Electrode polarization, effect frequency dependence

Figure 11 a illustrates the frequency dependence of e for Eq. (3-6). Note that e is midway between eu and er when co = l/id. The corresponding plots for s" are more complex, because one must assess the relative contributions of a and the dipole loss. The simplest case is for cr = 0 (Fig. lib), where the characteristic dipolar loss peak of amplitude (sr — eu)/2 is observed at frequency co = l/td. For non-zero ct, however, the 1/co dependence of e" greatly distorts the e" curve from the ideal Debye peak. Log-log scales are helpful, as illustrated in Fig. 12. The ct = 0 case is replotted from Fig. lib also plotted are the frequency dependences of e" for CTTd/Eo having various values relative to er — eu. Asct increases, it becomes increasingly difficult to discern the dipole loss peak. Roughly speaking, for CTTd/Eo greater than about three times er, the observed e" is entirely dominated by ct. (Ideally, even when cr dominates the dipolar contribution to e", it should still be possible to observe the dipolar contribution to e however, when o is large, electrode polarization effects tend to dominate the e measurement as well. See Sec. 3.2.1).

In addition, ionic conduction causes a charge qiit) to pass through the material, which rises from zero and then becomes linearly dependent on time to give a constant current I(t) = dgi/d. In contrast to qp(t), which becomes constant at long times (since the dipolar system reaches thermodynamic equilibrium in the presence of the steady field), qiit) increases without limit in the absence of interfacial and electrode polarization effects, giving a continual dissipation of energy via the conduction process. The fact that the steady conduction current takes time to get established means that the ac real conductivity a ico) is constant at low frequencies and becomes /-dependent at high frequencies. 

The results in Fig. 22 show that the RH-dependent spectra of a given PEC, can, indeed, be superimposed to a master curve. The agreement between the curves is excellent in all parts of the spectra except at low frequencies, where electrode polarization effects dominate however, these do not describe material properties. We can therefore claim that for the presented polyelectrolyte materials there is a time-humidity superposition-principle (THSP) in analogy to the well-established TTSP. Moreover, the special case of Summerfield-type scaling is fulhUed. The same holds true for other investigated PEC compositions not presented here. 

The third point is related to the quantization of the polarization effects at the electrodes, which are due to the acciunulation of carriers inside the material. It is therefore important to establish a model and a variation law depending on frequency. 

Method numbers 2 and 3 are based on the assumption that the metal/liquid interphase and thus the polarization impedance is invariable. This is not always the case. Measuring on dry samples for instance implies poor control of the contact electrolyte. Also a sample may contain local regions of reduced conductivity near the electrode surface. The currents are then canalized with uneven current density at the metal surface (shielding effect). Electrode polarization impedance, in particular at low frequencies, is then dependent on the degree of shielding. An example of method 4 is Krizaj and Pecar (2012), who described such a method for removing the contribution from electrode polarization impedance on measured impedance data of a suspension of microcapsules. 

Figure 14i exhibits the M spectra of the nanocomposites which approaches to zero at low frequencies suggesting that the effect of electrode polarization gives a negligible contribution. The frequency dependence of M" at room temperature is presented in the Fig. 14ii. A relaxation peak appears at high frequency which is attributed to Ag-PPy interfacial polarization effects. Accumulation of charges at the Ag-PPy interface takes place due to difference between the dielectric permittivity of silver and PPy phases in the nanocomposite giving rise to interfacial polarization.

Surface SHG [4.307] produces frequency-doubled radiation from a single pulsed laser beam. Intensity, polarization dependence, and rotational anisotropy of the SHG provide information about the surface concentration and orientation of adsorbed molecules and on the symmetry of surface structures. SHG has been successfully used for analysis of adsorption kinetics and ordering effects at surfaces and interfaces, reconstruction of solid surfaces and other surface phase transitions, and potential-induced phenomena at electrode surfaces. For example, orientation measurements were used to probe the intermolecular structure at air-methanol, air-water, and alkane-water interfaces and within mono- and multilayer molecular films. Time-resolved investigations have revealed the orientational dynamics at liquid-liquid, liquid-solid, liquid-air, and air-solid interfaces [4.307]. 

Yamamoto and Yamamoto (1981) studied human skin tissue and found the limit current of linearity to be about 10 pA/cm at a frequency of 10 Hz. Grimnes (1983b) studied electro-osmosis in human skin in vivo and found a strong polarity-dependent nonlinearity. The effect was stronger the lower the frequency, Figure 10.17 shows the dramatic effect with 20 V and 0.2 Hz, soon leading to skin breakdown. Nonlinearity of cardiac pacemaker CC electrodes made of noble metals and intended for use with pulses has been extensively studied (Jaron et al. 1969). 

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