Equivalent circuit analysis

Macdonald [1983] and by Lenhart, Macdonald, and Pound [1984] to model porous magnetite films on carbon steel in high-temperature chloride solutions and to describe the degradation of porous Ni(OH)2— NiOOH battery electrodes in alkaline solution upon cyclic charging and discharging. We will discuss the first case in some detail, because it is a good example of how a transmission line can provide a physical picture of the processes that occur with a complex corrosion reaction. 

Here R is the resistance of the magnetite per unit length of the pore, is the corresponding quantity for the solution, and I is the length of the pore. For an oxide consisting of n independent parallel pores, the total impedance of the film then becomes 

An effective means of reducing the rate of corrosion of a metal is to protect the surface with a coating. However, coatings generally are not impervious to water or even ions, so that corrosion reactions still proceed at the metal-coating interface. 

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Other Useful Information Obtained by Probes Both EIS and electrochemical noise probes can be used to determine information about the reactions that affect corrosion. Equivalent circuit analysis, when properly applied by an experienced engineer, can often give insight into the specifics of the corrosion reactions. Information such as corrosion product layer buildup, or inhibitor effectiveness, or coating breakdown can be obtained directly from analysis of the data from EIS or indirectly from electrochemical noise data. In most cases, this is merely making use of methodology developed in the corrosion laboratory. 

Ion transport across membranes can be evaluated by using mucosal and serosal electrodes to read transepithelial current (I) and potential difference OP). With these parameters, equivalent circuit analysis can be utilized to account for the relative contributions of transcellular and paracellular pathways. Ionic flux (J) is defined by the Nernst-Planck equation,... 

Equivalent Circuit Analysis. IS measurements yield values of V and Z the real and imaginary components of the impedance, as a function of f, the AC frequency. The data are usually displayed as Nvauist plots (Z, vs. Z ) or Bode plots (impedance modulus,... 

In conclusion, though the inhibitor chemistry is complex, IS sees only a slightly roughened surface covered with an adsorbed film. Since this is representable by a single type of equivalent circuit, analysis of the inhibition process per se is relatively straightforward, as will be discussed below. 

Figure 51. Zero-bias impedance of a 60%/40% LSM/YSZ composite cathode, measured at 950 °C as a function of The magnitude of the lowest-frequency arc ( 1 Hz) was quantified using equivalent circuit analysis and found to scale inversely with P02 and only weakly with temperature. (Reprinted with permission from ref 346. Copyright 2001 Elsevier.)...

Modeling and optimization of chemical sensors can be assisted by creating equivalent electrical circuits in which an ordinary electrical element, such as a resistor, capacitor, diode, and so on, can represent an equivalent nonelectrical physical parameter. The analysis of the electrical circuit then greatly facilitates understanding of the complex behavior of the physical system that it represents. This is a particularly valuable approach in the analysis and interpretation of mass and electrochemical sensors, as shown in subsequent chapters. The basic rules of equivalent circuit analysis are summarized in Appendix D. Table 3.1 shows the equivalency of electrical and thermal parameters that can be used in such equivalent circuit modeling of chemical thermal sensors. 

The diagnostic power of the equivalent circuit analysis is seen in Fig. 4.16, in which the effect of increasing dissipation (resistance R) on the shape of the spectrum is clearly visible. 

Equivalent circuit analysis is well suited for analysis of EIS measurements of conversion coatings and is the primary method for interpreting EIS spectra from conversion coated metal surfaces. A widely accepted generalized equivalent circuit model for the EIS response of pitted conversion coatings is shown in Fig. 22a (66,67). Several related models discussed below are also shown. In the gener-... 

This method of estimating Rc is useful when it can be applied, since the determination is not based on any presumed model of the corrosion damage process or any of the assumptions that come with assignment of an equivalent circuit model. This method is particularly helpful when there is more than one time constant in the spectrum, or the impedance spectrum is particularly complicated. Caution is warranted however. This method of estimation can be in serious error for samples with large capacitance-dominated low-frequency impedances. As a general rule, for this estimation method to be reasonably accurate, the impedance function must exhibit a clear DC limit, or a diffusional response that can be modeled by a constant phase element in equivalent circuit analysis (75). 

Breakdown of anodic films is yet another phenomenon for which EIS is well suited. Equivalent circuit analysis has been used to analyze EIS spectra from corroding anodized surfaces. While changes in anodic films due to sealing are detected at higher frequencies, pitting is detected at lower frequencies. Film breakdown leads to substrate dissolution, and equivalent circuit models must be amended to account for the faradaic processes associated with localized corrosion. 

Treatments of wire meshes can be found in the books of Chantry (1984) and in Goldsmith (1982, Chap. 5) and Holah (1982). These treatments are based mainly on the original work of Ulrich and co-workers (Ulrich et al, 1963 Ulrich, 1968, 1979), who derived an equivalent circuit analysis for wire meshes that works quite well in practice. 

Equivalent Circuit Analysis Technology, Sirotech Ltd., Ness-Ziona, Israel, 1994. 

T. Sun, C. Bemabini and H. Morgan, Single-colloidal particle impedance spectroscopy complete equivalent circuit analysis of polyelectrolyte microcapsules, Langmuir, DOT 10.1021/la903609u (2009). 

Based on the oriented dipole and the interfacial proton transfer mechanism described above, an equivalent circuit was established which described the relaxation time course of a photoelectric current generated by a single chemical reaction step of charge separation and recombination regardless of whether the charge separation is confined within the membrane or takes place across a membrane-water interface [21]. This equivalent-circuit analysis is notable for the absence of any adjustable parameters each and every parameter used for the computation can be measured experimentally (figure 10.2). An example of the... 

The role of the RC (resistive-capacitative) characteristics of the inert support elements in the thin film can be appreciated by the following experiment. Similar oriented BR thin films were deposited on Teflon films of various thicknesses (6.35, 12.7, 25.4 /zm). The relaxation time course varies with the thickness of the Teflon support, but the effect is predictable by the equivalent circuit. Figure 10.3(C) shows that the time course for the thin films of 12.7 and 25.4 fj.m thickness can be predicted by the equivalent-circuit analysis based solely on data obtained at the 6.35 /U,m thin film [10]. As expected, deconvolution of either the... 

The data shown in figure 10.3(C) indicate that the observed signal time course can be altered by varying the RC characteristics of inert support materials. Thus, it appears that the electrical behavior of thin-film devices constructed with electroactive biomaterials may be fundamentally similar to that of conventional microelectronic devices made of inorganic materials. In particular, equivalent-circuit analysis is useful as a design tool in biomolecular electronics. 

Figure 10.3 (A) Equivalent-circuit analysis of the B1 component. The multilayered method was used for the reconstitution. The temperature was 25 °C. The bathing electrolyte solutions contained 0.1 M KCl and 0.01 M L-histidine buffered at pH 2. The measurement was made at an access impedance of 39.2 kQ and an instrumental time constant of 0.355 /xs.

Both Trissl [58] and Rayfield [59] have constructed ultrafast biological photodiodes and Rayfield has demonstrated a rise time of the photoelectric of the order of a few picoseconds. That an oriented BR thin film constitutes a photocell is apparent from our equivalent-circuit analysis. However, the claim... 

The electrical properties of devices constructed with biomaterials follow the same physical laws as do conventional microelectronic devices and thus equivalent-circuit analysis can be used as a design tool for bioelectronics. What sets biomolecular (and synthetic molecular) electronic devices apart from conventional electronic devices is the exploitation of the vast repertoire of organic and biological chemical reactions and the fact that molecular devices can be constructed with a dimension in the nanometer scale (nanotechnology and nanobiology). 

Thus, unlike some kinetic models with many parameters that must be determined implicitly by curve fitting, the present equivalent circuit model offers a stringent test of the validity of our electrochemical analysis. The previously published (34, 36) derivation of the equivalent circuit implies that the equivalent circuit is intended for a photocurrent that arises from a single relaxation process that is, either first-order or pseudo-first-order processes. Thus, a composite photosignal that consists of both B1 and B2 is not expected to agree with the equivalent circuit. Therefore, a prerequisite to test the validity of the equivalent circuit analysis is to devise a successful method to separate the two components, for example, by elimination of the B2 component completely but leaving the B1 component intact. 

Taking into account that an electrolyte and aluminium are conductive materials and aluminium oxide is an insulator we can consider ac equivalent electrical circuit of this system as parallel-connected capacitors CP and CB with a resistor that represents the impedance of this system. On the basis of the equivalent circuit analysis we can define optimum duration of cathodic and... 

J. F. McCann and S. P. S. Badwal, Equivalent circuit analysis of the impedance response of semiconductor-electrolyte-counterelectrode cells, J. Electrochem. Soc. 129 (1982) 551-559. 

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