Dielectric relative

The same idea was actually exploited by Neumann in several papers on dielectric properties [52, 69, 70]. Using a tin-foil reaction field the relation between the (frequency-dependent) relative dielectric constant e(tj) and the autocorrelation function of the total dipole moment M t] becomes particularly simple ... 

Li) he so-called distance-dependent dielectric models. The simplest implementation of a dis-i.iiice-dependent dielectric is to make the relative permittivity proportional to the distance. Tine interaction energy between two charges qi and qj then becomes ... 

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. 

The dielectric constant is a property of a bulk material, not an individual molecule. It arises from the polarity of molecules (static dipole moment), and the polarizability and orientation of molecules in the bulk medium. Often, it is the relative permitivity 8, that is computed rather than the dielectric constant k, which is the constant of proportionality between the vacuum permitivity so and the relative permitivity. 

If this electrostatic treatment of the substituent effect of poles is sound, the effect of a pole upon the Gibbs function of activation at a particular position should be inversely proportional to the effective dielectric constant, and the longer the methylene chain the more closely should the effective dielectric constant approach the dielectric constant of the medium. Surprisingly, competitive nitrations of phenpropyl trimethyl ammonium perchlorate and benzene in acetic anhydride and tri-fluoroacetic acid showed the relative rate not to decrease markedly with the dielectric constant of the solvent. It was suggested that the expected decrease in reactivity of the cation was obscured by the faster nitration of ion pairs. 

Solvent Effects on the Rate of Substitution by the S l Mechanism Table 8 6 lists the relative rate of solvolysis of tert butyl chloride m several media m order of increasing dielectric constant (e) Dielectric constant is a measure of the ability of a material m this case the solvent to moderate the force of attraction between oppositely charged par tides compared with that of a standard The standard dielectric is a vacuum which is assigned a value e of exactly 1 The higher the dielectric constant e the better the medium is able to support separated positively and negatively charged species 8olvents... 

Solvent Structural formula Dielectric constant e Type of solvent Relative rate... 

The dielectric constant (permittivity) tabulated is the relative dielectric constant, which is the ratio of the actual electric displacement to the electric field strength when an external field is applied to the substance, which is the ratio of the actual dielectric constant to the dielectric constant of a vacuum. The table gives the static dielectric constant e, measured in static fields or at relatively low frequencies where no relaxation effects occur. 

This result, called the Clausius-Mosotti equation, gives the relationship between the relative dielectric constant of a substance and its polarizability, and thus enables us to express the latter in terms of measurable quantities. The following additional comments will connect these ideas with the electric field associated with electromagnetic radiation ... 

Under the same conditions. Maxwell s theory of radiation shows that the refractive index and the relative dielectric constant are simply related by... 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

In a medium where the relative dielectric constant is e, the force between fixed chages at a definite separation is decreased by the dimensionless factor e. This is true regardless of the system of units and is incorporated into Eqs. (10.101) and (10.102) by dividing the right-hand side of each by e. ... 

Relaxor Ferroelectrics. The general characteristics distinguishing relaxor ferroelectrics, eg, the PbMg 2N b2 302 family, from normal ferroelectrics such as BaTiO, are summari2ed in Table 2 (97). The dielectric response in the paraelectric-ferroelectric transition region is significantly more diffuse for the former. Maximum relative dielectric permittivities, referred to as are greater than 20,000. The temperature dependence of the dielectric... 

The 2eta potential (Fig. 8) is essentially the potential that can be measured at the surface of shear that forms if the sohd was to be moved relative to the surrounding ionic medium. Techniques for the measurement of the 2eta potentials of particles of various si2es are collectively known as electrokinetic potential measurement methods and include microelectrophoresis, streaming potential, sedimentation potential, and electro osmosis (19). A numerical value for 2eta potential from microelectrophoresis can be obtained to a first approximation from equation 2, where Tf = viscosity of the liquid, e = dielectric constant of the medium within the electrical double layer, = electrophoretic velocity, and E = electric field. 

Electrical Properties. Like unfluorinated siHcone counterparts, fluorosihcone elastomers have inherently good electrical insulating properties. The dielectric properties remain relatively unchanged when the elastomer is exposed to severe environments. 

Most glass-ceramics have low dielectric constants, typically 6—7 at 1 MHz and 20°C. Glass-ceramics comprised primarily of network formers can have dielectric constants as low as 4, with even lower values (K < 3) possible in microporous glass-ceramics (13). On the other hand, very high dielectric constants (over 1000) can be obtained from relatively depolymerized glasses with crystals of high dielectric constant, such as lead or alkaline earth titanate (11,14). 

Solvent Polarity and Temperature. The dielectric constant and polarizabihty are of Htde predictive value for the selection of solvents relative to polymerization rates and behavior. In spite of the similarity of the dielectric constants of CH2CI2, CH Cl, and C2H C1 these solvents yield quite different isobutylene polymerization rates that decrease in the same order. 

For most commercial voltages and frequencies used in power distribution, the capacitance effects are negligible. At relatively high voltages the current due to capacitance may reach sufficient value to affect the circuit, and insulation for such an appHcation is designed for a moderately low dielectric constant. 

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