Dielectric relaxation constant

The relaxation of the static dielectric constant is related to the transition dynamics of electrons from the valence band to the conduction band. The dielectric constant relaxation depends functionally on Eq expansion, electron-phonon coupling, and lattice relaxation, showing the trend of interaction-enhancement resulted depression [60]. The dielectric permittivity x — 1) of a semiconductor is approx-... 

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... 

The dielectric constant (permittivity) tabulated is the relative dielectric constant, which is the ratio of the actual electric displacement to the electric field strength when an external field is applied to the substance, which is the ratio of the actual dielectric constant to the dielectric constant of a vacuum. The table gives the static dielectric constant e, measured in static fields or at relatively low frequencies where no relaxation effects occur. 

A variety of experimental techniques have been employed to research the material of this chapter, many of which we shall not even mention. For example, pressure as well as temperature has been used as an experimental variable to study volume effects. Dielectric constants, indices of refraction, and nuclear magnetic resonsance (NMR) spectra are used, as well as mechanical relaxations, to monitor the onset of the glassy state. X-ray, electron, and neutron diffraction are used to elucidate structure along with electron microscopy. It would take us too far afield to trace all these different techniques and the results obtained from each, so we restrict ourselves to discussing only a few types of experimental data. Our failure to mention all sources of data does not imply that these other techniques have not been employed to good advantage in the study of the topics contained herein. 

R = factor for electrical relaxation D = dielectric constant of medium F = factor for size of spheres and = zeta potential. 

For many years the petroleum industry has defined nonconductive liquids as having conductivities less than 50 pS/m. A higher value of 100 pS/m is used here to address the higher dielectric constants of certain flammable chemicals in relation to petroleum products. For example the dielectric constant of ethyl ether is 4.6 versus 2.3 for benzene from Eq. (2-3.2), ethyl ether therefore has the same relaxation time at a conductivity of 100 pS/m as benzene at a conductivity of 50 pS/m. It is the relaxation time, not the conductivity alone, that determines the rate of loss of charge hence the same logic that makes 50 pS/m appropriate for identifying nonconductive hydrocarbons makes 100 pS/m appropriate for identifying nonconductive chemical products. 

The addition of salts modifies the composition of the layer of charges at the micellar interface of ionic surfactants, reducing the static dielectric constant of the system [129,130]. Moreover, addition of an electrolyte (NaCl or CaCli) to water-containing AOT-reversed micelles leads to a marked decrease in the maximal solubihty of water, in the viscosity, and in the electrical birefringence relaxation time [131],... 

Dielectric relaxation studies of phosphorylated polyethers from — 180° to 200 °C have been used to study their structures. The magnitude of the dielectric constants of high-phosphonic-acid-content polymers is much larger than predicted, which suggests a microphase-separated structure. Conductance studies on some aryl- and alkyl-phosphonium salts showed a higher conductance for the halides than for the nitrate. ... 

A larger protein dielectric constant of four was used by Eberini et al. [124] to fit the experimental pKa, in a case where the protein structural relaxation upon protonation was especially large. The need for a larger protein dielectric suggests a breakdown of the linear response assumption for this system. It may be preferable in such a case to simulate an additional point along the reaction pathway, such as the midpoint, rather than shifting to what is effectively a parameter-fitting approach. 

Mozumder (1969b) pointed out that in the presence of freshly created charges due to ionization, the dielectric relaxes faster—with the longitudinal relaxation time tl, rather than with the usual Debye relaxation time T applicable for weak external fields. The evolution of the medium dielectric constant is then given by... 

Equations (7.6) and (7.7) provide a means of determining excited dipole moments together with dipole vector angles, but they are valid only if (i) the dipole moments in the FC and relaxed states are identical, (ii) the cavity radius remains unchanged upon excitation, (iii) the solvent shifts are measured in solvents of the same refractive index but of different dielectric constants. 

The equivalent conductivity of an electrolyte solution decreases with increasing concentration due to interionic attractions described mainly by the electrophoretic and relaxation field effects 2-35>. This decrease is more pronounced if in addition the electrolyte is associated. Association of ionic salts by ion-pairing is commonly observed in solvents of low or moderate dielectric constant. The immediate goals in the analysis of conductance data are the. determination of the limiting equivalent conductance at infinite dilution, A0, and the evaluation of the association constant, KA, if ion-pairing occurs. 

Usually, the most general nonspecific effects of dipole-orientational and electronic polarization of the medium are discussed, and the results of the theory of relaxational shifts developed under the approximation of a continuous dielectric medium may be used.(86 88) The shift of the frequency of the emitted light with time is a function of the dielectric constant e0, the refractive index n, and the relaxation time xR ... 

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