Ideal dielectric

Figure 31.14 shows the temperature dependence of the dielectric constant of single-crystal BaTi03. The high value of k appears over a very short temperature range, close to 0c and far from room temperature. For this reason pure BaTiOs is not particularly useful as a dielectric. Ideally k must be... 

Figure 1.7 Normalized SPP dispersion relation for dielectric/ideal-free-electron-plasma interface for Sd = 1 and sa = 2. The straight dotted line represents the dispersion law of electromagnetic waves in a vacuum...

Figure 1.8 Normalized field penetrations for the dielectric/ideal free-electron plasma interface fors = 1 ande = 2.

The locations of the maxima of the -field and the E-field are different depending on the mode chosen for the EPR experuuent. It is desirable to design the cavity in such a way that the B field is perpendicular to the external field B, as required by the nature of the resonance condition. Ideally, the sample is located at a position of maxuuum B, because below saturation the signal-to-noise ratio is proportional to Simultaneously, the sample should be placed at a position where the E-field is a minimum in order to minimize dielectric power losses which have a detrimental effect on the signal-to-noise ratio. 

In the reaction field method, the space surrounding a dipolar molecule is divided into two regions (i) a cavity, within which electrostatic interactions are sunnned explicitly, and (ii) a surrounding medium, which is assumed to act like a smooth continuum, and is assigned a dielectric constant e. Ideally, this quantity will be... 

The first term represents the forces due to the electrostatic field, the second describes forces that occur at the boundary between solute and solvent regime due to the change of dielectric constant, and the third term describes ionic forces due to the tendency of the ions in solution to move into regions of lower dielectric. Applications of the so-called PBSD method on small model systems and for the interaction of a stretch of DNA with a protein model have been discussed recently ([Elcock et al. 1997]). This simulation technique guarantees equilibrated solvent at each state of the simulation and may therefore avoid some of the problems mentioned in the previous section. Due to the smaller number of particles, the method may also speed up simulations potentially. Still, to be able to simulate long time scale protein motion, the method might ideally be combined with non-equilibrium techniques to enforce conformational transitions. 

Solvents exert their influence on organic reactions through a complicated mixture of all possible types of noncovalent interactions. Chemists have tried to unravel this entanglement and, ideally, want to assess the relative importance of all interactions separately. In a typical approach, a property of a reaction (e.g. its rate or selectivity) is measured in a laige number of different solvents. All these solvents have unique characteristics, quantified by their physical properties (i.e. refractive index, dielectric constant) or empirical parameters (e.g. ET(30)-value, AN). Linear correlations between a reaction property and one or more of these solvent properties (Linear Free Energy Relationships - LFER) reveal which noncovalent interactions are of major importance. The major drawback of this approach lies in the fact that the solvent parameters are often not independent. Alternatively, theoretical models and computer simulations can provide valuable information. Both methods have been applied successfully in studies of the solvent effects on Diels-Alder reactions. 

In some cases it is possible to form bridges of metal using air as the dielectric (150). However, if more than two levels of wiring are required then dielectric spacing is necessary. The ideal dielectric film has excellent adhesion and alow dielectric constant to minimize parasitic capacitances. The most common films include siUcon oxide, siUcon nitride, and a number of spin-on dielectrics (216). 

This force equation can now be used to find the force in model systems such as that of an ideal dielectric sphere (relative dielectric constant Ko) in an ideal perfectly insulating dielectric fluid (relative dielectric constant K ). The force can now be written as... 

The satisfactory result shown in Table 12 suggests that one might give a more detailed and quantitative discussion of the variation with temperature. If we are to do this, we need some standard of comparison with which to compare the experimental results. Just as wq compare an imperfect gas with a perfect gas, and compare a non-ideal solution with an ideal solution, so we need a simple standard behavior with which to compare the observed behavior. We obtain this standard behavior if, supposing that. /e is almost entirely electrostatic in origin, we take J,np to vary with temperature as demanded by the macroscopic dielectric constant t of the medium 1 that is to say, we assume that Jen, as a function of temperature is inversely proportional to . For this standard electrostatic term we may use the notation, instead of... 

Carnie and Chan and Blum and Henderson have calculated the capacitance for an idealized model of an electrified interface using the mean spherical approximation (MSA). The interface is considered to consist of a solution of charged hard spheres in a solvent of hard spheres with embedded point dipoles, while the electrode is considered to be a uniformly charged hard wall whose dielectric constant is equal to that of the electrolyte (so that image forces need not be considered). 

The simplest way to treat the solvent molecules of an electrolyte explicitly is to represent them as hard spheres, whereas the electrostatic contribution of the solvent is expressed implicitly by a uniform dielectric medium in which charged hard-sphere ions interact. A schematic representation is shown in Figure 2(a) for the case of an idealized situation in which the cations, anions, and solvent have the same diameters. This is the solvent primitive model (SPM), first named by Davis and coworkers [15,16] but appearing earlier in other studies [17]. As shown in Figure 2(b), the interaction potential of a pair of particles (ions or solvent molecule), i and j, in the SPM are ... 

Replacement of gas by the nonpolar (e.g., hydrocarbon) phase (oil phase) has been sometimes used to modify the interactions among molecules in a spread film of long-chain substances. The nonpolar solvent/water interface possesses an advantage over that between gas and water in that cohesion (i.e., interactions between adsorbed molecules) due to dipole and van der Waals s forces is negligible. Thus, at the oil/water interfaces, the behavior of adsorbates is much more ideal, but quantitative interpretation may be uncertain, in particular for the higher chains, which are predominantly dissolved in the oil phase to an unknown extent. The oil phase is poured on the surface of an aqueous solution. Thus, the hydrocarbon, such as heptane or decane, forms a membrane a few millimeters thick. It is thicker than the adsorbed monolayer. Owing to the small difference in dielectric constant between the air and a hydrocarbon oil, the... 

An ideal (classical) electrostatic capacitor consists of two plane-parallel metal plates having surface areas S and a mutual distance 5, the gap being filled with air or a dielectric layer (the latter variety often is called a film capacitor). When a capacitor is charged (by applying an electrostatic potential difference A / between the two plates), electrical charges +Q m electron deficit) and Q (an efectron excess), which are equal in magnitude but opposite in sign, will accnmulate on the plates. The values of Q are proportional to the potential difference ... 

K = is the reciprocal Debye length and e, is the dielectric constant of the solvent. Through most of what follows we use the ideal conductor approximation, Eq. (66). Ionic effects will be considered in Section IV.D. 

In addition to the nonelectrostatic adsorptive force, there is an image force between a dipole and a metal, which will be present whenever charged or dipolar particles in a medium of one dielectric constant are near a region of another dielectric constant. If the metal is treated as an ideal conductor, the image-force contribution to the energy of a dipole in the electrolyte is proportional to p2j z3, where z is the distance of the dipole from the plane boundary of the metal (considered ideal, with no surface structure), and to 1 + cos2 0. This ideal term is, of course, the same for all metals. If... 

The electric field or ionic term corresponds to an ideal parallel-plate capacitor, with potential drop g (ion) = qMd/4ire. Itincludes a contribution from the polarizability of the electrolyte, since the dielectric constant is included in the expression. The distance d between the layers of charge is often taken to be from the outer Helmholtz plane (distance of closest approach of ions in solution to the metal in the absence of specific adsorption) to the position of the image charge in the metal a model for the metal is required to define this position properly. The capacitance per unit area of the ideal capacitor is a constant, e/Aird, often written as Klon. The contribution to 1/C is 1 /Klon this term is much less important in the sum (larger capacitance) than the other two contributions.2... 

From the point of view of biological relevance ideally EPR spectra should be taken from aqueous solution samples at physiological temperatures. Not-so-ideal reality brings along two major practical problems paramagnetic relaxation and dielectric absorption. 

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