Current oscillation impedance

The other effect considered in this section deals with transients in a single fuel cell. The transient models examine step changes in potential and related phenomena (e.g., gas flow rates, water production, and current density). Hence, they are aimed at examining how a fuel-cell system handles different load requirements, which may occur during automotive operation or start up and shut down. They are not trying to model slow degradation processes that lead to failure or the transients associated with impedance experiments (i.e., potential or current oscillations). These types of models are discussed in section 7. 

At potentials more positive than the second current plateau, Jx (see Fig. 5.2), where current oscillation occurs the impedance diagram is dominated by a set of loops characteristic of resonant behavior as shown in Fig. 5.35. ... 

FIGURE 5.35. Impedance diagrams in the current oscillation regime at 2 and 3.5V on p-Si (111) in an electrolyte of Cp = 0.05 M and pH 3. The measurement frequencies (in Hz) are indicated for some points on the diagrams. Notice the successive loops, corresponding to the fundamental resonance (the one closest to the origin) and to the successive overtones. After Ozanam el al (Reproduced by permission of The Electrochemical Society, Inc.)... 

When a sufficiently large external resistor is connected in series, the current oscillates on the branch with the positive polarization slope, though in a region where OH adsorption takes place (Fig. 21). (Recall that OH adsorption is the fast process that is responsible for a negative real impedance in an interval of nonzero frequencies.) The first three time series shown in Fig. 21(b) were obtained on the anodic scan, the last two... 

Comparison of the applied voltage and obtained current reveals that the current oscillates with the same frequency as the potential but is shifted in phase by the angle cp depending on the frequency, according to Eq. (2.112). The term IZI is the modulus of the impedance ... 

Survila, A. and Mockus, Z. (1999) Current oscillations and a negative impedance observed during the copper and tin codeposition from solutions involving laprol 2402C as a surface-active substance. Electrochim. Acta, 44 (11), 1707-1712. 

The second microwave heating mechanism arises from the migration of ions in the electric field. The resulting current from the oscillating ions gives rise to heat in the familiar way, following the i2r law, where / is the current and r reflects the resistance or impedence to ionic movement through collisions with other ions and molecules present in the medium. Ionic conduction is important in situations where the ions are free to move to some extent. 

In the EHD impedance method, modulation of the flow velocity causes a modulation of the velocity gradient at the interface which, in turn, causes a modulation in the concentration boundary layer thickness. As demonstrated previously in Section 10.3.3 and Fig. 10.3 the experiment shows a relaxation time determined solely by the time for diffusion across the concentration boundary layer. Although there is a characteristic penetration depth, 8hm, of the velocity oscillation above the surface, and at sufficiently high modulation frequencies this is smaller than the concentration boundary layer thickness, any information associated with the variation of hm with w is generally lost, unless the solution is very viscous. The reason is simply that, at sufficiently high modulation frequencies, the amplitude of the transfer function between flow modulation and current density is small. So, in contrast to the AC impedance experiment, the depth into the solution probed by the EHD experiment is not a function... 

The impedance of a capacitor is inversely proportional to the frequency of the oscillation of the voltage field across it. An equivalent way to state the same property is that the current through a capacitor is directly proportional to the time derivative of the potential field across it. 

To illustrate the technique, let s consider the case in which the system is stimulated by an applied voltage at a discrete frequency and the response current is measured at the same frequency. At zero frequency, or d.c., impedance is equivalent to resistance as defined by Ohm s law R = V/I. When the impressed voltage is oscillated at a particular frequency, the system responds by passing an oscillating current. If the amplitude of the input voltage is sufficiently small (typically < 10 mV), the system is linear, and the frequency of the response wave (current) matches the frequency of the perturbation (voltage). However, the response current wave may differ from the perturbation in amplitude and phase (Fig. 1). The ratio of the amplitudes of the perturbation to the response waveforms and the phase shift between the signals define the impedance function. 

As the potential that is applied across the electrodes is increased, the ionic velocities increase. Thus, the detector signal is proportional to the applied potential. This potential can be held to a constant value or it can oscillate to a sinusoidal or pulsed (square) wave. Cell current is easily measured however, the cell conductance (or reciprocal resistance) is determined by knowing the potential to which the ions are reacting. This is not a trivial task. Ionic behavior can cause the effective potential that is applied to a cell to decrease as the potential is applied. Besides electrolytic resistance that is to be measured, Faradaic electrolysis impedance may occur at the cell electrodes resulting in a double layer capacitance. Formation of the double layer capacitance lowers the effective potential applied to the bulk electrolyte. 

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