Permittivity also

The dielectric permittivity of a medium measures the polarization of the medium per unit applied electric field. The permittivity of free space, e, has the value 8.85 x 10 14 Farads/cm. Throughout this paper, we shall express the dielectric properties of a medium relative to e0. That is, the permittivity of a medium is written e eq, where e is the relative permittivity, also referred to as the dielectric constant of the medium (but remember that the dielectric constant changes with temperature and cure). 

It should be noticed that, in many theoretical works, the term solvent polarity is defined by the values of the relative electric permittivity, also called dielectric constant. However, such a definition is by no means precise. The existence of hydrogen bonds (H-bonds) between solute and solvent molecules is one of the important limitations of the use of the continuum models based on the theory of dielectrics. In modern physical chemistry of solutions in order to quantitatively describe the solvatochromism phenomenon various empirical scales of the polarity are used. The exhaustive reviews on this topic have been presented by Reichardt [1, 2],... 

The properties of the ions and the solvent which are ignored are similar to those ignored in the Debye-Hiickel treatment. These are very important properties at the microscopic level, but it would be a thankless task to try to incorporate them into the treatment used in the 1957 equation. Furthermore, Stokes Law is used in the equations describing the movement of the ions. This law applies to the motion of a macroscopic sphere through a structureless continuous medium. But the ions are microscopic species and the solvent is not structureless and use of Stokes Law is approximate in the extreme. Likewise, the equations describing the motion also involve the viscosity which is a macroscopic property of the solvent and does not include any of the important microscopic details of the solvent structure. The macroscopic relative permittivity also appears in the equation. This is certainly not valid in the vicinity of an ion because the intense electrical field due to an ion will cause dielectric saturation of the solvent immediately around the ion. In addition, alteration of the solvent stmcture by the ion is an important feature of electrolyte solutions (see Section 13.16). However, solvation is ignored. As in the Debye-Hiickel treatment the physical meaning of the distance of closest approach, i.e. a is also open to debate. 

Before beginning a discussion of non-aqueous solvents, we must define the relative permittivity, also referred to as the dielectric constant, of a substance. In a vacuum, the Coulom-bic potential energy of a system of two unit electronic charges is given by equation 8.1 where Eq is the (absolute)... 

Many 1,1-electrolytes show association to aggregates higher than ion pairs in pure solvents of classes 6 and 7 of Table I and in their mixtures of low permittivity, also in mixtures with solvents of other classes, e.g. PC, H O, ROH. The dependence of the... 

With dielectrically anisotropic materials such as textile filaments or fibers, it is important to state the direction of the electric field, and consequently it might in some cases be advisable to make measurements of permittivity in more than one direction. Permittivity also varies with the electrical frequency, and so it is advisable to make measurements of permittivity over as wide a range of frequencies as may be relevant to the material. The results should be plotted as permittivity against logm frequency. A typical plot is illustrated in Fig. 13. 

Relative permittivity also varies with the temperature, as well as frequency, so it is also advisable to determine the permittivity over a range of temperatures relevant to the material operating range, but obviously below the material softening temperature. The results can then be plotted as temperature over logu, frequency. 

Vacuum permittivity, also known as the permittivity of free space. 8.85 X 10- 2 F/m. 

The concept of constant dielectric permittivity in the double layer is also of concern. Different factors such as high ionic concentration or strong electric fields can affect the dielectric permittivity. In addition, description of the dielectric properties of solutions by a single parameter - the dielectric permittivity - also came under criticism and led to the development of nonlocal electrostatics. 

Througjiout this chapter the e parameter will be used in various equations that describe binding forces (such as Eq. 3.1, below). Mathematically, it is defined as the ratio of the permittivity of the medium (e ) to the permittivity of a vacuum ( o)- Hence, e = s lso- Therefore, it is a dimensionless parameter, which is often referred to as the relative permittivity (also known as the dielectric constant). 

The relative permittivity also correlates with refractive index (Fig. 2.3.19). In the case of aliphatic hydrocarbons, the relative permittivity increases slightly as refractive index increases. Both aromatic and aliphatic hydrocarbons have relative permittivities which follow the relation-ship s n. The relative permittivities of alcohols, esters and ketones decrease as the refractive corrstants increase but only alcohols and ketones form a similar relationship. The relative permittivities of ketones poorly correlate with then-refractive indices. 

The coefficients e and ex denote the (relative) dielectric permittivities, also called the dielectric constants, of the liquid crystal when the field and director are parallel and perpendicular, respectively. In terms of no it is simple to verify that (2.81) is equivalent to... 

N is the number of point charges within the molecule and Sq is the dielectric permittivity of the vacuum. This form is used especially in force fields like AMBER and CHARMM for proteins. As already mentioned, Coulombic 1,4-non-bonded interactions interfere with 1,4-torsional potentials and are therefore scaled (e.g., by 1 1.2 in AMBER). Please be aware that Coulombic interactions, unlike the bonded contributions to the PEF presented above, are not limited to a single molecule. If the system under consideration contains more than one molecule (like a peptide in a box of water), non-bonded interactions have to be calculated between the molecules, too. This principle also holds for the non-bonded van der Waals interactions, which are discussed in Section 7.2.3.6. 

Also use constant dielectric Tor MM+aiul OPLS ciilciilatimis. Use the (lislance-flepeiident dielecinc for AMBER and BlO+to mimic the screening effects of solvation when no explicit solvent molecules are present. The scale factor for the dielectric permittivity, n. can vary from 1 to H(l. IlyperChem sets tt to 1. .5 for MM-r. Use 1.0 for AMBER and OPLS. and 1.0-2..5 for BlO-r. 

A fourth correction term may also be required, depending upon the medium that surrounds the sphere of simulation boxes. If the surrounding medium has an infinite relative permittivity (e.g. if it is a conductor) then no correction term is required. However, if the surrounding medium is a vacuum (with a relative permittivity of 1) then the following energy must be added ... 

The apphcation of microwave power to gaseous plasmas is also of interest (see Plasma technology). The basic microwave engineering procedure is first to calculate the microwave fields internal to the plasma and then calculate the internal power absorption given the externally appHed fields. The constitutive dielectric parameters are useful in such calculations. In the absence of d-c magnetic fields, the dielectric permittivity, S, of a plasma is given by equation 10 ... 

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). 

Nonlinear properties of normal dielectrics can be studied in the elastic regime by the method of shock compression in much the same way nonlinear piezoelectric properties have been studied. In the earlier analysis it was shown that the shape of the current pulse delivered to a short circuit by a shock-compressed piezoelectric disk was influenced by strain-induced changes in permittivity. When a normal dielectric disk is biased by an electric field and is subjected to shock compression, a current pulse is also delivered into an external circuit. In the short-circuit approximation, the amplitude of this current pulse provides a direct measure of the shock-induced change in permittivity of the dielectric. 

The dielectric con.stant i.s also referred to a.s relative permittivity by physical chemi.sts. 

In contrast to bilateral triple-ion formation, unilateral triple-ion formation may also occur in solvents of high permittivity, when ion-pair association is increased by noncoulombic specific ion-ion interactions in solvents of low basicity such as PC or AN. Exclusive formation of anionic tripleions [A-C+A-] ", is observed in these solvents when large organic molecular anions A interact with small cations such as Li + or H+. For example, in contrast to lithium acetate in DMSO [97], where ion association is moderate, ion association as well as unilateral triple-ion formation is observed in the solvent PC [105] due to the much lower basicity of this solvent, (see Table 2)... 

The intrinsic properties of an electrolyte evaluated at low concentrations of the salt and from the viscosity and permittivity of the solvent also determine the conductivity of concentrated solutions. Various systems were studied to check this approach. The investigated parameters and effects were ... 

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