Electrochemistry impedance spectroscopy

Electrochemical impedance spectroscopy leads to information on surface states and representative circuits of electrode/electrolyte interfaces. Here, the measurement technique involves potential modulation and the detection of phase shifts with respect to the generated current. The driving force in a microwave measurement is the microwave power, which is proportional to E2 (E = electrical microwave field). Therefore, for a microwave impedance measurement, the microwave power P has to be modulated to observe a phase shift with respect to the flux, the transmitted or reflected microwave power APIP. Phase-sensitive microwave conductivity (impedance) measurements, again provided that a reliable theory is available for combining them with an electrochemical impedance measurement, should lead to information on the kinetics of surface states and defects and the polarizability of surface states, and may lead to more reliable information on real representative circuits of electrodes. We suspect that representative electrical circuits for electrode/electrolyte interfaces may become directly determinable by combining phase-sensitive electrical and microwave conductivity measurements. However, up to now, in this early stage of development of microwave electrochemistry, only comparatively simple measurements can be evaluated. 

This does not imply that this double layer is at its point of zero charge (pzc). On the contrary, as with every other double layer in electrochemistry, there exists for every metal/solid electrolyte combination one and only one UWr value for which this metal/gas double layer is at its point of zero charge. These critical Uwr values can be determined by measuring the dependency onUWR of the double layer capacitance, Cd, of the effective double layer at the metal/gas interface via AC Impedance Spectroscopy as discussed in Chapter 5.7. 

The technique of AC Impedance Spectroscopy is one of the most commonly used techniques in electrochemistry, both aqueous and solid.49 A small amplitude AC voltage of frequency f is applied between the working and reference electrode, superimposed to the catalyst potential Uwr, and both the real (ZRe) and imaginary (Zim) part of the impedance Z (=dUwR/dI=ZRc+iZim)9 10 are obtained as a function of f (Bode plot, Fig. 5.29a). Upon crossplotting Z m vs ZRe, a Nyquist plot is obtained (Fig. 5.29b). One can also obtain Nyquist plots for various imposed Uwr values as shown in subsequent figures. 

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. 

Warburg impedance is a well-known term in the field of impedance spectroscopy because of the early date at which it was published, the formulation came before the rest of the properties of the interface were known. In fact, for nearly all real situations examined in electrochemistry, the Warburg impedance is relatively small. Thus, for a concentration of 1 mol liter and a frequency of 1 kilocycle s l, and using the normal parameters for room temperature, the resistance is in the milliohm cm-2 range. 

Koryta, J., Dvorak, J., and Kavan, L. (1993) Principles of Electrochemistry, 2nd ed. Wiley. Macdonald, J.R. (1987) Impedance Spectroscopy. Wiley/Interscience. 

Gabrielli, C. (1995) Electrochemical impedance spectroscopy Principles, instrumentation and applications. In I. Rubinstein (Ed.) Physical Electrochemistry. Marcel Dekker. 

Impedance spectroscopy is one of the most informative methods in electrochemistry research [1,2], The essence of the method consists in investigating the response of a target taking place in stationary conditions to weak influences of a variable voltage or to an electric current in a wide range of frequencies. It is possible... 

The most common techniques for testing electrodes are sweep voltammetry, galvanostatic poten-tiometry, rotating disk electrochemistry, and impedance spectroscopy. Detailed information about these techniques may be found in most classical electrochemical textbooks [6-13], and we will present here the basics of these techniques. 

These examples and the general subjects mentioned above illustrate that ion conduction and the electrochemical properties of solids are particularly relevant in solid state ionics. Hence, the scope of this area considerably overlaps with the field of solid state electrochemistry, and the themes treated, for example, in textbooks on solid state electrochemistry [27-31] and books or journals on solid state ionics [1, 32] are very similar indeed. Regrettably, for many years solid state electrochemistry/solid state ionics on the one hand, and liquid electrochemistry on the other, developed separately. Although developments in the area of polymer electrolytes or the use of experimental techniques such as impedance spectroscopy have provided links between the two fields, researchers in both solid and liquid electrochemistry are frequently not acquainted with the research activities of the sister discipline. Similarities and differences between (inorganic) solid state electrochemistry and liquid electrochemistry are therefore emphasized in this review. In Sec. 2, for example, several aspects (non-stoichiometry, mixed ionic and electronic conduction, internal interfaces) are discussed that lead to an extraordinary complexity of electrolytes in solid state electrochemistry. 

Conventional two-electrode dc measurements on ceramics only yield conductivities that are averaged over contributions of bulk, grain boundaries and electrodes. Experimental techniques are therefore required to split the total sample resistance Rtot into its individual contributions. Four-point dc measurements using different electrodes for current supply and voltage measurement can, for example, be applied to avoid the influence of electrode resistances. In 1969 Bauerle [197] showed that impedance spectroscopy (i.e. frequency-dependent ac resistance measurements) facilitates a differentiation between bulk, grain boundary and electrode resistances in doped ZrC>2 samples. Since that time, this technique has become common in the field of solid state ionics and today it is probably the most important tool for investigating electrical transport in and electrochemical properties of ionic solids. Impedance spectroscopy is also widely used in liquid electrochemistry and reviews on this technique be found in Refs. [198 201], In this section, just some basic aspects of impedance spectroscopic studies in solid state ionics are discussed. 

Owing to its extraordinary chemical stability, diamond is a prospective electrode material for use in theoretical and applied electrochemistry. In this work studies performed during the last decade on boron-doped diamond electrochemistry are reviewed. Depending on the doping level, diamond exhibits properties either of a superwide-gap semiconductor or a semimetal. In the first case, electrochemical, photoelectrochemical and impedance-spectroscopy studies make the determination of properties of the semiconductor diamond possible. Among them are the resistivity, the acceptor concentration, the minority carrier diffusion length, the flat-band potential, electron phototransition energies, etc. In the second case, the metal-like diamond appears to be a corrosion-stable electrode that is efficient in the electrosyntheses (e.g., in the electroreduction of hard to reduce compounds) and electroanalysis. Kinetic characteristics of many outer-sphere... 

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. 

The most commonly used method for the electrochemical studies of Li electrodes was impedance spectroscopy (EIS). Table 5 provides a partial listing of papers published during the past two decades dealing with the EIS of Li electrodes. However, the following precautions must be taken into account in the application of EIS to Li electrochemistry and the data analysis ... 

Refs. [i] BardAJ, Faulkner LR (2001) Electrochemical instrumentation. In BardAJ, Faulkner LR (eds) Electrochemical methods, 2nd edn. Wiley, New York [ii] Brett CMA, Oliveira Brett AM (1996) Electrochemistry. Oxford University Press, Oxford [Hi] Retter U, Lohse H (2002) Electrochemical impedance spectroscopy. In ScholzF (ed) Electrochemical methods. Springer, Berlin... 

In electrochemistry, Fourier transformation is usually applied to the current resulting when a periodic (often sine-wave or square-wave) voltage is imposed on a cell. This may be the only signal applied, as in -> impedance spectroscopy or the periodic voltage may modulate an aperiodic ( DC ) potential as in -> AC voltammetry or... 

Finite-space diffusion takes place during the charging of insertion electrodes at moderate frequencies, transforming into mainly capacitive behavior within the limit of very low frequencies, in contrast to the semi-infinite diffusion for solution redox-species (except for thin-layer solution electrochemistry) electrochemical impedance spectroscopy becomes a very useful diagnostic tool for the characterization of insertion mechanisms ... 

Refs. [i] Schwall RJ, Bond AM, Loyd RJ, Larsen JG, Smith DE (1977) Anal Chem 49 1797 [ii] Ragoisha GA, Bondarenko AS (2005) Elec-trochim Acta 50 1553 [iii] Ragoisha GA, Bondarenko AS (2005) Potentiodynamic electrochemical impedance spectroscopy. In Nunez M (ed) Electrochemistry new research. Nova Science Publ, New York, chap 3... 

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. 

Figure 3.15. Schematic representation of the correlation between fuel cell impedance and polarization curve. (Modified from [23], with kind permission from Springer Science+Business Media Journal of Applied Electrochemistry, Characterization of membrane electrode assemblies in polymer electrolyte fuel cells using a.c. impedance spectroscopy, 32(8), 2002, 859-63, Wagner N. Figure 4.)...

Impedance spectroscopy (IS) is a measurement of the conductive and dielectric properties of electroactive systems over a wide range of frequencies. Its popularity and applicability has increased dramatically over the past 25 years with the advent of fast-response potentiostats and frequency response analyzers. Impedance spectroscopy has been applied extensively in electrochemistry, especially in battery and sensor research, and it has been used to study active transport in biological membranes. Skin impedance has also been investigated with IS, but many of these studies attempted to correlate impedance with hydration and provided no insight into the mechanism of charge transport. More recent studies have used IS to elucidate the pathways of ion transport through skin, with special emphasis on understanding the mechanism... 

Impedance spectroscopy is a well-established technique in electrochemistry, and it has been the topic of numerous articles and books. It is actually a subset of a broader category of spectroscopy that includes dielectric and conductance responses. All three terms (impedance, conductance, and dielectric response) are intimately related and are grouped under the general heading of immittance spectroscopy by MacDonald and Johnson [1]. For further detailed information on the various applications of immittance spectroscopy, the reader is directed to Ref. 1-4. 

The impedance spectroscopy method in electrochemistry has been greatly developed in recent years by the availability of state-of-the-art frequency-response analyzers capable of measuring ac impedance over wide frequency... 

A. Lasia, "Electrochemical Impedance Spectroscopy and its Applications," in Modern Aspects of Electrochemistry, R. E. White, B. E. Conway, and J. O. Bockris, editors, volume 32 (New York Plenum Press, 1999) 143-248. 

The promotional index, Pip [Eq. (2)]. After the establishment, via the use of surface spectroscopy (XPS [87,88], UPS [89], TPD [90], PEEM [91], STM [92], work function measurements [93]) but also electrochemistry (cyclic voltammetry [90], potential programmed reduction [94], AC impedance spectroscopy [43,95]), that electrochemical promotion is due to the potential-controlled migration (reverse spillover or backspillover) [13] of promoting ionic species (0 , Na", H, F ) from the solid electrolyte to the gas-exposed catalyst surface, it became clear that electrochemical promotion is functionally very similar to classical promotion and that the promotional index PI, already defined in Eq. (2), can be used interchangeably, both in classical and in electrochemical promotion. 

G. Hasse, M. Christophersen, J. Carstensen, and H. Foil, New insights into Si electrochemistry and pore growth by transient measurements and impedance spectroscopy, Phys. Status Solidi, (a)182, 1,... 

The technique of AC-impedance spectroscopy is one of the most commonly used techniques in electrochemistry, both aqueous and solid [7, 8], An AC voltage of small amplitude and frequency... 

Thus, in the metal/YSZ systems of solid-state electrochemistry, AC-impedance spectroscopy provides concrete evidence for the formation of an effective electrochemical double layer over the entire gas-exposed electrode surface. The capacitance of this metal/gas double layer is of the order of 100-500 pF cm-2 of superficial electrode surface area and of the order 2-10 pF cm-2 when the electrode roughness is taken into account and, thus, the true metal/gas interface surface area is used, comparable to that corresponding to the metal/solid electrolyte double layer. Furthermore AC-impedance spectroscopy... 

Kuang, R, Zhang, D., Li, Y., Wan, Y, and Hou, B. 2009. Electrochemical impedance spectroscopy analysis for oxygen reduction reaction in 3.5% NaCl solution. Journal of Solid State Electrochemistry 13, 385-390. 

Conventional kinetics is largely concerned with the description of dynamic processes in the time domain, and in consequence few conceptual problems are encountered in understanding time resolved experiments. By contrast, frequency resolved measurements often pose more of a challenge to understanding, in spite of the obvious correspondence between the time and frequency domains. This conceptual difficulty may explain why the only frequency resolved method to achieve universal acceptance in electrochemistry is electrochemical impedance spectroscopy (EIS) [27-29], which analyses the response of electrochemical systems to periodic (sinusoidal) perturbations of voltage or current. It is clear that EIS is a very powerful method, and there... 

Gassa, L.M., J.R. VUche, M. Ebert, K. Jiittner, and W.J. Lorenz, Electrochemical impedance spectroscopy on porous electrodes. Journal of Applied Electrochemistry, 1990. 20 pp. 677-685... 

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