Isotropic dielectrics

When a field E is applied across a dielectric (a simple parallel plate condenser, for example), the resulting displacement current, D is related to E as D = eE. In glasses, which are dielectrically isotropic, the permittivity, 8 behaves as a scalar quantity and is equal to D E. While E is an experimentally controlled alternating field of arbitrary frequency, D and s are the material dependent responses and Z), which represents the polarization current is not always in phase with E. s is, therefore, a complex frequency dependent quantity. The complex permittivity, e, is defined as... 

Within this model, the solute is described as a sphere of radius Oq with a dipole /x at the center of the cavity. The solvent is a dielectric isotropic medium described by its permittivity e (Figure 2.2b). Under this scheme, the Gibbs solvation energy is approximated as... 

E II Lo) for the B-effect. As follows from (4.1) the S- (B-)effect appears for the corresponding positive (negative) values of the dielectric anisotropy Ae. The dielectrically isotropic point Ac = 0 is stable for both types of the Prederiks transitions. 

Homogeneous, dielectric (isotropic, chiral) and perfectly conducting, ax-isymmetric particles (TAXSYM.fQO),... 

Formal Theory A small neutral particle at equihbrium in a static elecdric field experiences a net force due to DEP that can be written as F = (p V)E, where p is the dipole moment vecdor and E is the external electric field. If the particle is a simple dielectric and is isotropically, linearly, and homogeneously polarizable, then the dipole moment can be written as p = ai E, where a is the (scalar) polarizability, V is the volume of the particle, and E is the external field. The force can then be written as ... 

Conventionally RAIRS has been used for both qualitative and quantitative characterization of adsorbed molecules or films on mirror-like (metallic) substrates [4.265]. In the last decade the applicability of RAIRS to the quantitative analysis of adsorbates on non-metallic surfaces (e.g. semiconductors, glasses [4.267], and water [4.273]) has also been proven. The classical three-phase model for a thin isotropic adsorbate layer on a metallic surface was developed by Greenler [4.265, 4.272]. Calculations for the model have been extended to include description of anisotropic layers on dielectric substrates [4.274-4.276]. 

A normal dielectric may be characterized by Eq. (4.1) with the piezoelectric terms deleted. For an isotropic dielectric subject to uniaxial strain and a collinear electric field this equation takes the form... 

If we now transfer our two interacting particles from the vacuum (whose dielectric constant is unity by definition) to a hypothetical continuous isotropic medium of dielectric constant e > 1, the electrostatic attractive forces will be attenuated because of the medium s capability of separating charge. Quantitative theories of this effect tend to be approximate, in part because the medium is not a structureless continuum and also because the bulk dielectric constant may be an inappropriate measure on the molecular scale. Eurther discussion of the influence of dielectric constant is given in Section 8.3. 

Optical and electro-optical behavior of side-chain liquid crystalline polymers are described 350-351>. The effect of flexible siloxane spacers on the phase properties and electric field effects were determined. Rheological properties of siloxane containing liquid crystalline side-chain polymers were studied as a function of shear rate and temperature 352). The effect of cooling rate on the alignment of a siloxane based side-chain liquid crystalline copolymer was investigated 353). It was shown that the dielectric relaxation behavior of the polymers varied in a systematic manner with the rate at which the material was cooled from its isotropic phase. 

Wood and Blundy (2001) developed an electrostatic model to describe this process. In essence this is a continuum approach, analogous to the lattice strain model, wherein the crystal lattice is viewed as an isotropic dielectric medium. For a series of ions with the optimum ionic radius at site M, (A(m))> partitioning is then controlled by the charge on the substituent (Z ) relative to the optimum charge at the site of interest, (Fig. 10) ... 

An interesting hypothesis may be put forward. The interfacial pA lcm (Fig. 5.1) that a solute exhibits depends on the dielectric environment of its location in the bilayer. Simple isotropic water-miscible solvents may be used to approximate p mem pure methanol (e 32), may do well for the bilayer zone containing the phosphate groups pure 1,4-dioxane (e 2) may mimic some of the dielectric properties of the hydrocarbon region. It appears that psKa values of several weak bases, when extrapolated to 100% cosolvent, do approximate pvalues [119,162,172]. Fernandez and Fromherz made favorable comparisons using dioxane [448]. This idea is of considerable practical use, and has been largely neglected in the literature. 

Fig. 2.2 Self-Consistent Reaction Field (SCRF) model for the inclusion of solvent effects in semi-empirical calculations. The solvent is represented as an isotropic, polarizable continuum of macroscopic dielectric e. The solute occupies a spherical cavity of radius ru, and has a dipole moment of p,o. The molecular dipole induces an opposing dipole in the solvent medium, the magnitude of which is dependent on e.

These are the familiar orientational contributions to the DC dielectric response. This limit, /iE/kT <1, can be considered alternatively to be a restriction to nonsaturated alignments. For physical systems with orientational distributions intermediate between the isotropic and Ising limiting models the poling responses... 

The continuum model of solvation has evolved from these beginnings. The solvent is treated as a continuous polarizable medium, usually assumed to be homogeneous and isotropic, with a uniform dielectric constant e.11-16 The solute molecule creates and occupies a cavity within this medium. The free energy of solvation is usually considered to be composed of three primary components ... 

To answer this question, let us first consider a neutral molecule that is usually said to be polar if it possesses a dipole moment (the term dipolar would be more appropriate)1 . In solution, the solute-solvent interactions result not only from the permanent dipole moments of solute or solvent molecules, but also from their polarizabilities. Let us recall that the polarizability a of a spherical molecule is defined by means of the dipole m = E induced by an external electric field E in its own direction. Figure 7.1 shows the four major dielectric interactions (dipole-dipole, solute dipole-solvent polarizability, solute polarizability-solvent dipole, polarizability-polarizability). Analytical expressions of the corresponding energy terms can be derived within the simple model of spherical-centered dipoles in isotropically polarizable spheres (Suppan, 1990). These four non-specific dielectric in-... 

A method, integral equation formalism (lEF), can treat solvent effects. It exploits a single common approach for dielectrics of very different nature standard isotropic liquids, intrinsically anisotropic media like liquid crystals, and ionic solutions (Men-nucci et al., 1997). 

When structural and dynamical information about the solvent molecules themselves is not of primary interest, the solute-solvent system may be made simpler by modeling the secondary subsystem as an infinite (usually isotropic) medium characterized by the same dielecttic constant as the bulk solvent, that is, a dielectric continuum. Theoretical interpretation of chemical reaction rates has a long history already. Until recently, however, only the chemical reactions of systems containing a few atoms in the gas phase could be studied using molecular quantum mechanics due to computational expense. Fortunately, very important advances have been made in the power of computer-simulation techniques for chemical reactions in the condensed phase, accompanied by an impressive progress in computer speed (Gonzalez-Lafont et al., 1996). 

The spring model suggests that the symmetry of the crystal lattice determines the different forms of the dielectric tensor that is, they are related to the seven types of crystalline solid (amorphous solids and most liquids are isotropic). This is summarized as follows ... 

Further experimental evidence of shape effects in absorption spectra of SiC particles is found in the data of Pultz and Herd (1966), who investigated infrared absorption by SiC fibers with and without Si02 coatings. Although these measurements were not mass-normalized, they show a strong absorption band at 795 cm-1 and a weaker band at 941 cm-1. If the fibers are approximated as ellipsoids with L2 = L3 = and Lx = 0 (i.e., a cylinder), then the ellipsoid equation (12.27) predicts absorption peaks for particles in air at frequencies where c = -1 and c = — oo. This corresponds to absorption bands at 797 and 945 cm-1 for the dielectric function of isotropic SiC, in excellent agreement with the experimental peak positions for the fibers. 

The rotational diffusion coefficient Dr of a rodlike polymer in isotropic solutions can be measured by electric, flow, and magnetic birefringence, dynamic light scattering, and dielectric dispersion. However, if the polymer has some flexibility, its internal motion makes it difficult to extract Dr for the end-over-end rotation of the chain from data of these measurements. In other words, Dr can be measured only for nearly rodlike polymers. 

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