High-frequency intercept

The rate constants for electron transfer and recombination are readily separated because in the limit (w- 0), equation (8.31) tends to kir/(ktr + krec), and the maximum of the semicircle occurs when ca = 2ir f=kt + krec. In the absence of RC attenuation effects, the high frequency intercept of the IMPS plot (minority carriers. Measurements of gac as a function of potential (band bending) can be used to determine the minority carrier lifetime and absorption coefficient [46]. The main advantage of using the IMPS data rather than dc measurements of... 

The low frequency intercept corresponds to a quantum efficiency of 2, and the high frequency intercept tends towards a quantum efficiency of 1. The minimum of the semicircle occurs at an wr = 1, i.e., to = kin, the first order rate constant for majority carrier injection [36, 37]. 

The microwave response is therefore a semicircle in the lower complex plane with a high frequency intercept of zero and a low frequency intercept given by... 

The Nyquist plot of a Randles cell is always a semicircle. At high frequencies the impedance of Cdl is very low, so the measured impedance tends to Reh At very low frequencies the impedance of Cm becomes extremely high, and thus, the measured impedance tends to Rct + Rd. Accordingly, at intermediate frequencies, the impedance falls between Rd and Rct + Rd. Therefore, the high-frequency intercept is associated with the electrolyte resistance, while the low-frequency intercept corresponds to the sum of the charge-transfer resistance and the electrolyte resistance. The diameter of the semicircle is equal to the charge-transfer resistance. 

In the potential range -0.6 to -0.69 V, the high-frequency intercept changes with potential, indicating that the electronic resistance becomes comparable with the ionic resistance [12], The electronic and ionic resistances can be calculated by the following equations ... 

By using the impedance method, Freire et al. also demonstrated that thinner membranes not only show better performance but also are much less sensitive to humidification conditions, cell temperature, and current density. The dependence of the real resistance at high-frequency intercepts on membrane thickness at different current densities is illustrated in Figure 6.14. Linear dependence of the high-frequency resistance, RhJ. on the membrane thickness was observed at 80°C, whereas non-linear dependence of RhJ on membrane thickness was shown at 40°C and 60°C. They explained that this was due to better hydration of the membrane at higher temperatures. It is also observable that Rhf almost does not depend on current density at 80°C and at low current densities rather, Rhf dependence on membrane thickness is almost linear, which indicates that for thicker membranes at high current densities it no longer behaves as a pure resistor due to a capacitive effect caused by less effective back transport of water [9],... 

This behaviour contrasts with the IMPS response, where the high-frequency intercept is qjo and the low-frequency intercept is given by... 

Figure 12.34 LMMRS response of p-Si in HF, showing that the semicircular response persists at negative potentials that are in the photocurrent saturation region. Note that the high-frequency intercepts in the plots are at zero. For further details, see Schlichthorl et at. (1995).

It can be seen that diameters of the IMPS semicircles decrease as the potential becomes more negative. The high frequency intercept is almost constant, whereas the low frequency intercept moves away from the origin as the bend banding is increased. Although these trends correspond qualitatively to those predicted by the preceding... 

The theoretical treatment of the IMPS response predicts that if ka> kb> kc, each electron injection step should give rise to a corresponding semicircle in the lower quadrant of the complex plane plot. The low frequency intercept corresponds to a quantum efficiency of 4 and the high frequency intercept to a quantum efficiency of unity (RC attenuation is neglected here). Each semicircle has a diameter corre-... 

Fig. 41 shows that the complex plane IMPS plot of Eq. 93 is a semicircle with a positive real and a negative imaginary part. The low and high frequency intercepts are 1 and 0 respectively, and the inverse of the characteristic frequency (o i gives the transit time tj. 

Figure 16.3 Typical Nyquist plot recorded on a real anode-supported SOFC single cell. The high-frequency intercept (for CO —> oo) with the real axis corresponds to the purely ohmic resistance Rq. The difference between the low-and high-frequency intercept is the so-called polarization resistance Rpol of the cell (cell Zl 153).

The diameter of the semicircle is N/ J, and the high-frequency intercept on the real axis is NR. This semicircle appears when both R and R are large, and it is readily noted experimentally when the pol5nner is reduced. The semicircle decreases in magnitude as the polymer film becomes oxidized and therefore more conducting. 

Rq from the high frequency intercept on the real axis ... 

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