Film Impedance Response

Equation (11.41) governs the diffusion response of a stationary film. The steady-state boimdary conditions are applied at y = 3f and y = 0 as 

Equation (11.63) represents an as5mptotic limit for the solution presented as equations (11.53) and (11.54). 

Equation (11.41) can be written in terms of the oscillating concentration and dimensionless position as 

The appropriate boundary conditions for a diffusion layer of finite thickness are that 

The reciprocal of the derivative with respect to position is given by 

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A deterministic model for corrosion under SCW conditions was developed based on the model for oxide film growth on stainless steels in high-temperature, high-pressure aqueous environments proposed by Bojinov et al. [70—74]. The mixed conduction model (MCM) emphasizes the coupling between ionic and electronic defects in quasisteady-state passive films. It allows determination of the electronic properties of the oxide layer, the main kinetic and transport parameters needed to calculate the steady-state current density, the oxide film impedance response, and the thickness versus time relationship on many alloys. Such a model can provide insights into the effects of alloying elements on SCW oxidation resistance [70,75]. 

Figure 23. Impedance response of a thin film of LSC (x = 0.4) on GDC at 800 °C and Pq = 10 gxm as a function of polarization. (Reprinted with permission from ref 124. Copyright 2002 Electrochemical Society Inc.)...

Operational amplifier— An electronic device (available in numerous different forms, built with discrete components, in thick film or thin film technology, but mostly as an integrated solid state circuit IC). It is a an amplifier with ideally infinite input impedance, zero output impedance, response behavior independent of the rate of change of the input signal (amplification constant from DC to high frequency AC). It is schematically plotted as a triangle ... 

Surface films commonly form in electrochemical studies, and these films can influence the impedance response. The electrode coated with an inert porous layer may be considered to be an extension of the case described in Section 9.2.2 in which the film is thicker and the fractional surface coverage approaches unity. 

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. 

Starting with the material balance equation, develop the expression for the impedance response for mass transfer through a stagnant film. 

The impedance response of the films was observed with just one time constant (Ri, CPEi), except for the film formed for 10900 s. This film showed two time constants similar to the films formed at voltages > 30 V. In this case, the aluminium oxide film might be contaminated by anions migrating from the surface into the film. 

Figure 5.57 (a) Complex impedance response (plot of the imaginary part of the complex modulus M" versus the real part M in the complex plane) of a monolayer (3.5 nm diameter) of propanethiol pped Ag nanoparticles. The particle film response is characterized initially by an RC circuit equivalent, in conformity with a picture of capacitively determined hopping localized conductivity. As the particles are compressed to a separation of less than 0.6 nm, the film becomes inductive, indicating the presence of... 

The deviations of the impedance responses [23,28, 30,32, 59,64,66,69,71, 76,120,123,132,144-146] predicted by the theories have been explained by taking into account different effects, such as interactions between redox sites [30, 136], ionic relaxation processes [95], distributions of diffusion coefficients [28], migration [65, 118, 125, 132], film swelling [64, 137], slow reactions with solution species [22,138], nonuniform film thickness [23], inhomogeneous oxida-tion/reduction processes [123], etc. 

Cathodic Electrochromic Materials—Fluorinated Ti Oxide. Figure 4.3.18 shows two electrochemical three-electrode impedance spectra taken at different temperatures on a heavily intercalated Li containing flnorine doped Ti oxide film (Str0mme Mattsson et al. [1997]). The impedance response corresponds to that of the Randles circuit with a Zd of finite-length type. Details about the film preparation and the measurement conditions can be obtained from Strpmme Mattsson et al. [1996c, 1997]. The high frequency semicircle clearly has a center below the real... 

Cathodic Electrochromic Materials—Tungsten Trioxide. Figure 4.3.20 shows electrochemical impedance spectra on both amorphous and crystalline Li containing WO3 films together with fits to the Randles circuit (Strpmme Mattsson [2000]). For the amorphous film the high frequency semicircle overlaps with the diffusion response. In the case of the crystalline film, only a part of the semicircle due to Cdi and Ra, can be observed. As is obvious from the displayed spectra, the charge transfer resistance is much larger for the crystalhne sample than for the disordered one at an equilibrium potential of 2.9 V vs. the Li reference electrode used in the experiment. Impedance spectra were taken at several equihbrium potentials, and in all cases the impedance response corresponded to that of the Randles circuit with a Zd of semi-infinite type. 

Counter Electrode Materials. The anodic electrochromic materials and ion storage materials have not been so widely studied as the cathodic electrochromic materials discussed above. In general, the main features of the impedance spectra are similar to those shown above. The impedance response of nickel oxide films with... 

Inorganic Thin Film Ion Conductors— Tantalum Oxide. We give here a detailed account of the impedance response of thin tantalum pentoxide films. Firstly, the data illustrates several of the methods treated in Section 4.3.4.S. Secondly, Ta20s is a very interesting ion conductor for applications, in particular because it is possible to make the electronic leakage current very low. We also make some comments on Z1O2. 

Figure 44.22. Dependence of Z on for Type 304SS passivated in 0.1 N Na2HP04 solution (pH 9.1). (From C.-Y. Chao, L. F. Lin, and D. D. Macdonald, A Point Defect Model for Anodic Passive Films 111. Impedance Response, J. Electrochem Soc. 129, 1874-1879, [1982]. Reprinted by permission of the publisher. The Electrochemical Society, Inc.)...

Chao, C.Y, Lin, L.R and Macdonald, D.D. (1982) A point defect model for anodic passive films III. Impedance response. Journal of The Electrochemical Society, 129, 1874—1879. Macdonald, D.D. (1999) Passivity - the key to our metals-based civilization. Pure and Applied... 

This concludes our brief survey of fundamental concepts. In the following sections we discuss the complex impedance response of surface-deposited electroactive polymer films. We consider redox conductors and conjugated organic conductors separately, since mathematical models used to describe the impedance response of these two classes of electroactive macromolecules can be quite different. 

Complex Impedance Response of Redox Polymer Films... 

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