Units electric dipole moments

A ferroelectric crystal is one that has an electric dipole moment even in the absence of an external electric held. This arises because the centre of positive charge in the crystal does not coincide with the centre of negative charge. The phenomenon was discovered in 1920 by J. Valasek in Rochelle salt, which is the H-bonded hydrated d-tartrate NaKC4H406.4H 0. In such compounds the dielectric constant can rise to enormous values of lO or more due to presence of a stable permanent electric polarization. Before considering the effect further, it will be helpful to recall various dehnitions and SI units ... 

Molecules do not consist of rigid arrays of point charges, and on application of an external electrostatic field the electrons and protons will rearrange themselves until the interaction energy is a minimum. In classical electrostatics, where we deal with macroscopic samples, the phenomenon is referred to as the induced polarization. I dealt with this in Chapter 15, when we discussed the Onsager model of solvation. The nuclei and the electrons will tend to move in opposite directions when a field is applied, and so the electric dipole moment will change. Again, in classical electrostatics we study the induced dipole moment per unit volume. 

The electric dipole moments in units 1 X 10 18 e. s. u. of these molecules and their derivatives by hydrogenation measured19 in benzene solution are the following furan, 0.670 2,5-di-hydrofuran, 1.53 tetrahydrofuran, 1.68 pyrrole, 1.80 pyrroline, 1.42 pyrrolidine, 1.57 thiophene, 0.54 and tetrahydrothiophene, 1.87. We now give a very rough interpretation of these quantities based on the bond moments given... 

When the net charge on a species is zero but its electric dipole moment p is nonzero, classical electrostatics predicts that the interaction with an ion is described by an ion dipole interaction of the form (in atomic units)... 

The earliest approach to explain tubule formation was developed by de Gen-nes.168 He pointed out that, in a bilayer membrane of chiral molecules in the Lp/ phase, symmetry allows the material to have a net electric dipole moment in the bilayer plane, like a chiral smectic-C liquid crystal.169 In other words, the material is ferroelectric, with a spontaneous electrostatic polarization P per unit area in the bilayer plane, perpendicular to the axis of molecular tilt. (Note that this argument depends on the chirality of the molecules, but it does not depend on the chiral elastic properties of the membrane. For that reason, we discuss it in this section, rather than with the chiral elastic models in the following sections.)... 

All of the above-mentioned active materials show a crystal structure characterized by a continuous network of corner shared octahedral units of metal cations (TaC>6, NbOg, Ti06), which presumably allows for high charge carriers mobilities and efficient charge separation. A relevant role of local electric dipole moments cannot be excluded [111] (see also below). 

Dielectric polarization is the polarized condition in a dielectric resulting from an applied AC or DC field. The polarizability is the electric dipole moment per unit volume induced by an applied field or unit effective intensity. The molar polarizability is a measure of the polarizability per molar volume thus it is related to the polarizability of the individual molecules or polymer repeat unit. 

Let us first consider the dielectric constant of a gas. We assume that the molecules are far enough apart for them to contribute independently to the polarization and that the electric field E induces an electric dipole moment aE in each molecule. The quantity a is called the electric polarizability of the molecule. The number of moles per unit volume of gas is the density p divided by the tnolecular weight M, and the number of molecules in unit volume is this ratio multiplied by Avogadro s number A. Hence the polarization of the gas (the induced dipole moment per unit volume) is given by the following equation ... 

Material Media and Their Reaction to External Fields. In a material medium, a charge distribution can induce some charge separations, or dipoles, which help to minimize the total energy. Similarly, an external magnetic field will induce some magnetic dipoles in the medium to counteract this field. To handle these effects, an electric polarization (or electrical dipole moment per unit volume) P and a magnetization (or magnetic dipole moment per unit volume) M are defined. If the medium is linear and isotropic, these two new vectors P and M are proportional to E and to H, respectively ... 

Table 8.16. Molecular parameters for H35 Cl determined from the electric resonance spectra. All parameters are in kHz except for the electric dipole moment, n(v), which is in Debye units (D). The rotational and centrifugal distortion constants were obtained by Rank, Rao and Wiggins [102], S]2 is the spin-spin interaction constant, equal to [gig2ii2N(no/47t)/(2J + 3)(2J - 1)](R 3)vj...

Here the sum is over the three space-fixed cartesian axes and pp is a space-fixed component of the electric dipole moment. Inserting values for the fundamental constants the relation between Gji and Mji may be expressed in practical units as... 

To add to the confusion noted for conventions of polarizabilities, both cgs and recommended SI units for linear and non-linear optical polarizabilities coexist in the literature. We strongly advocate the use of SI units. The SI unit of the electric dipole moment is Cm (Cohen and Giacomo, 1987). Thus, consistent SI units of an nth-order polarizability are defined as C m(mV )" = C m " V ", cf. (34)-(37). Conversions from the SI to the esu system for the dipole moment, the first-, second-, and third-order polarizability, are given in (38)-(41). 

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