Dielectric response conducting materials

Rather than continue so formally, consider dielectric susceptibilities in terms of illustrative models. Conceptually the simplest picture of a dielectric response is that in an electric circuit. Think about a capacitor as a sandwich of interesting material between two parallel conducting plates (see Fig. L2.22). 

Alternatively, an equally powerful visualization of impedance data involves Bode analysis. In this case, the magnitude of the impedance and the phase shift are plotted separately as functions of the frequency of the perturbation. This approach was developed to analyze electric circuits in terms of critical resistive and capacitive elements. A similar approach is taken in impedance spectroscopy, and impedance responses of materials are interpreted in terms of equivalent electric circuits. The individual components of the equivalent circuit are further interpreted in terms of phemonenological responses such as ionic conductivity, dielectric behavior, relaxation times, mobility, and diffusion. 

When an alternating electric field (a.c.) is applied across an insulator, a time dependent polarization current flow is induced. This is because the electrical charges present in the atoms and molecules in the material respond to the changing directions of the field. This is also referred to as dielectric response of the material. When the frequency of the applied field is well below the phonon frequencies, the dielectric polarization of the bound charges is instantaneous. Therefore, the dielectric constant, e (oo), characterizing the bound charge response, is frequency independent. The frequency dependent part of dielectric constant is by definition related to the frequency dependent conductivity, CT (co) as... 

Stamires (35) investigated the effect of various adsorbed phases on the electrical conductivity of Linde synthetic crystalline zeolites type X and Y. He concluded that the potential energy barrier for cationic conduction is decreased by interaction with the adsorbed phases, but he did not investigate the dielectric response of the material. 

Nevertheless, a significant number of papers deal with the use of microwave measurements mainly for comprehension of transport properties of these materials. In particular, the dielectric response is important for understanding not only the intrinsic metallic nature of some conductive polymers but also charge localization. 

Two basic contributions are expected to the variation of dielectric properties of a hydrated material with respect to those of a dry one that of the polar water molecules themselves and the second one due to the modification of the various polarization and relaxation mechanisms of the matrix material itself by water [37]. In the low frequency region of measurements, there is a third contribution, often ignored in works dealing with high frequency measurements, which arises from the influence of moisture on conductivity and conductivity effects. The increase of electrical conductivity of the sample is the major effect present in wet samples dielectric response is often masked by conductivity, and it superposes the dielectric processes in the loss spectra and demands a conductivity correction of the dielectric loss spectra [9]. This dc conductivity strongly affects the modifled loss factor, e". In this case, it can be expressed as shown in the following equation ... 

In addition to the impedance, other derived quantities, such as the dielectric modulus (M), the complex dielectric constant (e), or susceptibility (x), can be calculated from the IS measurements their interrelations have been tabulated elsewhere (Macdonald 1987). Complementary information on the dielectric response of a given system can be obtained from the different impedance plots and the related magnitudes. It is important to point out the different nature of these magnitudes extensive or sample geometry dependent in the case of impedance or admittance, and intensive or characteristic of homogeneous materials in the case of conductivity and the dielectric constant. 

The time dependence of the dielectric properties of a material (expressed by e or CT ) under study can have different molecular origins. Resonance phenomena are due to atomic or molecular vibrations and can be analyzed by optical spectroscopy. The discussion of these processes is out of the scope of this chapter. Relaxation phenomena are related to molecular fluctuations of dipoles due to molecules or parts of them in a potential landscape. Moreover, drift motion of mobile charge carriers (electrons, ions, or charged defects) causes conductive contributions to the dielectric response. Moreover, the blocking of carriers at internal and external interfaces introduces further time-dependent processes which are known as Maxwell/Wagner/Sillars (Wagner 1914 Sillars 1937) or electrode polarization (see, for instance, Serghei et al. 2009). 

Electrical properties of materials are described by their behavior in the presence of an electric field. Basically, the response of any material to an electric field can be separated into two main parts dielectric response and electrical conduction. Polymer-based materials with good conduction properties have been the subject of fundamental scientific interest due to their tremendous potential in various applications (Gul 1996). Even though most polymeric materials are not conductors of electricity, they are easy to fabricate into complex shapes at a reduced expense. In particular, thermoplastics are moldable or extrudable into various shapes and sizes (Thomas et al. 2015). Besides this, the specific weight of industrial standard... 

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... 

Electrical response of materials in terms of dielectric (left) and conductive spectra (right). 

The above analysis applies to insulating materials. For electrically conductive materials such as metals, the dielectric constant is infinite and equations such as Eq. (2.47) do no longer apply. In this case, we can approximate the dielectric response function of the metal by... 

Choquette et al. investigated the possibilities of using a series of substituted sulfamides as possible electrolyte solvents (Table 12). These compounds are polar but viscous liquids at ambient temperature, with viscosities and dielectric constants ranging between 3 and 5 mPa s and 30 and 60, respectively, depending on the alkyl substituents on amide nitrogens. The ion conductivities that could be achieved from the neat solutions of Lilm in these sulfamides are similar to that for BEG, that is, in the vicinity of 10 S cm Like BEG, it should be suitable as a polar cosolvent used in a mixed solvent system, though the less-than-satisfactory anodic stability of the sulfamide family might become a drawback that prevents their application as electrolyte solvents, because usually the polar components in an electrolyte system are responsible for the stabilization of the cathode material surface. As measured on a GC electrode, the oxidative decomposition of these compounds occurs around 4.3—4.6 V when 100 fik cm was used as the cutoff criterion, far below that for cyclic carbonate-based solvents. 

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