Units dipole moment

Here Pi is the macroscopic induced polarization and for molecular materials, a, p, and y related to their macroscopic counterparts (1) (2) gjjjj (3) where polarization is dipole moment/unit volume. 

Table 13 Values of Restricted Bond Dipole Moments (units of 10 eA) ...

Fig. 17. Distribution of the cosine of the angle 3 between the dipole moment unit vector of the adsorbed water molecules fi) and the surface normal (z), which points into the liquid phase, for various homogeneous surface charge densities which are given in units of pC cm on the graphs. Data are from simulations of 700 TIP4P water molecules between Hg lll) surfaces.

Electric dipole moment unit—coulomb X meter (dipole electric moment of a pair of opposite charges equal in value and being 1 m apart)... 

The atomic unit (AU) of dipole moment is that of a proton and electron separated by a distance equal to the first Bohr orbit, oq. Similarly, the au of polarizability is Oq [125]. Express and o for NH3 using both the cgs/esu and SI approach. 

In order to describe the second-order nonlinear response from the interface of two centrosynnnetric media, the material system may be divided into tlnee regions the interface and the two bulk media. The interface is defined to be the transitional zone where the material properties—such as the electronic structure or molecular orientation of adsorbates—or the electromagnetic fields differ appreciably from the two bulk media. For most systems, this region occurs over a length scale of only a few Angstroms. With respect to the optical radiation, we can thus treat the nonlinearity of the interface as localized to a sheet of polarization. Fonnally, we can describe this sheet by a nonlinear dipole moment per unit area, -P ", which is related to a second-order bulk polarization by hy P - lx, y,r) = y. Flere z is the surface nonnal direction, and the... 

In stead, the electrostatic con tribn tion conies from definin g a set of bond dipole moments associated woth polar bonds. These bond moments are defined in the m m psir.LxL(dbf) file along with the bond stretching parameters and are given in units of Debyes. The cen ter of th e dipole Is defined to be th e m Idpoint of the bond an d two dipoles p. and pj. separated by Rjj. as shown beltnv ... 

Here r is the vector giving, together with e, the unit charge, the quantum mechanical dipole moment operator... 

Because the charge on an electron is 4 80 X 10 electrostatic units (esu) and the dis tances within a molecule typically fall m the 10 cm range molecular dipole moments... 

Debye unit (D) (Section 1 5) Unit customanly used for mea sunng dipole moments... 

Dipole moment (Section 1 5) Product of the attractive force between two opposite charges and the distance between them Dipole moment has the symbol p- and is measured in Debye units (D)... 

Figure 4 shows the measured angle of 105° between the hydrogens and the direction of the dipole moment. The measured dipole moment of water is 1.844 debye (a debye unit is 3.336 x 10 ° C m). The dipole moment of water is responsible for its distinctive properties in the Hquid state. The O—H bond length within the H2O molecule is 0.96 x 10 ° m. Dipole—dipole interaction between two water molecules forms a hydrogen bond, which is electrostatic in nature. The lower part of Figure 4 (not to the same scale) shows the measured H-bond distance of 2.76 x 10 ° m or 0.276 nm. 

The dipole moment in Eq. (2-73) is in debyes, while P is in atm and is in K. Units must be watched carefully. For hydrogen-bonding molecules, Eq. (2-71) can be used with a value of Bo calculated by Eq. 

The dipole moment of a molecule is another additive property since it arises from the difference in electronegativity of two atoms connected by a double bond. It should therefore be possible to associate a dipole moment with every linkage. Eucken and Meyer" have suggested the following moments for various linkages (in units of 10 e.s.cm)... 

The unequal distribution of electron density in covalent bonds produces a bond dipole, the magnitude of which is expressed by the dipole moment, having the units of charge times distance. Bonds with significant bond dipoles are described as being polar. The bond and group dipole moments of some typical substituents are shown in Table 1.7. 

The dipole moment p. is a molecular property defined as the product of charge (usually just a fraction of the electronic change, of course) and distance between the centers of positive and negative charge in the molecule. The dipole moment is usually expressed in debyes (D), where 1 D = 1(T esu in SI units 1 D = 3.3356 X 10 ° C-m. so, for example, the dipole moment of water is 1.84 D or 6.14 in units of 10 C-m. Again a rough correspondence is seen between this property of a molecule and its polarity, though e and p. are not precisely correlated. 

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 ... 

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