Dielectrics admittance

The interpretation of dielectric measurements assumes that the sample behavior can be represented by a linear, time-invariant admittance. The meaning of each of these terms is examined in turn. 

The effectiveness of these instruments for dielectric cure studies depends on sensitivity and accuracy. The sensitivity is related to the minimum resolvable phase angle, which for general cure studies, should ideally be less than about 0.10. Unfortunately, actual sensitivity in use depends strongly on the measurement frequency, on the admittance of the sample, on the details of the cabling and shielding, and on the electrical noise level of the environment. Therefore, analysis of published sensitivity specifications is difficult. It is easier to evaluate intrinsic instrument accuracy, which can be expressed in terms of either the tan8x accuracy or the conductivity accuracy. An example is useful. 

The LF measurements (a) are provided by means of impedance/admittance analyzers or automatic bridges. Another possibility is to use a frequency response analyzer. In lumped-impedance measurements for a capacitor, filled with a sample, the complex dielectric permittivity is defined as [3]... 

Impedance data are presented in different formats to emphasize specific classes of behavior. The impedance format emphasizes the values at low frequency, which t5rpically are of greatest importance for electrochemical systems that are influenced by mass transfer and reaction kinetics. The admittance format, which emphasizes the capacitive behavior at high frequencies, is often employed for solid-state systems. The complex capacity format is used for dielectric systems in which the capacity is often the feature of greatest interest. 

As shown in Example 16.1, the admittance format is ideally suited for analysis of dielectric systems for which the leading resistance can be neglected entirely. 

Example 16.1 Admittance of Dielectrics Find an expression for the admittance of the electrical circuit shown in Figure 16.9. Identify the characteristic frequencies. 

Remember 16.4 Like the admittance representation, the complex-capacitance representation emphasizes values at high frequency and is often used for solid-state and dielectric systemsfor which information is sought regarding system capacitance. 

The characteristic frequency evident as a peak for the imaginary part of the complex-capacitance in Figures 16.12(b) and 16.13(b) has a value corresponding exactly to fc = 27tReC) only for the blocking system. As found for data presentation in admittance format, the presence of a Faradaic process confounds use of graphical techniques to assess this characteristic frequency. Like the admittance format, the complex capacitance is not particularly well suited for analysis of electrochemical and other systems for which identification of Faradaic processes parallel to the capacitance represents the aim of the impedance experiments. It is particularly well suited for analysis of dielectric systems for which the electrolyte resistance can be neglected. 

Example 16.1 Admittance of Dielectrics Example 16.2 Complex Capacitance of Dielectrics Example 16.3 Evaluation of Double-Layer Capacitance... 

It has been known for some time that for efficiently reducing the reflectance of highly reflective substrate with a complex admittance (i.e. metals, or coated metals, such as an OLED), it is convenient to use simple metal-dielectric AR coatings similar to those used in black absorbers (Dobrowolski, 1981 Lemarquis Marchand, 1999) or heat-reflector in solar-cells applications (Macleod, 1978). This type of coatings has been demonstrated for the contrast-enhancement of electroluminescent (EL) displays (Dobrowolski et al., 1992) and on the cathode side of bottom-emitting OLED (see above) (Krasnov, 2002). 

As already mentioned, the lumped-circuit technique is the most widely used by the research community [16]. The dielectric response is measured in parallel-plate or coaxial geometry as an association of resistances (R) and capacitances (C) in parallel or series. In a.c. measurements only, the parallel and series electrical circuits can be forced to be equivalent [20] giving for the admittance, T((d) and impedance Z(co), the following equations ... 

This paper is primarily concerned with the techniques usually described as time domain spectroscopy (TDS) or time domain reflectom-etry (TDR). These have been most commonly applied to studies of time or frequency dependent behavior of dielectrics with negligible ohmic or d.c. conductance, but can be used for substances with appreciable conductance and indeed for studies of any electrical properties which can be characterized by an effective admittance or impedance. 

Two basically different kinds of cell arrangement can be distinguished those in which the dielectric filled section terminates the coaxial pulse generating and sampling line, and those in which this section is itself terminated by a further admittance. The former are usually simpler and more useful, but the latter can have advantages for some purposes. If the sample section is symmetrical with respect to interchange of its input and output connections, and is terminated by an arbitrary admittance yj, its input admittance is given from network theory by... 

In this even simpler cell shown in Figure 3b, the volume beyond the end of the coaxial line center conductor (supported by a disk with dimensions to match the coaxial line admittance) is filled with dielectric. The sample is thus in the fringing field at the end of the line, or more generally can be regarded as filling a section of circular wave guide used at frequencies below cutoff for wave propagation. 

A computer automated system, shown schematically in figure 5, has been developed to yield results for permittivity and dielectric loss over a range of temperatures. A real dielectric is considered to have an admittance, Y=j(oC. In practice, the measured admittance is found to have a conductive as well as a capacitive component, Y = G + jcoC. In order to account for this, the capacitance of the dielectric, C, is considered to be characterised by a complex relative permittivity, r ... 

Using this model, the measured components of admittance (conductance G, and capacitance C) are G = coer Co and C = 8r Co,where C()is the capacitance of the structure if the dielectric were replaced by free-space. By further manipulation, it is found that tan 6 is given by ... 

We revert to the basic capacitor model of Figure 3.1. The admittance Y of the capacitor is (sinusoidal AC voltage u, homogeneous dielectric, and no edge effects) ... 

In Figure 3.9(a), the case becomes quite different and much more complicated (see Section 12.2.3). The total immittance, and also the voltage at the interface between the two dielectrics, will be determined by the resistors at low frequencies, but by the capacitors at high frequencies. The analysis of Figure 3.9(a) will be very different dependent on whether a series (impedance) or parallel (admittance) model is used. 

In Section 7.5, we analyze the double layer charge in a solution as a function of the perpendicular distance from the solid surface. No double layer formations are considered in the Maxwell—Wagner theory (Section 3.5.1). However, in wet systems and in particular with a high volume fraction of very small particles, the surface effects from counter-ions and double layers usually dominate. This was shown by Schwan et al. (1962). By dielectric spectroscopy, they determined the dispersion for a suspension of polystyrene particles (Figure 3.10). Classical theories based on polar media and interfacial Maxwell—Wagner theory could not explain such results the measured permittivity decrement was too large. The authors proposed that the results could be explained in terms of surface lateral) admittance. 

What is the complex admittance Y of an ideal capacitor with dimensions area 1 cm and thickness 1 mm, and with a dielectric with 8i- = 3 and a = 2S/m ... 

In Section 3.8 about dispersions, the use of permittivity or conductivity parameters was discussed. From Section 2.3.4, we know that conductivity is dependent on the density of charge carriers and their mobility. In the frequency range less than 10 MHz, tissue admittance is usually dominated by the conductivity of the body electroljrtes, but at higher frequencies it is dominated by the dielectric constant. The electroljrtes without cells, in particular urine and cerebrospinal fluid (CSF), have the highest low-frequency conductivity thus, the higher the cell concentration, the lower the low-frequency conductivity. Tooth, cartilage and bone, lipids, fat, membranes such as the skin stratum comeum (SC), and connective tissue may contain many inorganic materials with low conductivity, but they are very dependent on body liquid perfusion. Tissue conductivity data are tabulated in Table 4.2. 

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