Anisotropy of the polarizability

The first term on the right corresponds to Raleigh scattering. The second term suggests an energy-exchange interaction that depends on the anisotropy of the polarizability and involves frequencies shifted from that of the incident radiation by an amount which depends on twice the rotational or vibrational frequency of the molecules in the sample. 

Note The phenomenon is due primarily to the anisotropy of the polarizability of the scattering medium. 

The anisotropy of the polarizability is described by the tensor invariant y2, which determines the depolarization ratio. This invariant y2 is averaged over all configurations of the chain molecule treated in the RIS approximation, interdependenca of rotations about neighboring bonds is taken into account. 

Here a designates the trace of the polarizability tensor of one molecule (l/47i o) times the factor of a represents the electric fieldstrength of the quadrupole moment q2. Other non-vanishing multipole moments, for example, octopoles (e.g., of tetrahedral molecules), hexadecapoles (of linear molecules), etc., will similarly interact with the trace or anisotropy of the polarizability of the collisional partner and give rise to further multipole-induced dipole components. 

Similarly as the trace, the anisotropy of the polarizability tensor of diatomic colli-sional systems can also be related to some macroscopic properties, namely to the refractive properties of atomic gases. The so-called Kerr constant, the anisotropy of the refractive index in the parallel and perpendicular directions to the external static electric field is given by,... 

This Van der Waals-London attraction is always present, also when there is a bond belonging to one of the other main types of the chemical bond. This interaction is always attractive, non-directional (apart from the anisotropy of the polarizability), non-specific, it does not lead to saturation and it acts only over distances of the order of magnitude of the radius of the particle and is dependent on the degree of polarizability of both particles. 

The association of nitrobenzene and nitronaphthalene in non-polar solvents, such as hexane and carbon tetrachloride, forms an exception. Here the association depends in the first place on interaction of the Keesom type with the very large moment (4.20 D). The stronger association of the last-mentioned compound points, however, in addition to an interaction due to complex resonance as observed between nitro compounds and aromatic hydrocarbons in general. It is plausible that when dissolved in benzene this association gives way to a solvation. This interaction between solute and solvent molecules is closely related to the association between like molecules. In benzene etc. no stoichiometric association is observed but, owing to the anisotropy of the polarizability, a more or less parallel... 

The authors used a [5 s4p 1 d/4s 1 p] basi s set in their calculations. In order to focus on the effects of the molecular interaction, they introduced the concept of a noninteracting dimer wherein the dimer wave function is a simple product (non-antisymmetrized) of the unperturbed monomer functions. The effects of the interaction are thus in evidence by comparison of the two columns in Table 3.31 from which it may be seen that the average polarizability is little affected, increasing from 16.48 to only 16.60. The anisotropy of the polarizability, however, as measured by y, undergoes a dramatic increase. Whereas the polarizability tensor is nearly spherical in the monomer, with all a.j values between 16.3 and 16.6, is increased up to 18 when the two molecules interact with one another. This increase is thus focused along the H-bond direction. 

This conclusion was reached, tentatively, by Frenkel, Shaltyko and Elyashevich A phenomenological analysis presented by Pincus and de Gennes predicted a first-order phase transition even in the absence of cooperativity in the conformational transition. These authors relied on the Maier-Saupe theory for representation of the interactions between rodlike particles. Orientation-dependent interactions of this type are attenuated by dilution in lyotropic systems generally. In the case of a-helical polypeptides they should be negligible owing to the small anisotropy of the polarizability of the peptide unit (cf. seq.). Moreover, the universally important steric interactions between the helices, regarded as hard rods, are not included in the Maier-... 

L. Frommhold and M. H. Proffitt. About the anisotropy of the polarizability of a pair of argon atoms. Molec. Phys., 35 681-689 (1978). 

M. H. Proffitt and L. Frommhold. Concerning the anisotropy of the polarizability of pairs of methane molecules. Chem. Phys., 36 197-200 (1979). 

Whereas the dielectric constant probes essentially the R-dependence of the isotropic polarizability, the collison induced depolarized Raman scattering depends on the increment in the anisotropy of the polarizability with varying R. Depolarized Raman scattering of noble gases has first been observed by MacTague and Bim-baum in 1968, and later investigated for many gases . Very recently also polarized Raman intensities have been measured for NCj and He ... 

We must add a remark with regard to polarisability. In what precedes we have taken account only of the mean value of a over all directions—a procedure which, in the case of a gas, whose molecules ban rotate freely, is certainly permissible as a first approximation. But by suitable experiments we can also determine the anisotropy of the polarizability, and so also form for ourselves a picture of the anisotropy of the electron cloud. We have already mentioned (p. 230) that the polarizability is a tensor, and can be represented by the so-called ellipsoid of polarization (see fig. 3). This has the following... 

Fig. 4.—Depolarization due to the anisotropy of the polarizability. a) In an isotropic molecule the induced dipole moment vibrates in the direction of the electric vector of the light wave.

Optical anisotropies characteristic of nematogenic molecules, comprising a linear array of aromatic groups, appear to play an important role in thermotropic LCs. Anisotropies of the polarizability tensors of the interacting molecules enhance parallel molecular alignment, providing a basis for the Maier-Saupe [1959, 1960] theory of the nematic LC state. The internal energy per mole is defined as... 

Second, for observing curvature structures induced by an externally applied electric field, one must also consider the interaction of the field with the anisotropy of the polarizability of the medium, which tends to align the director either parallel or perpendicular to the applied field. This can suppress the flexoelectrically induced curvature in many geometries. 

The anisotropy of the polarizability, Ae, is a good estimate of the order parameter in a nematic solution... 

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