Sinusoidal potential perturbation

In our opinion, the interesting photoresponses described by Dvorak et al. were incorrectly interpreted by the spurious definition of the photoinduced charge transfer impedance [157]. Formally, the impedance under illumination is determined by the AC admittance under constant illumination associated with a sinusoidal potential perturbation, i.e., under short-circuit conditions. From a simple phenomenological model, the dynamics of photoinduced charge transfer affect the charge distribution across the interface, thus according to the frequency of potential perturbation, the time constants associated with the various rate constants can be obtained [156,159-163]. It can be concluded from the magnitude of the photoeffects observed in the systems studied by Dvorak et al., that the impedance of the system is mostly determined by the time constant. 

The potential excitation and its current response are schematically shown in Figure 35 as sinusoidal excitations. The electrochemical impedance spectroscopy method is conducted according to the ASTM G-106 standard practice, in which a range of smaU-amphtude sinusoidal potential perturbation is applied to the electrode/sohition interface at discrete frequencies. These frequencies cause an out of phase current response with respect to the applied sinusoidal potential waveform. 

The lower part of Fig. 7-2 shows a stationary polarization curve with a sinusoidal potential perturbation... 

One of the earliest reports on the use of an AC perturbation in combination with SECM for the study of corrosion was by Tanabe et al. [12]. In what they termed an induced AC current mode, a small amplitude sinusoidal potential perturbation (0.3 mV p-p, IkHz) superimposed on a DC potential was applied to a steel substrate, which in turn induced an AC current at the tip (held at OV vs. Ag/AgCl, 20 pm above the surface). An increase in induced AC current was shown to correlate with a decrease in local pH and permitted mapping of pitting sites on the steel surface [12]. 

Another advantage of nonlinear impedance analysis is that measurement of several harmonics may facilitate extraction of kinetic parameters at a single DC "offset" potential V [8] not available from small-amplitude fundamental-frequency impedance measurement. NLEIS can be used to calculate all the harmonics of the current response to a sinusoidal potential perturbation -V+ V sin(( >t) and derive the nonlinear impedance. Results from a simulation study can be compared with experimental NLEIS data, leading to more accurate quantification and modeling of the impedance data and better interpretation of the electrochemical kinetic processes [8,9,10,11,12,13]. 

The current, A/, and mass, Am, responses of Prussian blue films to a small-amplitude sinusoidal potential perturbation. Aft, were studied at several imposed potentials, with respect to the frequency, to obtain extra information about the role of protons and potassium ions during the electrochemical redox reaction of Prussian blue. Figure 17 shows the transfer functions characteristic of a Prussian blue film at 0.375 V vs. SCE. In the same graphs, the theoretical curves are also represented. Good agreement between the theoretical and the experimental data was obtained for each of the five transfer functions not only regarding shape but also regarding frequencies. 

The basic experimental arrangements for photocurrent measurements under periodic square and sinusoidal light perturbation are schematically depicted in Fig. 19. In the previous section, we have already discussed experimental results based on chopped light and lock-in detection. This approach is particularly useful for measurement at a single frequency, generally above 5 Hz. At lower frequencies the performance of lock-in amplifier and mechanical choppers diminishes considerably. For rather slow dynamics, DC photocurrent transients employing optical shutters are more advisable. On the other hand, for kinetic studies of the various reaction steps under illumination, intensity modulated photocurrent spectroscopy (IMPS) has proved to be a very powerful approach [132,133,148-156]. For IMPS, the applied potential is kept constant and the light intensity is sinusoid-... 

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... 

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 ... 

The influence of large potential perturbations on the impedance response can be illustrated by an extension of the analysis presented in Section 7.3 for large-amplitude perturbations. The current density response to a 40 mV-amplitude (baAV = 0.78) sinusoidal potential input is presented in Figure 8.2 for Ae system presented in Section 7.3 with parameters Cji = 31 pF/cm, nFka = nFkc = 0.14 mA/cm, = 19.5 V be = 19.5 V , and V = 0.1 V. Following equation (7.4), these parameters yield a value of charge-transfer resistance Rt = 51.28 Ocm and a characteristic frequency of 100 Hz. The potential and current signals were scaled by the maximum value of the signal. 

The recursion is performed on new flow data using gradient techniques, which are then followed by the determination of control input. The RePOD method can also be used in isolation to compute the modal basis, potentially resulting in substantial savings in computational resources and time. The algorithm was applied to two classes of problems [15]. In the first, the problem of heat conduction through a one-dimensional rod with a sinusoidal heat perturbation source located inside the rod was considered. The objective is to reduce the temperature... 

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... 

The foregoing examples are valid for any potential perturbation. In the particular case of ac impedance, that is, when the applied potential perturbation is sinusoidal, one uses the ET (Eq. 2.127) ... 

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 ... 

We assume that the potential of the electrode is perturbed by a small-amplitude sinusoidal potential given by AA = A exp (/wt). Consequently the faradaic current is perturbed by an amount A/ = 1A/ exp jo)t + ). This perturbation induces a concentration change Ac in the layer that is described by the time-dependent Fick diffusion equation as follows... 

Figure 11.16 Solid arrows an AC current is applied to the electrode and an AC potential response is obtained. Dashed arrows an AC potential is applied to the electrode and an AC current is obtained. In both cases, the i-E relationship is recorded over a range of frequencies. Because of the small amplitude used, the current is proportional to the potential and the response is also sinusoidal. The perturbation is shown here around for the clarity of the drawing.

Recently, Lillard et al. (1992) developed a novel method for measuring the local impedance. The authors utilized a bi-elec-trode probe to measure the component of the ac current density normal to the electrode. The bi-electrode measures the ac potential differences of the two tips induced by the sinusoidal voltage perturbation of the working electrode with a lock-in analyzer or frequency response analyzer. The ac solution current density at the probe tip is obtained from the ac potential difference between the two probe tips according to Ohm s law... 

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