The impedance method

In Sects. 2.1.3, 2.2.6, and 2.3.2, the mathematics of the first-order small-amplitude techniques were formulated starting from the first-order 

The explicit expressions in the case of the linear rate equation have 

In Fig. 31, the potential dependence of In kt and of 21/2/X = p is illustrated for a selection of linear mechanisms using eqn. (120) with deliberately chosen values for the individual rate constants. Corresponding to a chosen set of rate constants, the rate control is governed by a typical mechanism as indicated. It may be noticed that closely resembling mechanisms cannot always be distinguished. Among the symmetrical examples considered here, the absence or presence of an intermediate chemical step is especially hard to demonstrate. 

If an overall reaction is relatively slow, i.e. kt is small, p cannot be obtained with sufficient accuracy. The kinetic information has then to be obtained from Rct. Here also, non-d.c. reversible behaviour has to be accounted for using eqn. (69) with eqn. (70) or (71). Then at each potential, Rct is a function of both fef and a, i.e. two unknowns. Therefore a fitting procedure of Rct vs. to a certain mechanism is inevitable [123). 

However, it may happen that a non-linear mechanism cannot a priori be excluded. Therefore we now consider the elaboration of Rct and X for the CECDC mechanism treated in Sect. 4.2.2. It is tedious, but not difficult, to derive from eqn. (123) expressions for the partial derivatives F, O and R in terms of f and the mean concentrations c and Cr. It can also be verified that these expressions reduce to simpler ones in the limiting cases for which eqn. (124) holds. The next step is to substitute c 0 and Cr by appropriate functions of c , Cr, and p. In the non-d.c. reversible case, this involves procedures similar to those mentioned in Sect. 4.3.1 and one may wonder whether the impedance parameters are of more diagnostic value than the d.c. current itself. 

---

Ga, In(Ga), Tl(Ga), and Hg in A-methylformamide + NaC104 solutions have been studied by the impedance method.359 The capacitance of the electrical double-layer for all electrodes in the frequency range 200 Hz < v < 5000 Hz was independent of v. The values of Ea=Q were usually... 

A modified immersion method has been used by Hamm et al.140 to obtain electrochemical cell by a closed-transfer system, and immersed in 0.1 M HCIO4 solution at various . was derived from the charge flowing during the contact with the electrolyte under potential control. For the reconstructed Au(l 11M22 X Vayo.l M HCIO4interface, =0.31 0.04V (SCE) (Table 9). Using the impedance method, = 0.34 V (SCE) for recon-... 

The electrical double layer of pc-Cd electrodes has been studied in many works,10,220,221,271,637,662 but the picture is still somewhat unclear. The first attempt to determine the electrical double layer parameters at solid Cd, Pb, and T1 electrodes by the impedance method was made by... 

Guidelli, and methods for the determination of, 63 Heusler and Lang, anisotropic surface potential and, 34 and the impedance method, 35 importance, 5... 

It can be seen that for severely degraded specimens, both the harmonic analysis and Impedance techniques are capable of detecting the presence of gross corrosion. The harmonics method provides a reasonable estimation of the corrosion rate when the Impedance data exhibits Warburg type behaviour. For less severely degraded specimens, especially those exhibiting blister attack, the Impedance method Is not as successful as the harmonic analysis technique. 

Several objective methods are available to determine the freshness of shrimp however, many require a) raw products for analysis, b) complex chemistry and equipment for testing, or c) highly trained technicians. Additionally, some of these methods require extensive analysis time making results meaningless if product has already spoiled or has been released to consumers. Results for the impedance method discussed in the present paper demonstrate that spoilage of raw or thermally processed shrimp can be detect in 30 min with easy sample preparation. The limitations of this method revolve around the requirement for authentic fresh frozen standards as a basis for comparison. Further research is necessary to define the effect of seasonal and geographical variations, and species and size difference. The sum of these factors will likely affect the reproducibility of this method. 

In studies of these and other items, the impedance method is often invoked because of the diagnostic value of complex impedance or admittance plots, determined in an extremely wide frequency range (typically from 104 Hz down to 10 2 or 10 3 Hz). The data contained in these plots are analyzed by fitting them to equivalent circuits constructed of simple elements like resistances, capacitors, Warburg impedances or transmission line networks [101, 102]. Frequently, the complete equivalent circuit is a network made of sub-circuits, each with its own characteristic relaxation time or its own frequency spectrum. 

A renewal of interest in the other rate-controlling processes started in those groups who were developing the impedance method [49, 53] and the a.c. polarographic method [12, 25], probably because it was found that, in many cases, Randles equivalent circuit did not hold and also because the appropriate mathematics are more tractable in the frequency domain. Still, it is recommended that the a.c. studies are combined with the diagnostic results which can be obtained from steady-state techniques and/or cyclic voltammetry. 

As this chapter is primarily dedicated to the study of electrode kinetics, we wish to deal only briefly with the fundamental consequences of reactant adsorption for the methodology of the relaxation techniques, again confined to the potential step and the impedance methods. In addition, we will review briefly the potentialities of these methods with regard to the study of adsorption itself in the case of the reversible electrode reaction. 

The complications and sources of error associated with the polarization resistance method are more readily explained and understood after introducing electrical equivalent circuit parameters to represent and simulate the corroding electrochemical interface (1,16-20). The impedance method is a straightforward approach for analyzing such a circuit. The electrochemical impedance method is conducted in the frequency domain. However, insight is provided into complications with time domain methods given the duality of frequency and time domain phenomena. The simplest form of such a model is shown in Fig. 3a. The three parameters (Rp, Rs, and C d,) that approximate a corroding electrochemical inter-... 

By using the impedance method, Freire et al. also demonstrated that thinner membranes not only show better performance but also are much less sensitive to humidification conditions, cell temperature, and current density. The dependence of the real resistance at high-frequency intercepts on membrane thickness at different current densities is illustrated in Figure 6.14. Linear dependence of the high-frequency resistance, RhJ. on the membrane thickness was observed at 80°C, whereas non-linear dependence of RhJ on membrane thickness was shown at 40°C and 60°C. They explained that this was due to better hydration of the membrane at higher temperatures. It is also observable that Rhf almost does not depend on current density at 80°C and at low current densities rather, Rhf dependence on membrane thickness is almost linear, which indicates that for thicker membranes at high current densities it no longer behaves as a pure resistor due to a capacitive effect caused by less effective back transport of water [9],... 

Figure 18. Pressure vs. particle velocity plot for the impedance method for shock transfer.

Application of the impedance methods in the described manner can be useful to the understanding of films of biochemical materials adsorbed at liquid-liquid interfaces and can provide some information for modeling ion transport across a biological membrane. 

As seen from Table 27.7, capacitance decreases at an increase in current, but to a different degree for different electrodes. For some samples, for example, for Kl, this decrease is too fast because of the very small pore size. For the K2.5 and K3 samples, the effect of current on capacitance is much lower because of the larger size of micropores. Table 27.8 presents the values of specific capacitance measured using the impedance method for the studied electrodes at three frequencies 1 Hz, 10 Hz, and 100 Hz. 

TABLE 27.8. The Values of Specific Capacitance Measured Using the Impedance Method for the Studied Electrodes at Three Frequencies 1, 10, and 100 Hz... 

TABLE 27.9. The Specific Capacitance Values Obtained Using the Impedance Method for Different Frequencies... 

Obviously, visual inspection measurement is the easiest method with the highest accuracy to date. The impedance method also uses it for calibration [10]. 

The theory of the impedance method for an electrode with diffusion restricted to a thin layer is well established [24,25,39,54,65,66,114-116,118,119,121,125,129, 130,133] however, the ideal response—separate Randles circuit behavior at high frequencies, a Warburg section at intermediate frequencies, and purely capacitive behavior due to the redox capacitance at low frequencies (see Fig. 3.7)—seldom appears in real systems. 

M. Rueda, Applications of the impedance method in organic electrode kinetics, in Research in Chemical Kinetics, ed. by R.G. Compton, G. Hancock, vol. 4 (Blackwell, Oxford, 1997), pp. 31-%... 

Thus, thallium ion discharge on thallium amalgam was investigated, using the impedance method, by Randles, and it was shown that log ks changes linearly with the change of the reversible potential as indicated by Eq. (25). The plot rendered (3 = 0.52 (similar results were obtained from Faradaic rectification measurements by Barker et... 

The Impedance Method Applied to the Investigation of Ion-Selective Electrodes, Ion-Selective Electrode Rev. 

The impedance method consists in measuring the response of an electrode to a sinusoidal potential modulation of small amplitude (typically 5-10 mV) at different frequencies. The ac modulation is superimposed either onto an applied anodic or cathodic potential or onto the corrosion potential. Another possibility is to modulate the current and to measure the potential. Impedance measurements as a function of modulation frequency are commonly referred to in the literature as electrochemical impedance spectroscopy, abbreviated EIS. Among the different transient methods discussed in this chapter, EIS is most widely used in corrosion studies. It serves for the measurement of uniform corrosion rates, fortheelucidationofreactionmechanisms, for the characterization of surface films and for testing of coatings. 

While it is often difficult to deduce a unique reaction mechanism from impedance measurements, a detailed knowledge of mechanism is not always required. Therefore, the impedance method finds many practical applications in corrosion science and engineering it is used, for example, in the measurement of corrosion rates, the development of organic coatings, and the characterization of surface films. 

The subject of the study of passivation processes by impedance analysis has been extensively reviewed by Epelboin et al [19]. Other areas where the impedance method has been developed include solid electrolytes and superionic conductors [20], electrocrystallisation [21] and state-of-charge testing of primary batteries [22]. Numerous other examples of the use of a.c. techniques have been collected together by Gabrielli [23],... 

There are excellent summaries on the characterization of polymeric membranes, using methods other than the electron micrograph [66], [67]. Among others, the adsorption method was used by Ohya et al. [68] [69], Broens et al. [70], and Han et al [71 ]. Thermoporometry was used by Bnin et al. [72], Zeman and Tkacik [73], and Cuperus et al [74]. The mo]ccular probe method was used by Michaels [75] and Zeman and Wales [76]. Recently, Dietz cl al. applied the impedance method to determine membrane porosity [77]. 

---