Capacitance blocking interface

Often a non-blocking interface will behave like a resistance (/ ct) and capacitance (Q,) in parallel. This leads to a semicircle in the impedance plane which has a high frequency limit at the origin and a low frequency limit at Z = (Fig. 10.4). At the maximum of the semicircle if the angular frequency is then ctQin>max = fro which dl can be evaluated. 

Many electrode processes are more complex than those discussed above. Besides this, the impedance of an interface is dependent on its microscopic structure which, in the case of a solid electrode, can have an important influence. Impedance measurements can be used to study complicated corrosion phenomena (Chapter 16), blocked interfaces (i.e. where there is no redox process nor adsorption/desorption), the liquid/liquid interface2425, transport through membranes26, the electrode/solid electrolyte interface etc. Experimental measurements always furnish values of Z and Z" or their equivalents Y and Y", or of the complex permittivities e and e" (e = Y/icoCc, Cc being the capacitance of the empty cell). In this section we attempt to show how to... 

Let us obtain some additional information from this experiment by considering what would happen if we left out KF from the internal compartment. The AgCl/KCl interface would still be nonpolarized and chloride ions would transfer from the internal solution to the solid AgCl phase, but the KC1 /LajF interface would be blocked (i.e., capacitive), because no charged species could transfer across it. Hence, the one-capacitor rule would be violated. The practical consequence would be uncontrollable drift of the Seen-... 

To estimate the effects of electrode polarization, the equivalent circuit of Fig. 16 can be used. It shows a blocking layer capacitance Cb (actually the series combination of two identical capacitors — one at each electrode interface) together with a parallel R — C circuit representing the bulk material. The separate thicknesses of the blocking layer 2tb and the total specimen length, L, must be used to construct the capacitances and resistance. The blocking layer capacitance Cb has the value... 

Figure 6.3 (a) Schematic representation of equivalent circuit for an ion conductor put between a pair of blocking electrode, and (b) the corresponding Nyquist plot. Ideally the sample-electrode interface is composed only of the double-layer capacitance. However, the practical Nyquist plot that corresponds to this frequency region is not vertical to the real axis. The rate-limiting process of this plot is that the ion diffuses to form a double layer. 

The phase transition was induced by Ca and Mg in the case of dipalmitoyl-phosphatidylserine to form a condensed monolayer at the nitrobenzene-water interface, which was stable throughout the potential window. The capacitance in the presence of the condensed monolayer was as low as 1.5 pF cm [101]. The phase transitions from the expanded to the condensed monolayer accompanied the concomitant decrease in the rate of ion transfer but even the condensed monolayers were unable to block it completely [100, 101]. 

Considering the possibility of the appearance of the blocking reaction layer on the surface of the solid electrolyte, it is necessary to consider the resistance Rf, which is connected in the parallel to the double electrical layer capacitance Co on the electrolyte/liquid-metal electrode interface, as shown in Figure 4.17, b. 

In this case, the dispersive capacitance can be described by another interfacial element capable of dealing with such low-frequency dispersion. A blocking capacitive interface response that takes into account a frequency dependency can generally be modeled by an interfacial impedance element such as ... 

For various illumination intensities, the diameter of the semicircle fitting the data at high frequencies equals approximately kT/ely pHl [45-47, 49]. In addition, it was shown that upon illumination, a capacitive peak appears in the C versus V plot of the n-GaAsjO.l M H2SO4 interface [45,46, 51], The peak value proved to be a function of the frequency and the photocurrent density as measured in region G [51]. This behavior is markedly different from the purely capacitive impedance (vertical line in the Nyquist plane and straight Mott-Schottky plot) expected for a blocking s/e interface (see Sect. 2.1.3.1). 

Figure 10 shows a solid electrolyte with two non-blocking electrodes. For non-blocking electrodes, no accumulation of charge occurs at the electrode-electrolyte interface.The Nyquist plot is expected to show a semicircle. The equivalent circuit may take the form of a resistor connected in parallel with a capacitor. In the presence of R, the expected Nyquist plot together with its equivalent circuit is depicted in Figure 11. On the other hand, for blocking electrodes, charge accumulates at the electrolyte-electrode interfaces. This contributes to the double layer capacitances at the interfaces, A vertical spike is thus expected to arise in the Nyquist plot due to the double layer capacitance (Figure 12).

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