Voltage perturbation

By polarization is meant the application of a voltage perturbing the equilibrium potential of the electrode. 

To carry out this type of study, a small AC amplitude voltage perturbation, AV ico,/), is applied, superimposed onto a DC bias voltage component, and the resulting alternating current response and its phase, A/(co,t), is measured [123,132], Then, the electrochemical impedance of the system is thus defined as... 

That is, in the specific case of electrochemical impedance spectroscopy (EIS), the steady, periodic linear response of a cell to a sinusoidal current or voltage perturbation is measured and analyzed in terms of gain and phase shift as a function of frequency, to, where the results are expressed in terms of the impedance, Z. In this regard, the impedance response of an electrode or a battery is given by... 

For the EIS evaluation, samples were exposed to an aerated 0.5 M NaCl solution for 24 h under free corrosion conditions. During this time, some amount of corrosion damage occurred that normally manifested itself as pitting. Replicate EIS spectra were collected from each sample between 10 kHz and 10 mHz using a 10 mV sinusoidal voltage perturbation. During the 24 h exposure period, sam-... 

Figure 54 LEIS admittance map of two scribe marks on 10 (im thick polyvinyl chloride/ polyvinyl acetate coating on A1 alloy 5182 (Al-2.5 Mg) after exposure to 3.5 wt% NaCl for 24 h. The map was collected using a 15 mV amplitude voltage perturbation at 500 Hz. Underfilm corrosion is occurring in association with the rightmost scribe, as indicated by the extended high admittance region located approximately at x = 2, y = 1. (From M. W. Wittmann, R. B. Leggat, S. R. Taylor. J. Electrochem. Soc. 146, 4071 (1999).)...

AC voltammetry — Historically the analysis of the current response to a small amplitude sinusoidal voltage perturbation superimposed on a DC (ramp or constant) potential [i]. Recent applications invoke large amplitude perturbation (sinusoidal, square wave or arbitrary wave... 

DC voltammetry — Voltammetry with an applied DC potential that varies, usually, linearly with time. That is, constant d V/dt without embellishments of the voltage perturbation as applies, for example, in AC voltammetry. See -> polarography, and subentry - DC polarography. Refs. [i] Bond AM (1980) Modern polarographic methods in analytical chemistry. Dekker, New York [ii] Galas Z (1994) Fundamentals of electrochemical analysis, 2nd edn. Ellis Horwood, New York, Polish Scientific Publisher PWN, Warsaw... 

Faradaic rectification voltammetry — A -> voltammetry technique utilizing an asymmetric current response to a symmetric voltage perturbation (usually sinusoidal and large enough to induce nonlinear effects) or visa versa [i-iv]. See also -> faradaic rectification. 

Low-amplitude perturbation — A potential perturbation (rarely a current perturbation) whose magnitude is small enough to permit linearization of the exponential terms associated with the relevant theory [i]. See for example -> electrochemical impedance spectroscopy where low-amplitude voltage perturbations (usually sinusoidal) are the sole perturbations see also AC -> po-larography where, historically, a small amplitude voltage perturbation was imposed on a DC ramp [ii]. 

Considering the charge transfer reaction (Ox + n e <=> Rd) with both oxidant (Ox) and reductant (Rd) being soluble, the electrode potential can be expressed as an equilibrium electrode potential plus a sinusoidal voltage perturbation ... 

There are two options for controlling the perturbation to the measured system one is to control the current perturbation then record the voltage response from the system the other is to control the voltage perturbation then record the current response. For a current control measurement, when the leads are all connected the electrical load is set to a DC constant current. The FRA will generate an AC current perturbation and interrupt the fuel cell through a load bank or a potentiostat. The response to the interruption from the fuel cell will enter into the FRA for analysis to obtain the AC impedance spectra. 

A small current or voltage perturbation also implies that the changes in concentration of the reactants and products near the electrode surface are small and the associated equations can be linearized when appropriate, to simplify the mathematical treatment. 

Figure 2. Representative drawing of the Na+ current (lm) response to a voltage-clamp step, shown as Vm, with superposed synthesized small perturbation (crosshatching). The acquisition of the current response to the small voltage perturbation, from which the admittance Y(jf) was calculated from eqs 2, 3, and 5 with YK(jf) = 0, occurred in the three intervals (20-100, 100-180, and 200-280 ms) marked by heavy horizontal lines under the time scale.

Coulometric titration of SOj, H2S In a cell containing Br-ZBrj in an acidic medium, elec-trolytically generated bromine is titrated with ambient levels of either SOj or HjS. The voltage perturbation seen by the analyzer as a result of the change in the redox potential when SO2 (or H2S) is introduced into the cell will be proportional to the SO2 concentration in the sample stream. 

For reversible systems there is no special reason to use these techniques, unless the concentration of the electrochemical active species is too low to allow application of DCP or cyclic voltammetry. For a reversible electrochemical system, the peak potentials in alternating current voltammetry (superimposed sinusoidal voltage perturbation) and in square-wave voltammetry (superimposed square-wave voltage... 

AC voltammetry/polarography An analysis of the current response to a small-amplitude sinusoidal voltage perturbation superimposed... 

Impedance analysis is used to study the response of electrochemical systems to sinusoidal perturbations about a steady state or equilibrium condition. In contrast to cyclic voltammetry which is a large amplitude technique, impedance measurements are carried out with small amplitude (voltage) perturbations. The voltage is typically 3-5 mV peak-to-peak about a d.c. voltage level so that the (current) response is linear. The frequency of perturbation is varied in order to separate the individual electrochemical relaxation processes which occur with different time constants. 

As the frequency of voltage perturbation is increased, one may limit the penetration depth (D/jco) of a concentration wave generated by the redox reaction so that it is much smaller than the thickness of the electroactive polymer film. In this region, one measures the kinetics of the charge injection process at the surface (Region III). The impedance characteristic is a semicircle in the Zreal vs —Zjmag impedance plane plot. For the impedance measurement, one may obtain Rct, the charge transfer resistance, and the double layer capacitance Cdl- This procedure was used to calculate the... 

Let us suppose that a small alternating voltage perturbation is applied to the working electrode around a constant dc potential,... 

We are interested in the current response of an electrode to a voltage perturbation of the form... 

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... 

In the EFM method, an a-c voltage pierturbation is applied at two frequencies, oji and (O2. As an example, the voltage perturbation could be given as ... 

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