Bulk material impedance Capacitance

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. 

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

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 ... 

ERF dielectric response can be appropriately described by the classical Debye circuit model (Section 4-4). The model contains 1 pF/cm bulk base oil capacitance in parallel with Tohm range base oil resistance This combination results in a circuit with a time constant on the order of 10 seconds, typical of the impedance behavior of dielectric materials with very low ionic content. The presence of 10 to 50 percent polarizable particles results in the development of a parallel bulk-solution conduction mechanism through the particles. When compared to the ions that transport current by electrophoretic mobility, the ERF particles have larger sizes and lower mobility and are capable of becoming polarized and reoriented in the external electric field. This percolation type of conduction mechanism can be represented by a series of the particle resistance and the contact impedance between the particles (Figure 12-8). As the ionic content is essentially absent in the... 

From the complex impedance spectnrm, depicted in the complex impedance plane, it is thus easy to separate the different contributions of the bulk material, the grain botmdaries and the electrodes, and to determine their respective electrical characteristics, i.e. resistance and capacitance. The last, but not the least, is that... 

Polarisation effects at electrodes become most prominent when the material of a specimen shows some appreciable bulk conductivity. Characteristically, there is an apparent increase in the relative permittivity at low frequencies. The anomaly originates in a high-impedance layer on the electrode surface. This may be caused by imperfect contact between the metal electrode and the specimen, aggravated by the accumulation of the products of electrolysis, etc. At low frequencies there is sufficient time for any slight conduction through the specimen to transfer the entire applied field across the very thin electrode layers, and the result is an enormous increase in the measured capacitance. For a purely capacitive impedance Ce at the electrodes, in.series with the specimen proper (geometrical capacitance C0), Johnson and Cole (1951) showed that the apparent relative permittivity takes the approximate form ... 

Sometimes, particularly when the electrode surface is rough and/or the bulk properties of the electrode material are inhomogeneous, the electronic properties of the interface cannot be described sufficiently well with a capacitive element, and a constant phase element (CPE) should be introduced instead of C i. CPEs are identified in impedance spectra due to the appearance of depressed semicircles in Nyquist plots (with their center below the real axis) and phase-angle values lower than 90° in Bode plots [9, 11, 12]. 

The shape of the ac impedance plots may deviate from that expected for the simple RC and Warburg elements. There are different reasons for deviations. Typical reasons are rough siufaces, constriction resistance, and distribution of elements with different characteristic parameters, mainly in the bulk. The constriction resistance is due to a smaller contact area of the electrode than the nominal electrode area. At low frequencies the capacitance reflects the actual contact area, while at high frequencies the capacitance reflects the area of the electrode material which may be larger. Thus the contact caimot be described by a single capacitance. It has also been shown that for a MIEC electrode the impedance of transfer of oxygen from the gas phase into the MIEC and the impedance of diffusion inside the MIEC, though coupled in series, do not yield separated parts in the Cole-Cole plot. 

The Debye circuit represents a transition from a conduction mechanism through the first capacitive C,g,g at high frequency to the second independent higher-value capacitive component C in a series with finite resistor R. At very high frequencies C,g,g, usually bulk capacitance Cg of ion-free "matrix" continuous-phase material such as nearly completely insulating oil, dominates the total impedance response. The finite resistor R prevents current from flowing through the secondary resistive-capacitive branch. This branch very often rep-... 

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