Isotropic molecules

Note that this also involves the assumption of isotropic molecules, which have the same polarizability in all directions. Unpolarized light consists of equal amounts of vertical and horizontal polarization, so the fraction of light scattered in the unpolarized (subscript u) case is given by... 

The fluctuations in the orientation of anisotropically polarizable molecules in liquids also cause frequency broadening of the scattered light, as investigated for CSj in CCI4 239). CS is a highly polarizable molecule with very different polarizabilities along and perpendicular to the internuclear axis. CCU on the other hand, is a poor scatterer because it is an isotropic molecule. Thus, if CSj is mixed with CCI4, the CSj molecules can be studied in a new environment. 

Measurement of the cross-relaxation rate in either the laboratory or the rotating frame suffices. This assumes that the respective correlation time function, /(tc), is the same for all spin pairs. If the calibration of the crossrelaxation rate is not feasible (e.g., no suitable spin pair, spectral overlap, motion not isotropic, molecule has internal mobility), the value of /(tc) for each spin pair (or for a group of selected pairs), i.e., the correlation time, must be explicitly determined. 

The relaxation time of C-5 of the B-type O-isopropylidene ring in each isotropic molecule 25,26, and 27 is, within experimental error, similar to the T, values of the furanose ring carbon atoms of each (see Table IV), indicating restricted rotation about the C-4—C-5 bond, which may be regarded as a very small oscillation. However, the fact that the AT, values for C-6 are larger than predicted by Eq. 16,... 

The constant of proportionality a is called the polarisability of the molecule. For isotropic molecules, which include the monatomic molecules of the inert gases, the average direction of the induced molecular dipoles is in the direction of the applied field. (Since the local field is, as we shall see later, proportional to the overall applied field, we have m = const.E.) The total dipole moment per unit volume developed in this way, the polarisation P, is then related to the number of molecules per unit volume Nq . 

Translational Fluctuations. We shall now discuss the general expression (191) for the Kerr constant, starting from the simple case of atomic liquids and ones composed of isotropic molecules. In substances like these, the above derived results (170) and (177), as well as (178), reduce to zero since in the case of isolated atoms the deviation tensors d and d vanish. Formula (191) now contains deviation tensors relating to the medium as a whole, which presents in general intense molecular fields. Taking into account Kirkwood-Yvon translational statistical fluctuations, one obtains in a first approximation of interaction between induced dipoles ... 

Isotropic molecules. For spherical symmetry, the contribution (200) vanishes and we have to revert to the general formula (191), inserting therein the deviation tensor (195a) accounting for the presence of translational fluctuations. By (199a), this yields ... 

Solution of a polar liquid in a solvent with isotropic molecules 313... 

This result (derived by Kielich ) states that in dense substances composed of atoms and isotropic molecules the presence of translational fluctuations is able to cause optical birefringence without the participation of the non-linear Voigt effect present in the gaseous state. 

The significance of (196c) lies in the conclusion that already binary correlations suffice for inducing local anisotropy in simple liquids. Pairs of atoms (or isotropic molecules), thus correlated, behave like anisotropic assemblages subject to reorientation by an external electric field, and cause an observable Kerr effect in carbon tetrachloride and similar liquids with almost symmetric molecules. ... 

Solution of a polar liquid in a solvent with isotropic molecules. Assume the molecules of the solvent to be isotropically polarizable, and those of the solute to be dipolar. Equation (227) now yields ... 

Pairwise Brownian dynamics has been primarily used for the analysis of diffusion controlled reactions involving the reaction between isotropic molecules with complex reactive sites. Since its introduction by Northrup et al. [58], the pairwise Brownian dynamics method has been considerably refined and modified. Some of the developments include the use of variable time steps to reduce computational times [61], efficient calculation methods for charge effects [63], and incorporation of finite rates of reaction [58,61,62]. We review in the following sections, application of the method to two example problems involving isotropic translational diffusion reaction of isotropic molecules with a spherical reaction surface containing reactive patches and the reaction between rodlike molecules in dilute solution. 

Two neutral molecules with no dipole moments can only interact through dispersion forces. Dispersion forces are always attractive, whatever the mutual orientation of the molecules. They are independant of temperature. The interaction energy between two isotropic molecules whose centers are separated by a distance r is ... 

The depolarization of gases composed of isotropic molecules at intermediate densities is reviewed by Thibeau and associates [182,187]. For argon and methane in the low-density limit, a comparison is made of the data obtained from the measurements of the depolarization ratios, CILS line-... 

M. Thibeau, G. C. Tabisz, B. Oksengorn, and B. Vodar. Pressure induced depolarization of the Rayleigh light scattered from a gas of optically isotropic molecules. J. Quant. Spectro. Rad. Trans., 70 839-856 (1970). 

M. Thibeau and B. Oksengorn. Some recent results about the depolarization of the Rayleigh light scattered by optically isotropic molecules. J. Phys. (Paris), 55 C1 247-C1 255 (1972). 

M. Thibeau. Rayleigh and Raman Depolarized Light Scattering by Isotropic Molecules. In B. Vodar and Ph. Marteau, (eds.). High Pressure Science and Technology, Pergamon, New York, 1980, pp. 724-726. 

M. Thibeau, B. Dumon, A. Chave, and V. Sergiescu. A dynamical Onsager model approach of field fluctuations and light scattering in a gas of isotropic molecules. Physica A, 7(75 219-228 (1981). 

M. Thibeau, J. Berrue, A. Chave, B. Dumon, Y. Le Duff, A, Gharbi, and B. Oksengorn. Depolarization Ratio of Light Scattered by a Gas of Isotropic Molecules. In G. Birnbaum (ed.), Phenomena Induced by Intermolecular Interactions, Plenum Press, New York, 1985, pp. 291-309. 

V. Sergiescu. On the usefulness of the lattice-gas model in the theory of the DID Rayleigh and Raman depolarized scattering by a fluid of isotropic molecules. Physica C, 97 292-298 (1979),... 

Scattering in the Rayleigh Frequency Region A. Optically Isotropic Molecules 1. Theory... 

V. Scattering in the Raman Vibrational Bands of Optically Isotropic Molecules... 

The influence of multipolar polarizabilities has been examined subsequently in several optically isotropic molecules such as CH4, CD4, neopentane, CF4, or SF6 [4,7-14,17,18]. In this review, our attention is focused on CF4 for which both Rayleigh [8,13] and Vi Raman [17,18] depolarized and isotropic bands have been studied and published by us. In the Rayleigh studies, we measured the /j (v) and / (v) intensities that are scattered by gaseous CF4 up to 340 cm-1, in... 

We calculate the pure rotational part of our spectrum taking into account all the light scattering mechanisms described in Eq. (56). Then the resulting spectrum takes the form of the convolution of the rotational and translational parts [see Eqs. (31) and (32)]. We deal numerically with the rotational and translational spectra and their convolution [15,16,36] by methods described in the previous section for optically isotropic molecules. 

V. SCATTERING IN THE RAMAN VIBRATIONAL BANDS OF OPTICALLY ISOTROPIC MOLECULES... 

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