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Dielectric inclusion

Finally, the dielectric properties of a nonpolar polymer are modified by inclusion of even small amounts of a polar comonomer. In coatings applications the presence of polar repeat units in an otherwise nonpolar polymer reduces the tendency for static buildup during manufacture, printing, and ultimate use. On the other hand, in dielectric applications this increases the power loss and must be kept to a minimum, even to the exclusion of polar initiator fragments. [Pg.469]

Historically, materials based on doped barium titanate were used to achieve dielectric constants as high as 2,000 to 10,000. The high dielectric constants result from ionic polarization and the stress enhancement of k associated with the fine-grain size of the material. The specific dielectric properties are obtained through compositional modifications, ie, the inclusion of various additives at different doping levels. For example, additions of strontium titanate to barium titanate shift the Curie point, the temperature at which the ferroelectric to paraelectric phase transition occurs and the maximum dielectric constant is typically observed, to lower temperature as shown in Figure 1 (2). [Pg.342]

Conceptually, the self-consistent reaction field (SCRF) model is the simplest method for inclusion of environment implicitly in the semi-empirical Hamiltonian24, and has been the subject of several detailed reviews24,25,66. In SCRF calculations, the QM system of interest (solute) is placed into a cavity within a polarizable medium of dielectric constant e (Fig. 2.2). For ease of computation, the cavity is assumed to be spherical and have a radius ro, although expressions similar to those outlined below have been developed for ellipsoidal cavities67. Using ideas from classical electrostatics, we can show that the interaction potential can be expressed as a function of the charge and multipole moments of the solute. For ease... [Pg.26]

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. 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.
As recently as 1965, Thoma and Stewart predicted that alterations in reaction rates [in the presence of the cycloamyloses] should be anticipated whose magnitude and sign will fluctuate with the reaction type, and added that at the present juncture, it is impossible to sort out confidently. . . which factors may contribute importantly to raising or lowering the activation energy of the reaction. In the short interval between 1965 and the present, a wide variety of cycloamylose-induced rate accelerations and decelerations have, indeed, been revealed. More importantly, rate alterations imposed by the cycloamyloses can now be explained with substantially more confidence. The reactions of derivatives of carboxylic acids and organo-phosphorus compounds with the cycloamyloses, for example, proceed to form covalent intermediates. Other types of reactions appear to be influenced by the dielectric properties of the microscopic cycloamylose cavity. Still other reactions may be affected by the geometrical requirements of the inclusion process. [Pg.258]

In this contribution, we describe and illustrate the latest generalizations and developments[1]-[3] of a theory of recent formulation[4]-[6] for the study of chemical reactions in solution. This theory combines the powerful interpretive framework of Valence Bond (VB) theory [7] — so well known to chemists — with a dielectric continuum description of the solvent. The latter includes the quantization of the solvent electronic polarization[5, 6] and also accounts for nonequilibrium solvation effects. Compared to earlier, related efforts[4]-[6], [8]-[10], the theory [l]-[3] includes the boundary conditions on the solute cavity in a fashion related to that of Tomasi[ll] for equilibrium problems, and can be applied to reaction systems which require more than two VB states for their description, namely bimolecular Sjy2 reactions ],[8](b),[12],[13] X + RY XR + Y, acid ionizations[8](a),[14] HA +B —> A + HB+, and Menschutkin reactions[7](b), among other reactions. Compared to the various reaction field theories in use[ll],[15]-[21] (some of which are discussed in the present volume), the theory is distinguished by its quantization of the solvent electronic polarization (which in general leads to deviations from a Self-consistent limiting behavior), the inclusion of nonequilibrium solvation — so important for chemical reactions, and the VB perspective. Further historical perspective and discussion of connections to other work may be found in Ref.[l],... [Pg.259]

As indicated, the power law approximations to the fS-correlator described above are only valid asymptotically for a —> 0, but corrections to these predictions have been worked out.102,103 More important, however, is the assumption of the idealized MCT that density fluctuations are the only slow variables. This assumption breaks down close to Tc. The MCT has been augmented by coupling to mass currents, which are sometimes termed inclusion of hopping processes, but the extension of the theory to temperatures below Tc or even down to Tg has not yet been successful.101 Also, the theory is often not applied to experimental density fluctuations directly (observed by neutron scattering) but instead to dielectric relaxation or to NMR experiments. These latter techniques probe reorientational motion of anisotropic molecules, whereas the MCT equation describes a scalar quantity. Using MCT results to compare with dielectric or NMR experiments thus forces one to assume a direct coupling of orientational correlations with density fluctuations exists. The different orientational correlation functions and the question to what extent they directly couple to the density fluctuations have been considered in extensions to the standard MCT picture.104-108... [Pg.29]

We take as our model of an inhomogeneous medium a two-component mixture composed of inclusions embedded in an otherwise homogeneous matrix, where e and are their respective dielectric functions. The inclusions are identical in composition but may be different in volume, shape, and orientation we shall restrict ourselves, however, to ellipsoidal inclusions. The average electric field (E) over a volume V surrounding the point x is defined as... [Pg.214]

Note that (8.49), which is a generalization of the Maxwell Garnett dielectric function (8.50), is not invariant with respect to interchanging the roles of matrix and inclusions if we make the substitutions e - em, em - t, and f - (1 — /), then eav is not, in general, unchanged. If, therefore, a two-component mixture is to be described by (8.49), a choice must be made as to which component is the matrix and which the inclusions (there may be physical reasons to guide this choice). The limiting values of eav are independent of 0 ... [Pg.216]

It is not difficult to extend (8.49) or (8.47) to multicomponent mixtures. If we make the same assumptions for each inclusion that were made preceding (8.48), then the average dielectric function is... [Pg.216]

An approach somewhat similar to that in Section 8.5 was taken by O Neill and Ignatiev (1978), who obtained an expression for the average dielectric function of a mixture containing spheroidal inclusions with ratios of semi-minor to semimajor axes given by a probability distribution function. [Pg.225]

The examples from the literature demonstrate the powerful methods available for the determination of the secondary structure. Although most of the referred studies have not included solvent interactions, the preferred conformation of the oligosaccharides when dissolved in water do not seem to be dependent on the inclusion of the water interaction. In contrast to this, the inclusion of polar terms in the calculation of the oligosaccharides causes problems and often leads to the prediction of wrong conformations, because of the difficulty of assessing the magnitude of the dielectricity constant in close proximity. [Pg.203]

The dielectric properties of charged inclusions contain an extra component due to double layer p olarization... [Pg.245]


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See also in sourсe #XX -- [ Pg.475 , Pg.498 ]




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