Equivalent circuit description

Equivalent Circuit Description of Mixed Conduction in Solids... 

A more quantitative description of the photocurrent responses, taking into account the contributions from back electron transfer and RuQi attenuation, was achieved by IMPS measurements [83]. Considering the mechanism in Fig. 11, excluding the supersensitization step, and the equivalent circuit in Fig. 18, the frequency-dependent photocurrent for a perturbation as in Eq. (42) is given by... 

To evaluate the magnitude of capacitive currents in an electrochemical experiment, one can consider the equivalent circuit of an electrochemical cell. As illustrated in Figure 24, in a simple description this is composed by a capacitor of capacitance C, representing the electrode/solution double layer, placed in series with a resistance R, representing the solution resistance. 

We have extended the technique of Relaxation Spectrum Analysis to cover the seven orders of magnitude of the experimentally available frequency range. This frequency range is required for a complete description of the equivalent circuit for our CdSe-polysulfide electrolyte cells. The fastest relaxing capacitive element is due to the fully ionized donor states. On the basis of their potential dependence exhibited in the cell data and their indicated absence in the preliminary measurements of the Au Schottky barriers on CdSe single crystals, the slower relaxing capacitive elements are tentatively associated with charge accumulation at the solid-liquid interface. 

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. 

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... 

The reaction of our investigator to the puzzle presented by the black box will differ according to whether he is a mathematician, electrical engineer, physicist or chemist. The mathematician will be satisfied by a description in terms of differential equations and the engineer by an equivalent circuit. However the physicist or chemist will want an interpretation in terms of the structure of the material whose response can be represented by the black box. The materials scientists will often be disappointed. 

The equivalent circuit should be as simple as possible to represent the electrochemical system and it should give the best possible match between the model s impedance and the measured impedance of the system, whose equivalent circuit contains at least an electrolyte resistance, a double-layer capacity, and the impedance of the Faradaic or non-Faradaic process. Some common equivalent circuit elements for an electrochemical system are listed in Table 2.1. A detailed description of these elements will be introduced in Section 4.1. 

Figure 69. Equivalent circuit for the description of generalized electrochemical processes in linear systems (see text).263 (Reprinted from J. Jamnik, Impedance spectroscopy of mixed conductors with semi-blocking boundaries Solid State Ionics, 157, 19-28. Copyright 2003 with permission from Elsevier.)...

In a recent study, Harrison et al. [485] used steady-state j-E and Z(co)-E data to characterize the chlorine evolution reaction at Ru02/Ti02 electrodes using a simple redox reaction description of the chlorine evolution process with HOC1 and CR as reactant and product, respectively. The impedance potential data were analyzed by the equivalent circuit method parameter curves such as CiX-E and Rct-E. It has been suggested by the authors [485] that this type of parametric analysis of impedance data can be useful for comparison of the activity of various types of electrodes. 

As mentioned in the introduction, the electrical nature of a majority of electrochemical oscillators turns out to be decisive for the occurrence of dynamic instahilities. Hence any description of dynamic behavior has to take into consideration all elements of the electric circuit. A useful starting point for investigating the dynamic behavior of electrochemical systems is the equivalent circuit of an electrochemical cell as reproduced in Fig. 1. The parallel connection between the capacitor and the faradaic impedance accounts for the two current pathways through the electrode/electrolyte interface the faradaic and the capacitive routes. The ohmic resistor in series with this interface circuit comprises the electrolyte resistance between working and reference electrodes and possible additional ohmic resistors in the external circuit. The voltage drops across the interface and the series resistance are kept constant, which is generally achieved by means of a potentiostat. 

The above analysis shows that in the simple case of one adsorbed intermediate (according to Langmuirian adsorption), various complex plane plots may be obtained, depending on the relative values of the system parameters. These plots are described by various equivalent circuits, which are only the electrical representations of the interfacial phenomena. In fact, there are no real capacitances, inductances, or resistances in the circuit (faradaic process). These parameters originate from the behavior of the kinetic equations and are functions of the rate constants, transfer coefficients, potential, diffusion coefficients, concentrations, etc. In addition, all these parameters are highly nonlinear, that is, they depend on the electrode potential. It seems that the electrical representation of the faradaic impedance, however useful it may sound, is not necessary in the description of the system. The systen may be described in a simpler way directly by the equations describing impedances or admittances (see also Section IV). In... 

Figure 8.21. Electrical equivalent circuit used for description of statistical sequences of emeraldine base and salt in polyaniline.

The Cole equations are descriptive in their nature. Even so, many have tried to use them for explanatory purposes but usually in vain. If a Cole model all the same is to be used not only for descriptive, but also for explanatory purposes, it is necessary to discuss the relevance of the equivalent circuit components with respect the physical reality that is to be modeled. Because the Cole models are in disagreement with relaxation theory, this is not easy. A more general dispersion model, Eq. 9.43, may help circumvent problems occurring when the characteristic frequency is found to vary and DC paths with independent conductance variables cannot be excluded. 

He discussed the three-component electric equivalent circuit with two resistors (one ideal, lumped, physically realizable electronic component one frequency-dependent not realizable) and a capacitor (frequency-dependent) in two different configurations. He discussed his model first as a descriptive model, but later discussed Philippson s explanatory interpretation (extra-/intracellular liquids and cell membranes). 

Kenneth S. Cole repeated the presentation from 1928, but now with a quasi-four-element equivalent circuit with two static resistors, his Z3 is a CPE. His model implies that the two resistors are not a part of the polarization process. This is exphcitly stated in Cole (1934). He did not discuss a microanatomical or relaxation-theory explanatory model. He pointed out that different equivalent circuits may equally well mimic measured data all are possible descriptive models. He did point out the similarity between data from tissue/cell suspensions and polarization on metal-electrolyte interphases. 

A description of the electrochemical kinetics of power sources requires treatment of two different kinds of processes. The first, intensive, can be thought of as localized, occurring in a specific volume, that is negligible compared to volume of the entire system, such as charge transfer or double-layer capacitance. These processes are described by ordinary differential equations and their equivalent circuits consist of basic building blocks representing losses and storage—resistors and capacitors. 

Chang B-Y, Park S-M (2006) Integrated description of electrode/electrolyte interfaces based on equivalent circuits and its vtsilication using impedance measurements. Anal Chem 78 1052-1060. doi 10.1021/ac0516411... 

The function of the AC technique is the following the equivalent circuit of a conductance cell (Fig. 19) is quite complex and the conditions of experiments must be such that the solution resistance R is the principal component that determines the observed cell response. The individual parts of the equivalent circuit in Fig. 19 should be easy to understand on the basis of the description given in section 2.2. 

The description of the transfer characteristic of solid-state actuators can be generalised if the system equations which have been introduced in Sect. 6.9.2 are not interpreted as electromechanical equivalent circuit diagrams but as signal flow charts [335]. The result is shown in Fig. 6.134. 

EIS changed the ways electrochemists interpret the electrode-solution interface. With impedance analysis, a complete description of an electrochemical system can be achieved using equivalent circuits as the data contains aU necessary electrochemical information. The technique offers the most powerful analysis on the status of electrodes, monitors, and probes in many different processes that occur during electrochemical experiments, such as adsorption, charge and mass transport, and homogeneous reactions. EIS offers huge experimental efficiency, and the results that can be interpreted in terms of Linear Systems Theory, modeled as equivalent circuits, and checked for discrepancies by the Kramers-Kronig transformations [1]. 

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