Admittance, impedance spectroscopy

Two such circuits having different relaxation time constants and connected in series lead to two semicircles as shown in Fig. 2.55(b). As in the case of any other spectroscopic analysis the separate responses may overlap and the experimental curve must then be resolved into its separate constituent semicircles. Impedance spectroscopy makes use of other electrical parameters, including the admittance (Y = Z 1), to assist in quantifying the circuit parameters. 

Admittance measurements were used extensively prior to the widespread use of impedance spectroscopy in the 1980s. Capacitance bridge methods are typically used, though this limits the lower bound on the measured frequency to several hundred hertz. Corrosion processes, whose time constants are normally measured at or below 1 Hz, cannot be directly interrogated with this method. 

Immittance — In alternating current (AC) measurements, the term immittance denotes the electric -> impedance and/or the electric admittance of any network of passive and active elements such as the resistors, capacitors, inductors, constant phase elements, transistors, etc. In electrochemical impedance spectroscopy, which utilizes equivalent electrical circuits to simulate the frequency dependence of a given elec-trodic process or electrical double-layer charging, the immittance analysis is applied. 

The immittance analysis can be performed using different kinds of plots, including complex plane plots of X vs. R for impedance and B vs. G for admittance. These plots can also be denoted as Z" vs. Z and Y" vs. Y, or Im(Z) vs. Rc(Z), and Im( Y) vs. Re( Y). Another type of general analysis of immittance is based on network analysis utilizing logarithmic Bode plots of impedance or admittance modulus vs. frequency (e.g., log Y vs. logo)) and phase shift vs. frequency ( vs. log co). Other dependencies taking into account specific equivalent circuit behavior, for instance, due to diffusion of reactants in solution, film formation, or electrode porosity are considered in - electrochemical impedance spectroscopy. Refs. [i] Macdonald JR (1987) Impedance spectroscopy. Wiley, New York [ii] Jurczakowski R, Hitz C, Lasia A (2004) J Electroanal Chem 572 355... 

Figure 2 Number of journal articles on electrochemical impedance spectroscopy identified on October 3, 2007 using the Engineering Village search engine. The key words used were (((impedance or admittance) and (Electrochemical)), Journal article only).

In impedance spectroscopy, spectral transmittance H(co) usually has a form of either complex impedance Z(o)) or complex admittance Y(co). 

Electrochemical impedance spectroscopy is extensively employed for the investigation of SAMs because the broad range of frequencies covered by this technique (usually from 10 to 10 Hz) may allow processes with different relaxation times taking place within the electrified interphase to be detected and sorted out. Unfortunately, the various relaxation times often differ by less than 2 orders of magnitude, thus requiring a certain amount of arbitrariness and of physical intuition for their separation. In fact, it is well known that the same impedance spectrum can often be equally well fitted to different equivalent circuits, which are consequently ascribed to different relaxation processes. Impedance spectra are frequently reported on a Y /co versus Y"/co plot, where Y and Y" are the in-phase and quadrature components of the electrochemical admittance and co is the angular frequency. This plot is particularly suitable for representing a series RC network. Thus, a series connection of R and C yields... 

Some authors have used the designation modulus spectroscopy to denote small-signal measurement of M vs. v or co. Clearly, one could also define admittance and dielectric permittivity spectroscopy. The latter is just another way of referring to ordinary dielectric constant and loss measurements. Here we shall take the general term impedance spectroscopy to include aU these other very closely related approaches. Thus IS also stands for immittance spectroscopy. The measurement and use of the complex (< ) function is particularly appropriate for dielectric materials, those with very low or vanishing conductivity, but aU four functions are valuable in IS, particularly because of their different dependence on and weighting with frequency. 

A pH sensor, based on a.c. conductivity measurements of a thin polymer film, has been developed. The sensor consists of a planar interdigitated electrode array coated with a polypyrrole multilayer, built-up using the Langmuir-Blodgett technique. Impedance spectroscopy has been used to investigate the complex admittance of the device when exposed to aqueous solutions of different pH. The experimental data have been fitted to the theoretical response of an equivalent electrical network of capacitors and resistors. A response over the pH range 3.5 to 8 has been measured. 

Surface Resistivity, Admittance, Hardness, HCl Bubble and Electrochemical Impedance Spectroscopy", Ap>phed Materials Confidential Technical Report, January 4,1994. 

McKubre and Syrett (1983, 1988) were the first to adapt the method of harmonic analysis for the control of the corrosion rate of cathodically polarized systems. They presented a theoretical description of the problem and developed the measuring technique by making measurements over a wide range of frequencies from 1 Hz to 10 kHz. The method applied by them is known in the literature as harmonic impedance spectroscopy (HIS). It is based on the measurement of the zero, first, second, and third harmonics of the current response of an electrode perturbed by a voltage sinusoid signal. The elaborate mathematical treatment of results theoretically gives the possibility of obtaining admittance data independent of the frequency. The numerical solution of a system of three equations with three unknowns allows the determination of required AE, b, and values, and finally the corrosion current. The authors of the HIS method carried out attempts to determine the corrosion rate of copper-nickel alloys, steel, and titanium under cathodic protec-... 

In most cases, the measurements are carried out isothermally in the frequency domain and the terms dielectric spectroscopy (DS) and dielectric relaxation spectroscopy (DRS) are then used. Other terms frequently used for DRS are impedance spectroscopy and admittance spectroscopy. Impedance spectroscopy is usually used in connection with electrolytes and electrochemical studies, whereas admittance spectroscopy often refers to semiconductors and devices. Isothermal measurements in the time domain are often used, either as a convenient tool for extending the range of measurements to low frequencies (slow time-domain spectroscopy, dc transient current method, isothermal charging-discharging current measurements) or for fast measurements corresponding to the frequency range of about 10 MHz - 10 GHz (time-domain spectroscopy or time-domain reflectometry). Finally, TSDC is a special dielectric technique in the temperature domain, which will be discussed in Section 2.2. 

This paper is primarily concerned with the techniques usually described as time domain spectroscopy (TDS) or time domain reflectom-etry (TDR). These have been most commonly applied to studies of time or frequency dependent behavior of dielectrics with negligible ohmic or d.c. conductance, but can be used for substances with appreciable conductance and indeed for studies of any electrical properties which can be characterized by an effective admittance or impedance. 

Table 1 list some important phenomenological length scales which influences the phenomena like charge transfer, screening (electronic and ionic), diffusion, adsorption, ohmic loss and diffusion length w.r.t experimental techniques like chronoamperometry, electrochemical impedance or admittance spectroscopy and cyclic voltammetry. 

---