Capacitive loop

Consider first the corrosion of low alloy steel in HC1 per se, i.e. before the addition of organic inhibitors. As shown in Figures 1 and 2 for N80 steel in 15% and 28% HC1 at 65 C, Nyquist plots for steel in concentrated HC1 typically have only one distinct feature a single capacitance loop (a loop above the Z axis) with a hint of a second capacitance loop at lower frequencies. The low-frequency loop is more fully developed in 28% HC1 than in 15% HC1. Mass transport limitations are not evident except under extreme conditions, e.g. above 28% HC1 and 65 C. 

Thus, it appears that in most cases we can treat steel corrosion in concentrated HC1 adequately with the circuit Rq+P/R. In cases where the two capacitance loops are sufficiently distinguishable, we must resort to the full circuit Rq+P/(Rt+Ra/Pa)> where Pa is the CPE counterpart of Ca when the full circuit is prescribed, the fitted n-value of Pa is always less than the n-value of P. 

An interesting incidental effect observed when an inhibitor is present in such a great excess that it forms a separate phase is the appearance of a large low-frequency capacitance loop which we attribute to precipitation (physical adsorption). This effect, however, plays no role in the experiments discussed above, since they all deal with aqueous single-phase solutions. 

Figures 7.4 and 7.5 are the polarization curves and EIS of pyrite under different concentration of the NaOH media. The results show that its corrosive potential move towards negatively and the corrosive ciurent density decreases with the increase of NaOH concentration. The capacitance loop radius increases with the...

The complex plane plots in Fig. 18 illustrate the characteristic components of the impedance response for p-type silicon and heavily doped n-type silicon in the absence of illumination. In the region of pore formation where dt//dlog(/) = 60 mV, the impedance response is characterized by an inductive loop at low frequencies and a capacitive loop at higher frequencies, as shown in Fig. 18 a. In the transition region, a second capacitive loop is observed related to oxide formation at the surface (Fig. 18 b). At more positive potentials in the electropolishing domain (Fig. 18 c) only the two capacitive loops are seen. 

The corresponding time constant mil be T(2 = 9 x 10 s, and the corresponding characteristic frequency mil be f(2 = 7 x 10 Hz or 700 MHz. This frequency is well above the capabilities of electrochemical impedance instrumentation. Thus, the capacitive loop corresponding to the outer layer will not be observed experimentally. The resistance of the layer influences measurements at all frequencies thus, the presence of a growing layer thickness will be manifested as an apparent increase cf the Ohmic resistance. For the situation described in this example, the circuit shown in Figure 9.5 should be amended as shown in Figure 9.6P- The ability to measure the capacitive loop associated with the outer porous layer does not depend on layer thickness, but it is sensitive to the effectixje conductivity of the layer. The effective conductivity of paints and polymer films is much... 

It is easy to show that (B + ARt) always has a positive value. The easiest way to determine whether the low-frequency loop is inductive or capacitive is to calculate (Z — Rp ) at zero frequency. If the value is positive, an inductive loop is present if the value is negative, a capacitive loop appears. Thus the same impedance expression (10.77) can yield two completely different equivalent circuits according to the potential and the constant parcimeter values. 

The local Ohmic impedance Zg accounts for the difference between the loccil interfacial and the local impedances. The calculated local Ohmic impedance for Tafel kinetics with 7 = 1.0 is presented in Figure 13.9 in Nyquist format with normalized radial position as a pcirameter. The results obtained here for the local Ohmic impedance are very similar to those reported for the ideally polarized electrode and for the blocking electrode with local CPE behavior. ° ° At the periphery of the electrode, two time constants (inductive and capacitive loops) are seen, whereais at the electrode center only an inductive loop is evident. These loops are distributed around the asymptotic real value of 1/4. 

Solution The imaginary part of the impedance is plotted on a logarithmic scale in Figure 17.12. A line with slope —0.856 0.007 is shown, which was fitted to the high-frequency data for t = 0.5 h of immersion. This slope has the value of —a, and departure from -1 provides an indication of distributed processes. The low-frequency portion of the high-frequency capacitive loop has a slope o/0.661 0.008. The lack of symmetry suggests that the high-frequency capacitance is in parallel with other reactive processes. Observation of... 

The logo for the 2004 International Symposium on Impedance Spectroscopy, shown in Figure 1, was intended to evoke the lessons of the blind men and the elephant. The multiple loops resemble the Nyquist plots obtained in some cases for the impedance of corroding systems influenced by formation of surface films. The low-frequency inductive loop was deformed to evoke the image of the elephant s trunk, and the capacitive loops resemble the head and body of the elephant. 

A second capacitive loop, loop n, starts to be seen at potential values about -0.3 Vsce which is about 0.1 V more positive than that shown in Fig. 5.32a, and gains... 

Another problem of data modeling is connected with the fact that the same data may be represented by different equivalent circuits. For example, a system containing one capacitive loop (Fig. 4) may be exactly described by either of the two equivalent circuits shown in Fig. 43. In fact, the admittance of these two circuits may be written in the general form ... 

Figure 43. Alternative circuits for the impedance behavior of a system containing one capacitive loop.

The effect of DC bias on a contaminated sample at 100% RH is shown in Figure 5. At bias levels corresponding to threshold and super-threshold levels for electrochemical reactions, the impedance spectrum shows the capacitive loop that intersects the real axis at low frequency (.1 Hz). Zero-DC-bias data, which are not shown, form a similar arc that is large compared to the scale of this plot. This behavior is modelled by a parallel RC circuit, whose resistance decreases from 1 x 10 to 1.6 x 10 and whose capacitance remains constant at approximately 30000 pF, as DC bias is raised from 0 to 3.0 V. The resistances agree with those measured in DC leakage current experiments. The capacitances are 100 times larger than those measured on the clean sample at 100 % RH. 

Figure 12 shows the current-voltage curve and the impedance for bi > b2- For potentials lower than Ec, the impedance has an inductive loop, whereas there is a capacitive loop for potentials greater than Ec. Ec is defined when the two steps have equal rates. At this particular potential, where 9s = 0.5, the impedance is reduced to the charge transfer resistance Ri. It is possible to ascertain that the polarization resistance, Rp, which is the limit of Zp when ct) —> 0, always remains positive and equal to the slope of the current-voltage curve. 

Ren et al. [40] investigated PPy/PANI-coated steel by EIS measme-ments. Comparing with the bare steel, the impedance diagrams of the PPy-coated steel exhibit clearly at least two time constants, with much larger impedance. The capacitive loop expands with the immersion time during the initial stage, and then contracts. As mentioned in the test section, the high-frequency section reflects the responses from the films, and... 

For ZA27samples and those containing 15%SiC at high frequencies seems to be defined one second capacitive loop corresponding to corrosion processes controlled by precipitation and dissolution of ions Zn, see Figure 7 (b, c and d). The equivalent circuit corresponds to that showed in Figure 8 (b). 

The passivating feature attributed to Cr at point D (capacitive loop of characteristic frequency 4 Hz) is therefore already visible at the beginning of the active domain (point A). Simulations of the current-voltage curves and of the impedance diagrams were performed on the basis of a mechanistic description derived from the reaction pattern previously elaborated for pure iron [61,62]. Therefore, coverages by five surface species were introduced in the derivation. The whole body of data led to taking into consideration, at the same time, liie three types of interaction between Fe and Cr listed earlier namely... 

There was a capacitive loop in the high-frequency range due to the double layer capacitance, Cj,. There was a capacitive loop in the low-frequency range caused by the faradic electrochemical reaction process when (8//8X)ss... 

In the corrosion process, there are capacitive loops and inductive loops in the intermediate frequency range induced by area fraction of the partially protective film (0) on the alloy surface, the concentration of intermediate species Mg (Cm), respectively [5],... 

From the above theoretical calculation, the EIS of AZ91D alloy in NaCl aqueous solution consists of one capacitive loop in the high-frequency range (double layer), a capacitive loop (surface state variable Cm) and an inductive... 

The LIS was carried out at open circuit potential (Fig. 4.13), which was aimed at confirming the results of cathodic polarization curve and at demonstrating the ohmic drop between working and reference electrode. The EIS of Mg-Gd-Y alloy under TEL consisted of two capacitive loops in the high and low frequency ranges. 

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