Constant dielectric coefficient

Garrett and Poladian demonstrate the uniqueness of the nonlinear PB equation for the case of a constant dielectric coefficient. The extension for a variable (and positive) dielectric coefficient is readily shown by a suitable modification of Green s theorem based on Eq. [3]. However, care must be taken in the numerical solution of some modified PB theories as nonuniqueness has been observed. ... 

Clausius-Mossotti equation). In this expression, V designates the mole volume and Ae, Be, Cf,... are the first, second, third,... virial dielectric coefficients. A similar expansion exists for the refractive index, n, which is related to the (frequency dependent) dielectric constant as n2 = e (Lorentz-Lorenz equation, [87]). The second virial dielectric coefficient Be may be considered the sum of an orientational and a polarization term, Be = B0r + Bpo, arising from binary interactions, while the second virial refractive coefficient is given by just the polarization term, B = Bpo at high enough frequencies, the orientational component falls off to small values and the difference Be — B may be considered a measurement of the interaction-induced dipole moments [73],... 

The basic properties of water such as viscosity, dissociation constant, dielectric constant, compressibility, and the coefficient of thermal expansion play a major role in determining optimal reaction conditions for obtaining maximum benefits in both SCWO and WAO processes. The properties of water change dramatically with temperature, particularly near the critical point [24-26]. A well-known example, the variation of pAw with temperature at the saturation pressure, is shown in Fig. 3. The dissociation constant of water goes through a maximum around 250°C (pAw minimum), and then undergoes a sharp decline as the temperature approaches the critical point. The density and the dielectric constant of water also show sharp changes close to the critical point, as shown in Fig. 4. 

These simplified expressions depend on the assumption of a constant Hamaker coefficient with dielectric responses e1, e2, and em of similar magnitudes. 

A full set of optical functions consists of reflectivity R and absorption coefficients, p, the imaginary 82 and real 81 parts of the dielectric function 8, the absorption and refraction indices k and n, the product of the integral joint density of states (DOS) function and the transition probability, equal within constant factor to the effective number of valence electrons n E) participating in the transitions to given energy level A the effective dielectric coefficient Sef, and the characteristic electron energy functions for volume (-Imc ) and surface (-Im(l+8) ) losses. 

The Helmholtz capacitance may be described by Ch = e o/d, where e is the local value of the dielectric coefficient and d is the Stem layer thickness. Under conditions where e is independent of surface charge density, we can identify two domains of nearly constant capacitance under varying surface charge densities (i.e., pH). When Cq Ch (at high ionic strength), C == Ch when Cq Ch (lower ionic strength), C Cq. When the surface potential is small, for example, less than 25 mV, then Cq = eeox = 2.3 (25°C) (equation... 

A dielectric sphere of dielectric coefficient e embedded in an infinite dielectric of permittivity 82 is an important case from many points of view. The idea of a cavity formed in a dielectric is routinely used in the classical theories of the dielectric constant [67-69], Such cavities are used in the studies of solvation of molecules in the framework of PCM [1-7] although the shape of the cavities mimic that of the molecule and are usually not spherical. Dielectric spheres are important in models of colloid particles, electrorheological fluids, and macromolecules just to mention a few. Of course, the ICC method is not restricted to a spherical sample, but, for this study, the main advantage of this geometry lies just in its spherical symmetry. This is one of the simplest examples where the dielectric boundary is curved and an analytic solution is available for this geometry in the form of Legendre polynomials [60], In the previous subsection, we showed an example where the SC approximation is important while the boundaries are not curved. As mentioned before, using the SC approximation is especially important if we consider curved dielectric boundaries. The dielectric sphere is an excellent example to demonstrate the importance of curvature corrections . 

In this entry, the classification, preparation, properties, fabrication, safety considerations, and economics of fluoropolymers are discussed. Monomer synthesis and properties have also been discussed. Increasing the fluorine content of a polymer increases chemical and solvent resistance, flame resistance, and photostability, improves electrical properties, such as dielectric constant, lowers coefficient of friction, raises melting point, increases thermal stability, and weakens mechanical properties. 

The order parameter S is a very important quantity in a partially ordered system. It is the measure of the extent of the anisotropy of the liquid crystal physical properties, e.g., elastic constants, viscosity coefficients, dielectric anisotropy, birefringence, and so on. S is temperature dependent and decreases as the temperature increases. The typical temperature dependence of S is shown in Figure 1.16. 

A-methylacetamide (NMA) is another solvent which has received considerable interest in recent years because of its high degree of association and dielectric constant. Activity coefficients for a large number of... 

The simple electrostatic model of charges in a continuum was ex-tended to take account of dielectric saturation, a phenomenon which is only significant for the association of small ions. To correct the predicted association for dielectric saturation, a distance-dependent dielectric coefficient e must replace the static dielectric constant of the solvent. Eqn. 5.3.8 for then becomes... 

A parallel-plate capacitor consists of two closely spaced conductive Plates. A nonconductive material is termed a dielectric. When the space between the two plates is occupied by a dielectric material, the capacitance is increased by a factor K that is characteristic of the dielectric and is known as the dielectric constant or dielectric coefficient [8] ... 

It is known that the value of dielectric constant is a function of the local electric field. Since the electric field near the interface is not a constant, but a function of distance from it, the further refinement of EDL theory and potential profile at the BLM interface should include this positional dependency of dielectric coefficient. The local value of this coefficient is of course a measure of the influence of uncharged species such as water or lipid molecules on the interaction between charges in their vicinity. The dielectric coefficient of bulk aqueous electrolyte at... 

This handbook contains extensive tables of data for the more common Inorganic and organic aqueous electrolyte solutions. Properties covered include dielectric constants, activity coefficients, relative partial molar enthalpies, equilibrium constants, solubility products, conductivities, electrochemical potentials, Gibbs energies and enthalpies of formation, entropies, heat capacities, viscosities, and diffusion coefficients. Unfortunately, only a few of the tables contain references to the sources of the data. 

This equation derives directly from the fundamental electromagnetism relations, the Maxwell equations, and relates the electrostatic potential, yr, at any point in space with the charge density (i.e., electrical charge per unit volume), at the same point. In Equation 3.4, is a fixed charge distribution, e is the dielectric coefficient (or constant) of the medium, given by c = e e p where e, is the relative dielectric constant, and q is the vacuum permittivity. 

The dielectric coefficient e is in general not constant but can vary for several reasons one of them is the restructuring of water due to a preferential molecular orientation in the presence of strong electric fields and surfaces the latter is the case for water near a surface, where e will have a value lower than that of the bulk water. 

Beryllium oxide materials are particularly attractive for use in power vacuum tubes because of their electrical, physical, and chemical properties. The thermal conductivity of BeO is approximately 10 times higher than that of alumina-based materials. Figure 5.35 compares the thermal conductivity of BeO to that of alumina and some alternative materials. As the chart iUustrates, BeO has a lower dielectric constant and coefficient of thermal expansion than alumina, ft is, however, also sHghtly lower in strength. 

Mechanical and thermal characterization of ultra low k dielecteics is very similar to the characterization of dense low k dielectrics however the introduction of porosity requires the development of new characterization techniques in order to understand the pore structure. The dielectric constant, dielectric breakdown and coefficient of diermal expansion can be measured using the same techniques used for dense low k electrics. Modulus and hardness can also be measured by die same techniques, however, if using nanoindentation, measurements firom porous dielectrics may have larger substrate contributions at equivalent film thicknesses. Therefore, the modulus values... 

Some requirements to use these polymers for interlayer and intermetal dielectrics in advanced microelectronic applications are high thermal stability, high glass transition temperature, good mechanical properties, low dielectric constant, low coefficient of thermal expansion and low moisture absorption. The dielectric constant of polyimides depends mainly on the... 

After a piezoelectric ceramic is poled by a DC field higher than the coercive field Ec, the sample has symmetry of 00mm. For this piezoelectric ceramic, a typical process chart for the determination of dielectric constant, piezoelectric constant, elastic coefficient and electromechanical coupling factor is shown in Figure 22-13. 

Commercial fluoropolymers are based on TFE, vinylidene fluoride, and, to a lesser extent, CTFE. Examples of other comonomers include perfluoro-methyl vinyl ether, perfluoroethyl vinyl ether, PPVE, HFP, CTFE, and perfluorobutyl ethylene. The general consequences of the substitution of fluorine for hydrogen in a polymer include increased chemical and solvent resistance, enhanced electrical properties such as lower dielectric constant, lower coefficient of friction, higher melting point, increased photostability and thermal stability, improved flame resistance and weakened mechanical properties. The ultimate, most useful and sought-after properties are achieved in perfluorinated polymers. 

The literature on the molecular theory of liquid crystals is enormous and in this chapter we have been able to cover only a small part of it. We have mainly been interested in the models for the nematic-isotropic, nematic-smectic A and smectic A-smectic C phase transitions. The existing theory includes also extensive calculations of the various parameters of the liquid crystal phases Frank elastic constants, dielectric susceptibility, viscosity, flexoelectric coefficients and so... 

Koyama et al. [24] have shown that in the planar cell geometry it is possible to determine all three bulk elastic constants as well as the dielectric coefficients and and the magnetic anisotropy A in one cell under simultaneous application of an electric field and a magnetic field and using different orientations of the celt. 

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