Dielectric constant, alternating currents

Some important dielectric behavior properties are dielectric loss, loss factor, dielectric constant, direct current (DC) conductivity, alternating current (AC) conductivity, and electric breakdown strength. The term dielectric behavior usually refers to the variation of these properties as a function of frequency, composition, voltage, pressure, and temperature. 

If an alternating current potentiaHs appHed to an electrical condenser, each reversal of the potential results ia a reversal of the charge stored ia the coadeaser. There is, therefore, an alternating current apparently flowing through the condenser proportional to the capacitance of the condenser, hence proportional to the dielectric constant of the iasulation material forming the dielectric of the condenser. 

There is an important practical distinction between electronic and dipole polarisation whereas the former involves only movement of electrons the latter entails movement of part of or even the whole of the molecule. Molecular movements take a finite time and complete orientation as induced by an alternating current may or may not be possible depending on the frequency of the change of direction of the electric field. Thus at zero frequency the dielectric constant will be at a maximum and this will remain approximately constant until the dipole orientation time is of the same order as the reciprocal of the frequency. Dipole movement will now be limited and the dipole polarisation effect and the dielectric constant will be reduced. As the frequency further increases, the dipole polarisation effect will tend to zero and the dielectric constant will tend to be dependent only on the electronic polarisation Figure 6.3). Where there are two dipole species differing in ease of orientation there will be two points of inflection in the dielectric constant-frequency curve. 

The physical approach uses alternating current (ac-) dielectrophoresis to separate metallic and semiconducting SWCNTs in a single step without the need for chemical modifications [101]. The difference in dielectric constant between the two types of SWCNTs results in an opposite movement along an electric field gradient between two electrodes. This leads to the deposition of metallic nanotubes on the microelectrode array, while semiconducting CNTs remain in the solution and are flushed out of the system. Drawbacks of this separation technique are the formation of mixed bundles of CNTs due to insufficient dispersion and difficulties in up-scaling the process [102]. 

When a solution containing dipolar molecules is placed between electrodes and subjected to an alternating current, the molecules tend to rotate in phase with the current, thus increasing the dielectric constant of the solution. As the frequency is increased, it becomes more difficult for the dipolar molecules to overcome the viscous... 

The most important dielectric properties are the dielectric constant, e, and the dielectric loss factor, tan 8. These properties are of interest for alternating currents indicates the polarizability in an electric field, and, therefore, it governs the magnitude of the alternating current transmitted through the material when used in a capacitor. For most polymers e is between 2 and 5, but it may reach values up to 10 for filled systems. 

The electrical properties of polyelectrolyte complexes are more closely related to those of biologically produced solids. The extremely high relative dielectric constants at low frequencies and the dispersion properties of salt-containing polyelectrolyte complexes have not been reported for other synthetic polymers. Neutral polyelectrolyte complexes immersed in dilute salt solution undergo marked changes in alternating current capacitance and resistance upon small variations in the electrolyte concentration. In addition, their frequency-dependence is governed by the nature of the microions. As shown in... 

With an alternating current (AC) field, the dielectric constant is virtually independent of frequency, so long as one of the multiple polarization mechanisms usually present is active (see Section 8.8.1). When the dominating polarization mechanism ceases as the frequency of the applied field increases, there is an abmpt drop in the dielectric constant of the material before another mechanism begins to dominate. This gives rise to a characteristic stepwise appearance in the dielectric constant versus frequency curve. For each of the different polarization mechanisms, some minimum dipole reorientation time is required for reahgnment as the AC held reverses polarity. The reciprocal of this time is referred to as the relaxation frequency. If this frequency is exceeded, that mechanism wUl not contribute to the dielectric constant. This absorption of electrical energy by materials subjected to an AC electric held is called dielectric loss. 

There is much to think about here. If one wishes to measure the dielectric constant of a liquid, not a conducting ionic solution, one simply uses an alternating current (ac) bridge containing a capacitor in one of the arms. Then the capacitance is measured in the presence of the liquid, the dielectric constant of which is to be measured, and then without it, i.e., in the presence of air. Since the dielectric constant is near to unity in the latter case, this gives rise to knowledge of the dielectric constant of the liquid because the capacitance of the cell in the bridge arm increases as the dielectric constant increases. 

Polarization can be classified as electronic (electron cloud distortion), atomic, molecular, ionic, and crystalline. The point of maximum polarization in a system would occur when all dipoles reacted to the applied field and aligned. This is difficult to obtain even in a static situation. In an alternating field situation, the dielectric remains the same or decreases as the frequency increases past the microwave region (11). In the microwave region, attainment of equilibrium is more difficult, and there is an observable lag in the dipole orientation which is commonly called relaxation. The polarization then acquires a component out of phase with the field thermal dissipation of some of the energy of the field. This dissipation and its relation to the normal charging current can be related by Equation 1 where c is the measured dielectric constant of the material and e"... 

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... 

The extraction techniques described in this book fulfill many of Anastas and Warner s principles. For example, the use of supercritical carbon dioxide (SC-CO2) as the sole extraction solvent results in a nonpolluting process (prevention of waste and safer solvents and auxiliaries). Other beneficial properties of supercritical CO2 include fast diffusivity and nearly zero surface tension, which lead to extremely efficient extractions. In Chapters 2-4, applications of SC-CO2 as an extraction solvent are described. Ethanol and water are also environmentally friendly solvents that can be used as extraction media in many applications (see Chapters 5-7). Pressurized hot water ( 100-200 °C) in particular is a safe and nonpolluting solvent that has a similar dielectric constant to polar organic solvents, such as ethanol or acetone. Hence, pressurized hot water is a viable green alternative to many current extraction processes that use toxic organic solvents. Similarly, pressurized hot ethanol is an excellent solvent for the extraction of most medium polar to nonpolar organic molecules. Some of the techniques, such as membrane-assisted solvent extraction, described in Chapter 10, use organic solvents but in much smaller amounts compared to classical extraction techniques. Other techniques, for instance solid-phase microextraction and stir-bar sorptive extraction, described in Chapter 11, use no solvents. 

The dielectric constant is ordinarily measured in an alternating current circuit. The direction of the field across the capacitor changes back and forth with the frequency of the applied potential. If we imagine a single polar molecule between the plates of a capacitor, then if the frequency is not too high, this single molecule will flip back and f orth as the field oscillates, always adjusting its orientation to match the direction of the field. 

---