Resultant-current sine wave

A small sinusoidal perturbation is applied potentiostatically to the system under investigation and the resulting current sine wave is analysed in terms of its second and third harmonics ( 2 and 13), i being the fundamental. The corrosion current is calculated... 

And finally, the equation for the resultant-current sine wave is ... 

In this procedure, a constant sine wave a.c. potential of a few millivolts is superimposed upon the usual d.c. potential sweep. The applied d.c. potential is measured in the usual way and these results are coupled with measurements of the alternating current. 

Harmonic analysis was carried out on the specimens 7 days after the impedance measurements in order to allow the specimens to settle down again. An Ono Sokki CF 910 dual channel FFT analyser was used in conjunction with a potentiostat (Thompson Mlnistat 251) to hold the specimen at its rest potential and to provide the low frequency sine wave perturbation. The second channel was used to measure the harmonic content of the resulting current. The Ono Sokki produces a dlgltially generated high purity sine wave at a chosen frequency, in this instance, 0.5 Hz. The total harmonic content of the input sine wave was less than 0.45% measured over 10 harmonics. Only the first 3 harmonics are used to calculate the corrosion current. 

It can be seen that it was again difficult to obtain results from specimens where no stable rest potential could be measured. The harmonic currents in all cases were low and for certain specimens were of the same order as the distortion resulting from the input sine wave. The Tafel slopes obtained were in general anomalously high and the corrosion rates varied over several orders of magnitude. 

In electrochemistry, Fourier transformation is usually applied to the current resulting when a periodic (often sine-wave or square-wave) voltage is imposed on a cell. This may be the only signal applied, as in -> impedance spectroscopy or the periodic voltage may modulate an aperiodic ( DC ) potential as in -> AC voltammetry or... 

The angle ip is the phase shift between the applied sine-wave voltage and the resulting sine wave current. 

In ACIS, a small-amplitude sine wave is superimposed on a constant potential, and the resulting current is recorded. The current lags behind the alternating potential by a degree proportional to the impedence of the SAM. From a plot of the imaginary versus real parts of the complex impedence, both the capacitance of the SAM and the electron-transfer kinetics can be extracted. Because the bulk of the studies described in this chapter make use of cyclic voltammetric or chromo-amperometric methods, ACIS is not discussed further here. Leading references are provided for the interested reader [23, 43, 76]. 

In some very favorable situations, several techniques can have comparable effectiveness. However, when complex heterogeneous reactions interact with mass transport, analyses of the current or potential time transients lead to poor results if a reaction mechanism has to be resolved. A frequency analysis is then more efficient. Therefore, impedance measurements, by means of a perturbation sine wave... 

Fig. 5.19 Voltage sine wave v t) applied across resultant "ac" current waveform /(f) for capacitor.

Another interesting photoelectroanalytical method for the characterization of polymer films is a method which might be called photoimpedance spectrum. A small-amplitude sine-wave signal is applied to the working electrode and the resulting absorbance response is recorded at different frequencies. Alternatively, several frequencies are applied simultaneously and the response analyzed by using Fourier transform. The main advantage compared with the conventional electrical impedance measurements is naturally that only faradaic current... 

If R and B are nonideal with current depending values, as in an electrolytic electrode system, the DC approach cannot be used. A better approach is to superimpose a small, continuous sine wave voltage on the applied DC voltage. Our current measuring device must then be able to measure both AC current with phase and DC. The battery (being ideal with zero internal resistance) will not influence the AC current, and we consequently measure the resistance of R at AC, but a different R at DC. Because there is no phase shift, we then know that the battery is in the circuit. If we repeat the measurement on many frequencies and the results are identical, we know that there is no capacitor inside the black box. 

If linear, a sine excitation input results in a sine response. However, the immittance concept can be extended to nonlinear networks, where a sine wave excitation leads to a nonsinusoidal response. Including a separate immittance value for each harmonic component of the response performs the necessary extension. In the linear region, the principle of superposition is valid. This means, for example, that the presence of strong harmonics in the applied current or voltage would not affect immittance determination at the fundamental frequency or a harmonic (Schwan, 1963). Some lock-in amplifiers can measure harmonic components, making it possible to analyze nonlinear phenomena and extend measurement to nonsinusoidal responses. 

The harmonic pattern of a full wave diode bridge is well known and well documented in literature. In the diagram of Figure 2, six diodes are used for full wave rectification of a three phase AC supply, feeding the intermediate DC circuit of a VFD. The AC current will exhibit a 6 pulse pattern, resulting from each half of the AC sine wave conducting via a particular diode. This AC current does not have a pure sinusoidal shape anymore it now includes the combination of a fundamental component (50 or 60 Hz) to which additional frequencies are superimposed. 

In EIS one can use potential or current sinusoidal perturbations. In practice, the potential perturbation of 10 mV peak to peak or a 5 mV amphtude is usually used because EIS is based on the linearization of nonlinear electrochemical equations. This also means that as the sum of sine waves is appUed, its total amplitude cannot exceed 5 mV. In practice amplitude of 5 mV rms is usually used for diffusion and adsorption limited processes, see Sect. 13.2, but in certain cases of surface processes where sharp voltammetric peaks appear the amplitude should be much lower. The linearity can be simply checked by decreasing amplitude and comparing the obtained results. Sect. 13.2. It should be kept in mind that the apparatus used in electrochemistry displays the root-mean-squared (rms) amplitude, which is the effective amplitude measured by an ac voltmeter. This rms amplitude is equal to the real amplitude divided by V ... 

The methods reviewed in this chapter, electrochemical impedance and conductivity, have common features the measured object is a specialized electrochemical cell subjected to a periodic electrical perturbation signal (in most cases the sine-wave signal) and the resulting periodic current flowing through the cell is used for the evaluation of the overall cell impedance. This cell impedance consists of the individual impedance contributions of both electrodes and a solution placed in the cell. The techniques mentioned above are aimed at the determination of only one predominant contribution of the overall impedance by using experimental conditions that enable other cell impedances to be ignored. 

Both harmonic and electrochemical frequency modulation (EFM) methods take advantage of nonlinearity in the E-I response of electrochemiced interfaces to determine corrosion rate [47-50]. A special application of harmonic methods involves harmonic impedance spectroscopy [5i]. The EFM method uses one or more a-c voltage perturbations in order to extract corrosion rate. The electrochemical frequency modulation method has been described in the literature [47-50] and has recently been reviewed [52]. In the most often used EFM method, a potential perturbation by two sine waves of different frequencies is applied across a corroding metal interface. The E-I behavior of corroding interfaces is typically nonlinear, so that such a potential perturbation in the form of a sine wave at one or more frequencies can result in a current response at the same and at other frequencies. The result of such a potential perturbation is various AC current responses at various frequencies such as zero, harmonic, and intermodulation. The magnitude of these current responses can be used to extract information on the corrosion rate of the electrochemical interface or conversely the reduction-oxidation rate of an interface dominated by redox reactions as well as the Tafel parameters. This is an advantage over LPR and EIS methods, which can provide the Z( ) and, at = 0, the polarization resistance of the corroding interface, but do not uniquely determine Tafel parameters in the same set of data. Separate erqreriments must be used to define Tafel parameters. A special extension of the method involves... 

The sinusoidal wave (Figure 2-5A) is the most frequently encountered type of periodic electrical signal. A common example is the current produced by rotation of a coil in a magnetic field (as in an electrical generator). Thus, if the instantaneous current or voltage produced by a generator is plotted as a function of time, a sine wave results. 

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