Charge Transfer Resistance, Rct

The capacitance CH and the charge transfer resistance Rct representing the Helmholtz layer. 

Figure 4 Dark currents in DSSCs with the standard I /I2 redox couple (solid line) and with a kinetically much faster redox couple, ferrocene/ferrocenium, FeCp2 + /0. A = tetrabutylammonium. The charge-transfer resistance, Rct (see Fig. 1), of the 1 2 couple is 106 times greater than that of the FeCp2+/0 couple, leading to what is sometimes mistaken as diode behavior in the dark for the cell containing the 1 2 couple. (Data from Ref. 49.)...

The three partial derivatives describe the kinetics of the reaction and (dE/dl) is the charge transfer resistance, Rct. It can be shown, using Laplace transformation, that... 

Equation (1) is similar to - Ohms law, thus we may define a resistance that is called charge transfer resistance (Rct) [i—iii] ... 

The above formulas may become inapplicable for systems with adsorption processes or/and coupled chemical steps in solution whose characteristic times are comparable with the inverse frequency within the impedance measurement interval. In this case the charge-transfer resistance, Rct, must be replaced by a complex charge-transfer impedance, Zct. Another restriction of this treatment is its assumption of the uniform polarization of the m s interface which requires to ensure a highly symmetrical configuration of the system. Refs. [i] Sluyters-Rehbach M, Sluyters JH (1970) Sine wave methods in the study of electrode processes. In Bard A/ (ed) Electroanalytical chemistry, vol. 4. Marcel Dekker, New York, p 1 [ii] Bard A], Faulkner LR (2001) Electrochemical methods, 2nd edn. Wiley, New York [iii] Retter U, Lohse H (2005) Electrochemical impedance spectroscopy. In Scholz F (ed) Electroanalytical methods. Springer, Berlin, pp 149-166 [iv] Bar-soukov E, Macdonald JR (ed) (2005) Impedance spectroscopy. Wiley, Hoboken... 

The simplest case for estimating the initial values of the circuit parameters is when the semicircle arcs in the impedance spectrum are not overlapping. In this situation the charge-transfer resistance, Rct, can be estimated using the intercepts of the arc with the real axis, and the associated double-layer capacitance, Cdh is then obtained from mm r. = peak value of the frequency. 

A charge-transfer resistance, Rct, and an impedance called Warburg impedance, Z , which describes the mass transport of the electroactive... 

If the impedance // is subdivided into a charge-transfer resistance, Rct, and the Warburg impedance, Zw, we easily obtain... 

Under this electrochemical configuration, it is commonly accepted that the system can be expressed by the Randles-type equivalent circuit (Fig. 6, inset) [23], For reactions on the bare Au electrode, mathematical simsulations based on the equivalent circuit satisfactorily reproduced the experimental data. The parameters used for the simulation are as follows solution resistance, Rs = 40 kQ cm2 double-layer capacitance, C = 28 /iF cm-2 equivalent resistance of Warburg element, W — R = 1.1 x 109 2 cm2 equivalent capacitance of Warburg element, W — T = 1.1 x 109 F cm2 (

charge-transfer resistance, Rct = 80 k 2 cm2. Note that these equivalent parameters are normalized to the electrode geometrical area. On the other hand, results of the mathematical simulation were unsatisfactory due to the nonideal impedance behavior of the DNA adlayer. This should... 

In the limit of small overpotentials (rj 0), the Butler-Volmer equation can be linearized to yield the charge transfer resistance (Rct) ... 

Complexation of alkali metal ions by 15-crown-5 and 12-crown-4 terminated SAMs was studied by EIS [78,80]. The impedance of SAM-covered electrodes in the presence of a redox probe (usually Ru(NH3)g ) was described by the Randles equivalent circuit, and the charge-transfer resistance Rct changed systematically with the metalion concentration. Binding of Na" " ions... 

Figure 2. Dependence of the charge transfer resistance Rct of the P-CD monolayer on the concentration of anionic guest (1,8-ANS) obtained by electrochemical impedance spectroscopy measurements. The solid line is a fitted Langmuir isotherm [20]. (Adapted with permission from reference 11. Copyright 2000 American Chemical Society.)...

Nyquist diagram of an electrode with parallel capacitance C and charge transfer resistance Rct Re and an ohmic resistance Ro in series. 

Randles circle for the electrical circuit of Figure 1.31 with a Warburg impedance Z in series to the charge transfer resistance Rct nd the related Nyquist diagram. 

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