Sinusoidal current perturbation

Electrochemical Impedance Spectroscopy (EIS) consists in measuring the voltage response to sinusoidal current perturbation with different frequencies. This method can yield important information about mass transport limitations, but the interpretation of the results must be done very carefully. In particular, it has been shown that the cell global impedance spectrum is strongly affected by gas consumption along the channels [22]. Even on the scale of a differential cell, local effects on the rib/channel scale can dominate the resulting spectrum [23]. 

The fundamental principles of impedance spectroscopy are outlined in a number of basic textbooks/ and review articles/ " and so only a very brief summary of the fundamental ideas are presented here. In essence we examine the sinusoidal voltage response of an electrochemical system to a small-amplitude sinusoidal current perturbation. Let the perturbation have the form A/ = / sin [Pg.164]

The electrical impedance spectra of initial and final cell suspensions were measured using a PGSTAT 204 AUTOLAB potentiostat and a tetrapolar probe (figure 1) with a 4pA sinusoidal current perturbation in the range Ifom 1 Hz to 1 MHz. 

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... 

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]. 

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... 

Here, lAEI is the amplitude, U = 2 is the radial frequency in radians per second (fis the frequency expressed in hertz). In order to maintain a linear response of the electrode, the modulation amplitude must not exceed about 10 mV. The sinusoidal perturbation of the potential induces a sinusoidal current AI, superimposed onto the steady state current, with the phase shift of 0 with respect to the potential. 

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.

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. 

In the conventional EIS approach, a small sinusoidal voltage perturbation is imposed on the electrode. Impedance data for the whole electrode are then generated by measuring the ratio of the voltage perturbation and its current response as a function of frequency. In the case of a nonuniform electrode surface with sites of different electrochemical reactivity, interpretation of the data using transfer functions becomes complex and quantirication of derived values becomes difficult. 

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... 

The local electrochemical impedance spectroscopy (LEIS) " is another scanning probe technique that can map the ac impedance distribution over an electrode surface. In LEIS a sinusoidal voltage perturbation between the working and reference electrode is maintained by driving an ac current between the working... 

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]. 

The measurement of electrochemical impedance usually involves applying a small sinusoidal voltage perturbation superimposed on a fixed value of applied potential at frequencies which typically vary from 100 kHz down to 1 mHz. The current response to this perturbation is measured in terms of its amplitude and change in phase which leads to the impedance. 

EIS, which involves the application of a sinusoidal electrochemical perturbation (potential or current) over a wide range of frequencies, allows for the measurement of impedance changes in the forms of double-layer capacitance and the... 

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. 

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