Diffusion impedance Resistance

Zs is the faradaic impedance due to the substrate for a redox system it consists of a series combination of a charge-transfer resistance Rt and a convective diffusion impedance Zds (2s - ts+2os)-... 

The electrolyte resistance Re is added in series with the previous impedance. If the electrochemical reaction is mass-trai3sport limited, the previous equivalent circuit is still valid, but the Faradaic impedance includes a diffusion impedance as described in Chapter 11. 

Diffusion through a stagnant layer of finite thickness can also yield a uniformly accessible electrode. The diffusion impedance response of a coated (or film-covered) electrode, imder the condition that the resistance of the coating to diffusion is much larger than that of the bulk electrol5M e, is approximated by the diffusion impedance of file coating. This problem is also analyzed in Section 15.4.2. 

Example 11.5 Diffusion Impedances in Series If, as is shown in eqmtion (4.23), the impedance corresponding to two resistors in series is equal to the sum of the resistances, why is it incorrect to treat diffusion through two layers by adding two diffusion impedances ... 

Nernst applied the electrical bridge invented by Wheatstone to the measurement of the dielectric constants for aqueous electrolytes and different organic fluids. Nemst s approach was soon employed by others for measurement of dielectric properties and the resistance of galvanic cells. Finkelstein applied the technique to the analysis of the dielectric response of oxides. Warburg developed expressions for the impedance response associated with the laws of diffusion, developed almost 50 years earlier by Fick, and introduced the electrical circuit analogue for electrolytic systems in which the capacitance and resistance were functions of frequency. The concept of diffusion impedance was applied by Kruger to the capacitive response of mercury electrodes. ... 

Cadmium atomic layer electrodeposition above reversible Cd2+/Cd potential (underpotential deposition, upd) on bulk tellurium and Te atomic layer predeposited on gold has been characterised with potentiodynamic electrochemical impedance spectroscopy (PDEIS) by variations, with the electrode potential E, of double layer pseudocapacitance Q,u, charge transfer resistance Rrt and Warburg coefficient Aw of diffusion impedance. 

Figure 10a shows the Nyquist plot for a situation when diffusion impedance is much larger compared to the charge transfer resistance. The 45° Warburg line dominates the... 

Impedance spectroscopy in the high-frequency region is another way of eliminating diffusion overpotential. The equations were given in Chapter 5. The combination of the double-layer equivalent circuit with the diffusion impedance was described in Section 5.23 and examples for the determination of the charge transfer resistance at high frequencies were given. 

Determination of Parameters from Randles Circuit. Electrochemical three-electrode impedance spectra taken on electrochromic materials can very often be fitted to the Randles equivalent circuit (Randles [1947]) displayed in Figure 4.3.17. In this circuit R /denotes the high frequency resistance of the electrolyte, Ra is the charge-transfer resistance associated with the ion injection from the electrolyte into the electrochromic film and Zt, is a Warburg diffusion impedance of either semi-infinite, or finite-length type (Ho et al. [1980]). The CPEdi is a constant phase element describing the distributed capacitance of the electrochemical double layer between the electrolyte and the film having an impedance that can be expressed as... 

Impedance Spectroscopy. Impedance spectroscopy has been carried out on devices with WO3 as the cathodic electrochromic layer, counter electrodes of iridium oxide, polyaniline or Prussian blue, and polymers as electrolytes (Katsube et al [1986], Friestad et al [1997]). The equivalent circuit for a whole device becomes very complicated. In the works quoted above simplified, Randles-type circuits were used for the two electrochromic layers, while the ion conductor was modeled by a pure resistance, or neglected. Extraction of device parameters from the data fitting was reported. However, it is clear that in many cases it will be difficult to distinguish the contributions from the different layers in a device, in particular if the migration impedances, ion diffusion impedances, etc. are of the same order of magnitude. When it comes to characterizing electrochromic devices, impedance spectroscopy is a very time-consuming process, since a spectrum down to low frequencies should be taken at a number of equilibrium potentials. Thus we believe that transient current measurements in many cases offer a faster alternative that sometimes allows a simple determination of diffusion coefficients. 

On the basis of this model and the equivalent circuit shown in Figure 4.5.67, the changes and differences, depending on the used anode in the fuel cell (Pt/C or PtRu/C) in the impedance spectra during the experiment, are dominated by the changes of the charge transfer resistance of the anode (Raj), the surface relaxation impedance (Rg, tg) and the finite diffusion impedance (Z ). 

The impedance of CPE is described according to eq. 3 (Zoltowski 1998). When a is close to 0, the CPE describes a resistance, close to -1 it describes an inductance, close to 1 it describes a capacity and finally, for the value of 0.5, the result is equivalent to the Warburg diffusion impedance. 

The kinetic impedance Zj represents the faradaie impedance in the absence of a concentration overpotential. In the simplest case, the kinetie impedance corresponds to the transfer resistance Rt, but in more complicated situations it may include several circuit elements. The diffusion impedance Z describes the contribution of the concentration overpotential to the faradaic impedance and therefore depends on the transport phenomena in solution. In the absence of convection, it is referred to as the Warburg impedance and, in the opposite case, as the Nernst impedance Z. ... 

Figure 8-11. Equivalent circuit of a polarized electrode obtained by modification of the Randles diagram, where / s is the electrolyte resistance, Q the double layer capacity, R, the charge transfer resistance, Rg the anodic process resistance, R the cathodic process resistance, CPE the constant phase element, and the diffusion impedance.

Figure 3. (a) Nyquist plot and (b) Bode plot, obtained from the equivalent circuit of Figure 2. The impedance spectra were theoretically determined by arbitrarily taking Rq=5 Q, Rj=20 Q, Cj=10 jjF, Rc=35 Q, and C =2 mF. The diffusion impedance is expressed as Zji AjJa>) hanh[5(ja)f ] (where, Sis defined as L/D , a is the angular frequency, and A is the Warburg coefficient expressed as Ri/5). Rd=400 Q, L=I0 /am, and D=10 cm /s were taken for the calculation of The elemental resistance r and capacitance c in the TML were estimated to be 4x10 and 2.5x10 s C2 m respectively.

The equivalent circuits of Figure 15 are still valid to model the impedance spectra for the cathode and anode. The diffusion impedance was substituted for the transmission line, and its elementary resistance and capacitance were evaluated in the same manner as in previous sections. All of the electric... 

Figure 22 Different stages in behavior of a coated system with progressing exposnre time to water. (Left to right) System, impedance response, and eqnivalent circnit Stages (A) Water permeation (B) corrosion initiation (C) qnasi-stationary corrosion. (R = resistance, C = capacitance, Z = diffusion impedance, pf = paint film, cat = cathodic, an = anodic, dl = double layer, u = electrolyte.)...

The electrode reaction rate may be controlled by diffusion or by chemical reaction. The impedances associated with these cannot be derived so simply. All that needs to be said here is that they are not pure resistances, i.e. they include a reactive part which, for convenience, is called pseudocapacity to distinguish it from the true capacity of the double layer. The diffusion impedance is also often referred to as Warburg impedance . 

Figure 3.51 shows the impedance spectra for a Pt/FTO sandwich cell at different bias potentials reported by Hauch and Georg.The impedance element on the left of the spectrum (high frequencies) is the Pt/ electrolyte interface (charge-transfer resistance and double layer capacitance) on the right (low frequencies) there is the Nernst diffusion impedance. The diameter of the high frequency semicircle in the impedance... 

Diffusion and charge-transfer kinetics are usually coupled. A typical electrochemical (or "Faradaic") reaction is composed of both mass-transport processes of charged species to the electrode surface and their redox discharge at the interface. The Faradaic impedance can be represented by a series combination of Warburg diffusion impedance and charge-transfer resistance ... 

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