Fundamentals of electrochemical impedance spectroscopy

It is hoped that the more advanced reader will also find this book valuable as a review and summary of the literature on the subject. Of necessity, compromises have been made between depth, breadth of coverage, and reasonable size. Many of the subjects such as mathematical fundamentals, statistical and error analysis, and a number of topics on electrochemical kinetics and the method theory have been exceptionally well covered in the previous manuscripts dedicated to the impedance spectroscopy. Similarly the book has not been able to accommodate discussions on many techniques that are useful but not widely practiced. While certainly not nearly covering the whole breadth of the impedance analysis universe, the manuscript attempts to provide both a convenient source of EK theory and applications, as well as illustrations of applications in areas possibly u amiliar to the reader. The approach is first to review the fundamentals of electrochemical and material transport processes as they are related to the material properties analysis by impedance / modulus / dielectric spectroscopy (Chapter 1), discuss the data representation (Chapter 2) and modeling (Chapter 3) with relevant examples (Chapter 4). Chapter 5 discusses separate components of the impedance circuit, and Chapters 6 and 7 present several typical examples of combining these components into practically encountered complex distributed systems. Chapter 8 is dedicated to the EIS equipment and experimental design. Chapters 9 through 12 

I owe thanks to many others who have helped with this project. I am especially grateful to John Wiley Sons, Inc. and Lone Wolf Enterprises, Ltd. for their conscientious assistance with many details of preparation and production. Over the years many valuable comments and encouragement have been provided by colleagues through the electrochemical community who assured that there would be a demand for this book. I also would like to thank my wife Laura and my son William for affording me the time and freedom required to undertake such a project. 

The concept of electrical impedance was first introduced by Oliver Heaviside in the 1880s and was soon afterward developed in terms of vector diagrams and complex numbers representation by A. E. Kennelly and C. P. Steinmetz [1, p. 5]. Since then the technique has gained in exposure and popularity, propelled by a series of scientific advancements in the field of electrochemistry, improvements in instrumentation performance and availability, and increased exposure to an ever-widening range of practical applications. 

In spite of the ever-expanding use of EIS in the analysis of practical and experimental systems, impedance (or complex electrical resistance, for a lack of a better term) fundamentally remains a simple concept. Electrical resistance R is related to the ability of a circuit element to resist the flow of electrical current. Ohm s Law (Eq. 1-1) defines resistance in terms of the ratio between input voltage V and output current I  

FIGURE 1-2 Impedance experiment sinusoidal voltage input Vat a single frequency/and current response / 

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It is not necessary to deal with these techniques in detail here, since there are several books and monographs on the subject. The fundamental theory and practice of electrochemical and spectroelectrochemical methods can be found in [1,2] and also in [3-5], where investigations of polymeric surface layers are emphasized. Excellent monographs on EQCM [6-9] and PBD [10] are also recommended for further studies. Infrared, Mdssbauer spectroscopy, ellipsometry, etc., are described in [I I], while electron spin resonance is discussed in [12], radiotracer in [13], scanning tunneling microscopy in [14], and scanning electrochemical microscopy in [15]. The fundamentals of electrochemical impedance spectroscopy are treated in [1,2,16] however, the different models elaborated for electrochemically active films and membranes can be found in various papers (see later), while the most important methods for analyzing impedance spectra, as reported before 1994, are well summarized in [3]. Nevertheless, the essential elements of these techniques are briefly discussed here, in order to help the reader to understand the experimental material presented in this book. 

This chapter has provided basic electrical fundamentals, including concepts and definitions for circuit elements, and their relationships within electric circuits. Various basic AC electric circuits were also presented. Following upon primary circuit theories, the concept of electrochemical impedance spectroscopy and basic information about EIS was introduced. This chapter lays a foundation for readers to expand their study of EIS and its applications in PEM fuel cell research and development. 

However, EIS is a very sensitive technique and must be used with great care. In addition, it is not always well understood. This may be because it is often difficult for nonspecialists to understand existing reviews on EIS and frequently the articles do not show the complete mathematical development of equations connecting the impedance with the physicochemical parameters. It should be stressed that EIS cannot give all the answers. It is a complementary technique and other methods must also be used to elucidate the interfacial processes. The purpose of this chapter is to fill this gap by presenting a modem and relatively complete review of electrochemical impedance spectroscopy, including the mathematical development of the fundamental equations. 

Refs. [i] Oldham KB, Myland JC (1994) Fundamentals of electrochemical science. Academic Press, San Diego, p 20, 400 [ii] Westphal WH (ed) (1952) Physikalisches Worterbuch. Springer, Berlin [Hi] Macdonald JR (1987) Impedance spectroscopy. Wiley, New York... 

Potentiodynamictechniques— are all those techniques in which a time-dependent -> potential is applied to an - electrode and the current response is measured. They form the largest and most important group of techniques used for fundamental electrochemical studies (see -> electrochemistry), -> corrosion studies, and in -> electroanalysis, -+ battery research, etc. See also the following special potentiodynamic techniques - AC voltammetry, - DC voltammetry, -> cyclic voltammetry, - linear scan voltammetry, -> polarography, -> pulse voltammetry, - reverse pulse voltammetry, -> differential pulse voltammetry, -> potentiodynamic electrochemical impedance spectroscopy, Jaradaic rectification voltammetry, - square-wave voltammetry. 

To increase fundamental knowledge about ionic resistance, it is important to develop a methodology to experimentally isolate the contributions of the various cell components. Electrochemical impedance spectroscopy has been widely used by Pickup s research group to study the capacitance and ion conductivity of fuel cell catalyst layers [24-27] they performed impedance experiments under a nitrogen atmosphere, which simplified the impedance response of the electrode. Saab et al. [28] also presented a method to extract ohmic resistance, CL electrolyte resistance, and double-layer capacitance from impedance spectra using both the H2/02 and H2/N2 feed gases. In this section, we will focus on the work by Pickup et al. on using EIS to obtain ionic conductivity information from operational catalyst layers. 

Electrochemical impedance spectroscopy is a mature technique, and its fundamental mathematical problems are well understood. Impedances can be written for any electrochemical mechanism using standard procedures. Modem electrochemical equipment makes it possible to acquire data in a wide range of frequencies and with various impedance values. The validity of experimental data can be verified by standard procedures involving Kramers-Kronig transforms. Several programs either allow for the use of predefined simple and distributed elements in the construction of electrical equivalent circuits or directly fit data to equations (which should be defined by the user). 

E. Ivers-Tiffee, A. Weber, H. Schichlein, Electrochemical impedance spectroscopy (methods in electrocatalysis for fuel cells), in Handbook of Fuel Cells Fundamentals, Technology, Applications, ed. by W. Vielstich, A. Lamm, H. Gasteiger, vol. 2 (Wiley, Chichester, 2003), pp. 220-235... 

AC conductance is noninvasive, quick and the test instruments are relatively inexpensive. There are, however, some fundamental problems. Most commercial testers use only one frequency, which is commonly below 100 Hz. Multi-frequency systems would be more accurate but require complex data interpretation software and expensive hardware. In this section we focus on electrochemical impedance spectroscopy (EIS), a method that overcomes some of the shortcomings of AC conductance. 

Electrochemical Impedance Spectroscopy (EIS) is a powerful technique for the characterization of electrochemical systems. The fundamental approach of all impedance methods is to apply a small-amplitude sinusoidal excitation signal to the system xmder investigation and measure the response (current or voltage or another signal of interest). An advantage of EIS compared to amperometry or potentiometry is that labels are no longer necessary, thus simplifying sensor preparation. However, the use of labels (like enzymes or nanoparticles) increases a lot the sensitivity of the method [23-26]. 

Various planar membrane models have been developed, either for fundamental studies or for translational applications monolayers at the air-water interface, freestanding films in solution, solid supported membranes, and membranes on a porous solid support. Planar biomimetic membranes based on amphiphilic block copolymers are important artificial systems often used to mimic natural membranes. Their advantages, compared to artificial lipid membranes, are their improved stability and the possibility of chemically tailoring their structures. The simplest model of such a planar membrane is a monolayer at the air-water interface, formed when amphiphilic molecules are spread on water. As cell membrane models, it is more common to use free-standing membranes in which both sides of the membrane are accessible to water or buffer, and thus a bilayer is formed. The disadvantage of these two membrane models is the lack of stability, which can be overcome by the development of a solid supported membrane model. Characterization of such planar membranes can be challenging and several techniques, such as AFM, quartz crystal microbalance (QCM), infrared (IR) spectroscopy, confocal laser scan microscopy (CLSM), electrophoretic mobility, surface plasmon resonance (SPR), contact angle, ellipsometry, electrochemical impedance spectroscopy (EIS), patch clamp, or X-ray electron spectroscopy (XPS) have been used to characterize their... 

Analysis based on electrochemical impedance spectroscopy (EIS also called AC impedance spectroscopy) allows estimation of frequency behavior, quantification of resistance, and the ability to model equivalent circuits (ECs) of ES systems. The fundamental EC for a double-layer circuit, as discussed in Chapter 2, contains series resistance and double-layer capacitance. In addition, there is often a faradic parallel resistance from impurities in the carbon. In the pseudocapacitive case, the faradic resistance is a related reciprocal of the overpotential-dependent charge transfer [2,21]. 

In short, there is little research related to the study of mechanical and electrochemical properties of Zn-Al alloys as well as Zn-Al alloys MMCs containing SiC and AI2Q3 particulations with different grain structures in the matrix. Also there is lack of fundamental study on the performance of Zn-Al alloys and their MMCs in corrosive environments when both solidification microstructure and type of particle distribution are in consideration. In the present research, Zn-Al-SiC and Zn-Al-AI2O3 composites are prepared and solidified by vertical directional solidification method. By means of voltammograms and electrochemical impedance spectroscopy, the corrosion resistances of Zn-Al matrix composite materials with different types of particles are obtained and analyzed and the results are compared. 

Electrochemical impedance spectroscopy (EIS) has also been discussed in Chapter 3. EIS is generally used to diagnose the performance limitations of fuel cells. There are three fundamental sources of voltage loss in fuel cells kinetic losses (charge-transfer activation), ohmic losses (ion and electron transport), and mass transfer losses (concentration). EIS can be used to distinguish and... 

It should also be recalled that a full electrochemical, as well as spectroscopic and photophysical, characterization of complex systems such as rotaxanes and catenanes requires the comparison with the behavior of the separated molecular components (ring and thread for rotaxanes and constituting rings in the case of catenanes), or suitable model compounds. As it will appear clearly from the examples reported in the following, this comparison is of fundamental importance to evidence how and to which extent the molecular and supramolecular architecture influences the electronic properties of the component units. An appropriate experimental and theoretical approach comprises the use of several techniques that, as far as electrochemistry is concerned, include cyclic voltammetry, steady-state voltammetry, chronoampero-metry, coulometry, impedance spectroscopy, and spectra- and photoelectrochemistry. 

With all its complications and uncertainties, impedance spectroscopy, as seen at the end of the twentieth century, is a growing technique in fundamental electrodic analysis [cf. the seminal contributions of (independently) D. D. and J. R. MacDonald]. Among its advantages is that the necessary equipment is less expensive than that of competing spectroscopic equipment and that it can provide information on any electrochemical situation (e.g., it is not limited by, say, the need for specular reflectance, as in ellipsometry). 

Fleig reviews fundamental aspects of solid state ionics, and illustrates many similarities between the field of solid state electrochemistry and liquid electrochemistry. These include the consideration of mass and charge transport, electrochemical reactions at electrode/solid interfaces, and impedance spectroscopy. Recent advances in microelectrodes based on solid state ionics are reviewed, along with their application to measuring inhomogeneous bulk conductivities, grain boundary properties, and electrode kinetics of reactions on anion conductors. 

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