Electrolyte relaxation frequency

The double layer takes time to distort. If the applied field frequency is much greater than the electrolyte relaxation frequency, that is if cb is large, there is not enough time... 

The power generation of SC-SOFC is dependent on the resistance of the materials. The electrolyte itself, the chemical reactions, and the overpotential contribute to the impedance, which is measured with a load of half the short circuit current applied to the cell. Figure 3 shows the impedance spectra of a particular cell, fitted to an equivalent resistor/capacitor (RC) circuit. Usually, R1 is considered to be the electrolyte resistance with R2 and R3 as the overpotential of the electrodes. The inductance of the cables and the relaxation frequency of R2 and C2 tended to introduce error into the measurement of Rl. Therefore, R1 is usually measured together with R2 as R1 + R2 [31], Some cells may be significantly affected by the electrolyte resistance, which depends on thickness. 

There is a duality in the electrical properties of tissue. Tissue may be regarded as a conductor or a dielectric. In frequencies of 100 kHz or less, most tissues are predominantly electrolytic conductors. Therefore, we start Chapter 2 with a look at electrolytes. Bulk electrolyte continuity is broken in two important ways by electrode metal plates and by cell membranes. This break in continuity introduces capacitive current flow segments. At the electrodes, electric double layers are formed in the electrolyte the cell interiors are guarded by membranes. With high-resolution techniques, it is possible to extract important capacitive (i.e., dielectric) properties even at low frequencies, such as 10 Hz. At higher frequencies, such as 50 kHz, the dielectric properties of tissue (discussed in Chapter 3) may dominate. At the highest frequencies, tissue properties become more and more equal to that of water. Pure water has a characteristic relaxation frequency of approximately 18 GHz. 

Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simplified equivalent circuit for the liquid-liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clarified later, the photoinduced ET... 

The appearance of capacitive or inductive impedance depends essentially on the value of the rate constants. Low frequency loops, in a general case, are all very sensitive to the pH of the electrolyte. The different time constants are attributed to the relaxation of surface coverage by a corresponding number of reaction Intermediates. 

We have extended the technique of Relaxation Spectrum Analysis to cover the seven orders of magnitude of the experimentally available frequency range. This frequency range is required for a complete description of the equivalent circuit for our CdSe-polysulfide electrolyte cells. The fastest relaxing capacitive element is due to the fully ionized donor states. On the basis of their potential dependence exhibited in the cell data and their indicated absence in the preliminary measurements of the Au Schottky barriers on CdSe single crystals, the slower relaxing capacitive elements are tentatively associated with charge accumulation at the solid-liquid interface. 

Fig. 9. A rotation spectrum is produced by observing the motion of a cell in a rotating electric field of constant amplitude and plotting the rotation speed of the cell against frequency of the field. In solutions of low conductivity, the cell rotates in the opposite direction to the field (anti-field rotation) at low frequencies. This rotation reaches a peak when the field frequency corresponds to the charge relaxation time of the membrane. The position of this peak therefore contains information about membrane permittivity and conductivity. As the frequency increases further, the rate of cell spinning falls, becoming zero at about 1 MHz. Above this frequency, the cell starts to spin with the field (co-field rotation) and a second peak is reached. The frequency at which this peak occurs depends in practice mainly on the conductivity of the interior of the cell. It may be used for non-destructive determination of cytosolic electrolyte concentration.

As expected, the capacitance of the cell increases when the frequency is decreased (Figure 1.25a) below the knee frequency, the capacitance tends to be less dependent on the frequency and should be constant at lower frequencies. This knee frequency is an important parameter of the EDLC it depends on the type of the porous carbon, the electrolyte as well as the technology used (electrode thickness, stack, etc.) [20], The imaginary part of the capacitance (Figure 1.25b) goes through a maximum at a given frequency noted as/0 that defines a time constant x0 = 1 lf0. This time constant was described earlier by Cole and Cole [33] as the dielectric relaxation time of the system, whereas... 

Debye-Falkenhagen effect - Debye and - Falken-hagen predicted, that in - electrolyte solutions the ionic cloud may not be established properly and maintained effectively when the ion and the cloud are exposed to an alternating (AC) electric field in particular of high frequency. Thus the impeding effect of the ion cloud on the ion movement should be diminished somewhat resulting in an increased value of the ionic conductance. Above frequencies of v 107 to 108 s-1 this increase has been observed, see also - Debye relaxation time. 

Debye-Falkenhagen effect. In the absence of a complete and perfectly shaped ionic cloud movement of the ions is less impeded by the ionic cloud, thus electrolytic conductivity should increase. Above frequencies / 107 to 108 s-1 this increase has been observed, accordingly the Debye relaxation time is r 10-8 s. 

Fig. 4.100. Argand diagrams of a completely dissociated electrolyte and its pure solvent. Full circles experimental data from frequency domain measurements on aqueous potassium chloride solutions at 25 °C. Curve 1 Argand diagram of pure water. Curve 2 Argand diagram, ff = f(E ), of an 0.8 Waqueous KCI solution, Curve 3 Argand diagram, e"=f(e )r obtained from curve 2. (Reprinted from P. Turq, J. Barthel, and M. Chemla, in Transport, Relaxation and Kinetic Processes in Electrolyte Solutions, Springer-Verlag, Berlin, 1992, p. 78).

Ionic Equilibria and Their Effect on the Permittivity of Electrolyte Solutions. Most of the commonly used solvents exhibit several relaxation processes that show up in the change of dielectric constant with frequency (see Section 2.12). These relaxation processes include rotation and libration of the molecules of the solvents, aggregates of ionic species, and H-bonding dynamics. 

Industrial applications of moisture measurement by nucrowave absorption are numerous they are relative rather than absolute measurements, strongly dependent upon calibration they must compete with othe-techniques, such as neutron absorption. A popular frequency band is 3—10 GHz at lower frequencies the electrolytic conductivity can mask the absorption due to dipolar relaxation, so that the technique becomes inconveniently electrolyte-sensitive at higher frequendes the penetration is usually insufficient the technique is normally carried out in transmission, but measurement by reflection is also possible. Kilohertz frequencies are also popular in studies of systems containing bound water. 

This proposal represents a distinct advance from the previous state of our knowledge of aqueous solutions of non-electrolytes. The multiplicity of relaxation times may be present in other solutions the frequency ranges studied are inadequate to enable generalizations to be made. 

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