Semicircle rotation

In the study of impedance plots, we may observe the depression of semicircles. This is the so-called semicircle rotation of the impedance. This phenomenon is associated with electrode/electrolyte interface double-layer properties. For example, the rough surface of the electrodes or porous electrodes can result in an uneven distribution of the double-layer electric field. This semicircle rotation can be explained using the equivalent circuit presented in Figure 3.10, where R is inversely proportional to the frequency CO (and b is a constant). 

Figure 3.10. Equivalent circuit for explaining the semicircle rotation of the impedance...

Figure 3.11. Semicircle rotation of the total impedance Z in Cartesian coordinates...

In the presence of the faradaic reaction, assuming that the faradaic impedance can be expressed as a simple equivalent resistance, the complex plane plots represent a rotated semicircle p ig. 28(b)], instead of a semicircle centered on the Z axis. Similarly, the double-layer capacitance in the presence of the faradaic reaction may be obtained as... 

Classification of Flow. The flow near bodies like that in Fig. 4.1a can be classified into one of three types two-dimensional (2D), axisymmetric, and three-dimensional (3D). The flow is 2D if the body is invariant in cross-sectional shape along a long horizontal axis (e.g., a long horizontal circular cylinder). An axisymmetric flow takes place near a body (Fig. 4.3ft) whose shape can be generated by revolving a body contour about a vertical line for example, a sphere is generated by rotating a semicircle. If the body meets neither the 2D or axisymmetric requirements, its flow is classified as 3D this class includes the flow around 2D and axisymmetric bodies whose axes have been tilted. 

TMs effective design, made out of coloured card (cardboard), is variation I of the Double sat Cut Away technique, repeated many times on a diagonally pleated sheet of card. The repeated use of even the simplest Cut Away form (here, a semicircle), can create patterns of gyeat beauty. Suspended from a thread and allowed to rotate, the ever-changng pattern of //gjhf and shade across the planes adds greatly to the effect. 

The complex plane plots represent sunken or rotated semicircles with their center located below the real axis [304]. There are also changes in the Bode plots. 

In most corrosion systems the capacitive semicircle exhibits significant deviation from an ideal semicircle. This has often been referred to as frequency dispersion attributed to surface inhomogeneities and distributed circuit elements. Detailed analysis of the experimental data shows that this deviation can be described by a rotation of the semicircle below the real axis by an angle Y, as shown in Fig. 7-7. A good approxima-... 

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