Ac voltammetry

Ac signals (controlled potential or current) can be considered simply as signals varying in time in a known manner. They can be followed (sampled) discretely in the same manner as, for example, a linear potential sweep and this has, in fact, been done. Sine-wave signals, however, are a special category and a great body of mathematical theory is available from the electrical engineering field. 

Simulations of ac voltammetry are rare. There is the work of Hayes et al (1974A, 1974B) and Bond et al (1976). These authors examined specific electrochemical situations Hayes et al (1974A) dealt with disproportionation and (1974B) irreversible dimerisation Bond et al (1976) with the interplay of ac and LSV. No analytical solutions for these exist as yet. These workers assumed that the dc and ac components of all quantities are independent. The assumption is reasonable for sufficiently small ac amplitudes and sufficiently high frequencies of the ac modulation. Then, the ac solution can be obtained analytically from the dc solution, and one needs only to simulate the latter. 

Ac voltammetry is one of the techniques based on the analysis of faradaic impedance. A low-amplitude sinusoidal voltage (E ) is applied to the working electrode, which is also biased at some dc potential (E ) with respect to the reference electrode. Because of the difference in the time scale, the ac component of the total current can be readily separated from the dc component. The kinetic parameters can be extracted either from the amplitude of ac current, which is measured as a function of E, or from the phase angle between the ac current and ac voltage, p. 

There are several modifications of this technique. In ac polarography, which employs a dropping mercury working electrode, 4 is changed step-wise (one step per drop lifetime) and the diffusion layer is completely renewed after every drop fall. In linear sweep ac voltammetry, the working electrode is stationary, and dc is a linear function of time. However, when the sweep rate is slow, the polarographic and voltammetric responses are quite similar, and we will neglect the difference between those two modifications. For more details, one should consult Chapter 10 in reference (1) and the review articles cited therein. 

Although it is possible to determine a from the peak potential [equation (15.11a)] and then use its value to find k° from equation (15.11b), it is more common to extract the kinetic parameters from the phase angle p. The dependence of cot( on the ac frequency (ft)) and dc potential is given by equation (15.12), which is vahd for both quasi-reversible and irreversible ET kinetics  

Kinetic parameters can be determined by fitting experimental cot0 vs. - Ei ) dependences obtained at different ac frequencies to equation (15.12) (10). 

More recently, ac voltammetry was carried out at pm-sized UMEs to further diminish the effect of the resistive potential drop in studies of fast ET reactions (11). These experiments yielded kinetic parameters for several rapid electrode processes in agreement with the results obtained by steady-state techniques. 

AC voltammetry is an extension of classical linear sweep electrochemical techniques such as cyclic voltammetry (CV) [1]. Analogous to CV, in AC voltammetry the mean DC potential V is imposed potentiostatically at arbitrary values that usually are different from the equilibrium value. A DC ramp with a comparatively slow sweep rate v and an AC signal sin (Of with 

The magnitude of Faradaic impedance for a simple reversible system is determined by both diffusion and charge-transfer resistance (Section 5-6) as  

A reversible redox process involving oxidized species with a bulk-solution concentration determined by the amplitude of the AC current output 

At the peak maximum, the applied DC-potential V equals the standard potential V. Since for this condition V=Vg and cosh 0) = 1, the peak current becomes . — 

From Eq. 13-3 it can be seen that the peak current is proportional to 2 and C. This concentration dependence allows analytical electrochemistry applications of AC voltammetry. 

The detection of the ac component allows one to separate the contributions of the faradaic and charging currents. The former is phase-shifted by 45° relative to the applied sinusoidal potential, while the background component is 90° out of phase. The charging current is thus rejected using a phase-sensitive lock-in amplifier (able to separate the in-phase and out-of-phase current components). As a result, reversible electrode reactions yield a detection limit of 5 x 10 7 M. 

Using either a lock-in amplifier or frequency response analyzer it is possible to study impedance during cyclic voltammetric dc potential cycling. During a slow voltammetric sweep, an ac signal can be superimposed and the ac response measured at one frequency at a time as a function of potential. If such an experiment is repeated at various frequencies, a complete impedance curve can be acquired, although for individual sweeps complex admittance is usually registered. 

Effectively removes noise Wide Irequency range 

Reduces harmonic distortion Removes harmonic distortion 

Suppresses dc noise Direct output to external device 

This technique was applied, for example, to Pt oxidation [86], electrocatalysis of methanol [87], formic acid oxidation [88], or hydrogen adsorption [89]. There is a limitation on the smallest frequency at a given sweep rate, v during the ac cycle the electrode potential cannot change too much [86]  

Application of the FT-IFT strategy to the analysis of S W voltammetry provides entirely different patterns in the harmonics. Now, all odd harmonics contain both faradaic and nonfaradaic components while even harmonics, being almost purely faradaic, manifest themselves only when departure from reversibility of the electrochemical kinetics occurs or the // -drop is significant [30, 32]. Thus, the electroanalytical advantages furnished by FT AC voltammetry are again moderated by the influence of the scourge of all voltammetric methods. 

The current magnitude of each harmonic component of an AC voltammogram increases with an increase in AP (to a limiting value defined by frequency,/(Hz)), while the presence of // -drop suppresses the current. Nevertheless, the accuracy in the determination of Ip available with FT AC voltammetry is vastly superior to that possible in the DC mode. A careful selection of frequency of the periodic component in FT AC voltammetry provides a straightforward possibility to tune the sensitivity of the method to the kinetics of interest, analogous to varying the scan rate in DC voltammetry. The upper limit of frequency in an experiment is usually determined by the f a-CjjL time constant of the electrochemical cell, and by instrumental limitations. 

In contrast to DC voltammetry, where an evaluation of iP can be achieved by using look-up tables (see Section 2.1.2), the quantitative analysis of FT AC voltammetric 

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FIGURE 3-11 Potential-time waveform used in alternating current (AC) voltammetry. 

Substantial loss in sensitivity is expected for analytes with slow electron-transfer kinetics. This may be advantageous for measurements of species with fast electron-transfer kinetics in the presence of a species (e.g., dissolved oxygen) that is irreversible. (For the same reason, the technique is very useful for the study of electron processes.) Theoretical discussions on AC voltammetry are available in the literature (16-18). 

The term polarography basically refers to a method, where the current flowing across the electrochemical interface is recorded as a function of the applied electrode potential, historically in most cases a mercury electrode is involved. Thus polarography might be called also voltammetry. This sometimes results in confusing terms like e.g. AC voltammetry, which is obviously equivalent to AC polarography (see following entry). (Data obtained with this method are labelled DCP.)... 

For the in situ characterization of modified electrodes, the method of choice is electrochemical analysis by cyclic voltammetry, ac voltammetry, chronoamperometry or chronocoulometry, or rotating disk voltametry. Cyclic voltammograms are easy to interpret from a qualitative point of view (Fig, 1). The other methods are less direct but they can yield quantitative data more readily. 

The methods of ac voltammetry are widely used for kinetic studies of different electrochemical reactions. The sensitivity for analytical purposes is about 10 M. It can be raised by about an order of magnitude when versions are used in which the ac signal is recorded not at the fundamental frequency of the ac voltage, but at its second harmonic, or when still more complicated effects are used. 

Topics discussed above are some basic principles and techniques in voltammetry. Voltammetry in the frequency domain where i-E response is obtained at different frequencies from a single experiment known as AC voltammetry or impedance spectroscopy is well established. The use of ultramicroelectrodes in scanning electrochemical microscopy to scan surface redox sites is becoming useful in nanoresearch. There have been extensive efforts made to modify electrodes with enzymes for biosensor development. Wherever an analyte undergoes a redox reaction, voltammetry can be used as the primary sensing technique. Microsensor design and development has recently received... 

Redox potentials for i-2 were determined in butyronitrile containing O.IM tetra-n-butylammonium perchlorate using a Pt disc electrode at 21. These potentials were measured relative to a saturated calomel electrode using ac voltammetry.(lQ) Both the one electron oxidations and reductions of i-2 exhibited good reversibility. The half-wave potentials for the one-electron oxidation and reduction of i-2, ZnTPP, and two model quinones are given in Table I. 

Recently, Alvarez et al. [136] have studied interfacial and electrochemical behavior of diphenylselenide on HMDE in DMF-water mixture (3 7, v v). Applying ac voltammetry and chronocoulometry, it has been shown that a multilayer film of chemisorbed diselenide of the progressively increasing thickness is formed. 

Cyclic voltammetric methods, or other related techniques such as differential pulse polarography and AC voltammetry,3 provided a convenient method for the estimation of equilibrium constants for disproportionation or its converse, comproportionation. In this respect, the experimentally measured quantity of interest in a cyclic voltammetric experiment is E>A, the potential mid-way between the cathodic and anodic peak potentials. For a one-electron process, E,A is related to the thermodynamic standard potential Ea by equation (4).13 In practice, ,/2 = E° is usually a good approximation. 

Before introducing further examples, the significance of phase shifts upon measurement error in ac voltammetry should be explored. Since the basic pur-... 

Recently, Lenhard (43) has used phase-selective second-harmonic ac voltammetry to obtain more nearly reversible redox potentials for a group of cyanine dyes. The main advantage of this approach is the short time scale of the ac measurements. 

MB has been shown useful also for detection of cocaine by means of specific DNA aptamer [50]. The MB-tagged aptamer has been immobilized via thiol group onto a gold support. In absence of cocaine, the aptamer was partially unfolded. Addition of cocaine resulted in folding of aptamer into three-way junction, moving MB to a close proximity with the electrode surface. This resulted in an increase in reduction peak measured by AC voltammetry. Sensor was regenerable and allowed to detect cocaine within several seconds with sensitivity below 10pmol/L. 

It was also found that the hybridization kinetics were found to be faster in a moving sample, as compared to a stationary sample [939]. In another report, active acoustic mixing was used to achieve a five-fold faster DNA hybridization rate. Hybridization was detected electrochemically (by AC voltammetry) based on the ferrocene redox chemistry [62],... 

Sequaris, J.-M. Valenta, P. Nurnberg, H.W. A new electrochemical approach for the in vitro investigation of damage in native DNA by small G-radiation doses. Int. J. Radiat. Res. 1982, 42, 407-415. Sequaris, J.-M. Valenta, P. AC voltammetry A control method for the damage to DNA caused in vitro by alkylating mutagens. J. Electroanal. Chem. 1987, 227, 11-20. 

A third electrochemical technique, phase selective second harmonic AC voltammetry has recently been successfully used for determining reversible redox potentials for systems where species formed undergo fast follow-up reactions (Ahlberg et al., 1978 Ahlberg and Parker, 1980 Jaun et al., 1980). 

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... 

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