Equivalent circuit system

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, = 40 kS2 cm double-layer capacitance, C = 28 /xF cm equivalent resistance of Warburg element, W — R = 1.1 x 10 cm equivalent capacitance of Warburg element, IF—7 =l.lxl0 F cm (

charge-transfer resistance, R = 80 kf2 cm. 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... 

FIG. 6 Complex impedance plots for the electrode reaction of [Fe(CN)6] on bare (open circle) and DNA-modilied (filled circle) An electrodes. An equivalent circuit for the electrode system is shown in the inset and solid lines represent theoretical responses from the circuit. Parameters used in simulation are cited in the text. Electrode potential, + 205 mV (vs. Ag/AgCl) AC amplitude, 25 mV (p-p). Other conditions are the same as those in Fig. 5. 

In an analysis of an electrode process, it is useful to obtain the impedance spectrum —the dependence of the impedance on the frequency in the complex plane, or the dependence of Z" on Z, and to analyse it by using suitable equivalent circuits for the given electrode system and electrode process. Figure 5.21 depicts four basic types of impedance spectra and the corresponding equivalent circuits for the capacity of the electrical double layer alone (A), for the capacity of the electrical double layer when the electrolytic cell has an ohmic resistance RB (B), for an electrode with a double-layer capacity CD and simultaneous electrode reaction with polarization resistance Rp(C) and for the same case as C where the ohmic resistance of the cell RB is also included (D). It is obvious from the diagram that the impedance for case A is... 

When the rate of the electrode reaction is measurable, being characterized by a definite polarization resistance RP (Eq. 5.2.31), the electrode system can be characterized by the equivalent circuit shown in Fig. 5.22. 

Nevertheless, we will show that all of the systems studied exhibited relatively straightforward electrochemical phenomenology and could be represented by simple equivalent circuits involving primarily passive electrical elements. 

Electrical parameters of the system under consideration have been estimated using an equivalent circuit presented by Fig. 2. Thus, the anode capacitance can be written as follows ... 

Equivalent circuit In impedance analyses, a collection of electrical components used to mimic the frequency behaviour of a cell or electrochemical system. 

The next set of models examined in this section is impedance models. Impedance is often used to determine parameters and understand how the fuel cell is operating. By applying only a small perturbation during operation, the system can be studied in situ. There are many types of impedance models. They range from very simple analyses to taking a complete fuel-cell model and shifting it to the frequency domain. The very simple models use a simple equivalent circuit just to understand some general aspects (for examples, see refs 302—304). 

EIS data is generally interpreted based on defining an appropriate equivalent circuit model that best fits the acquired data. The elements of the circuit model involve a specific arrangement of resistors, capacitors, and inductors that tacitly represent the physicochemical reality of the device under test. Under these circumstances the numerical value for chemical properties of the system can be extracted by fitting the data to the equivalent circuit model. Impedance measurements are typically described by one of two models ... 

To a first approximation, the BLM can be considered to behave like a parallel plate capacitor immersed in a conducting electrolyte solution. In reality, even such a thin insulator as the modified BLM (designated by and R, in Fig. 108) could block the specific adsorption of some species from solution and/or modify the electrochemical behavior of the system. Similarly, System C may turn out to be a semiconductor(l)-insulator-semiconductor(2) (SIS ) rather than a semiconductor(l)-semiconductor(2) (SS ) junction. The obtained data, however, did not allow for an unambiguous distinction between these two alternative junctions we have chosen the simpler of the two [652], The equivalent circuit describing the working (Ew), the reference (Eg), and the counter (Ec) electrodes the resistance (Rm) and the capacitance (C of the BLM the resistance (R ) and capacitance (Ch) of the Helmholtz electrical double layer surrounding the BLM as well as the resistance of the electrolyte solution (RSO ) is shown in Fig. 108a [652],... 

Deposition of a particulate semiconductor on the cis side of the BLM (System A) alters the equivalent circuit to that shown in Fig. 108b, where Rf and... 

Impedance Spectroscopy for More Complex Interfacial Situations. The electrochemical interfacial equivalent circuits shown in Figs. 7.48 and 7.49 are the simplest circuits that can be matched to actual electrochemical impedance measurements. The circuit in Fig. 7.49 would be expected to apply to an electrode reaction that involves only electron transfer (e.g., redox systems of the type Fc3+ + e Fe2+), no adsorbed intermediate. 

Modeling and optimization of chemical sensors can be assisted by creating equivalent electrical circuits in which an ordinary electrical element, such as a resistor, capacitor, diode, and so on, can represent an equivalent nonelectrical physical parameter. The analysis of the electrical circuit then greatly facilitates understanding of the complex behavior of the physical system that it represents. This is a particularly valuable approach in the analysis and interpretation of mass and electrochemical sensors, as shown in subsequent chapters. The basic rules of equivalent circuit analysis are summarized in Appendix D. Table 3.1 shows the equivalency of electrical and thermal parameters that can be used in such equivalent circuit modeling of chemical thermal sensors. 

This expression is the basic description for the use of the pyroelectric effect in a host of sensor applications including the well known optical detection devices (82,83). A particularly useful way of describing this type of system is with an equivalent circuit where the pyroelectric current generator drives the pyroelectric impedance and the measuring amplifier circuit as shown in Figure 11. 

Figure 36. Plots of different system functions for the Equivalent Circuit given by Eq. (62) and special cases of it.3,15 Reprinted from J. Maier, Evaluation of Electrochemical Methods in Solid State Research and Their Generalization for Defects with Variable Charges , Z. Phys. Chem. NF, (1984) 191-215. Copyright 1984 with permission from Oldenbourg Verlagsgruppe.223...

If we switch-off the current after the steady state has been reached, the voltage relaxes to the initial zero-level. The electrical behavior can be taken into account by introducing in the simple equivalent circuit (eqc) (Eq. (60)) a capacitor Cl in series to Rioa or to R,.ml (if ions or electrons are blocked) In the language of system theory the equivalent circuit of the bulk represents a PDTi-element and reads3 15 e.g., for cells 3 and 4 Par (Cx. Par (Rm , Ser ( AJrai, Cl))). 

According to the superposition theorem of system theory for linear responses, this response to a step-function in the current can be employed to deduce the impedance behavior. As regards a qualitative discussion, one can adopt the above description by just replacing short/long times by high/small frequencies. Quantitatively the impedance is given by a Laplace transformation of Eq. (64) (or equivalently by applying Kirchhoff s laws to the equivalent circuit (Eq. (63))) with the result... 

Fig. 6.16. Equivalent circuit representing the electrode system Ti02 Ag nanoparticles electrolyte and calculated Mott-Schottky curves for different portions of the electrode surface covered by metal particles (m) 0 (curve 1) 0.02 (curve 2) 0.2 (curve 3). CH = 10 pF/cm2 CM = 20 pF/cm, Nd = 1.5xl018 cm 3.

Consider the application of a small sinusoidal potential ( AE sin cut) on a corroding sample, which results in a signal along with the current flow of harmonics 2cq, 3co, etc. Then the impedance A/ sin ( of + r/j) is the relation between AE/ Al and phase (j). In the case of corrosion studies, the sample is made part of a system known as equivalent circuit,24 which consists of the solution resistance Rs, charge transfer resistance Rqt and the capacitance of the double layer Cdi- The measured impedance plot appears in the form of... 

The interpretation of measured data for Z(oi) is carried out by their comparison with predictions of a theoretical model based either on the (analytical or numerical) integration of coupled charge-transport equations in bulk phases, relations for the interfacial charging and the charge transfer across interfaces, balance equations, etc. Another way of interpretation is to use an -> equivalent circuit, whose choice is mostly heuristic. Then, its parameters are determined from the best fitting of theoretically calculated impedance plots to experimental ones and the results of this analysis are accepted if the deviation is sufficiently small. This analysis is performed for each set of impedance data, Z(co), measured for different values of external parameters of the system bias potentials, bulk concentrations, temperature... The equivalent circuit is considered as appropriate for this system if the parameters of the elements of the circuit show the expected dependencies on the external parameters. 

Figure 2.37 shows an example impedance spectrum of an electrochemical system with two time constants. Figure 2.37a, b, and c are the equivalent circuit, simulated Nyquist diagram, and Bode plot, respectively. 

Figure 2.38. Typical Nyquist plots for electrochemical systems 2.6.3 Equivalent Circuit Models...

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