Faradaic admittance,

Here also, the Laplace transform method is particularly useful [130]. First, the two rate equations for v1 and vu are linearized and subsequently written in the Laplace domain. 

The explicit expression for YF(s) can be found in a recent review together with a brief discussion of some limiting cases, where the general formula can be simplified [53]. The complex faradaic admittance is obtained after substituting s = ico. Only in the limiting cases is it possible to visualize it by means of an equivalent circuit. 

The partial derivatives in eqns. (153) will be functions of the potential-dependent rate constants, kj, etc. and the mean concentrations c 0,c z, and cR. So, for application to experimental data, the results of the present section have to be combined with those of Sects. 5.1.1 or 5.1.2. The interested reader can find extensive theoretical predictions of the a.c. polarogram in ref. 131. 

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FIG. 10 Faradaic admittance coefficient Yq for the interface between 0.1 M LiCl in water and 0.02 M tetrabutylammonium tetraphenylborate ( ) or tetrapentylammonium tetrakis[3,5-bis(tri-fluoromethyl)phenyl]borate ( ) in o-nitrophenyl octyl ether as a function of the interfacial potential difference A y. (From Ref 73.)... 

It is quite easy to derive the faradaic admittance from eqns. (63) using eqn. (57). For the sake of simplicity, we introduce the parameter p defined by... 

Fig. 17. (a) The components of the faradaic impedance plotted against to. (b) The components of the faradaic admittance plotted against to1/2. System parameters fict = lficm1, p = 0.03. The solid parts of the plots indicate the frequency range that is normally accessible for meaningful analysis of data with the simple theory described in this section... 

Formulations of the general expressions for YF (s) and of some limiting cases can be found in ref. 53. It is to be noted that this faradaic admittance is connected in parallel to the double-layer admittance Yc (s). The latter may well be influenced by the presence of the adsorbed intermediate. Nevertheless, the quite specific frequency dependence of Yf can be applied to detect the presence of a mechanism of the type discussed here [53, 132]. 

Anticipating the treatment of the faradaic admittance in Sect. 7.4, we derive the a.c. parts of the interfacial concentrations for two cases described in the literature. 

The ratio of the imaginary to real faradaic admittances equals... 

The faradaic admittance of reactions (116) and (117) is described by Eq. (135). Analysis of the complex plane plots in such a case was presented by Cao. Bai and Conway presented three-dimensional plots for such a reaction. Two general cases should be considered, depending on the sign of the parameter B ... 

Equations (157)-(159) present a system of three equations with three unknowns j, 02, and7/fj. The faradaic admittance is determined as... 

Grahame DC. (1952). Mathematical theory of the Faradaic admittance. I. Pseudocapacity and polarization resistance./oaraa/ of The Electrochemical Society 99 370C-385C. Hamed J, Acar YB, Gale RJ. (1991). Pb(II) Removal from kaolinite by electrokinetics. 

The relationship between the AC fluorescence and the faradaic admittance also allows us to study the dynamics of ion transfer responses as a function of the frequency modulation. For a quasi-reversible ion transfer process featuring planar diffusion profiles, the real and imaginary components of the AC fluorescence can be expressed as [15, 23]... 

Faradaic admittance experiments on a mercury surface blocked by tribenzy-lammine [208] and in situ STM experiments with physisorbed hydrogen-bonded monolayers of guanine and adenine on HOPG [209, 210] revealed an average... 

EXPERIENCES OF AN ON-LINE FOURIER TRANSFORM FARADAIC ADMITTANCE MEASUREMENT (FT-FAM) SYSTEM BASED ON DIGITAL SIGNAL PROCESSORS... 

The theory and practical implementation of the Fourier Transform Faradaic Admittance Measurement technique was introduced and developed by Smith and coworkers.This elec-troanalytical technique now rests on a sound theoretical basis and has been proven in many experimental situations. In this method a multiple-frequency perturbation waveform is used and the cell admittance is calculated at each of these frequencies using the measured current and potential. Measurements over a substantial range of frequencies, at least over two orders of magnitude, are required before any conclusive interpretations can be made concerning the mechanism and kinetics of an electrochemical system. The main advantage of this Fourier transform approach is that the cell admittance can simultaneously by measured at a large number of frequencies. 

FOURIER TRANSFORM FARADAIC ADMITTANCE MEASUREMENTS (FT-FAM) A DESCRIPTION AND SOME APPLICATIONS... 

Cell admittance at any frequency is the cell current response divided by the amplitude of the a.c. input at that frequency. Faradaic admittance is the faradaic current response divided by the amplitude of the a.c. input. 

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