Effective permittivity

Fi. 4.30 A sigmoidal dielectric model smoothly varies the effective permittivity from SO to 1 as shown. 

It is necessary to use the bulk permittivity of the solvent in the equation, instead of the unknown but more correct effective permittivity of the medium between the charges in the transition state. 

The method used in determining the dense dielectric permittivity of a definite material consists in defining a fluid in which the material cannot dissolve and further to measure the effective permittivity of various particulate media/fluid mixtures corresponding to various porosity. The interception point of the curves representing the variation of the permittivity of the material with porosity (through the effective medium equation, see section 3.2) gives the dense state permittivity. 

Units based on SrTi03 are more stable with respect to field and temperature than those based on BaTi03. Their capacitance is only reduced by 5% under maximum d.c. field and their variation with temperature can be kept within 20% over a — 20 to + 85 °C range their effective permittivity is 10 000-20 000. BaTi03 units have effective permittivities of up to 50 000. 

Applications that have received attention, and the material properties that enable them, are shown in Figure 27.1. These applications are reviewed in detail in Waser and Ramesh. Decoupling capacitors and filters on semiconductor chips, packages, and polymer substrates (e.g., embedded passives ) utilize planar or low aspect ratio oxide films. These films, with thicknesses of 0.1 to 1 J,m, are readily prepared by CSD. Because capacitance density is a key consideration, high-permittivity materials are of interest. These needs may be met by morpho-tropic phase boundary PZT materials, BST, and BTZ (BaTi03-BaZr03) solid solutions. Phase shifters (for phase array antennas) and tunable resonator and filter applications are also enabled by these materials because their effective permittivity exhibits a dependence on the direct current (DC) bias voltage, an effect called tunability. 

Solids and adsorbed phases Solid surfaces almost invariably have absorbed molecules derived from the gas or liquid medium to vhich the surface is exposed. The amount of such absorbed material depends upon the chemical nature of the solid surface. The absorbed layer can greatly affect the properties of the solid surface. The absorbed molecules may reorient by libratory oscillation betv een deflned orientational positions (see Orienting effect of a static electric field in Section 1.1.2.1). Such a restricted process could account for the reduced effective permittivity. The extensive use of silicates (clays and soils) as catalysts in chemistry adds interest to their study. 

Thus, if the wavelength of the light is much greater than the grain size, the long wavelength approximation and effective medium theory can be applied to determine the effective value of the composite dielectric constant and, consequently, describe composites optical properties. However, if the size of the structure is of the order of tens and even units of nanometers, then the effective medium approach is not applicable. Indeed, within this approximation, the effective permittivity of a composite is determined as a function of the permittivity for each composite component and, in turn, the nanocomposite components are characterized by the same tensor of permittivity as those used for bulk media. ... 

According to Frohlich, a pure condensed dielectric consisting of polarizable molecules with a permanent dipole moment p may be formally represented by a continuum permittivity accounting for the molecular polarizability, embedded in the bulk continuum with the effective permittivity 8. The fundamental polarization equation for such a polar dielectrics is... 

A chemicapacitive sensor is a capacitor that has a selectively absorbing material such as a polymer as a dielectric As chemicals are absorbed into the dielectric, effective permittivity of the capacitive sensor is changed. This leads a change of the capacitance. A cross-secti(Mial view of the basic structure of micromachined parallel plates is shown in Fig. 5 [9]. The conductance of the polymer depends on the types and quantities of biochemicals. 

T, R) is the temperature and size dependent dielectric permittivity of incipient ferroelectric nanoparticles of radius R, (x is the fermion effective mass, is the effective permittivity of the particle environment, 8q is the dielectric permittivity of vacuum (in SI units). Due to the high values of e(r, R) the radius (T, R) > 5 nm is much higher than the lattice constant a = 0.4 nm, proving the validity of the effective mass approximation as well as the self-consistent background for the introduction of dielectric permittivity in the continuous medium approach [60]. 

Interaction of BSA with A-300 causes an increase in the temperature of dipolar relaxation in comparison with BSA alone, e.g., the main peak in the HT region shits by 26 K (Figure 6.22). This effect is accompanied by an increase in the free energy of activation of relaxation (Table 6.3, AG ) for both BSA fragments bound to silica and bound water, an increase in the effective permittivity (e), relaxation time (x), and activation energy of depolarization (Figure 6.25). One can assume that the sizes of relaxed structures increase because of aggregation of oxide NP with macromolecules. 

The fact that in the absence of specific ion adsorption, variations in practically coincide with those may be explained assuming that, under such conditions, the effective permittivity, hence, the capacity for the layer between the electrode and discharging ion localization plane, are much lower than the corresponding values for the layer between the inner and outer Helmholtz planes. Then, the potential drop is concentrated, mainly, in the layer between the electrode and discharging ions, i.e., ( 1 — ( 0, is a relatively small value. Model-based evaluations of respective permittivity values corroborate this picture. 

Results showed that the textile-based sensor behavior is close to the expected one and already at this stage the stmcture might be used to indicate the presence of a pressure. The deviation was mainly due to the lateral movement of the conductive layers. As the distance decreases the rigidity of the spacer stmcture produces a shear force, which makes the conductive layers move laterally so that the overlapping area is no longer constant. Future work should aim to resolve the unwanted lateral motion of the conductive layers as well as to make a precise model of the partially filled capacitor in order to predict the effective permittivity of the dielectric. If fliese issues are taken care of the stmcture will also be suitable for making absolute measurements of either distance or pressure. 

Temperature dependence of extracted parameters relative effective permittivity, effective conductivity and inverse conductivity relaxation time... 

In gas-solids systems the volume fraction of solids is inferred from the measurements of the effective dielectric constant (or effective permittivity), expressed by... 

Major results In non-interacting spheres, the effective permittivity, eff where e is polymer permittivity and ( ) is filler firaction. Figure... 

The anion position in the series (II) determines its influence on the surface activity of alkylammonium salts upon adsorption from the aqueous phase. The value of the effective permittivity of the electrical double layer is lower than in the bulk phase due to dielectric saturation caused by the strong electric field and the presence of the adsorbed monolayer [89]. Therefore, the less hydrated anions permeate more easily to the plane formed by the adsorbed alkylammonium ions and form ionic pairs due to the interaction. 

Such a dependence of the attraction constant makes it possible to assume that there should be no essential interaction between the adsorbed cations at the interface of water with an organic solvent with an intermediate permittivity value (D = 17). Actually, the adsorption of CetMe3NCl at the water-methylbutylketone interface (Z> = 14.6) is described by the Langmuir iso term. Apparently, the values of the effective permittivity are equal in the Helmholtz layer of both phases and no definite conclusion can be drawn what so ever concerning the location of the adsorbed cation sites. The adsorption isotherms of the above systems are given in Fig. 4. 

Future work should scrutinize these structural aspects and refine corresponding approaches. The effective permittivity of water in pores increases with pore size, resulting in lower osmotic pressures, compared to the constant permittivity case due to a modified proton distribution. Consequently, the water uptake should be less steep at large RH. The inclusion of a Stern layer would further affect the proton distribution and, hence, water sorption. In fact, a modified Poisson-Boltzmann approach might be better suited to describe the electrostatic phenomena in such PEM pores. 

Pendry et al. [310] have shown that a surface wave propagating along a 2D array of apertures in metal film one can be described by an effective permittivity as... 

The effective permittivity c for a dielectric with permittivity C incoeporatiag uniformly distributed spherical inclusions of ceramic material with permittivity Cj can be also calculated from the equation... 

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