Relative permittivity defined

The influence of a particular dielectric on the capacitance of a condenser is conveniently assessed by the dielectric constant, also known as the relative permittivity or rarely specific inductive capacity. This is defined as the ratio of the relative condenser capacity, using the given material as a dielectric, to the capacity of the same condenser, without dielectric, in a vacuum (or for all practical intents and purposes, air). 

The insulating property of any insulator will break down in a sufficiently strong electric field. The dielectric strength is defined as the electric strength (V/m) which an insulating material can withstand. For plastics the dielectric strength can vary from 1 to 1000 MV/m. Materials may be compared on the basis of their relative permittivity (or dielectric constant). This is the ratio of the permittivity of the material to the permittivity of a vacuum. The ability of a... 

In addition to the Peclet number, one can also define other dimensionless groups that compare either relevant time scales or energies of interaction. Using some of the concepts previewed in Section 4.7c and Table 4.4, one can define an electrostatic group (in terms of the zeta potential f and relative permittivity cr of the liquid) as... 

These properties are sometimes grouped as the dielectric properties but this is not entirely logical as dielectric simply means insulating. Relative permittivity of a material can, for practical purposes, be defined as the ratio of the capacitance of a condenser having the material as the dielectric to the capacitance of a similar condenser having air, or more precisely, a vacuum as the dielectric. The word relative is usually dropped and the property simply called permittivity and is the same thing as used to be called dielectric constant (this term is apparently still used in the USA). 

The dielectric constant (or relative permittivity) is usually expressed using the symbol c. The dielectric e is defined as the ratio of electric fields EJE for a vacuum and a substance placed between the plates of a capacitor. The dielectric constant of a vacuum is 1 and substances that can orient to greater or lesser extents in the applied field will have higher dielectric constants. The dielectric constant of heptane at 20°C is 1.9. Acetonitrile, CH3C=N , has a dielectric constant at 20°C of 37.5. The dielectric constant for water is near 80. 

The relative permittivity tensor for the system ik is defined (see, for example, Born and Wolf 1970 Landau et al. 1987) by the relation... 

The written relations define the relative permittivity tensor for the system, which is formulated below to within second-order terms in the orientation tensor... 

Equation (10.6), formulated in the previous section, defines the relative permittivity tensor in terms of the mean orientation of certain uniformly distributed anisotropic elements, which we shall interpret here as the Kuhn segments of the model of the macromolecule described in Section 1.1. We shall now discuss the characteristic features of a polymer systems, in which the segments of the macromolecule are not independently distributed but are concentrated in macromolecular coils. 

Let us consider the anisotropy of polymer system undergoing simple steady-state shear. This situation can be realised experimentally in a simple way (Tsvetkov et al. 1964). The quantity measured in experiment are the birefringence An and the extinction angle x which are defined by formulae (10.19) and (10.20), correspondingly, through components of the relative permittivity tensor. 

One can turn to discussion of the dynamo-optical coefficient, defined by equation (10.22). The expression for the relative permittivity tensor (10.10) and equation (2.41) for the moments allow one to write... 

Relative - permittivity of a dielectric (an electronic - insulator) or relative dielectric constant or, shorter, dielectric constant er is the proportionality constant between the electric field strength and the charge density for a plate condenser with a dielectric medium between the two plates. In case of vacuum this constant is called the permittivity of free space 0 and its value is 8.85418782 x 10-12 CV 1m 1. When a dielectric is present between the two plates, an increase of the charge density is observed compared to the case with a vacuum. This relative increase is called the relative dielectric constant er, i.e., it is unity for vacuum. The dielectric constant can be determined from the capacity of a condenser with the dielectric to be studied between the plates. The electric susceptibility of the dielectric is defined as = cr - 1. 

The dielectric susceptibility, like magnetic suscephbUity, is a second-rank tensor. The dielectric constant (also known as the relative permittivity), k, is defined as ... 

Since both the relative permittivity and the dipole moment p are important complementary solvent properties, it has been recommended that organic solvents should be classified according to their electrostatic factor EE (defined as the product of r... 

Evidently, solvent polarity , as so-defined, is badly described in a quantitative manner by means of individual physical constants such as relative permittivity, dipole moment, etc. It is no surprise therefore, that the macroscopic relative permittivities are an unsuitable measure of molecular-microscopic interactions. This has often been demonstrated experimentally. One reason is that the molecular-microscopic relative permit-... 

Another problem that has been tackled by multivariate statistical methods is the characterization of the solvation capability of organic solvents based on empirical parameters of solvent polarity (see Chapter 7). Since such empirical parameters of solvent polarity are derived from carefully selected, strongly solvent-dependent reference processes, they are molecular-microscopic parameters. The polarity of solvents thus defined cannot be described by macroscopic, bulk solvent characteristics such as relative permittivities, refractive indices, etc., or functions thereof. For the quantitative correlation of solvent-dependent processes with solvent polarities, a large variety of empirical parameters of solvent polarity have been introduced (see Chapter 7). While some solvent polarity parameters are defined to describe an individual, more specific solute/solvent interaetion, others do not separate specific solute/solvent interactions and are referred to as general solvent polarity scales. Consequently, single- and multi-parameter correlation equations have been developed for the description of all kinds of solvent effects, and the question arises as to how many empirical parameters are really necessary for the correlation analysis of solvent-dependent processes such as chemical equilibria, reaction rates, or absorption spectra. 

A second limitation of the Hughes-Ingold theory concerns the fact that the solvent is treated as dielectric continuum, characterized by one of the following its relative permittivity, e, the dipole moment, fi, or by its electrostatic factor, EF, defined as the product of and [27]. The term solvent polarity refers then to the ability of a solvent to interact electrostatically with solute molecules. It should be remembered, however, that solvents can also interact with solute molecules through specific inter-molecular forces like hydrogen bonding or EPD/EPA complexation cf. Section 2.2). For example, specific solvation of anionic solutes by pro tic solvents may reduce their nucleophilic reactivity, whereas in dipolar aprotic solvents solvation of anions is less,... 

Here and t] are, respectively, the relative permittivity and the viscosity of the electrolyte solution. This formula, however, is the correct limiting mobility equation for very large particles and is valid irrespective of the shape of the particle provided that the dimension of the particle is much larger than the Debye length 1/k (where k is the Debye-Htickel parameter, defined by Eq. (1.8)) and thus the particle surface can be considered to be locally planar. For a sphere with radius a, this condition is expressed by Ka l. In the opposite limiting case of very small spheres (Ka 3> 1), the mobility-zeta potential relationship is given by Hiickel s equation [2],... 

The investigation of the absorption [47] has shown that in the temperature interval between two phase transitions (T, 120 K to To = 213 K) the relative intensities of the absorption maximum (for the lattice 99-cm 1 mode) and the scattering maximum (for the intracellular 756-cm 1 mode) have changed very markedly. The first mode decreased by approximately a factor of two at 213 K. The second one increased by approximately a factor of five at 213 K. Since the imaginary part of the permittivity defines the absorption (scattering) maximum, the expression (D32) has to describe the real temperature behavior of the two aforementioned anomalous modes. 

In this chapter, the properties of polar solvents are discussed, especially as they relate to the formation of electrolyte solutions. Polar solvents are arbitrarily defined here as those liquids with a relative permittivity greater than 15. Solvents with zero dipole moment and a relative permittivity close to unity are non-polar. These include benzene, carbon tetrachloride, and cyclohexane. Solvents with relative permittivities between 3 and 5 are weakly polar, and those with values between 5 and 15 are moderately polar. The latter systems are not considered in the discussion in this chapter. 

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