Dielectric behavior

Dielectric spectroscopy has been shown to be of great interest in dealing with transitions involving reorientation of permanent dipoles [93]. By monitoring the temperature and frequency dependence of the complex dielectric permittiv- 

In particular, VF2/F3E copolymers have also been the subject of extensive research [6,17,96]. As an example to illustrate the dielectric behavior of these copolymers, the temperature dependence of the real and the imaginary part of the complex permittivity at two different frequencies (1 and 100 kHz) are shown in Figs. 23a and 23b respectively. The measurements correspond to the 60/40 copolymer. The data have been collected by using a sandwich geometry with gold evaporated electrodes [95]. Frequencies of 103 and 106 Hz have been used by employing a 4192 A HP Impedance Analyzer. From inspection of Fig. 23b 

As an example of the Curie transition for other VF2/F3E compositions, measurements of e and e as a function of temperature and f = 1 kHz are shown in Figs. 25a and 25b. The complex permittivity function of polymeric materials has been shown to follow the Havriliak-Negami phenomenological equation [99]  

Il is interesting to discuss, next, the available e data for the various compositions in the light of the classical theory of ferroelectricity. According to this theory [100] for T Tc the temperature dependence of e can be written as 

In Fig. 27 experimental 1/e values are represented as a function of the temperature for samples with different compositions. As shown, the experimental values qualitatively follow Eq. 7 although 1/e achieves a non-zero value at the critical temperature. The intrinsic composite structure of semicrystalline polymers has been invoked to understand this effect [8, 6]. The order of magnitude of the constant A has been reported to be around 103 °C [11] which is consistent with the relatively high polarizability of these materials. At this point it is important to emphasize that the knowledge of morphological aspects of these copolymers might help, in future, to develop a theoretical framework capable of accounting for the experimental observations. 

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Dielectric Behavior of Adsorbed Water. Determination of the dielectric absorption of adsorbed water can yield conclusions similar to those from proton NMR studies and there is a considerable, although older literature on the subject. Figure XVI-7 illustrates how the dielectric constant for adsorbed water varies with the frequency used as well as with the degree of surface coverage. A characteristic relaxation time r can be estimated... 

As our discussion of scattering proceeds, we shall examine the coupling between the oscillating electrical field of light and the electrons of the scatterer in detail. First, it is useful to consider the interaction of an electric field with matter, as this manifests itself in the dielectric behavior of a substance. This will not only introduce us to the field-matter interaction, but will also provide some relationships which will be useful later. 

E. H. Grant, R. J. Sheppard, and G. P. South, Dielectric Behavior of Biological Molecules in Solutions, Clarendon Press, Oxford, U.K., 1978. 

The information presented in this work builds upon developments from several more established fields of science. This situation can cause confusion as to the use of established sign conventions for stress, pressure, strain and compression. In this book, those treatments involving higher-order, elastic, piezoelectric and dielectric behaviors use the established sign conventions of tension chosen to be positive. In other areas, compression is taken as positive, in accordance with high pressure practice. Although offensive to a well structured sense of theory, the various sign conventions used in different sections of the book are not expected to cause confusion in any particular situation. 

In this chapter nonlinear piezoelectric and dielectric behavior shock-induced electrical conductance semiconductors elastic physical properties. 

The trends of variation of the activation parameters are correlated with the solvation mechanism and dielectric behavior of the medium. Thus, AH, AG and A5 for the acidic resin-catalyzed hydrolysis of isopropyl acetate were calculated using the Wynne-Jones and Eyr-... 

Water absorption can also cause significant changes in the permittivity and must be considered when describing dielectric behavior. Water, with a dielectric constant of 78 at 25°C, can easily impact the dielectric properties at relatively low absorptions owing to the dipolar polarizability contribution. However, the electronic polarizability is actually lower than solid state polymers. The index of refraction at 25°C for pure water is 1.33, which, applying Maxwell s relationship, yields a dielectric constant of 1.76. Therefore, water absorption may actually act to decrease the dielectric constant at optical frequencies. This is an area that will be explored with future experiments involving water absorption and index measurements. 

It might be useful in some cases to raise the dielectric constant of mixed solvents by addition of suitable substances and it is known that dipolar molecules such as amino acids do so in pure water. These amino acids are virtually insoluble in nonpolar solvents but they dissolve readily in aqueous salt solutions and in most mixed solvents according to their highly polar structure. Most of what is known about their dielectric behavior concerns aqueous solutions, in which they were studied up to concentrations near saturation. 

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. 

The dielectric behavior is often studied by employing charging or polarization currents. Since polarization currents depend on the applied voltage and the dimensions of the condenser, it is customary to eliminate this dependence by dividing the charge, Q, by the voltage, V, to get a parameter called the capacitance (capacity), C ... 

Banerjee S, Kumar A (2010) Dielectric behavior and charge transport in polyaniline nanofiber reinforced PMMA composites. J Phys Chem Solids 71 381... 

On physical grounds, relaxation of permanent dipoles is expected to be highly dependent on temperature this is in contrast with Lorentz oscillators, the dielectric behavior of which is relatively insensitive to changes in temperature. Debye (1929, Chap. 5) derived a simple classical expression for the relaxation time of a sphere of radius a in a fluid of viscosity tj ... 

The dielectric behavior of PBLG in other helicogenic solvents has been investigated by several later workers. Thus Marchal and Marchal (112) concerned themselves with samples of Mw ranging from 2 x 104 to 22 x 104 in three solvents chloroform containing 0.5% formamide, EDC containing 0.8%... 

From a chemical perspective, dielectric- and conductor-like continuum models give sufficiently similar electrostatic results that the differences in their underlying assumptions appear to have no impact. Conductor-like models seem to be slightly more computationally robust in some instances, which may make tliem a better choice if instability is manifest in an SCRF calculation. Some concerns were raised initially that the post facto correction for dielectric behavior might render the models appropriate only for media having reasonably high dielectric constants, but a systematic study by Dolney et al. (2000) indicated non-polar solvents to be equally amenable to treatment by a COSMO model. 

The dielectric behavior of nonionized PAAm network and a ionized P(AAm/MNa) network with xMNa = 0.03 in deionized-water-acetone mixtures was also studied [33]. High values of complex permittivity e were found for both networks (Fig. 19). For the PAAm network, the dependence of both component e and e" on acetone a is continuous. On the other hand, for the ionized network the jumpwise decrease in swelling at the transition is accompanied by a jumpwise increase in the values of both components of e at all... 

Smyth, C. P. Dielectric behavior and structure, p. 125. New York McGraw-Hill 1955. 

Dipolar Absorption. When the dielectric behavior of hydrated Na+-zeolites is investigated between two electrodes blocked from the sample with thin mica sheets, the conduction process is eliminated and two absorp-... 

Onsager Theory for C(t) for Non-Debye Solvents. Generally solvents have more complex dielectric responses than described by the Debye equation (Eq. (18)). To obtain the time dependence of the reaction field R from Eqs. (12, (15), (16) and (7) an appropriate model for dielectric behavior of a specific liquid should be employed. One of the most common dielectric relaxation is given by the Debye-type form, which is applicable to normal alcohols. 

A much better representation of the dielectric behavior of polar liquids is given by the Onsager equation... 

The symmelrical loss-frequency curve predicted by this simple theory is commonly observed for simple substances, but its maximum is usually lower and broader because of the existence of more than one relaxation time. Various functions have been proposed to represent the distribution of relaxation times. A convenient representation of dielectric behavior is obtained, according to the method of Cole and Cole, by writing the complex dielectric constant as... 

It is thus again demonstrated that an understanding of the mechanisms of dielectric behavior of mixtures must be understood in detail in order to extract diagnostic information from the microwave spectrum. 

Finally, an area which is in need of much further research is that of the dielectric properties of two-phase systems such as frozen foods, emulsions, whips and foams. It is well known that the dielectric behavior of particles of one dielectric property imbedded in a substrate of another, behave very differently from a distributive mixture of both. Fricke (1955) developed a model for randomly oriented oblate spheroids suspended in a continuous medium. It is expected that this model may be used successfully to model two-phase food systems, but to date there is very little literature reporting such studies. 

El-Rays, M. and Ulaby, F. 1987. Microwave Dielectric Behavior of Vegetation Material. Ann Arbor, Michigan Radiation Laboratory, University of Michigan. (Available through National Technical Information Service, Springfield, VA). 

There are two parameters which appear to be of major importance in determining the occurrence and observability of electron solvation. The first is the polarizability of the liquid, as expressed by its dielectric behavior. On the basis of theory, which will be discussed later, a necessary condition for electron solvation appears to be that the static dielectric constant of the liquid be substantially greater than one. The second parameter, which seems at present to be unpredictable, is the natural lifetime of the solvated electron—i.e., its lifetime with respect to reaction with the solvent itself. 

The theory relates the energy states of the electron to the dielectric behavior of the continuous medium, assuming the electron to be bound in the potential field of the oriented dipoles. Davydov (8) has derived the expression ... 

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