Specific impedance

The other important consideration concerns the transmission of ultrasound (and other forms of energy) from one medium to another and the importance of impedance matching . When wave energy is transferred from one medium to another then a part is transmitted and the rest reflected. The ratio of reflected to transmitted energies depends on the characteristic impedances of the two media and the transmission is total if these are matched. In the case of acoustic waves the specific impedance (Z) of a medium is given by the product of the density p and the velocity of sound v. that is... 

The property of the interface which controls the relative amounts reflected and transmitted is termed the specific acoustic input impedance Z which is defined as the ratio of the acoustic pressure to the particle velocity associated with the wave motion at the boundary. Note that this definition is similar to that used previously in defining the specific impedance of the media z. The use of the term impedance for both input impedance at the boundary and specific impedance of the media occasionally leads to some confusion if care is not taken. 

As mentioned previously, the reflectivity and transmissibility of the surface is entirely controlled by the ratio of the specific impedance of media 1 and the input impedance at the boundary with media 2. As additional complexities are included in the formulation, they simply present themselves as modifications to these impedances. 

For sound incident at other than the perpendicular direction the equations for reflectivity and transmissibility become significantly more complicated. If the deviation from perpendicular is small and the speed of sound in all three materials is similar, then the behavior can be closely approximated by correcting the specific impedances of the media using Equation 9. However when these conditions are not met, an expression such as that derived by Barnard (6) must be used. 

The quality of a regression can also be assessed by visual inspection of plots. Of course, some plots are more sensitive than others to the level of agreement between model and experiment. As will be demonstrated in this chapter, the plot types can be categorized as given in Table 20.1. The comparison of plot types is presented in the subsequent sections for regression of models to a specific impedance data set. 

Nicholson, P.W. Specific impedance of cerebral white matter. Exp. Neurol. 1965 13 386-401. 

Ranck, J.B., Jr. Analysis of specific impedance of rabbit cerebral cortex. Exp. Neurol. 1963 7 153-174. 

In plane waves, the particle velocity v and the sound pressure are related by the specific impedance of the liquid... 

Fig. 3.10a,b Schematics of the two models for polymer-modified electrodes, a Homogeneous model Zjf j/f, interfacial impedances (s f soIution fiIm f s film substrate), Zb impedance of the bulk phase, R -. solution resistance b porous (heterogeneous) model Z the impedance per unit length of the transport channel in the polymer phase, Z2 the impedance per unit length of the transport channel in the pores, Z3 the specific impedance at the iimer interface, which corresponds to charge transfer and charging processes, solution resistance. (From [68], reproduced with the permission of Elsevier Ltd.)... 

The specific impedance of the pore walls is Zei = /jeoCQ cm ), where... 

For systems where the outer layer does not form, or where the outer layer presents little impediment to the transport of species to or from the barrier layer/outer layer (bl/ol) interface, the specific impedance in the absence of redox couples is very high ( 10 -10 Qcm for NiO on Ni, for example) but in the presence of redox couple [e.g. Fe(CN)6 ] the impedance is often low. This demonstrates that the barrier layers may be good electronic conductors but, generally, are poor ionic conductors. 

The specific impedance is a measure of the AC resistance, and is a function of p and e. Figure 26.2 illustrates schematically the effect of grading in stress distribution. 

A first difficulty results from the fact that the impedance data reflect the overall state of the tested surface integrating the contributions of non-rubbed and rubbed surfaces. Such data must thus be de-convoluted in order to obtain the specific impedances of these two types of surface states. A first approach to this problem might be to use models similar to those describing the impedance of a sample undergoing a localized corrosion (Oltra Keddam, 1990). In that specific case, the overall impedance can be considered as the result of two impedances in parallel, namely the impedance of the non-rubbed surface and the one of the rubbed surface. A strict interpretation requires further an evaluation of the areas of these surfaces, e.g. by using profilometry and surface observations by light optical or scanning electron microscopy. 

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