Relaxation time electrode polarization

Schwan was one of the founders of biomedical engineering as a new discipline. Before World War II, in the laboratory of Rajewski at the Frankfurter Institut fiir Biophysik, he had started with some of the most important topics of the field on low-frequency blood and blood serum conductivity, counting of blood cells, selective heating and body tissue properties in the ultra-high-frequency range, electromagnetic hazards and safety standards for microwaves, tissue relaxation, and electrode polarization. He also worked with the acoustic and ultrasonic properties of tissue. In 1950, he revealed for the first time the frequency dependence of muscle... 

Alternating-current and frequency effects. With an AC rather than a DC voltage applied to the electrodes, the processes above reverse themselves with the period of the alternating voltage. But each process proceeds at a different rate (with a characteristic relaxation time) so that their relative contributions to energy dissipation vary with frequency. As the frequency is increased concentration-polarization can be reduced or eliminated, particularly if the electrode reaction is reversible (fast electron transfer in both directions). 

Two more difficulties require comment. The first is that in most of the early literature, authors did not recognize the importance of electrode polarization, and, hence, failed to make quantitative allowance for the presence of blocking and/or release layers. Thus, in most cases, it is not possible to reconstruct quantitative bulk properties from the data presented. (The present authors were not immune. They reported a correlation between a dielectric relaxation time and viscosity54), failing at that time to realize that the relaxation time being studied was actually the characteristic time for electrode polarization, and, hence was dominated by conductivity.)... 

While our method works well with most situations, it is limited when (oo) exhibits a low-frequency tail. Such a situation is characteristic of percolation, electrode polarization, or other low-frequency process, where the reciprocal of the characteristic relaxation time for the process is just below our frequency window. In this case, aliasing effects distort the transform result. 

If vdielectric permittivity in vacuum will then be equal to 80. This is the so-called static permittivity. The permittivity of the vaccum is 0.855x 10 C m. The static dielectric permittivity near the ion or the surface of the charged electrodes, however, will exhibit smaller values. For instance, in the case of water at the electrode surface is assumed to approach 6. When applying the Marcus theory [8] both static and optical permittivities are used in calculations. These parameters therefore are listed in Table 1. In other calculations and correlations of the rate constants of electrode reactions and the dynamic relaxation properties of the solvents, the relaxation time of the solvents is used (Thble 1). 

The polarization curves showed that a large scan rate affects the polarization curves. This phenomenon can be illustrated by the capacitance effect of the electric double layer on the working electrode surface. Based upon the model of M. Hishida, et al. ( ), assume C i is the capacitance of electric double layer, Rf is the polarization resistance, and Rsoi is the solution resistance. A characteristic relaxation time can be defined as ... 

Interpreting the experimental data in this form nowadays is a commonly employed method to obtain information about the relaxation processes in ionic conductive materials and polymer-conductivity nanoparticles composites. In this representation, interfacial polarization and electrode contributions are essentially suppressed [44, 45]. The peak in the imaginary part of M" depends on temperature, which can be related to the translational ionic motions. The corresponding relaxation time = l/(27r/p), where /p is the peak frequency, therefore is called conductivity relaxation time. 

In the ease of TDS we can present a double layer with a capacitanee Cp that is eonneeted in series to the sample eell filled with the eonduetive material (Fig. 9). The charaeter-istic charge time of Cp is mueh larger than the relaxation time of the measured sample. This allows us to estimate the parameters of parasitic capacitance in the long-time window where only the parasitic electrode polarization takes plaee. Considering the relationship for the eurrent i(s)... 

The electrical properties of nail resemble those of SC and hair. However, note that the low-frequency susceptance plateau in Figure 4.24 represents a deviation from a simple model with a distribution of relaxation times for a single dispersion mechanism (cf. Section 9.2), and it must be due to another dispersion mechanism such as, for example, electrode polarization, skin layers, etc. The admittance of nail is also logarithmically dependent on water content, as shown in Figure 4.25 (Martinsen et al., 1997c). 

The time dependence of the dielectric properties of a material (expressed by e or CT ) under study can have different molecular origins. Resonance phenomena are due to atomic or molecular vibrations and can be analyzed by optical spectroscopy. The discussion of these processes is out of the scope of this chapter. Relaxation phenomena are related to molecular fluctuations of dipoles due to molecules or parts of them in a potential landscape. Moreover, drift motion of mobile charge carriers (electrons, ions, or charged defects) causes conductive contributions to the dielectric response. Moreover, the blocking of carriers at internal and external interfaces introduces further time-dependent processes which are known as Maxwell/Wagner/Sillars (Wagner 1914 Sillars 1937) or electrode polarization (see, for instance, Serghei et al. 2009). 

Here a is the bulk ionic or dc conductivity is the angular frequency (27rf) r is the dipole relaxation time is the relaxed dielectric constant or low frequency/high temperature dielectric constant (relative permittivity due to induced plus static dipoles) is the unrelaxed dielectric constant or high frequency/low temperature dielectric constant (relative permittivity due to induced dipoles only) o is the permitivity of free space E p is the electrode polarization term for permittivity and E"-p is the electrode polarization term for loss factor. The value of E p and E"p is usually unity, except when ionic conduction is very high (75). 

Many polymeric materials consist of dipoles (chemical bonds which have an unbalanced distribution of charge in a molecule) and traces of ionic impurities. If a polymer containing polar groups is heated so that an immobile dipole becomes mobile, an increase in permittivity is observed as the dipole starts to oscillate in the alternating electric field. This effect is referred to as a dipole transition and has a characteristic relaxation time (t) associated with it (76). When exposed to an electric field, the dipoles tend to orient parallel to the field direction and the ions move toward the electrodes, where they form layers. The dipole relaxation time... 

The polarizations discussed above have different relaxation times, as they are governed by the different physical origins. Figure 7 schematically shows the wide frequency spectrum of the dielectric properties of a heterogeneous system. All polarizations are depicted in Figure 7 on the basis of their relative relaxation times. The dielectric dispersion of the electronic polarization appears at the highest frequency, more than lO FIz. With the polarization entity size increase, the dielectric dispersion peak gradually appears at low frequencies in the sequence of the atomic, Debye, interfacial polarization, and the electrode polarization. The Debye polarization usually appears at 10 Hz, the interfacial polarizations appears around 1000 Hz, and the electrode polarization appears below 100 Hz. The Debye, interfacial, and electrode polarizations arc rather slow processes as compared with the electronic and the atomic polarizations. Usually, the former three... 

For electrode polarization, the relaxation time should be controlled by the time of building up the elcetrical double layer. Suppose that the cations and anions have a same diffusion coeillcient D ol the dimension area/second, the ion velocity vi in an electrical double layer of thickness k can be expressed as ... 

Eq.(32) indicates that the relaxation time of the electrode polarization decreases with the number concentration of ions and increases witli the size of ions, the dielectric constant and the viscosity of medium. Detailed discussion on the electrode polarization will be given further on. 

Eq. (46) indicates that tlie natural logrithium of the relaxation time of double layer build up should have a linear relationship with (l/T), which can be used to determine if the dielectric relaxation peak is resulted from the electrode polarization. Note that where / , is the frequency... 

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