Impedance measurement

Integrating this equation between the limits of f = 0 and t, taking into account that at f = 0 the potential E = E, and performing simple transformations, we obtain an equation for the potential decay curve  

When alternating current is used for the measurements, a transient state arises at the electrode during each half-period, and the state attained in any half-period changes to the opposite state during the next half-period. These changes are repeated according to the ac frequency, and the system will be quasisteady on the whole (i.e., its average state is time invariant). 

For measurements, an ac component = / sin at with the amphmde / and angular frequency co (co = 2jt/, where/is the ac frequency) is passed through the electrode (alone or in addition to a direct current). Alternating potential (polarization) changes 

FIGURE 12.12 Equivalent circuits with resistance and capacitance in series (a) and in parallel b). 

AE having the same frequency and an amphtude AE are the response. Sometimes alternating potential components are apphed, and the resulting alternating current component is measured, hi aU cases the potential changes are small in amphtude ( 10 mV). 

The high temperature value for the activation energy will be composed of two terms, 

The conductivity of an ionic conductor can be assessed by direct current (dc) or alternating current (ac) methods. Direct current methods give the resistance R and the capacitance C. The corresponding physical quantity when ac is applied is the impedance, Z, which is the total opposition to the flow of the current. The unit of impedance is the ohm (fl). The impedance is a function of the frequency of the applied current and is sometimes written Z(to) to emphasize this point. Impedance is expressed as a complex quantity  

The impedance of a ceramic material such as an oxide is often considered to be made up of a resistive part in parallel with a reactive part (Fig. 6.1a). The impedance of this combination is 

Ideally, the reactance is made up only of a capacitive component in which case the impedance can be written  

Actually developed for polymer electrolytes [467], the method is also used for liquid electrolytes. Nonetheless, the drawback is the time-consuming procedure until equilibrium is adjusted. 

Every method has its advantages and disadvantages, and it is remarkable that different methods give different results. There is always a model applied on the calculation and it should be acted with caution which method is applicable. As can be seen in Table 17.18, measured transference numbers vary widely with different methods, caused by the different assumptions made in every method. In Ref. [456], two different methods were used for the same system and in accordance with investigations from this group [528], completely contrary tendencies of the concentration dependence of the transference number were obtained. Nevertheless, the transference number is an important parameter, which is also reflected by increasing interest in recent years. 

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The determined eddy-eurrent parameter is the inductance of the eomplex impedance measured by impedance analyzer at j=100 kHz. Therefore the impulse response function from chapter 4.2.1. is used for calculation. The depth of the cracks is big in comparison to coil size. For presentation the measured and pre-calculated data are related to their maxima (in air). The path X is related to the winding diameter dy of the coil. 

Aperture impedance measurements of cell volume must take into account the osmolaUty and pH of the medium. A hypotonic medium causes cells to swell a hypertonic medium causes them to shrink. Some manufacturers of aperture impedance counters deHberately provide hypertonic electrolytic media for red blood cell measurements. The shmnken red cells not only become more nearly spherical and thus less affected by orientation, but also less deformable than cells in isotonic media and thus less affected by differences in hemoglobin content. 

The use of impedance electrochemical techniques to study corrosion mechanisms and to determine corrosion rates is an emerging technology. Elec trode impedance measurements have not been widely used, largely because of the sophisticated electrical equipment required to make these measurements. Recent advantages in micro-elec tronics and computers has moved this technique almost overnight from being an academic experimental investigation of the concept itself to one of shelf-item commercial hardware and computer software, available to industrial corrosion laboratories. 

In maldug electrochemical impedance measurements, one vec tor is examined, using the others as the frame of reference. The voltage vector is divided by the current vec tor, as in Ohm s law. Electrochemical impedance measures the impedance of an electrochemical system and then mathematically models the response using simple circuit elements such as resistors, capacitors, and inductors. In some cases, the circuit elements are used to yield information about the kinetics of the corrosion process. 

The magnitudes of symmetrical and non-symmetrical fault currents, under different conditions of fault and configurations of faulty circuits, can be determined from Table 13.5, where Z] = Positive phase sequence impedance, measured under symmetrical load conditions. The following values may be considered ... 

A.c. impedance. Measurements of the frequency variation of impedance allow separation of the change transfer resistance from the contributions to the total impedance of the environment resistance, surface films, adsorbed layers, etc. Robust instruments utilising a two-frequency technique have been developed . 

Neufeld, P. and Queenan, E. D., Frequency Dependence of Polarisation Resistance Measured with Square Wave Alternating Potential , Br. Corros. J., 5, 72-75, March (1970) Fontana, M. G., Corrosion Engineering, 3rd edn., McGraw-Hill, pp 194-8 (1986) Dawson, J. L., Callow, L. M., Hlady, K. and Richardson, J. A., Corrosion Rate Determination By Electrochemical Impedance Measurement , Conf. On-Line Surveillance and Monitoring of Process Plant, London, Society of Chemical Industry (1977)... 

Recently, a constant-phase element has been found607 to be present at pc-Pb/KF + HaO interfaces by impedance measurements. The Pb electrode was cathodically reduced before use. The assumption has been made that the CPE is due to the inhomogeneity of the metal surface. Frequency-... 

Metal/molten salt interfaces have been studied mainly by electrocapillary833-838 and differential capacitance839-841 methods. Sometimes the estance method has been used.842 Electrocapillary and impedance measurements in molten salts are complicated by nonideal polarizability of metals, as well as wetting of the glass capillary by liquid metals. The capacitance data for liquid and solid electrodes in contact with molten salt show a well-defined minimum in C,E curves and usually have a symmetrical parabolic form.8 10,839-841 Sometimes inflections or steps associated with adsorption processes arise, whose nature, however, is unclear.8,10 A minimum in the C,E curve lies at potentials close to the electrocapillary maximum, but some difference is observed, which is associated with errors in comparing reference electrode (usually Pb/2.5% PbCl2 + LiCl + KC1)840 potential values used in different studies.8,10 It should be noted that any comparison of experimental data in aqueous electrolytes and in molten salts is somewhat questionable. 

After this step, the understanding of microwave electrochemical mechanisms deepened rapidly. G. Schlichthorl went to the laboratory of L. Peter to combine potential-modulated microwave measurements with impedance measurements, while our efforts focused on laser pulse-induced microwave transients under electrochemical conditions. It is hoped that the still relatively modest knowledge provided will stimulate other groups to participate in the development of microwave photoelectrochemistry. 

As with alternating electrical currents, phase-sensitive measurements are also possible with microwave radiation. The easiest method consists of measuring phase-shifted microwave signals via a lock-in technique by modulating the electrode potential. Such a technique, which measures the phase shift between the potential and the microwave signal, will give specific (e.g., kinetic) information on the system (see later discussion). However, it should not be taken as the equivalent of impedance measurements with microwaves. As in electrochemical impedance measurements,... 

Figure 9. (a) Electrode and representative circuit for phase-sensitive electrochemical measurements (impedance measurements) compared with (b) setup for phase-sensitive microwave (impedance) measurements. 

The combination of photocurrent measurements with photoinduced microwave conductivity measurements yields, as we have seen [Eqs. (11), (12), and (13)], the interfacial rate constants for minority carrier reactions (kn sr) as well as the surface concentration of photoinduced minority carriers (Aps) (and a series of solid-state parameters of the electrode material). Since light intensity modulation spectroscopy measurements give information on kinetic constants of electrode processes, a combination of this technique with light intensity-modulated microwave measurements should lead to information on kinetic mechanisms, especially very fast ones, which would not be accessible with conventional electrochemical techniques owing to RC restraints. Also, more specific kinetic information may become accessible for example, a distinction between different recombination processes. Potential-modulation MC techniques may, in parallel with potential-modulation electrochemical impedance measurements, provide more detailed information relevant for the interpretation and measurement of interfacial capacitance (see later discus-... 

Electrochemical impedance spectroscopy leads to information on surface states and representative circuits of electrode/electrolyte interfaces. Here, the measurement technique involves potential modulation and the detection of phase shifts with respect to the generated current. The driving force in a microwave measurement is the microwave power, which is proportional to E2 (E = electrical microwave field). Therefore, for a microwave impedance measurement, the microwave power P has to be modulated to observe a phase shift with respect to the flux, the transmitted or reflected microwave power APIP. Phase-sensitive microwave conductivity (impedance) measurements, again provided that a reliable theory is available for combining them with an electrochemical impedance measurement, should lead to information on the kinetics of surface states and defects and the polarizability of surface states, and may lead to more reliable information on real representative circuits of electrodes. We suspect that representative electrical circuits for electrode/electrolyte interfaces may become directly determinable by combining phase-sensitive electrical and microwave conductivity measurements. However, up to now, in this early stage of development of microwave electrochemistry, only comparatively simple measurements can be evaluated. 

At present, the microwave electrochemical technique is still in its infancy and only exploits a portion of the experimental research possibilities that are provided by microwave technology. Much experience still has to be gained with the improvement of experimental cells for microwave studies and in the adjustment of the parameters that determine the sensitivity and reliability of microwave measurements. Many research possibilities are still unexplored, especially in the field of transient PMC measurements at semiconductor electrodes and in the application of phase-sensitive microwave conductivity measurements, which may be successfully combined with electrochemical impedance measurements for a more detailed exploration of surface states and representative electrical circuits of semiconductor liquid junctions. 

Figure 15. Complex plane impedance plots for polypyrrole at (A) 0.1, (B) -0.1, (C) -0.2, (D) -0.3, and (E) -0.4 V vs. Ag/AgCl in NaCl04(aq). The circled points are for a bare Pt electrode. Frequencies of selected points are marked in hertz. (Reprinted from X. Ren and P. O. Pickup, Impedance measurements of ionic conductivity as a probe of structure in electrochemi-cally deposited polypyrrole films, / Electmanal Chem. 396, 359-364, 1995, with kind permission from Elsevier Sciences S.A.)...

Impedance Measurements in Electrochemical Systems Macdonald, D. D. McKubre, M. C. H. 14... 

Measurements of the interfaeial eapacitance (the differential double layer capacity Cdl) have been used widely, the method has been labelled tensammetry [46Bre, 52Bre, 51Dosl, 52Dosl, 63Bre]. Various experimental setups based on arrangements for AC polarography, lock-in-amplifier, impedance measurement etc. have been employed. In all reports evaluated in the lists of data below the authors have apparently taken precautions in order to measure only the value of Cdl-... 

Lyden et al. [92] used in situ electrical impedance measurements to investigate the role of disorder in polysulfide PEC with electrodeposited, polycrystalline CdSe photoanodes. Their results were consistent with disorder-dominated percolation conduction and independent of any CdS formed on the anode surface (as verified by measurements in sulfide-free electrolyte). The source of the observed frequency dispersion was located at the polycrystalline electrode/electrolyte interface. 

Systems at Elevated Temperatures Impedance Measurements in Electrochemical 14... 

Transient measnrements (relaxation measurements) are made before transitory processes have ended, hence the current in the system consists of faradaic and non-faradaic components. Such measurements are made to determine the kinetic parameters of fast electrochemical reactions (by measuring the kinetic currents under conditions when the contribution of concentration polarization still is small) and also to determine the properties of electrode surfaces, in particular the EDL capacitance (by measuring the nonfaradaic current). In 1940, A. N. Frumkin, B. V. Ershler, and P. I. Dolin were the first to use a relaxation method for the study of fast kinetics when they used impedance measurements to study the kinetics of the hydrogen discharge on a platinum electrode. 

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