Birefringence, polarizability measurements

Polarizability is related to birefringence, and measurements were carried out in the nematic phases of [IrCl(CO)2(8-OPhVPy)], PdCl2( -OCB)2], and [Ag(n-OPhVPy)2][DOS] the data are summarized in Table 68. 

The polarizability tensor, a, introduced in section 4.1.2, is a measure of the facility of the electron distribution to distortion by an imposed electric field. The structure of the electron distribution will generally be anisotropic, giving rise to intrinsic birefringence. This optical anisotropy reflects the average electron distribution whereas vibrational and rotational modes of the molecules making up a sample will cause the polarizability to fluctuate in time. These modes are discrete, and considering a particular vibrational frequency, vk, the oscillating polarizability can be modeled as... 

This approach is based on the introduction of molecular effective polarizabilities, i.e. molecular properties which have been modified by the combination of the two different environment effects represented in terms of cavity and reaction fields. In terms of these properties the outcome of quantum mechanical calculations can be directly compared with the outcome of the experimental measurements of the various NLO processes. The explicit expressions reported here refer to the first-order refractometric measurements and to the third-order EFISH processes, but the PCM methodology maps all the other NLO processes such as the electro-optical Kerr effect (OKE), intensity-dependent refractive index (IDRI), and others. More recently, the approach has been extended to the case of linear birefringences such as the Cotton-Mouton [21] and the Kerr effects [22] (see also the contribution to this book specifically devoted to birefringences). 

Birefringences are mostly observed in condensed phases, especially pure liquids or solutions, since the strong enhancement of the effects allows for reduced dimensions (much shorter optical paths) of the experimental apparatus. Nowadays measurements of linear birefringences can be carried out on liquid samples with desktop-size instruments. Such measurements may yield information on the molecular properties, molecular multipoles and their polarizabilities. In some instances, for example KE, CME and BE, measurements (in particular of their temperature dependence) have been carried out simultaneously on some systems. From the combination of data, information on electric dipole polarizabilities, dipole and quadrupole moments, magnetizabilities and higher order properties were then obtained. 

The simplified schematic in Figure 2a shows the essential features of the effect. Optically anisotropic molecules in the solution are preferentially oriented by the applied field E(t), resulting in a difference of refractive indices for components of polarized light parallel and perpendicular to the bias field which is measured as a birefringence. The basic theoretical problem is to evaluate this effect in terms of anisotropies of polarizability Aa. referred to molecular axes which produce a time dependent effect when the molecules are preferentially oriented by the field. For no anisotropy in absence of the field, the effect must be an evgn function of field strength, and at low fields proportional to E. A remarkable feature of the effect is that for molecules with permanent dipole moments the response af-... 

On the assumption of total symmetry of the tensor of third-order nonlinear polarizability c(— co coi, cog, cog), its non-zero and independent elements are the same as those of Table 12. Direct theoretical calculations of c = c(0 0,0,0) have been performed for the atoms of inert gases and some simple molecules. Values of the tensor elements = c(— cu cu, 0,0) have been determined for numerous molecules from static Kerr effect studies and values of c = c(— cd ot>,coi — col) from measurements of optical birefringence induced by laser li t. Measurements of second-harmonic generation by gases in the presence of a static electric field yield the tensor elements c " = c( — 2co co, to, 0), which can also be obtained from second-harmonic scattering in centro-symmetric liquids. The elements of the tensor c = c(— 3co co, co, co)... 

Electric birefringence (EB) or the Kerr effect is widely used in molecular optics as a method for the investigation of the molecular structure of low molecular weight substances. The study of the Kerr effect in the gas phase or in solutions in combination with other methods, such as refraction, light scattering, dielectric measurements etc. permits to ascertain the spatial arrai ement of atoms in the molecule and thus to calculate the main values of the polarizability tensor of the molecule and to obtain information about the value and direction of its dipole moment ... 

Birefringence can be defined as the difference in the refractive indices of two perpendicular directions as measured with light polarized along these respective directions. Molecular orientation will in general give rise to non-zero birefringence. This results because the polarizability... 

In the future, sonic measurements could lead to an estimate of the form birefringence term. It is doubtful whether such estimates could be confirmed since most theoretical predictions of maximum birefringence depend on the earlier measurements by Denbigh (If) or Bunn and Danbery (7) of bond polarizabilities which are not in agreement. 

Tricot M, Houssier C. Electro-optical studies on sodium polystyrene-sulfonate). 1. Electric polarizability and orientation function from electric birefringence measurements. Macromolecules 1982 15 854-865. 

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