Bulk material impedance

In many other highly resistive materials with associated bulk impedance values above 1 Mohm, the range of frequencies corresponding to the bulk-material impedance can still cover several decades of frequency range—often from MHz to low Hz. When conduction through the bulk is not ionic, there would be no significant accumulation of charges at the interface and essentially no double-layer capacitance develops. The total circuit is represented by and the total thickness of the sample d can be used to estimate this capacitive response. 

An excellent reference describing appropriate ways of measuring the piezoelectric coefficients of bulk materials is the IEEE Standard for Piezoelectricity [1], In brief, the method entails choosing a sample with a geometry such that the desired resonance mode can be excited, and there is little overlap between modes. Then, the sample is electrically excited with an alternating field, and the impedance (or admittance, etc.) is measured as a function of frequency. Extrema in the electrical responses are observed near the resonance and antiresonance frequencies. As an example, consider the length extensional mode of a vibrator. Here the elastic compliance under constant field can be measured from... 

In chitin, CS and PVA complex dielectric spectra (Z" versus Z plot shown in Fig. 2.3), two different behaviors are identified (i) a typical semicircle at high frequencies, which corresponds to the bulk material signal and (ii) a quasilinear response at low frequencies associated with interfacial polarization in the bulk of the films and/or surface and contact effects [46, 47]. This low frequency part of the electrical response is easily influenced by imperfect contact between the metal electrode and the sample as it was previously tested elsewhere [5], there is no influence of gold contact on the polymer impedance spectra (high frequency part of the spectra corresponding to the bulk of the film) and it is discarded for further analysis. 

Clearly, an undervaluation of education in this field is impeding progress towards radical improvements in industrial performance. An important aspect of securing improvement in this field is achieving an understanding of bulk material behaviour, and its significance in the selection and... 

By fitting of the impedance data, the resistance and the capacitance of the bulk material Q, and the... 

This section presents two examples of composite cathodes for SOFC. For these systems, the most commonly used cathode material and solid electrolyte are LSM and YSZ, respectively. Electrode impedances appear over a small space scale, characteristic of atomic dimensions, and as a result their spectra differ from those of bulk materials in several ways listed below. 

Flow resistance is also known as static flow resistance and is the ratio of the pressure drop across a porous element to the volume velocity flowing through it under conditions of steady low speed flow. The flow resistance is almost independent of the volume velocity at low speeds. However, flow resistance is dependent on the acoustic frequency. Dynamic specific flow resistance of a thin (compared to acoustic wavelengths) porous textile layer is the real part of the complex specific flow impedance at a specified frequency, which is defined as the complex ratio of the pressure drop across the layer to the relative face velocity through the layer. When the frequency tends to zero, the dynamic specific flow resistance varies little with frequency, so it is almost equal to the static flow resistance. In the international standard, flow resistance is defined as the real part of the ratio between the pressure drop and the flow velocity through a layer of material of unit thickness (ISO 9053,1991). Flow resistance characterizes a layer of specified thickness, whereas flow resistivity characterizes a bulk material in terms of resistance per unit thickness. 

Nevertheless, historically a differentiation exists between "dielectric" and "impedance" spectroscopies. Traditional dielectric analysis has been applied primarily to the analysis of bulk "dielectric" properties of polymers, plastics, composites, and nonaqueous fluids with very high bulk material resistance. The dielectric method is characterized by using higher AC voltage amplitudes, temperature modulation as an independent variable, lack of DC voltage perturbation, and often operating frequencies above 1 kHz or measurements at several selected discrete frequencies [2, p. 33]. 

Impedance Representation of Bulk Material and Electrode Processes... 

If an aqueous solution is replaced by a tissue or a dielectric medium, a more complex circuit consisting of both resistive and capacitive elements replaces the resistor. This more complicated circuit is represented by a parallel combination of Rgm, with impedance response to bulk solution processes dominating the kHz-MHz frequency ranges (Chapter 11). As will also be shown in Chapter 7, in complex multicomponent media several relaxations represented by a combination of several 1 elements may be present. As the first approximation, a single Cg element can be selected to represent the bulk-material relaxation. For the bulk processes in dielectrics the Rgu represents a lossy part of the relaxation mechanism, and is a dipolar capacitive contribution [1, p. 68]. 

An important task of practical impedance measurements is to identify the frequency ranges for correct evaluation of characteristic parameters of an analyzed sample, such as bulk-media resistance capacitance and interfacial impedance. These parameters can be respectively evaluated by measuring the current inside the cell of known geometry, especially in the presence of uniform electric field distributions. For instance, many practical applications often report "conductivity" of materials (o), the parameter inversely proportional to the bulk-material resistivity p and resistance Rgy x soi)- permittivity parameter e, determined from capacitance measurements and Eq. 1-3, is another important property of analyzed material. 

For accurate measurements of media conductivity, it is necessary to realize that the measured resistance value of a sample at an arbitrarily chosen AC sampling frequency may not be a correct representation of the media bulk resistance. The measured total resistance may contain contributions from electrode polarization, Faradaic impedances, lead cables, and other artifacts. To make accurate measurements of the bulk resistive properties of a material, it is necessary to know the measurement frequency range where both capacitive interference from the double layer (and other electrode interfacial impedance effects such as adsorption/desorption) and the bulk capacitance are absent [5]. A sampling frequency has to be chosen that is within the frequency region where the impedance spectrum is dominated by the bulk-material resistance. This task essentially involves the development of a concept of spatially distributed impedance. 

The following analysis will be shown for a realistic system equivalent circuit model (Figure 6-1), further simplified by replacing CPE with as shown in Figure 2-6A. The resistance of the material dominates the lower cutoff frequency/j. At lower frequencies the double-layer capacitance and other interfacial processes will cause the impedance to decrease with increasing frequency. This will continue until the impedance from the double-layer capacitor becomes lower than the impedance representing the bulk-material resistance RguLK/ which occurs at the frequency ... 

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