Permittivity dielectric medium

The uncharged ion is transferred into a solvent with permittivity e = De0y where D is the relative permittivity (dielectric constant) of the medium. No work is gained or lost in this process. In the solvent, the ion is again recharged to the value of the electric potential at its surface,... 

The interface is, from a general point of view, an inhomogeneous dielectric medium. The effects of a dielectric permittivity, which need not be local and which varies in space, on the distribution of charged particles (ions of the electrolyte), were analyzed and discussed briefly by Vorotyntsev.78 Simple models for the system include, in addition to the image-force interaction, a potential representing interaction of ions with the metal electrons. 

Thus, we see the initial connection between optical properties and the electrical and magnetic properties from the two previous sections. Substimtion of Eqs. (6.78) and (6.79) into (6.77) shows that the refractive index can be expressed in terms of the relative electric permittivity (dielectric constant), (cf. Table 6.5), and relative magnetic permeability of the medium, (1 - - x) [cf. Eq. (6.63)], where x is the magnetic susceptibility ... 

There are several physical properties of a solvent that are of importance in determining its behavior. Two of the most important from a pragmatic point of view are the melting and boiling points. These determine the liquid range and hence the potential range of chemical operations. More fundamental is the permittivity (dielectric constant). A high permittivity is necessary if solutions of ionic substances are 10 form readily. Coulombic attractions between ions are inversely proportional to the permittivity of the medium ... 

If two charges, qt and q2, are placed at a distance of d meters apart in a dielectric medium of relative permittivity equal to eR, the force (F) acting between the two charges is given by Coulomb s law ... 

We now consider the same parallel-plate condenser immersed in the dielectric medium. The charges on the two plates are represented again by the symbols +Q and — Q. The permittivity of the fluid, s, is defined by... 

A linear dielectric medium is characterized by a linear relation between the polarization density and the electric field, P = e0xE, where eo is the permittivity of free space and x is the electric susceptibility of the medium. A nonlinear dielectric medium, on the other hand, is characterized by a nonlinear relation between P and E, as illustrated in Figure 4.19. 

The quantity er is the relative dielectric constant or permittivity of a dielectric medium, eo = 8.85 x 10 12 As/Vm. The quantity tan 6 represents the loss tangent of a dielectric medium. Metals in the microwave range are usually described by a complex conductivity with dominant real part for normal metals and dominant imaginary part for superconductors. 

The dispersion interaction between an atom and a metal surface was first calculated by Lennard-Jones in 1932, who considered the metal as a perfect conductor for static and time-dependent fields, using a point dipole for the molecule [44], Although these results overestimate the dispersion energy, the correct l/d3 dependence was recovered (d is the metal-molecule distance). Later studies [45 17] extended the work of Lennard-Jones to dielectrics with a frequency-dependent dielectric constant [48] (real metals may be approximated in this way) and took into account electromagnetic retardation effects. Limiting ourselves to small molecule-metal distances, the dispersion interaction of a molecule characterized by a frequency-dependent isotropic polarizability a embedded in a dielectric medium with permittivity esol (note that no cavity is built around the molecule) reads ... 

Not to be forgotten is the assumption that neither the presence of the electrolyte nor the interface itself changes the dielectric medium properties of the aqueous phase. It is assumed to behave as a dielectric continuum with a constant relative dielectric permittivity equal to the value of the bulk phase. The electrolyte is presumed to be made up of point charges, i.e. ions with no size, and responds to the presence of the charged interface in a competitive way described by statistical mechanics. Counterions are drawn to the surface by electrostatic attraction while thermal fluctuations tend to disperse them into solution, surface co-ions are repelled electrostatically and also tend to be dispersed by thermal motion, but are attracted to the accumulated cluster of counterions found near the surface. The end result of this electrical-thermodynamic conflict is an ion distribution which can be represented (approximately) by a Boltzmann distribution dependent on the average electrostatic potential at an arbitrary point multiplied by the valency of individual species, v/. 

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. 

Dielectric relaxation — Dielectric materials have the ability to store energy when an external electric field is applied (see -> dielectric constant, dielectric - permittivity). Dielectric relaxation is the delayed response of a dielectric medium to an external field, e.g., AC sinusoidal voltage, usually at high frequencies. The resulting current is made up of a charging current and a loss current. The relaxation can be described as a frequency-dependent permittivity. The real part of the complex permittivity (e1) is a measure of how much energy from an external electric field is stored in a material, the imaginary part (e") is called the loss factor. The latter is the measure of how dissipative a material is to an exter-... 

Molecular distortion polarizability is a measure of the ease with which atomic nuclei within molecules tend to be displaced from their zero-field positions by the applied electric field. (3) Orientation polarizability is a measure of the ease with which dipolar molecules tend to align against the applied electric field. The electron polarizability of an individual molecule is related to the -> permittivity (relative) of a dielectric medium by the -> Clausius-Mossotti relation. 

Polarization density (of a dielectric medium) — The polarization density P is the difference between the electric displacement in a - dielectric medium Dc and the electric displacement in a vacuum Do- (Note The electric displacement is defined as the product of the electric field strength E and the - permittivity e.) The polarization density of a dielectric medium may also be... 

The Polarizable Continuum Model (PCM)[18] describes the solvent as a structureless continuum, characterized by its dielectric permittivity e, in which a molecular-shaped empty cavity hosts the solute fully described by its QM charge distribution. The dielectric medium polarized by the solute charge distribution acts as source of a reaction field which in turn polarizes back the solute. The effects of the mutual polarization is evaluated by solving, in a self-consistent way, an electrostatic Poisson equation, with the proper boundary conditions at the cavity surface, coupled to a QM Schrodinger equation for the solute. 

This also means that the permittivity of a dielectric medium, e(ir), is exactly the same as the relative permittivity or dielectric constant er, so that only one of these quantities is required—which is usually simply called the permittivity, e. Finally, since e0(ir) = h equations (3) and (5) require that /io(ir) = 1/co2. 

The electric field flux within a fluid volume of charge density pe in a continuous dielectric medium, such as water, can be described in terms of the permittivity... 

Many of the different susceptibilities in (18)-(21) correspond to important experiments in linear and non-linear optics. The argument in parentheses again describes the kind of interacting waves. TWo waves interact in a first-order process as described above in (9), three waves in a second-order process, and four in a third-order process. x ° describes a possible zeroth-order (permanent) polarization of the medium t- (0 0) is the first-order static susceptibility which is related to the relative permittivity (dielectric constant) at zero frequency, e,.(0), by (22). 

Here Cyoi is the capacitance per unit volume k, the dielectric constant (or, relative permittivity), and t is the thickness of the dielectric medium. 

A. 15.5 Three of the following. (1) A central reference ion of a specific charge can be represented as a point charge. (2) This central ion is surrounded by a cloud of smeared-out charge contributed by the participation of all of the other ions in solution. (3) The electrostatic potential field in the solution can be described by an equation that combines and linearizes the Poisson and Boltzmann equations. (4) No ion — ion interactions except the electrostatic interaction given by a l/z dependence are to be considered (i.e., dispersion forces and ion - dipole forces are to be excluded). (5) The solvent simply provides a dielectric medium, and the ion — solvent interactions are to be ignored, so that the bulk permittivity of the solvent can be used. 

The Born model [11] provides a means of estimating the Gibbs energy of solvation for an ion in an infinitely dilute solution. It is based on a continuum description of the solvent as a uniform dielectric with a relative permittivity of The work of transferring the ion from vacuum to the dielectric medium is estimated on the basis of the following three-step process (a) the ion is reversibly discharged in vacuum (b) the discharged ion, which is assumed to be a sphere of radius, r, is... 

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