Frequency dependence electrode

Frequency dependent electrode impedance is also important in bioelectric stimulation applications, where relatively larger currents and complex waveforms are often used to stimulate excitable tissues. 

Impedance Some of the errors arising from the use of linear polarisation resistance led to interest and development in a.c. systems.An early development used a fixed a.c. frequency and a commercial instrument was produced in the UK. Inaccuracies still occurred, however, and were due to the electrode impedance which is fequency dependent. Electrode reactions have a capacitance component, in addition to resistance, resulting in a requirement to measure the impedance. However, the total impedance comprises values for the reaction, solution, diffusion and capacitance. Measurements at different frequency are more reliable, particularly where high solution resistances occur. Simplifications for industrial monitoring have been developed consisting of two measurements, i.e. at a high (10 kHz) and low frequency (0-1 Hz). The high-frequency measurement can identify the... 

Fig. 109. Frequency dependence of conductivity (G) for single crystals of MsNbjOFis and KsNb3OF,g (electrodes were deposited onto the (001) faces). Reproduced from [443], A. I. Agulyansky, J. Ravez, R Von Der Mtihll, A. Simon, Ferroelectrics 158 (1994) 139, Copyright 1994, with permission of Taylor Francis, Inc., http //www.routledge-ny.com.

But when considered over a wide range of frequencies, the properties of a real electrode do not match those of the equivalent circuits shown in Fig. 12.12 the actual frequency dependence of Z and a does not obey Eq. (12.21) or (12.22). In other words, the actual values of R and or R and are not constant but depend on frequency. In this sense the equivalent circuits described are simplified. In practice they are used only for recording the original experimental data. The values of R and Cj (or R and C ) found experimentally for each frequency are displayed as functions of frequency. In a subsequent analysis of these data, more complex equivalent circuits are explored which might describe the experimental frequency dependence and where the parameters of the individual elements remain constant. It is the task of theory to interpret the circuits obtained and find the physical significance of the individual elements. 

In the presence of Bi or Te, the C=0 bond is weakened, as concluded from the displacement of the CO stretching band to lower wavenumbers. There is also a change in the dependence of the band frequency on electrode potential, with the slope dv/dE increasing for the adatom-modified surfaces. These changes indicate that the adatom alters the electronic properties of the surface, increasing the amount of electronic backdonation and stabilizing the adsorbed CO molecule. No catalytic enhancement is expected from this effect. 

Fig. 5.9 Frequency dependence of impedance of fresh electrodes of different Ru content in 5 M NaCl at room temperature at OCP. 

A constant phase element (CPE) rather than the ideal capacitance is normally observed in the impedance of electrodes. In the absence of Faradaic reactions, the impedance spectrum deviates from the purely capacitive behavior of the blocking electrode, whereas in the presence of Faradaic reactions, the shape of the impedance spectrum is a depressed arc. The CPE shows power law frequency dependence as follows129 130... 

The voltammetric features of a reversible reaction are mainly controlled by the thickness parameter A = The dimensionless net peak current depends sigmoidally on log(A), within the interval —0.2 < log(A) <0.1 the dimensionless net peak current increases linearly with A. For log(A )< —0.5 the diSusion exhibits no effect to the response, and the behavior of the system is similar to the surface electrode reaction (Sect. 2.5.1), whereas for log(A) > 0.2, the thickness of the layer is larger than the diffusion layer and the reaction occurs under semi-infinite diffusion conditions. In Fig. 2.93 is shown the typical voltammetric response of a reversible reaction in a film having a thickness parameter A = 0.632, which corresponds to L = 2 pm, / = 100 Hz, and Z) = 1 x 10 cm s . Both the forward and backward components of the response are bell-shaped curves. On the contrary, for a reversible reaction imder semi-infinite diffusion condition, the current components have the common non-zero hmiting current (see Figs. 2.1 and 2.5). Furthermore, the peak potentials as well as the absolute values of peak currents of both the forward and backward components are virtually identical. The relationship between the real net peak current and the frequency depends on the thickness of the film. For Z, > 10 pm and D= x 10 cm s tlie real net peak current depends linearly on the square-root of the frequency, over the frequency interval from 10 to 1000 Hz, whereas for L <2 pm the dependence deviates from linearity. The peak current ratio of the forward and backward components is sensitive to the frequency. For instance, it varies from 1.19 to 1.45 over the frequency interval 10 < //Hz < 1000, which is valid for Z < 10 pm and Z) = 1 x 10 cm s It is important to emphasize that the frequency has no influence upon the peak potential of all components of the response and their values are virtually identical with the formal potential of the redox system. 

Electrode polarization, represented by the second term in equation (5), in general is a significant and difficult to account for factor at frequencies below 10 Hz and/or for high values of a usually associated with a highly fluid resin state. The frequency dependence e due to dipolar mobility is generally observed at frequencies in the KHz and MHz regions. For this reason an analysis of the frequency dependence of e, equations 3 and 5, in the Hz to... 

Capacitive reactance is a frequency-dependent quantity, decreasing with increasing frequency. Typically, double-layer capacitances for aqueous solutions are 10-100 nF/cm2. Thus the capacitive reactance for a 1-cm2 electrode with a 10-fxF capacitance at an applied frequency of 104 rad/s (1.6 kHz) is... 

Now we show that the validity of the cascade Langevin approach extends beyond the limits of validity of Boltzmann equation. Consider a frequency-dependent noise in a chaotic cavity, i.e. in a metallic island of irregular shape connected to the electrodes L, R via two quantum point contacts of conductances Gl,r e1 /h and arbitrary transparencies / /. . As the dwell time of... 

Fig. 3. The frequency dependence of Pt L electrode impedance active component. L 1-0.5M K2S04 2- 0.1M K3Fe(CN)6 / 0.1M K4Fe(CN)6 3- 0.5M H2S04.

Fig. 5. The frequency dependence of Pt 0.5M H2S04 electrode impedance reactive component at relative length of extended conductor electrode parties equal to 1- 1.0 2- 0.8 3-0.64 4- 0.52 5- 0.40.

The electrochemical impedance of a real electrode is frequently represented by an equivalent circuit containing constant phase element (CPE) showing power-law frequency dependence as follows... 

Conventional two-electrode dc measurements on ceramics only yield conductivities that are averaged over contributions of bulk, grain boundaries and electrodes. Experimental techniques are therefore required to split the total sample resistance Rtot into its individual contributions. Four-point dc measurements using different electrodes for current supply and voltage measurement can, for example, be applied to avoid the influence of electrode resistances. In 1969 Bauerle [197] showed that impedance spectroscopy (i.e. frequency-dependent ac resistance measurements) facilitates a differentiation between bulk, grain boundary and electrode resistances in doped ZrC>2 samples. Since that time, this technique has become common in the field of solid state ionics and today it is probably the most important tool for investigating electrical transport in and electrochemical properties of ionic solids. Impedance spectroscopy is also widely used in liquid electrochemistry and reviews on this technique be found in Refs. [198 201], In this section, just some basic aspects of impedance spectroscopic studies in solid state ionics are discussed. 

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