Generalized permittivity

Relaxor Ferroelectrics. The general characteristics distinguishing relaxor ferroelectrics, eg, the PbMg 2N b2 302 family, from normal ferroelectrics such as BaTiO, are summari2ed in Table 2 (97). The dielectric response in the paraelectric-ferroelectric transition region is significantly more diffuse for the former. Maximum relative dielectric permittivities, referred to as are greater than 20,000. The temperature dependence of the dielectric... 

Principles in Processing Materials. In most practical apphcations of microwave power, the material to be processed is adequately specified in terms of its dielectric permittivity and conductivity. The permittivity is generally taken as complex to reflect loss mechanisms of the dielectric polarization process the conductivity may be specified separately to designate free carriers. Eor simplicity, it is common to lump ah. loss or absorption processes under one constitutive parameter (20) which can be alternatively labeled a conductivity, <7, or an imaginary part of the complex dielectric constant, S, as expressed in the foUowing equations for complex permittivity ... 

The internal field is that microwave field which is generally the object for solution when MaxweU s equations are appUed to an object of arbitrary geometry and placed in a certain electromagnetic environment. The is to be distinguished from the local field seen by a single molecule which is not necessarily the same (22). The dielectric permittivity as a function of frequency can be described by theoretical models (23) and measured by weU-developed techniques for uniform (homogeneous) materials (24). 

Although the continuum model of the ion could be analyzed by Gauss law together with spherical symmetry, in order to treat more general continuum models of electrostatics such as solvated proteins we need to consider media that have a position-specific permittivity e(r). For these a more general variant of Poisson s equation holds ... 

Meanwhile, the R-R coupling (see Sect. 2.2) has evidently found general acceptance as the main reaction path for the electropolymerization of conducting polymers The ionic character of the coupling species explains why polar additives such as anions or solvents with high permittivity accelerate the rate of polymerization and function as catalysts. Thus, electropolymerization of pyrrole is catalyzed in CHjCN by bromide ions or in aqueous solution by 4,5-dihydro-1,3-benzenedisulfonic acid The electrocatalytic influence of water has been known since the work... 

An alternative electrical method that has been used in the study of glass-ionomer cements has been the measurement of dielectric properties. Tay Braden (1981, 1984) measured the resistance and capacitance of setting cements at various times from mixing. From the results obtained, relative permittivity and resistivity were calculated. In general, as these cements set, their resistivity was found to fall rapidly, then to rise again. Both these results and the results of relative permittivity measurements were consistent with the cements comprising highly ionic and polar structures. 

The interface is, from a general point of view, an inhomogeneous dielectric medium. The effects of a dielectric permittivity, which need not be local and which varies in space, on the distribution of charged particles (ions of the electrolyte), were analyzed and discussed briefly by Vorotyntsev.78 Simple models for the system include, in addition to the image-force interaction, a potential representing interaction of ions with the metal electrons. 

The general equation for complex dielectric permittivity is then given by Eq. (11) ... 

The assumption of linear response played a prominent role in the derivation (given above) of the SCRF equations, and one aspect of the physics implied by this assumption is worthy of special emphasis. This aspect is the partitioning of Gp into a solute-solvent interaction part Gss and a intrasolvent part Gss The partitioning is quite general since it follows entirely from the assumption of linear response. Since classical electrostatics with a constant permittivity is a special case of linear response, it can be derived by any number of classical electrostatic arguments. The result is [114, 116-119]... 

In Eqs. (16) and (17), a and P refer to atoms of the solute and solvent, respectively q is the permittivity of free space, Qa and Qp are atomic charges, and Rap is the distance between atoms a and p. The parameters eap, aap, Aap, Bap and Cap can either be assigned by fitting to experimental data or can be the arithmetic or geometric means of literature values for the individual atom types.10,65,66 The atomic charges are commonly determined by requiring that they reproduce the calculated molecular electrostatic potentials.10 In order to provide better descriptions of the solvent s structure, Eqs. (16) and (17) are generally extended to include solvent-solvent intermolecular interactions. 

Methods for measuring the resistivity of insulating materials are based on IEC 60093 [24] and insulation resistance is covered by IEC 60167 [25]. For conducting and antistatic materials the methods for rubbers, ISO 1853 [26] for resistivity and ISO 2878 [27] for resistance, could be adapted and there is a draft IEC standard. The general method for electric strength is IEC 60243 [28] and methods for power factor and permittivity are often based on IEC 60250 [29]. 

Permittivity measurements have been used to study hydrogen bonding of phenol or carboxylic acids with trialkylphosphine oxides (154). The results can be explained in terms of a simple electrostatic model. The properties of trimethylphosphine oxide were different from the general properties of the series.189... 

A similar conclusion arises from the capacitance data for the mercury electrode at far negative potentials (q 0), where anions are desorbed. In this potential range, the double-layer capacitance in various electrolytes is generally equal to ca. 0.17 F Assuming that the molecular diameter of water is 0.31 nm, the electric permittivity can be calculated as j = Cd/e0 = 5.95. The data on thiourea adsorption on different metals and in different solvents have been used to find the apparent electric permittivity of the inner layer. According to the concept proposed by Parsons, thiourea can be treated as a probe dipole. It has been cdculated for the Hg electrode that at (7 / = O.fij is equal to 11.4, 5.8, 5.1, and 10.6 in water, methanol, ethanol, and acetone, respectively. 

Figure 5-11 shows a simple model of the compact double layer on metal electrodes. The electrode interface adsorbs water molecules to form the first mono-molecular adsorption layer about 0.2 nm thick next, the second adsorption layer is formed consisting of water molecules and hydrated ions these two layers constitute a compact electric double layer about 0.3 to 0.5 nm thick. Since adsorbed water molecules in the compact layer are partially bound with the electrode interface, the permittivity of the compact layer becomes smaller than that of free water molecules in aqueous solution, being in the range from 5 to 6 compared with 80 of bulk water in the relative scale of dielectric constant. In general, water molecules are adsorbed as monomers on the surface of metals on which the affinity for adsorption of water is great (e.g. d-metals) whereas, water molecules are adsorbed as clusters in addition to monomers on the surface of metals on which the affinity for adsorption of water is relatively small (e.g. sp-metals). 

When the relative permittivity of the organic solvent or solvent mixture is e < 10, then ionic dissociation can generally be entirely neglected, and potential electrolytes behave as if they were nonelectrolytes. This is most clearly demonstrated experimentally by the negligible electrical conductivity of the solution, which is about as small as that of the pure organic solvent. The interactions between solute and solvent in such solutions have been discussed in section 2.3, and the concern here is with solute-solute interactions only. These take place mainly by dipole-dipole interactions, hydrogen bonding, or adduct formation. 

It is not difficult to generalize the results of this section to an anisotropic ellipsoid the axes of which coincide with the principal axes of its permittivity tensor. The principal values of the polarizability tensor of such a particle are... 

More general ellipsoidal particles in an anisotropic medium, where there is no restriction on the principal axes of either the real or imaginary parts of the permittivity tensors, have been treated by Jones (1945). 

Physical properties of liquid crystals are generally anisotropic (see, for example, du Jeu, 1980). The anisotropic physical properties that are relevant to display devices are refractive index, dielectric permittivity and orientational elasticity (Raynes, 1983). A nematic LC has two principal refractive indices, Un and measured parallel and perpendicular to the nematic director respectively. The birefringence An = ny — rij is positive, typically around 0.25. The anisotropy in the dielectric permittivity which is given by As = II — Sj is the driving force for most electrooptic effects in LCs. The electric contribution to the free energy contains a term that depends on the angle between the director n and the electric field E and is given by... 

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