Bulk material impedance Resistance

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... 

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. 

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. 

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]. 

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 ... 

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... 

Data from electrochemical impedance diagrams yield a simplified quantitative analysis for an appropriate interpretation of the linear sweep voltammetry (LSV) experiments. In fact, the Si electrode potential measured with respect to the reference electrode represents the value within the bulk of the material. The direct current flow for the electrochemical reaction has to overcome the resistance of the space charge layer, which can reach extremely high values when a depletion layer is formed. For p-type Si in the potential range for the HER onset, this excess surface resistance is over 10 f2 cm. Thus, even with a bias of —1 V, the DC... 

By the method of introducing Pt into the DLC, the platinum metal is assumed to be distributed over the carbonaceous material bulk as discrete atoms or clusters [154], Essentially, Pt is not a dopant in the DLC, in the sense that the term is used in semiconductor physics. Nor is the percolation threshold surpassed, since the admixture of Pt (not exceeding 15 at. %) did not affect the a-C H resistivity, as was shown by impedance spectroscopy tests p 105 Q, cm, like that of the undoped DLC (see Table 3). It was thus proposed that the Pt effect is purely catalytic one Pt atoms on the DLC surface are the active sites on which adsorption and/or charge transfer is enhanced [75], (And the contact of the carbon matrix to the Pt clusters is entirely ohmic.) This conclusion was corroborated by the studies of Co tetramethylphenyl-porphyrin reaction kinetics at the DLC Pt electrodes [155] redox reactions involving the Co central ion proceed partly under the adsorption of the porphyrin ring on the electrode. 

Recently, it was reported by Pyun et al. thatthe CTs of transition metal oxides such as Lii 8CoO2 [14,77-79], l i,, AiO. [11,12], Li, sMii.O [17,80,81], Lij + 8[Ti5/3Lii/3]O4 [11, 28], V2O5 [11, 55] and carbonaceous materials [18, 82-84] hardly exhibit a typical trend of diffusion-controlled lithium transport - that is, Cottrell behavior. Rather, it was found that the current-potential relationship would hold Ohm s law during the CT experiments, and it was suggested that lithium transport at the interface of electrode and electrolyte was mainly limited by internal cell resistance, and not by lithium diffusion in the bulk electrode. This concept is referred to as cell-impedance-controlled lithium transport. 

A polarization ratio can he defined as the ratio of polarization impedance to the bulk resistance of the electrolyte. Mirtaheri et al. (2005) measured the ratio as a function of frequency (10 —10 Hz) and NaCl concentration (2.4—77.0 mmol/L) and found that the polarization ratio diminished as a function of concentration regardless of electrode material. Medical stainless steel ratio was concentration independent hut had high electrode polarization impedance values compared with the other metals studied. Aluminum showed small ratio changes at low concentrations. However, the changes were more pronounced at higher concentrations. Gold, platinum, and silver showed a moderate concentration dependency at low concentrations. 

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