Orientational energy

Hindered Rotation (Figure 4b). This mode characterizes the orientational energy associated with the bond. For HoO the tilt energy Is very small ( . 1 eV) until the protons get close to the surface and the Coulomb repulsion takes over abruptly, resulting In a... 

For NHj the orientational energy is quite large. However, since in the ground state the permanent dipole is perpendicular to the surface, the dynamical dipole for this mode is zero, so that the mode is EELS-lnactlve. 

Exact Treatment for the Freely Jointed Chain (or Equivalent Chain).4 >5— Consider one of the bonds of a freely jointed chain acted upon by a tensile force r in the x direction. Letting xpi represent the angle between the bond and the o -axis, its component on the x-axis is Xi = l cos pi. The orientation energy of the bond is —rXi, and the probability that its x component has a value between Xi and Xi- -dxi therefore is proportional to... 

The orientation energy—partial reorientation of solvent molecules caused by the presence of the solute. 

AE/kT. The second term gives the deviation from the uniform distribution over attractive and repulsive configurations which results in attraction. It can be seen readily that the Keesom or orientation energy will be proportional to — (n2/r3) (AE/kT), therefore to [j,4/r6 T. The numerical factor 2/3 only appears on accurate averaging by integration over all orientations. 

It is obvious that for larger molecules and for small molecular distances in the solid and liquid state the directive forces are quite insufficiently represented by the dipole action. For these one has simply to replace the left-hand side of (20) by the classical orientation energy in order to obtain a reasonable estimate for the limit of free motion. 

Orientational energy from this source provides the basis for the Maier and Saupe theory asymmetry of molecular shape and its influence on molecular packing in the fluid are not taken into account. Consequently, in order to reconcile this theory with experiments, it has been necessary to postulate unreasonably large orientation-dependent energies and, by implication, excessively large value of Aa... 

There are other forces, principally electrical in nature, present in molecular arrays whose constituents possess a permanent dipole (H2O, NH3). The energy resulting from such dipole-dipole interaction is also called the orientation energy. A charged species can also induce a dipole (induction energy). 

Note that temperature is a parameter of the equation. As the material temperature rises during processing, the value of orientation energy becomes negligible. In a typical system conflicting dipole fields are created which significantly reduce dipole-dipole net interaction. Keesom forces, unlike London forces, do not apply to nonpolar substances because both dipoles, which participate in the interaction, must be permanent dipoles (London forces do not require the presence of permanent dipoles). 

Fig. 2. Results of the DFT calculations for the potential energy of the HOMO in a lying (left side) and a standing (center) monolayer of PEN. The right side shows the DOVS of the two layers with different orientation. Energy reference is the vacuum level (Evac).

See Figure 7-3). Since it turns out that experimentally we are interested in conditions where kT is large compared with orienting energies, the exponential in equation (7-44) may be expanded and terms higher than... 

E20.32(b) The orientational energy of an electron spin system in a magnetic field is =... 

In all important cases, therefore, the potential energy of the attraction varies as , the orientation energy being the only term which depends significantly upon the temperature. 

We assume that each molecule is subject to an average internal field which is independent of any local variations or short-range ordering. Consistent with the symmetry of the structure, viz, the cylindrical distribution about the preferred axis and the absence of polarity, we may postulate that the orientational energy of a molecule... 

The behaviour is slightly more complicated in the case of electric birefringence because, as explained in 2.3.4, the orientational energy in an electric field E arises from the anisotropy of low frequency polarizability and also from the net permanent dipole moment p. An interesting example is that of PAA in which the Kerr constant actually changes sign at about T -I-5K (fig. 2.5.3). The sign reversal is easily understood. The... 

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