Light-scattering polarizability measurements

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 ... 

The influence of Van der Waals interactions on the polarizability of interacting molecules manifests itself in deviations from the Clausius-Mosotti equation , in the Kerr effect and in collision induced light scattering . Although measurements of these effects are all performed on bulk systems in thermodynamical equilibrium and not on Van der Waals molecules per se, we will nevertheless say a few words about pair polarizabilities, because, just as in the case of the collision induced IR absorption, much can be learned about Van der Waals interactions from the comparison of experimental and computational results. 

The assumption of no interaetion between the rotating molecules is not correet in a dense dipolar liquid where the moleeules may possess a dipole moment in addition to being polarizable. In sueh a situation, dynamic light-scattering experiments measure the eolleetive property. The polarizability can be expanded in terms of spherieal harmonies and, for a moleeule of ellipsoidal or cylindrieal symmetry, the only terms that appear are Y2m. So the dynamic quantity is T2m(k,0 and the eorrelation funetions, C2m(k, t), are defined as... 

Equations (10.17) and (10.18) show that both the relative dielectric constant and the refractive index of a substance are measurable properties of matter that quantify the interaction between matter and electric fields of whatever origin. The polarizability is the molecular parameter which is pertinent to this interaction. We shall see in the next section that a also plays an important role in the theory of light scattering. The following example illustrates the use of Eq. (10.17) to evaluate a and considers one aspect of the applicability of this quantity to light scattering. 

In order to be able to use the fluctuation of the intensity around the average value, we need to find a way to represent the fluctuations in a convenient manner. In Section 5.3b in our discussion of Rayleigh scattering applied to solutions, we came across the concept of fluctuations of polarizabilities and concentration of scatterers and the role they play in light scattering experiments. In the present section, what we are interested in is the time dependence of such fluctuations. In general, it is not convenient to deal with detailed records of the fluctuations of a measured quantity as a function of time. Instead, one reduces the details of the fluctuations to what is known as the autocorrelation function C(s,td), as defined below ... 

In the absence of electron dispersion and absorption, the tensor of second-order non-linear polarizability ft(— cog coi, tog) can be dealt with as totally symmetric, and the numbers of its non-zero and independent elements are to be found in Table 11. Static values of the nonJinear polarizability = i(0 0,0) have been calculated theoretically for some molecules. Tensor elements A" = fi(— Kerr effect or molecular light scattering in liquids. ... 

In general, the polarizability is a tensor whose invariants, trace and anisotropy, give rise to polarized and fully depolarized light scattering, respectively. Collision-induced light scattering is caused by the excess polarizability of a collisional pair (or a larger complex of atoms or molecules) that arises from the intermolecular interactions. In Section I.l, we are concerned with the definition, measurement, and computation of interaction-induced polarizabilities and their invariants. 

In summary, since the early 1980s or so, collision-induced light scattering experiments on molecular fluids have demonstrated that the study of the collision-induced absolute-unit spectra (depolarized and/or isotropic ones) is an useful tool, and up to now the only one, to measure multipolar polarizabilities of molecules. 

The polarization P of a molecule has three frequency components v and v v and the vibrational polarization emits light with its frequency. Therefore in general light scattering experiments, scattered light with these frequencies can be observed. In contrast a Raman spectrum can be measured only in the case where there are changes in molecular polarizability in the various vibrational modes, since Eq. (4.16) is expected to hold at dA/dQ 0 (Raman active). 

In the light scattering experiment, by measuring the intensity of the incident beam, Iq, and the scattered beam, Iq, we obtain the Rayleigh ratio. Before this equation can be used to determine the molar mass we must have a relation between a and the molar mass. We obtain it by using Eq. (26.14), but we replace by the square of the refractive index and note that the polarizability is the sum of two contributions, Nq ao from the solvent and Na from the solute that is, we rewrite Eq. (26.14) in the form... 

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