Impedance frequencies, surface-bound

By using the imaginary component of the measured impedance data for PtO-OTS and PtO-OTS-Rh electrodes (Table II) at a frequency of 1000 Hz (after subtracting Ru), the calculated Cm is 867 nF/cm2 and Cbl is thus 584 nF/cm2 using = 10 jiF/cm2 and 0 = 0.97, which are close to the theoretical values derived from the best curve fit simulation. We conclude that the simplified equivalent circuit may be adequate for the surface-bound membrane electrode. The thickness of the tightly packed membrane bilayer, d, can be calculated from d = e0e/Cbl, where e is the dielectric constant of... 

Devise and justify an equivalent circuit for a system in which O and R are bound to the surface of the electrode as the result of a chemical modification. Follow the steps in Sections 10.2 and 10.3 to evaluate the expected frequency dependence of the faradaic impedance for the case in which the electrode reaction is nemstian. What phase angle is expected ... 

But how do we explain that surface waves are present only in a limited frequency range, namely 6.3-8.3GHz This is explained in Fig. 4.16 in a qualitative way. It shows the scan impedance plotted earher in Fig. 4.2 but here plotted at three frequencies, namely 6, 7.7, and 10 GHz. Furthermore, these scan impedance curves are shown a bit more realistic by the fact that they for end-fire condition do no go to infinity but just to a large value depending on how large the array actually is. This point is easy to see by application of the mutual impedance concept. It simply tells that the magnitude Za of the scan impedance can never exceed Ylq=-Q Zo, , where Zo,q is the mutual impedance between the reference element in column 0 and all the elements in column q (see Chapter 3 for details). Since Zo, j and Q are bounded, so is the finite sum Za. As already shown in Fig. 4.2 and repeated in Fig. 4.16 for easy comparison, we... 

Using Eq. 1-2 for resistance R and Eq. 1-3 for capacitance C, which are frequency-dependent parameters when analyzed over a broad frequency range, a general impedance equation (Eq. 1-10) can be developed as a function of the frequency-dependent characteristic electrical properties of the analyzed material or system. This expression takes into account the frequency-dependent values of relative permittivity e((o) and resistivity p(co) or its inverse, electrical conductivity a(co), combined with the geometry factors of the electrode surface area (/4) and the sample s thickness between the bounding electrodes (d) ... 

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