Bulk impedance

Most of the olefins shown so far, for which reversibility of the bromonium ion formation had been demonstrated, are particular olefins, in which either steric bulk impedes the product forming step, or ring strain in the dibromide product retards this step. In order to check the general occurrence of the reversibility during the bromination reaction, a further approach, based on the cis-trans isomerization of stilbene derivatives during the bromination of the cis isomers, was devised. 

Fig. 10.3 Impedance diagrams for (a) a blocking interface (b) a blocking interface when the associated bulk impedance is taken into account.

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. 

A reasonable approximation of the impact of such a boundary in series to the current flow is provided by a parallel R-C circuit (R, C ) in series to the bulk impedance... 

In the case of electron blocking the indices eon and ion have to be exchanged, but also the total equivalent circuit has to be complemented by circuit elements that take account of the bulk impedance of the blocking electrodes (e.g., YSZ). 

To obtain an adequate impedance match, the desired bulk impedance of the material used can be calculated from equation 9, knowing the speed of sound in the material and the wedge angle. For materials with sound speeds less than that of water the desired bulk impedance is seen to be somewhat less than water. In practice, however, the range of acceptable impedance values is so wide that this... 

Steps 5 to 7 are the same as steps 1 to 3 in the opposite direction The permeation mechanism can be simplified by considering only the series connection of three main steps (i) the surface resistance on the upstream side of the membrane due to the surface dissodation of molecular hydrogen and leading to the formation of sub-surface H ad-atoms (ii) the bulk impedance associated with the transport of hydrogen ad-atoms and (iii) the surface resistance on the downstream side of the membrane due to the surface recombination of hydrogen ad-atoms into molecular hydrogen and subsequent transport of gas away from the interface. 

Each of the circular arcs found in the polycrystalline materials was of the form shown in Figure 2.1.16. It seems that polycrystalUnity introduces anomalous frequency dispersion into the bulk impedance behavior before a second and separate... 

If the bulk impedance is ignored, the phase angle corresponding to the contact impedance is given by... 

In many other highly resistive materials with associated bulk impedance values above 1 Mohm, the range of frequencies corresponding to the bulk-material impedance can still cover several decades of frequency range—often from MHz to low Hz. When conduction through the bulk is not ionic, there would be no significant accumulation of charges at the interface and essentially no double-layer capacitance develops. The total circuit is represented by and the total thickness of the sample d can be used to estimate this capacitive response. 

However, these segments are yet again very small compared to the typical thickness of the sample, and the total thickness of the sample d can be used to estimate the bulk impedance responses. In practice there is no real difference between the two position choices for As the first approximation, we may consider that the "bulk" region ends at the Helmholtz outer layer [1, p. 100], resulting in the representation of Rg... 

As can be seen from Eq. 8-25, this transition frequency value depends on the relative magnitudes of the interfacial impedance (in this case the charge transfer resistance R ) and the bulk impedance RsoJ-1 highly conductive systems the bulk impedance is very small (R j, 0 ohm), the transition fre-... 

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