Interfaces equivalent circuit

FIGURE 8.19 Electrochemical reaction at the electrode-electrolyte interface equivalent circuit. 

Under potentiostatic conditions, the photocurrent dynamics is not only determined by faradaic elements, but also by double layer relaxation. A simplified equivalent circuit for the liquid-liquid junction under illumination at a constant DC potential is shown in Fig. 18. The difference between this case and the one shown in Fig. 7 arises from the type of perturbation introduced to the interface. For impedance measurements, a modulated potential is superimposed on the DC polarization, which induces periodic responses in connection with the ET reaction as well as transfer of the supporting electrolyte. In principle, periodic light intensity perturbations at constant potential do not affect the transfer behavior of the supporting electrolyte, therefore this element does not contribute to the frequency-dependent photocurrent. As further clarified later, the photoinduced ET... 

In particular, the coupling between the ion transfer and ion adsorption process has serious consequences for the evaluation of the differential capacity or the kinetic parameters from the impedance data [55]. This is the case, e.g., of the interface between two immiscible electrolyte solutions each containing a transferable ion, which adsorbs specifically on both sides of the interface. In general, the separation of the real and the imaginary terms in the complex impedance of such an ITIES is not straightforward, and the interpretation of the impedance in terms of the Randles-type equivalent circuit is not appropriate [54]. More transparent expressions are obtained when the effect of either the potential difference or the ion concentration on the specific ion adsorption is negli-... 

The distribution of potential in TC is practically the same as that near the flat surface if the electrolyte concentration is about 1 mol/1 [2], So the discharge of TC may be considered as that of a double electric layer formed at the flat electrode surface/electrolyte solution interface, and hence, an equivalent circuit for the TC discharge may be presented as an RC circuit, where C is the double layer capacitance and R is the electrolyte resistance. 

Very often, the electrode-solution interface can be represented by an equivalent circuit, as shown in Fig. 5.10, where Rs denotes the ohmic resistance of the electrolyte solution, Cdl, the double layer capacitance, Rct the charge (or electron) transfer resistance that exists if a redox probe is present in the electrolyte solution, and Zw the Warburg impedance arising from the diffusion of redox probe ions from the bulk electrolyte to the electrode interface. Note that both Rs and Zw represent bulk properties and are not expected to be affected by an immunocomplex structure on an electrode surface. On the other hand, Cdl and Rct depend on the dielectric and insulating properties of the electrode-electrolyte solution interface. For example, for an electrode surface immobilized with an immunocomplex, the double layer capacitance would consist of a constant capacitance of the bare electrode (Cbare) and a variable capacitance arising from the immunocomplex structure (Cimmun), expressed as in Eq. (4). 

Figure 18b.5b shows the equivalent circuit of the metal solution interface composed of C(i and the solution resistance Rs. When a voltage pulse, E, is applied across such a Rc circuit, the transient current flow... 

Fig. 18b.5. (a) The capacitor-like metal solution interface, the double layer, (b) The equivalent circuit with solution resistance and overall double-layer capacitor, (c) Charging current transient resulting from a step-potential at... 

Fig. 10.1 Equivalent circuits used to represent the semiconductor-electrolyte interface, (a) A more complete approach taking into account the series resistance (Ry), the depletion layer (Csc, Rsc), an oxide surface film...

However, although the WO3 surface is filled , ions still move from the electrolyte reservoir toward the WO3-electrolyte interface. Such a situation results in the accumulation of charge at this interface. In effect, we have a structure which is physically very similar to that of a typical plate capacitor (see Figure 5.3). For this reason, the equivalent circuit (see Figure 8.12(b)) also contains a capacitor Q (where the subscript denotes surface ). 

Figure 20. Equivalent circuit based on surface layer formation on cathode materials (a. top) and the electrolyte/ cathode interface (b. bottom). (Reconstructed based on ref 295.)...

Most often, the electrochemical impedance spectroscopy (EIS) measurements are undertaken with a potentiostat, which maintains the electrode at a precisely constant bias potential. A sinusoidal perturbation of 10 mV in a frequency range from 10 to 10 Hz is superimposed on the electrode, and the response is acquired by an impedance analyzer. In the case of semiconductor/electrolyte interfaces, the equivalent circuit fitting the experimental data is modeled as one and sometimes two loops involving a capacitance imaginary term in parallel with a purely ohmic resistance R. 

Generally, depending on the bias potential, the EIS leads to RC equivalent circuit loops representing both the space charge and the interface impedance components. The complete set of imaginary versus real impedance data leads to the construction of a semicircle that can be... 

Andrade and Molina [46] have performed electrochemical impedance studies of mercury electrodes with hematite particles adhered at different electrode potentials. Adhesion of such particles was strong and the decrease in the impedance was accompanied by an increase in the number of attached particles. Experimental results were analyzed in terms of an equivalent circuit including the constant phase element (CPE), the magnitude of which appeared to be directly related to the electrode coverage. A pore model for the metal/hematite particles interface has been proposed. 

Fig. 108a-c. Proposed equivalent circuits for. a an empty and b a semiconductor-particle-coated BLM. Porous structure of the semiconductor particles allowed c the simplification of the equivalent circuit. Rm, RH, and Rsol are resistances due to the membrane, to the Helmholtz electrical double layer, and to the electrolyte solutions, while C and CH are the corresponding capacitances Rf and Cf are the resistance and capacitance due to the particulate semiconductor film R m and Cm are the resistance and capacitance of the parts of the BLM which remained unaltered by the incorporation of the semiconductor particles R and Csc are the space charge resistance and capacitance at the semiconductor particle-BLM interface and Rss and C are the resistance and capacitance due to surface-state on the semiconductor particles in the BLM [652]... 

Fig. 6.33. (a) The equivalent circuit for an electrified interface is a capacitor and resistor connected in parallel, (b) In the equivalent circuit for an ideally polarizable interface, the resistance tends to infinity, and fora nonpolarizable interface, the resistance tends to zero. 

In drawing an appropriate equivalent circuit, it is clear that the resistance of the solution should be placed first in the intended diagram, but how should the capacitative impedance be coupled with that of the interfacial resistance One simple test decides this issue. We know that electrochemical interfaces pass both dc and ac. It was seen in Eq. (7.103) that for a series arrangement of a capacitor and a resistor, the net resistance is infinite for = 0, i.e., for dc. Our circuit must therefore have its capacitance and resistance in parallel for under these circumstances, for = 0, a direct current can indeed pass the impedance has become entirely resistive.51... 

How does the simplest electrochemical interface look, in terms of an equivalent circuit The appropriate circuit element is shown in Fig. 7.49. It is worth noting that the famous Warburg impedance has been left out The reason is that for most situations in which relatively fast electrode reactions occur, it is negligible. 

Fig. 7.49. Simplest electrochemical interface, in terms of an equivalent circuit.

In the Cole-Cole (or complex impedance ) plot, one takes the real as ordinate and the Zimag part as abscissa. Each point on the resulting diagram is made up of a Z resolved into two components measured at a chosen frequency. There may be 20-30 points, each at different frequencies. Such plots tend to be semicircles (see Fig. 7.47), but even simple equivalent circuits have some structure (i.e., deviations from the semicircle), and these deviations provide information concerning events at the elec-trode/solution interface. 

A more complicated model situation is demanded if one thinks of the equivalent circuit for an electrode covered with an oxide film. One might think of A1 and the protective oxide film that grows upon it during anodic polarization. One has to allow for the resistance of the solution, as before. Then there is an equivalent circuit element to model the metal oxide/solution interface, a capacitance and interfacial resistance in parallel. The electrons that enter the oxide by passing across the interfacial region can be shown to go to certain surface states (Section 6.10.1.8) on the oxide surface, and they must be represented. Finally, on the way to the underlying metal, the electron... 

Cases in which Impedance Spectroscopy Becomes Limited. One might say that if one understands an interface well, the results of Z-to measurements can be readily understood. Of course, the interest is in the other direction, in using Z-to plots when one does not understand the interlace. Then the task is to find an interfacial structure and mechanism (and its resulting equivalent circuit) that provides a Z that is consistent in its dependence on to with the experimental results of the impedance measurement. This requires finding reasonable parameters to fit the value of the C s and R s as a function of to for the individual elements in the various equivalent circuits. If the shape of the calculated Z-to plot can only be made to match experiment by using C s and R s that are physically unreasonable, the proposed structure and the equivalent circuit to match it are not acceptable and another must be tried. 

Here is more impedance study the simplest cell. In a real-life experiment, one can only work with a complete circuit, which consists of at least two electrodes. Now, to test our newly acquired impedance knowledge on a real-life problem, let s consider a circuit consisting of two identical electrodes. Draw its equivalent circuit and make a try at its impedance expression. Try harder to imagine its Cole-C ole plot You may also use a computer to simulate the situation by using reasonable parameters. To make the situation less complicated, we assume the interface is ideally polarizable. (Kang)... 

Impedance spectroscopy a single interface. Draw the equivalent circuits for the following electrode/electrolyte interfaces, then derive their impedance expression and explain what their Cole-Cole plot will look like (a) An ideally polarizable interface between electrode and electrolyte, (b) An ideally nonpolarizable interface between electrode and electrolyte, (c) A real-life electrode/... 

Now, it has already been seen in Chapter 7 that one may write an equivalent circuit for a simple electrode/solution interface as given in Fig. 7.52, where Rsoln is the resistance of the solution RF is the Faradaic resistance and DL the double-layer capacitance then the relaxation time6 is given by ... 

Fig 29. A simple equivalent circuit for the artificial permeable membrane. Physical meaning of the elements C, membrane capacitance (dielectric charge displaceme-ment) R, membrane resistance (ion transport across membrane) f pt, Phase transfer resistance (ion transport across interface) Zw, Warburg impedance (diffusion through aqueous phase) Ctt, adsorption capacitance (ion adsorption at membrane side of interface) Cwa, aqueous adsorption capacitance (ion adsorption at water side of interface). From ref. 109. 

Figure 7.1 (A) Typical controlled-potential circuit and cell OA1, the control amplifier OA2, the voltage follower (Vr = Er) OA3, the current-to-voltage converter. (B) Equivalent circuit of cell Rc, solution resistance between auxiliary and working electrodes Ru, solution resistance between reference and working electrodes, Rs = Rc + Ru and Cdl, capacitance of interface between solution and working electrode. (C) Equivalent circuit with the addition of faradaic impedance Zf due to charge transfer. Potentials are relative to circuit common, and working electrode is effectively held at circuit common (Ew = 0) by OA3.

An equivalent circuit of the three-electrode cell discussed in Chapters 6 and 7 is illustrated in Figure 9.1. In this simple model, Rr is the resistance of the reference electrode (including the resistance of a reference electrode probe, i.e., salt bridge), Rc is the resistance between the reference probe tip and the auxiliary electrode (which is compensated for by the potentiostat), Ru is the uncompensated resistance between the reference probe and the working-electrode interphase (Rt is the total cell resistance between the auxiliary and working electrodes and is equal to the sum of Rc and Ru), Cdl is the double-layer capacitance of the working-electrode interface, and Zf is the faradaic impedance of the electrode reaction. 

Figure 2. Assumed generalized equivalent circuit of the semiconductor—electrolyte interface. Reduced equivalent circuit at high frequencies and the expression for the impedance at low and high frequencies.

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. 

It has been said that interfaces separate charges. Explain the charge separation and draw the equivalent circuit diagram of the following materials interfacing with an electrolyte containing only NaCl and water. 

The equivalent circuit corresponding to this interface is shown in Fig. 6.1b. The charge-transfer resistances for the exchange of sodium and chloride ions are very low, but the charge-transfer resistance for the polyanion is infinitely high. There is no direct sensing application for this type of interface. However, it is relevant for the entire electrochemical cell and to many practical potentiometric measurements. Thus if we want to measure the activity of an ion with the ion-selective electrode it must be placed in the same compartment as the reference electrode. Otherwise, the Donnan potential across the membrane will appear in the cell voltage and will distort the overall result. 

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