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Warburg line

Figure 10.2 shows data, both experimental and simulated, for hexacyanofer-rate(ii) ion at a gold disc electrode. The Warburg line at 45° indicates a diffusion process (see Section 8.2.2). The continuous line represents impedance data simulated by the Eco Chimie GPES software (as described below). Here, the fit between theory and experiment is seen to be very good. [Pg.293]

The impedance plot in the Nyquist plane as presented in Figure 1.20 shows two different parts a loop at high frequency and a line at low frequency, also named Warburg line, at 45° angle with the real axis [10]. [Pg.27]

Figure 10a shows the Nyquist plot for a situation when diffusion impedance is much larger compared to the charge transfer resistance. The 45° Warburg line dominates the... [Pg.150]

In the high-frequency limit the circuit behaves like the two resistances in parallel. The impedance is dominated by the smaller of the resistances as the current takes the most conducting pathway. The second term in Eqn. 23 describes a 45° Warburg line, but now it is displaced from the origin by Eqn. 24. It has the same type of dimensionless frequency term as the classical line. [Pg.452]

Reality tells us that a simple model with two resistances and a capacitor is a long way from being capable of representing all of the phenomena observed. Indeed, experience shows that for very low frequencies, the curve does not stop at the point R + Rot, 0. A line appears which symbolizes the phenomena of diffusion of ions in the materials of the electrodes (of the interfaces and/or the electrolyte). This is known as the Warburg line." " From an electrical point of view, we add a series impedance with R. This impedance is determined using the laws of electrochemical diffusion. It is of the form /VJ > where Aw is the Warburg coefficient. [Pg.53]

Figure 2.13. Representation of the impedance of an electrochemical cell with the Warburg line... Figure 2.13. Representation of the impedance of an electrochemical cell with the Warburg line...
Reality is often less simple. The transition between the semi-circle and the Warburg line may be more gentle (see the dashed line in Figure 2.14) ... [Pg.54]

The diffusion with reflecting boundary produces a transmission line terminated by an open circuit (as = °o), revealing a straight -90° capacitive line at low frequencies following the high frequency -45° Warburg line (Fig-... [Pg.84]

Yes, in principle, D can indeed be determined from analysis of the time-dependence of Z, by using only those frequencies represented by the Warburg, as follows. First, we draw a graph ofZ and 71 (both on the y axis) against (o (as The Warburg is seen in such a plot by the frequencies at which the two lines, for 7 and 7", are parallel (see Figure 8.14). [Pg.268]

The interface impedance for a case such as Ag/Ag4Rbl5 will consist of a capacitance (derived from the Helmholtz formula) in parallel with i et so that in the complex plane impedance a semi-circle will be found from which Qi and can be evaluated. Rq will cause this semicircle to be offset from the origin by a high frequency semicircle due to the bulk impedance between the interface and the reference electrode (Fig. 10.12). There can be no Warburg impedance (a line at 45° to the real axis generally due to diffusion effects) in this case. [Pg.282]

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. [Pg.277]

The same consideration applies to the impedance measurement according to Fig. 8.1b. It is a normal electrochemical interface to which the Warburg element (Zw) has been added. This element corresponds to resistance due to translational motion (i.e., diffusion) of mobile oxidized and reduced species in the depletion layer due to the periodically changing excitation signal. This refinement of the charge-transfer resistance (see (5.23), Chapter 5) is linked to the electrochemical reaction which adds a characteristic line at 45° to the Nyquist plot at low frequencies (Fig. 8.2)... [Pg.243]

For a constant phase process, as a diffusion process, the plot is represented as a straight line with one slope (see Figure 8.22) [75], This is evident from Equation 8.86, because when Z, is plotted versus Zr, the Warburg component is represented as a straight line with a unitary slope. [Pg.406]

This low-frequency limit is a straight line of unit slope, which extrapolated to the real axis gives an intercept of (Ra + Rct - 2o2Cd). The line corresponds to a reaction controlled solely by diffusion, and the impedance is the Warburg impedance, the phase angle being jt/4, see Fig. 11.6. [Pg.234]

In contrast, Fig. 11.6 shows a typical Nyquist plot for the layer after switching between the oxidised and reduced forms in background electrolyte for several days (Fig. 11.4(c)). A pronounced semicircular region, Warburg 45° line and vertical capacitive region can clearly be seen. We have fitted these data to the transmission line circuit (Fig. 11.1). The value of Cs obtained is found to vary with dc potential (Fig. 11.7) and with the... [Pg.452]

In a situation where a charge transfer is also influenced by diffusion to and from the electrode, the Warburg impedance will be seen in the impedance plot. This circuit model presents a cell in which polarization is controlled by the combination of kinetic and diffusion processes. The equivalent circuit and the Nyquist and Bode plots for the system are all shown in Figure 2.40. It can be seen that the Warburg element is easily recognizable by a line at an angle of 45° in the lower frequency region. [Pg.87]

The Nyquist plot is presented in Figure 4.9b. At high frequencies (real axis at a value of R. At low frequencies ( 0), it intercepts the real axis at a value of R+R0. Note that the bounded Warburg impedance is easily recognized from its Nyquist plot. At high frequencies, this circuit element looks like a traditional Warburg impedance and shows a 45° line on the Nyquist plot. At low frequencies, it looks like the semicircle of a Randles cell,... [Pg.152]


See other pages where Warburg line is mentioned: [Pg.184]    [Pg.451]    [Pg.104]    [Pg.232]    [Pg.85]    [Pg.91]    [Pg.155]    [Pg.184]    [Pg.451]    [Pg.104]    [Pg.232]    [Pg.85]    [Pg.91]    [Pg.155]    [Pg.270]    [Pg.288]    [Pg.560]    [Pg.169]    [Pg.31]    [Pg.64]    [Pg.83]    [Pg.206]    [Pg.383]    [Pg.265]    [Pg.229]    [Pg.4]    [Pg.5]    [Pg.79]    [Pg.246]    [Pg.349]    [Pg.680]    [Pg.680]    [Pg.680]    [Pg.117]    [Pg.141]    [Pg.224]    [Pg.228]    [Pg.77]    [Pg.232]   
See also in sourсe #XX -- [ Pg.150 ]

See also in sourсe #XX -- [ Pg.104 ]




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