Spectroscopy impedance

Impedance spectroscopy is discussed in depth in the monograph edited by J.Ross Macdonald [17]. It has its origins in the classical work of K.S. Cole and R.H. Cole, published more than 60 years ago, concerned with methods of plotting the response of a dielectric material to applied voltages as a function of frequency. The method assists in identifying observed relaxation effects with processes at the atomic and microstructural levels. For a system having a single well-defined 

This can be verified by eliminating (cox) between the two equations, leading to 

It is instructive, and more elegant, to prove the form of the plot as follows. In the complex plane vectors , roo, rs, u and v are defined as shown in Fig. 2.53. 

A point on the curve (e (co) and e (co) at a particular frequency) is defined by the vector . From the figure 

From the figure = roo+ u and substituting this, and the expression for (firs — roo) given by Eq. (2.134), into Eq. (2.135) leads to v= —jcoxu. This shows that in the complex plane u and v are at right angles to each other that is they define points on a semicircle of diameter (ers - eroo). 

Impedance spectroscopy is an effective technique for probing the features of chemically-modified electrodes and for understanding electrochemical reaction rates (87,88). Impedance is the totally complex resistance encountered 

Example 2.1 The reversible oxidation of dopamine (DA) is a 2e process. A cyclic voltammetric anodic peak current of 2.2 pA is observed for a 0.4-mM solution of dopamine in phosphate buffer at a glassy carbon disk electrode of 2.6 mm2 with a scan rate of 25mV/s. What will ip be for v = lOOmV/s and 1.2mM DA  

Example 2.2 The following cyclic voltammogram was recorded for a reversible couple  

Calculate the number of electrons transferred and the formal potential for the couple. 

Example 2.3 The electropolymeric growth of 2ng polyphenol onto a gold QCM crystal (A = 1cm2 /0 = 5MFLz) resulted in a frequency change of 12.5 Hz. Calculate the frequency change associated with the deposition of 4ng polyphenol onto a 0.5-cm2 crystal (/0 = 8MHz). 

Impedance Spectroscopy (IS) is an a.c. technique for electrical characterization of materials and interfaces based on impedance measurements carried out for a wide range of frequencies (10 f(Hz) 10 ), which can be used for the determination of the electrical properties of homogeneous (solids and liquids) or heterogeneous systems formed by a series array of layers with different electrical and/or structural properties (for example membrane/electrolyte systems), since it permits us a separate evaluation of the electrical contribution of each layer by using the impedance plots and equivalent circuits as models, where the different circuit elements are related to the structural/transport properties of the systems [40, 41). 

When a linear system is perturbed by a small voltage (a sine wave input) v(t) = Vo sin cot, the current intensity is also a sine wave  

The analysis of the impedance data can be carried out by complex plane Z ( ) method by using the Nyquist plot (—Zimg versus Zreai)- The equation for a (RC) circuit gives rise to a semi-circle in the Z ( )) plane with intercepts on the Zreai axis at R o (ra oo) and Rq ( )- 0), being (Rq—Rqo) = Rs the resistance of the system 

The Bode plot versus f) is another common impedance plot which allows 

However, complex systems usually present a distribution of relaxation times and the resulting plot is a depressed semi-circle, which is associated with a non-ideal capacitor or constant phase element (CPE), and its impedance is given by [42]  

In impedance spectroscopy a sinusoidally varying potential with a small amplitude is applied to the interface, and the resulting response of the current measured. It is convenient to use a complex notation, and write the applied signal in the form  

Typically, the frequency lu of the modulation is varied over a considerable range, and an impedance spectrum Z(lS) recorded. Various electrode processes make different contributions to the total impedance. In many cases it is useful to draw an equivalent circuit consisting of 

We consider a simple redox reaction obeying the Butler-Volmer equation. From Eq. (5.15), valid for small overpotentials, the charge- 

At high frequencies diffusion of the reactants to and from the electrode is not so important, because the currents are small and change sign continuously. Diffusion does, however, contribute significantly at lower frequencies solving the diffusion equation with appropriate boundary conditions shows that the resulting impedance takes the form of the Warburg impedance  

There are several ways to plot the impedance spectrum Z(uj) or Z(u). A common procedure is to plot the absolute value Z of the 

Clearly, the oxidation state is Z = 2. Thus, the corrosion rates are 

The electrochemical impedance spectroscopy (EIS) method is very useful in characterizing an electrode corrosion behavior. The electrode characterization includes the determination of the polarization resistance (/J ), corrosion rate (Cfl), and electrochemical mechanism [1,4,6,19-28]. The usefulness of this method permits the analysis of the alternating current (AC) impedance data, which is based on modeling a corrosion process by an electrical circuit. Several review papers address the electrochemical impedance technique based on the AC circuit theory [22-24,29-30]. 

The transfer functions depend on the angular frequency and are expressed as impedance Z (u ) and admittance Y (u ). It should be emphasized that Z (ta) is the frequency-dependent proportionality factor of the transfer function between the potential excitation and the current response. Thus, for a sinusoidal current 

In addition. Ohm s law can be viewed in two different current imposition cases as per ASTM G-106 standard testing method. Hence, 

If a sinusoidal potential excitation is applied to the electrode/solution interface, the potential, current and impedance can be predicted as per Bam and Faulkner mathematical models [6]. Thus, 

The electrical properties of an electrode represented by its capacity C and its parallel charge transfer resistance R r and an ohmic resistance in series for the electrolyte between the electrode and the HL capillary of the RE. 

The impedance of a system is the resistance for alternating current (Equation 1.132). Voltage AE and current AI follow Equations 1.133 with a phase shift I between them. 

If the system behaves like an ohmic resistor, i.e., with Z = R, the applied voltage and the current are in phase, i.e., with a phase shift O = 0. If only a capacitance C is effective, the impedance equals the capacitive resistance Z = l/coC with a phase shift of O = ji/2 with CO = 27i/with the frequency/ An in-series connection of C and R requires the addition of both resistances  

Impedance Z given as a presentation of complex numbers with the real and the imaginary part, and respectively and the phase shift, (a) for C in series, (b) for parallel R r and C (inverse addition of the 

Nyquist diagram of an electrode with parallel capacitance C and charge transfer resistance Rct Re and an ohmic resistance Ro in series. 

Under general conditions it is helpful to select a basic input function, which can easily be used to construct the stimulus under consideration. The response to this basic input will be termed transfer function. If we select the delta function , then 

Rsp arbitrary function = Rsp delta function arbitrary function. (7.115) 

According to Eq. (7.115), the desired response is obtained by convolution of the basic response (Rsp delta function ) with the respective excitation function. The delta function is now just the derivative of the step function of interest to us, so that instead of Rsp delta function it is also possible to use the time derivative of the response to the step function, that we already know (5/ Rsp step function ) . Since the Laplace transformation ( ) converts the convolution into a multiplication it is more concise to write 

In the last equation we exploited the fact that the Laplace transformation of a derivative means to multiply the transform by the function p = (more generally  

If h s Rsp H is the response to the step function H, then it follows according to the previous footnote 107, after exploiting linearity that Rsp Snfn(H(t—uAr)—H(t-nAr—At)) = E fn([h(t-nAr) — h(t — nAr — At)]/At)At. The limit At — 0 provides the convolution integral with a s f, b = dh/dt. Equation (7.115) follows from this, but with h instead of Rsp 5. That both 

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AC impedance spectroscopy is widely employed for the investigation of both solid- and liquid-phase phenomena. In particular, it has developed into a powerfiil tool m corrosion teclmology and in the study of porous electrodes for batteries [, and ]. Its usage has grown to include applications ranging from... 

An essential introduction to the field of microeiectrodes. MacDonald J R 1987 impedance Spectroscopy (New York Wiley) For in-depth theory of impedance. 

Other techniques to detennine the corrosion rate use instead of DC biasing, an AC approach (electrochemical impedance spectroscopy). From the impedance spectra, the polarization resistance (R ) of the system can be detennined. The polarization resistance is indirectly proportional to j. An advantage of an AC method is given by the fact that a small AC amplitude applied to a sample at the corrosion potential essentially does not remove the system from equilibrium. 

Electrochemical Impedance Spectroscopy (EIS) and AC Impedance Many direct-current test techniques assess the overall corrosion process occurring at a metal surface, but treat the metal/ solution interface as if it were a pure resistor. Problems of accuracy and reproducibility frequently encountered in the application of direct-current methods have led to increasing use of electrochemical impedance spectroscopy (EIS). 

Although the above experiments involved exposure to the environment of unbonded surfaees, the same proeess oeeurs for buried interfaces within an adhesive bond. This was first demonstrated by using electrochemical impedance spectroscopy (EIS) on an adhesive-covered FPL aluminum adherend immersed in hot water for several months [46]. EIS, which is commonly used to study paint degradation and substrate corrosion [47,48], showed absorption of moisture by the epoxy adhesive and subsequent hydration of the underlying aluminum oxide after 100 days (Fig. 10). After 175 days, aluminum hydroxide had erupted through the adhesive. 

Impedance spectroscopy This technique is essentially the extension of polarization resistance measurements into low-conductivity environments, including those listed above. The technique can also be used to monitor atmospheric corrosion, corrosion under thin films of condensed liquid and the breakdown of protective paint coatings. Additionally, the method provides mechanistic data concerning the corrosion processes, which are taking place. 

Electrical characteristics of surface films formed electrochemically can be analysed using frequency response analysis (FRA) (sometimes called electrochemical impedance spectroscopy, or This technique is... 

The capacitance. The electrical double layer may be regarded as a resistance and capacitance in parallel see Section 20.1), and measurements of the electrical impedance by the imposition of an alternating potential of known frequency can provide information on the nature of a surface. Electrochemical impedance spectroscopy is now well established as a powerful technique for investigating electrochemical and corrosion systems. 

The method is referred to as electrochemical impedance spectroscopy (EIS), by Mansfield... 

Electrochemical Impedance Spectroscopy see Frequency Response Analysis. 

Frequency Response Analysis the response of an electrode to an imposed alternating voltage or current sign of small amplitude, measured as a function of the frequency of the perturbation. Also called Electrochemical Impedance Spectroscopy. 

J- R. Macdonald, Impedance Spectroscopy, John Wiley, New York, 1987. 

Electrochemical impedance spectroscopy (EIS) in a sufficiently broad frequency range is a method well suited for the determination of equilibrium and kinetic parameters (faradaic or nonfaradaic) at a given applied potential.268,269 EIS has been used to study polycrystalline Au, Cd, Ag, Bi, Sb, and other electrodes.152249 270-273... 

Light intensity and potential-modulated microwave measurements <5//. SDU—t Microwave 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. 

In situ electron transport measurements on conducting polymers are commonly made by using a pair of parallel-band electrodes bridged by the polymer [Fig. 9(A)].141142 Other dual-electrode techniques in which the polymer film is sandwiched between two electrodes [Fig. 9(B)],139,140 rotating-disk voltammetry [Fig. 9(C)],60,143 impedance spectroscopy,144,145 chronoamperometry,146 and chronopotentiometry147 have also been used. 

Impedance spectroscopy is best suited for the measurement of electronic conductivities in the range 10 -7to 10 2S cm 1.145 In principle, it is perhaps the best method for this range, but it is often difficult to interpret impedance data for conducting polymer films. The charge-transfer resistance can make measurements of bulk film resistances inaccurate,145 and it is often difficult to distinguish between the film s ionic and electronic resistances.144 This is even more of a problem with chronoamperometry146 and chronopotentiometry,147 so that these methods are best avoided. 

Impedance, for measurement of the potential of zero charge, 35 Impedance blocks, for polypyrrole, 577 Impedance spectroscopy of electronically conducting polymers, 576 Indium... 

A.D. Frantzis, S. Bebelis, and C.G. Vayenas, Electrochemical promotion (NEMCA) of CH4 and C2H4 oxidation on Pd/YSZ and investigation of the origin of NEMCA via AC impedance spectroscopy, Solid State Ionics 136-137, 863 (2000). 

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. 

For the experiments shown in Fig. 5.30 the ratio Cdi2/Cdi] is on the average 2500, very close to the ratio NG/Ntpb ( 3570)54 where N0 is the gas-exposed electrode surface area and Ntpb is the surface area of the three phase boundaries. These quantities were measured via surface titration and via SEM and the techniques described in section 5.7.2, respectively. Thus once N0 has been measured, AC Impedance spectroscopy allows for an estimation of the three-phase-boundary (tpb) length via ... 

Similar are the conclusions from the work of Kek, Pejonic and Mogensen55 who were first to use AC Impedance spectroscopy for the detailed investigation of Pt, Au and Ni films deposited in YSZ and exposed... 

In summary 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 100-300 pF/cm2, comparable to that corresponding to the metal/solid electrolyte double layer. Furthermore it permits estimation of the three-phase-boundary length via Eq. 5.62 once the gas exposed electrode surface area NG is known. 

Thus, due to the lack of sufficient Ds data for most metals, other than Pt, the most reliable method for measuring Kpb and N,Pb,n is based on AC Impedance spectroscopy as outlined in the previous section and using equation (5.62), i.e. 

Thus the difference jJ02-(S) Po2 (M) is the thermodynamic driving force for O2 backspillover from the support onto the catalyst surface as already discussed in Chapter 3 and as proven by AC Impedance spectroscopy, STM, TPD and XPS as reviewed in Chapter 5. It should be noted in equations (11.4) and (11.5) that the Fermi level of the metal is also the Fermi level of the support. 

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