Orientation of dipoles

Figure 4-16 Orientation of Dipole Moment Vectors to give Vj,.

When A = B, the expression at Eq. (8) represents the usual interaction energy of permanent dipoles. When A < B, parallel orientations of dipoles are favoured and when A > B, the interaction energy has a minimum for antiparallel dipoles. 

Fig. 2.9. Ground state for a square lattice of dipoles a. Orientations of dipole moments b. wave vectors of the structure in the first Brillouin zone c. and d. orientations of dipole moments in infinitely small and large external electric fields, respectively.

The parallel or antiparallel orientations of dipoles to each other may form certain angles 9 or 9k with the Ox axis of the lattice, which is drawn along the chains with the smallest intersite distances46 (ai a2 < aj - a2 < ai + a2 ). The energies of these ground states can also be conveniently calculated in the chain representation with somewhat more awkward46 expressions than Eqs. (2.2.10) and (2.2.11). 

Note in figure 9.1 that bulk potential depends greatly on the mutual orientation of dipoles molecules with parallel dipoles form more stable bonds than molecules with antiparallel dipoles. Note, moreover, as already stated, that repulsive and dispersive forces are not alfected by the state of dipole orientation. 

The potential due to the net preferential orientation of dipoles in the inlcrphase region... 

What happens when the metal is charged Would other types of forces be involved The forces of attraction between the metal and the water molecules still operate, but in addition, the charge on the metal will stimulate the water molecules to orient themselves. The process is similar to the orientation of dipoles in the solvent sheath around an ion (see Chapter 2). 

The orientation of dipoles can be assessed by comparing otherwise identical molecules. For example, amino is electron releasing and nitro is electron withdrawing. The molecular dipoles (1.53 D for aniline and 4.22 D for nitrobenzene) add to give an overall molecular dipole of 6.3 D for 4-nitroaniline. The importance of two polar C—O bonds should be large... 

The electrostatic free energy of ionization, as calculated from (11) with ZA = +1 and ZB = — 1, is always positive. The quantity d In D/dT is always negative because thermal motion overcomes the orientation of dipoles in an electric field therefore A8el is always negative. The values of D, AFel, AHa, and ASel for several representative solvents are given in Table 8 (Frost and Pearson, 1961). Comparison with the data in... 

In the case of a liquid phase, the/ potential is associated with the net preferential orientation of dipoles at the surface. This arrangement is equivalent to a charge separation and a potential difference occurs across the surface dipole layer. The estimation of / remains unsolved [8]. 

It may be convenient to regard the Galvani potential difference between two phases in contact as being due to two effects the orientation of dipoles in the interface between them and the separation of independently mobile charged species across the phase boundary in an analogous way to that discussed for the separation of (f> into outer and surface potentials [5, 6]. 

There also exist dispersion, or London-van der Waals forces that molecules exert towards each other. These forces are usually attractive in nature and result from the orientation of dipoles, and may be dipole-dipole (Keesom dispersion forces), dipole-induced dipole (Debye dispersion forces), or induced dipole-induced dipole... 

Van der Waals postulated that neutral molecules exert forces of attraction on each other which are caused by electrical interactions between dipoles. The attraction results from the orientation of dipoles due to any of (1) Keesom forces between permanent dipoles, (2) Debye induction forces between dipoles and induced dipoles, or (3) London-van der Waals dispersion forces between fluctuating dipoles and induced dipoles. (The term dispersion forces arose because they are largely determined by outer electrons, which are also responsible for the dispersion of light [272].) Except for quite polar materials the London-van der Waals dispersion forces are the more significant of the three. For molecules the force varies inversely with the sixth power of the intermolecular distance. 

The total electrostatic free energy per unit area, between the two parallel plates, due to the orientation of dipoles m z) in the local field E = m(z)/y is given by26... 

D. This wave is p-polarized, giving information about the spatial orientation of dipoles interacting with the SPP. 

For ideally polarizable electrodes - since as a whole, the double layer is electrically neutral - the absolute value of the -> surface charge on the metal (opposite charge accumulated at the solution phase near the metal (surface charge density and for the ideally polarizable electrode it is equal to the surface charge density (Q), i.e., electrocapillary measurements. When oM = os = 0, i.e., at the -> potential of zero charge (pzc, Ea = Eq = 0) the - Galvani potential difference between the two phases is due to the orientation of dipoles (e.g., water molecules) [i.v]. 

Fig. 11 Relative size and orientation of dipole moment vectors of the ground state black) and the excited states JMLCT (bJA ), 3IL (b3A"), and 3MLCT (a3A") of [Re(Etpy)(CO)3(bpy)]+, projected onto the optimized ground-state molecular structure. Dipole moment vectors originate in the center of charge calculated using Mulliken population analysis. They lie in the molecular symmetry plane. (Calculated by TD-DFT G03/PBE0/vacuum at the optimized ground state geometry.) Reproduced with permission from [76]...

Comparing Equations (3.55) and (3.56) with the Debye Equations (3.25) and (3.26), we can appreciate that the composite displays a dielectric relaxation that is indistinguishable in form from that due to orientation of dipoles. Equation (3.59) shows that the relaxation time decreases as the conductivity... 

Fig. 2.26. The orientation of dipoles in the dielectric sets up an internal field that is directed counter to the external field produced by the charges on the plates.

Some difficulties in comparing the experimental kinetic data with the outer-sphere reorganization energy calculated from the Marcus formula (28) result from several assumptions made in this theory. The reactant was assumed to have a spherical shape with a symmetric charge distribution. No field penetration into the metal was considered. Also, the spatial dispersion of the dielectric permittivity of the medium was not taken into account. In fact, the positions and orientations of dipoles around a given ion are correlated with each other therefore the reorientation of one dipole, under the influence of the external field, changes to some extent the reorientation of other dipoles within the distance defined by the correlation length. 

III) When there are charges on the surface, their effect on the water structure, notably on the orientation of dipoles, is only noted in the very few first layers adjacent to the surface. If this observation is confirmed then there is an argument for considering water in the diffuse part of a double layer (sec. 3.5) as having bulk properties. 

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