Impedance model

Numerical solutions have been presented for the impedance response of semiconducting systems that accoimt for the coupled influence of transport and kinetic phenomena, see, e.g., Bonham and Orazem. Simplified electrical-circuit analogues have been developed to account for deep-level electronic states, and a graphical method has been used to facilitate interpretation of high-frequency measurements of capacitance. The simplified approaches are described in the following sections. 

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Other types and aspects of polymer-electrolyte fuel cells have also been modeled. In this section, those models are quickly reviewed. This section is written more to inform than to analyze the various models. The outline of this section in terms of models is stack models, impedance models, direct-methanol fuel-cell models, and miscellaneous models. 

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). 

While a good equivalent-circuit representation of the transport processes in a fuel cell can lead to an increased understanding, it is not as good as taking a 1-D sandwich model and taking it into the frequency domain. These models typically analyze the cathode side of the fuel cell. °2.3i3 3i4 pj g j ost comprehensive is probably that of Springer et al. °2 The use of impedance models allows for the calculation of parameters, like gas-phase tortuosity, which cannot be determined easily by other means, and can also allow for the separation of diffusion and migra-... 

Thus it appears that by incorporating parameters such as pore resistance and coating capacitance to the existing theoretical impedance model dealing with metal dissolution one would obtain valuable overall information (14,27). Complemented by results from regular immersion and salt spray tests it should be possible to find satisfactory solutions to corrosion problems of coated metals (9 ). 

Apparatus and Procedure. Surface Isotherms. The technique for determining the n-A and AV-A curves of the lipid films has been described (6). Briefly, the Wilhelmy plate method was used to measure surface tension, from which the surface pressure was calculated (n = 7h2o—yfiim) The surface potential was measured by means of a radioactive (226Ra) air electrode and a saturated calomel electrode connected to a high impedance model 610 B Keithley electrometer (Keithley Instruments, Cleveland, Ohio). 

Impedance models are constructed according to the electrochemical phenomena. The total impedance of an electrochemical system can be expressed by different combinations of the electrical elements. This section covers the features of basic equivalent circuits commonly used in electrochemical systems. In Appendix D, the effect of an element parameter change on a spectrum related to a given equivalent circuit is described in detail. 

The general expression (10.3) guides development of impedance models from proposed reaction sequences. The reaction mechanisms considered here include reactions dependent only on potential, reactions dependent on both potential and mass transfer, coupled reactions dependent on both potential and surface coverage, and coupled reactions dependent on potential, surface coverage, and mass transfer. The proposed reaction sequence has a major influence on the frequency dependence of the interfacial Faradaic impedance described in Qiapter 9. 

Remember 12.1 The development of impedance models for semiconductors is similar to that for electrolytic systems with the exception that the capacity associated with the diffuse region of charge is modeled explicitly. 

The impedance models developed in Chapters 9,10,11, and 12 are based on the assumption that the electrode behaves as a uniformly active surface where each physical phenomenon or reaction has a single-valued time constant. The assumption of a uniformly active electrode is generally not valid. Time-constant dispersion can be observed due to variation along the electrode surface of reactivity or of current and potential. Such a variation is described in Section 13.1.1 as resulting in a 2-dimensional distribution. Time-constant dispersion can also be caused by a distribution of time constants that reflect a local property of the electrode, resulting in a 3-dimensional distribution. 

Poor Sensitivity Modulus The Bode magnitude representation is singularly incapable of distinguishing between impedance models unless they provide extremely poor fits to impedance data. 

The similarity between the spectra of a model with just three components and a complex material such as tissue is of course limited. The first step of refinement is often to replace an ideal capacitor found in the Debye models of Figures 10.3 and 10.4 with a CPE. They are then called Cole impedance models (Cole 1940) and Cole-Cole permittivity models (Cole and Cole 1941). 

Figure 11.16 Impedance model of Vorotyntsev et and Q represent the properties of the metal/ polymer interface, and Cj the properties of the metal/electrolyte interface, and the resistance of the buUc polymer.

For the dynamic lung impedance model to be useable in Finite Difference Method or Finite Element Method impedance signal simulations, the dynamic tissue sample model is discretized into volume data. At first 3D data with 35 x 35 x 35 voxel resolution is prepared from each of the 40 time frames. This allows for easy import into MATLAB or COMSOL based calculation. The volume data includes percentage of blood vessels (blood) for each of the 35 X 35 X 35 X 40 voxels. It can readily be transformed into electric/dielectric properties for each voxel with tissue data available on the internet. But data can also be exported with arbitrary resolution depending on calculation-simulation requirements. The simulations are run separately for each of the 40 time-frames to get full frequency characteristic of impedance measurement across the tissue sample. Finally we can get 40 frequency characteristics—one for each time-frame and to see a dynamic electrical impedance signal on a certain frequency, we just need to plot the impedance value at the chosen frequency from the 40 time-frames. 

A. Haffehn, J. Joos, M. Ender, et al., Time-Dependent 3D Impedance Model of Mixed-Conducting Solid Oxide Fuel Cell Cathodes, Journal of the Electrochemical Society, vol. 160, no. 8, F867-F876, 2013. 

Ever since Feldberg s original model separating faradaic and capacitance current associated with a conducting polymer that behaves like a porous metal, " there have been various attempts to rationalize experimentally the nature of the current at a conducting polymer. Apart from impedance models, there has not been so much effort placed on modeling the system. Experimental efforts to examine processes at conducting-polymer-modified electrodes consisted of voltam-metry, " impedance, " and quartz crystal microbalance. However the... 

Mathias M. and Haas 0., An alternating current impedance model including migration and redox-site interactions at polymer-modifed electrodes,/. Phys. Chem., 1992,96,3174-3182. 

First, Eq. 2 shows that the basic impedance model actually is an admittance model. The conductive and capacitive (quadrature) parts are physically in parallel in the model of Figure 3.1. 

The Cole single-dispersion impedance model (Eq. 9.26) is based upon an ideal conductance as a dependent variable and a characteristic time constant as an independent variable. Usually, however, the characteristic time constant of tissue or cell suspensions is a function of conductance according to relaxation theory (see Section 3.4). The Cole model is therefore not in accordance with relaxation theory (Figures 9.21 and 9.22). 

Figure 9.21 Dispersion model in accordance with relaxation theory (Eq. 9.43). (a) Impedance model and (b) admittance model.

Grimnes, S., Martinsen, 0.G., 2005. Cole electrical impedance model — a critique and an alternative. IEEE Trans. Biomed. Eng. 52 (1), 132—135. 

Bisquert, J., Gratzel, M., Wang, Q., Fabregat-Santiago, F. Three-channel transmission line impedance model for mesoscopic oxide electrodes functitmalized with a conductive coating. J. Phys. Chem. B 110, 11284-11290 (2006)... 

Impedance Model of the Hand-Arm System. A 4-degree-of-freedom model consisting of four of the models sketched in Fig. 10.6, arranged in series (i.e., on top of each other), has been used to predict idealized values for the input impedance to the hand (ISO 10068, 1998). As is the case for the lumped whole-body models, Ae parameters of the hand-arm model do not possess direct anatomical correlates. 

Fig. 4.2 illustrates the geometric definitions of a cantilevered IPMC beam. The beam is clamped at one end (2 = 0), and is subject to an actuation voltage producing the tip displacement w t) at the other end z = L). The neutral axis of the beam is denoted by x = 0, and the upper and lower surfaces are denoted hy x = h and x = —h, respectively. We are interested in obtaining the relationships between the applied voltage and both the resulting current (impedance model) and the tip displacement (actuation model). 

Fig. 4.3 Illustration of the IPMC impedance model with surface resistance. The Dynamics of Ion Movement block captures the original PDEis in Section 4.2.1. Reprinted from [Chen and Tan (2008)] with permission from IEEE, Copyright 2008.

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