Perturbation Signal

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  

This means that to have an amphtude of 5 mV, the rms value should be set to firms = 5/ 3.5 mV. 

Nowadays it is possible to carry out automatic impedance measurements with modem equipment that uses frequency analyzers, lock-in amplihers, and FT techniques. This equipment comes with its own software for data acquisition and analysis. Usuahy, ten frequencies per decade are acquired and one must use the appropriate ac amphtude. 

Equipment dedicated to simultaneous FT analysis at a constant potential or during ac sweep is still less common. More details on how to choose the ac amplitude and to assure that good impedances will be obtained will be discussed in Sect. 13.2. 

Exercise 3.1 Simulate the sum of odd harmonic functions YAi cos 27rVit + Ttb for Frequencies, v,/Hz 

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Most of the PKIs currently in clinical trials are small molecules that compete for the ATP-binding site [3,5]. They prevent the phosphate donor ATP to bind to the protein kinase, and hence the target protein will not become phosphorylated and the perturbed signalling can be terminated. 

Fig. 22. Schematic representation of the electrochemical cell connected to a perturbation circuit and a detection circuit for second-order responses. In this case, it is supposed that the perturbation signal has a high frequency and the response signal a low frequency.

Ross, J.A., Maingay, J.P., Fearon, K.C., Sangster, K., and Powell, J.J., Eicosapentaenoic acid perturbs signalling via the NFkappaB transcriptional pathway in pancreatic tumor cells, Ini. J. Oncol., 23,1733, 2003. 

The galvanostatic intermittent titration technique (GITT) has been first proposed by Weppner and Huggins in 1977 [22], This method is of particular interest for the measurement of ion transport properties in solid intercalation electrodes, used in lithium-ion batteries, for instance [18]. The determination of the diffusion constants relies on Fick s law. The GITT method records the transient potential response of a system to a perturbation signal a current step (/s) is applied for a set time xs, and the change of the potential (E) versus time (0 is recorded (Figure 1.11) [18,22],... 

The measurement is done by applying a perturbation signal 8 (0)) to the constant potential EST where the system was initially at the steady state, with the pulsation co = 2nf. The whole potential of the electrode is then... 

Fig. 11. 13. Perturbing signals and responses for (a) faradaic rectification (b) demodulation type 1 (c) demodulation type 2.

An electrical system with linear properties does not generate harmonics in response to the perturbation signal, and the response to two or more superimposed excitation signals is equal to the sum of the two responses obtained by excitation independently. With electrochemical systems this linearity is possible to a good approximation for perturbations rather less than the thermal potential (lcBT/e) = 25 mV at 298K. 

Fuel cell researchers have also investigated other reference electrodes, such as a pseudo-reference electrode constructed by inserting a micro-sized carbon filament between two polymer electrolyte membranes [73], The main advantage of pseudoreference electrodes is their easy implementation, although one disadvantage is that their DC potential is unknown. However, this DC potential may not be that critical because EIS measurements mainly rely on the AC perturbation signal from which the impedance is calculated. 

Popkirov GS, Schindler RN (1993) Optimization of the perturbation signal for electrochemical impedance spectroscopy in the time domain. Rev Sci Instrum 64 3111-15... 

When using sine wave signals, the perturbation signal and the current response are U(t) = U0 (af) sin(fl>f) (A. 27)... 

Figure 14.5 Experimental setup used to determine the variation of interface capacitance with a low frequency perturbing signal.

Figure 4.29 Perturbation signals recorded on a four-compound plateau. Top, experimental results. Bottom signal calculated with the equilibrium-dispersive model and the best coefficients of a competitive quaternary bi-Langmuir isotherm. Compoxmds enantiomers of methyl- and ethyl-mandelate on a chiral phase. Perturbation as in Eq. 4.104 Reproduced with permission from J. Lindholm, P. Porssen, T. Fomstedt, Anal. Chem., 76 (2004) 5472 (Fig. 3). 2004, American Chemical Society.

In general, the perturbing signal may have an arbitrary form. However, in practice, the most often used perturbation signals are ° (l) pulse, (2) noise, and (3) sum of sine waves. 

White noise, that is, noise consisting of a continuous spectrum of frequencies (or a computer-generated pseudo-random white noise), may be used as a perturbation signal in practical impedance measurements. However, single-frequency components obtained by the FFT have relatively low amplitudes and a long data acquisition time is necessary to... 

This technique was introduced and used extensively by D. E. Smith In it, the perturbation signal is composed of a... 

The solution of nonlinear evolution equations in the time domain is known analytically only in very simple cases such as reversible redox processes limited by diffusion. For electrochemical nonlinear systems, the treatment of nonsteady-state techniques generally requires calculations that are at least partially numerical. In addition, the solutions found to express the response to a perturbing signal depend specifically on the form of the perturbation. These drawbacks are largely eliminated if the amplitude perturbation is limited to a sufficiently low value to allow the equations to be linearized. In this case, analyses in the frequency domain are very powerful. 

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