and corrosion mechanisms, primarily because of the ability to probe electrochemical systems at very low frequencies. It is evident that the use of EIS in identifying reaction mechanisms makes use of pattern recognition, currently through inspection. It is argued that, in the future development of EIS, this would be most efficiently done by using artificial neural networks operating in the pattern recognition mode. This strategy would require the creation of libraries of reaction mechanisms for which the theoretical impedance functions are known.

A theoretical approach of impedance spectroscopy during the passivation of steel in alkaline media

A theoretical impedance function is deduced for a proposed mechanism of passive film formation of steel in contact with alkaline aqueous media involving two reaction intermediates: mixed oxide with similar stoichiometry to magnetite and Fe(III)-oxides. The reduction reaction of dissolved oxygen is considered as the only cathodic reaction compensating the anodic current induced by the formation of iron oxides at open circuit potential. The iron dissolution takes place through a chemical dissolution of ferric oxide. A two-layered passive film with 3D structure is considered. A satisfactory agreement between the digital simulations on the basis of the theoretical impedance function and experimental spectra validates the proposed model.

A kinetic interpretation of a negative time constant in impedance equivalent circuits for the dissolution/passive transition

A theoretical impedance function is proposed for the active/passive transition of nickel in an acid sulphate medium. It is considered that passivating species progressively covers the electrode surface. This approximated model predicts the appearance of negative time constants in the impedance spectra when coverage coefficient θ values for passive species are greater than 0.5.

An approximate theoretical impedance analysis of the anodic dissolution of nickel across nickel(II) stabilised by means of competitive anions

A theoretical impedance function for the anodic dissolution of nickel is developed by considering the hypothesis that there are two competitive anions which participate in the stabilization of the electrogenerated Ni(II) species. The experimental effect of chloride ion concentration on nickel electrodissolution process is analyzed by means of a mechanism that considers this competency. It is observed that an increased Cl − concentration causes an increase in Ni(I) surface concentration and a decrease in the kinetic constant rates of the considered mechanism. Moreover, an increased chloride concentration causes a flattening in the low frequencies inductive loop in the Nyquist plot recorded at relatively low stabilization potentials. In the active anodic dissolution/passive transition potential range chloride ions favours a salt layer precipitation which interferes with the passive layer formation.

Reflections on the history of electrochemical impedance spectroscopy

The history of electrochemical impedance spectroscopy (EIS) is briefly reviewed, starting with the foundations laid by Heaviside in the late 19th century in the form of Linear Systems Theory (LST). Warburg apparently was the first to extend the concept of impedance to electrochemical systems at the turn of the 19th century, when he derived the impedance function for a diffusional process that still bears his name. Impedance spectroscopy was next employed extensively using reactive bridges to measure the capacitance of ideally polarizable electrodes (mostly mercury), leading to the development of models for the electrified interface. However, it was the invention of the potentiostat in the 1940s and the development of frequency response analyzers in the 1970s that led to the use of EIS in exploring electrochemical and corrosion mechanisms, primarily because of their ability to probe electrochemical systems at very low frequencies. These inventions have led to an explosion in the use of EIS for exploring a wide range of systems and processes, ranging from conduction in the solid and liquid states, ionic and electronic conduction in polymers, heterogeneous reaction mechanisms, and the important phenomenon of passivity. It is evident that the use of EIS in identifying reaction mechanisms makes use of pattern recognition, currently through inspection. It is argued that, in the future development of EIS, reaction mechanism analysis (RMA) would be most efficiently done by using artificial neural networks operating in the pattern recognition mode. This strategy would require the creation of libraries of reaction mechanisms for which the theoretical impedance functions are known.

Analysis of an impedance function of zinc anodic dissolution

Zinc anodic dissolution has been studied by means of electrochemical impedance spectroscopy (EIS). The kinetic study of the oxidation mechanism has allowed us to propose a theoretical impedance function for this system in deaerated sulphate medium. Relevant information on the faradaic process is provided by analysis of the theoretical impedance function. Kinetic parameters of this system can be calculated from the fitting of experimental data to the faradaic impedance function deduced theoretically. The physical measurements of this function are analysed by means of the dependence of simulated EIS spectra on kinetic parameters.

A time-domain viscous damping model based on frequency-dependent damping ratios

This paper introduces the mathematics and procedures used in developing a time-dependent damping model for integration analyses of structural response. To establish the time-dependent viscous damping model, frequency-dependent damping ratios of the structure under a series of steady-state unit impulses corresponding to actual loads are first calculated. For simplicity, the ratios can be incorporated with the static stiffness of the structure to model approximately the impulse induced damping spectrum. According to the nature of the problem, these ratios can be calculated from the theoretical impedance functions and experimental observations. With the computed damping spectrum, the damping coefficient in the time domain can be obtained with the Fourier transform technique. Adopting the impulse–response method, the damping can be modeled rationally through integration with changing loads. Numerical examples are presented to show the feasibility of this model while the transform criterion is satisfied.

Review of mechanistic analysis by electrochemical impedance spectroscopy

The use of electrochemical impedance spectroscopy (EIS) for mechanistic analysis is briefly reviewed with particular emphasis on the mathematical techniques that may be used to derive theoretical impedance functions and to extract kinetic data. The advantages of EIS for kinetic and mechanism analysis include the fact that it is a steady-state technique, that it employs small signal analysis, and that it is capable of probing relaxations over a very wide frequency range (from <1 mHz to ⪢1 MHz) using readily available instrumentation. EIS also has an enormous advantage over classical transient techniques in that the validity of the data is readily checked using the Kramers—Kronig transforms. The principal disadvantage of the method is that many workers are discouraged by the level of mathematics required to properly analyze impedance data. This has led many researchers to analyze their data in terms of simple equivalent electrical circuits, and hence to ignore the great power of EIS for deriving mechanistic and kinetic information for processes that occur at electrochemical interfaces.

Foundation Impedance Functions: Theory Versus Experiment

Forced‐haimonic‐vibration tests, using an eccentric‐mass shaker, were conducted on two small but different concrete foundations. One foundation (Cholame 1E), located in central California, consisted of a 4‐in.–(10‐cm‐) thick, 50‐in.‐ (1.27‐m‐) square slab with corner piers embedded in moderately stiff alluvial deposits. The other foundation (Station 6), a 6‐in.‐ (15‐cm‐) thick, 48‐in.‐×45‐in.‐(1.22‐m‐×1.14‐m‐) rectangular slab, rested directly on softer deposits in the Imperial Valley of southern California. Experimental foundation‐impedance functions, computed from the vibration‐response data, were similar to theoretical predictions for Station 6; however, significant differences were observed between the experimental and theoretical impedance functions for Cholame 1E. These differences probably resulted from overestimation of the shear‐wave velocities of the top layers of soil directly underneath the Cholame IE foundation, and to a lesser extent from the use of a simple embedded disk to model the founda...

The transfer function of a ferrite head

In read-channel analysis, the head transfer function is usually derived on the basis of a simple equivalent circuit which does not take into account the frequency-dependent complex permeance of the magnetic circuit. In the present work, equations for the transfer function and the impedance of the head are derived taking this permeance into account. It is shown that some of the head parameters which are required for computing the transfer function, but which are very difficult to determine either analytically or by direct measurement, can be found by measuring the head impedance at several frequencies and fitting theoretical impedance function to the experimental results. The transfer function of a ferrite head with 27 bifilar turns was computed with the method.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

An acoustic impedance sensor with two reciprocal transducers

A sensor has been built with two capacitive reciprocal transducers, one used to emit sound, the other acting as a microphone. Since the theoretical impedance functions of tubes are easily obtained, the calibration and the control of the functioning of the sensor are realized by taking detailed measurements of the input impedance of such tubes. This apparatus allows a variety of acoustical impedances to be measured with facility over a frequency range from 0.2–7 kHz.

Experimental study of soil-structure interaction at an accelerograph station

AbstractForced harmonic vibration tests, using eccentric mass shakers, were conducted at the Jenkinsville, South Carolina, accelerograph station to determine the effect of soil-structure interaction on the motions recorded during four small magnitude earthquakes. The station consisted of a 4′ × 4′ × 2′ concrete pad that was embedded in a stiff clayey to medium sandy silt with a shear-wave velocity estimated at 500 fps. A five-foot-high wooden hut was attached to the pad and provided shelter to the SMA-1 accelerograph, which was bolted directly to the pad. The real parts of complex foundation impedance functions, which were obtained by solving the equations of motion for the vibration tests, were generally similar to the theoretical impedance functions for an embedded rectangular foundation. However, the imaginary parts, which are a measure of the foundation damping, were closer to the theoretical prediction for a surface foundation. The tests also showed that the soil-pad-hut system had two strongly coupled translational and rocking modes of vibration in the frequency range of 1 to 60 Hz. The first mode occurred at approximately 11 Hz (N40°W direction) and 17 Hz (N50°E direction) and involved mostly the response of the hut, while the second mode occurred at approximately 50 Hz in both directions and involved mostly the response of the concrete pad. Approximate transfer functions between the motions recorded at the station during the earthquakes and the free-field motions were computed from the experimental data. These functions showed significant amplification in the frequency band 20 to 50 Hz with a maximum amplification of 3 occurring at 50 Hz. Some measurable amplification also was observed at the fundamental natural frequencies in both directions. Calculations based on the transfer functions indicated that the average response spectra of the recorded earthquake motions were amplified by an average of about 30 per cent for frequencies greater than 15 Hz. These results suggest that careful attention must be given to the design of accelerograph stations if they are to record true ground motions over a wide frequency range.