Einstein-Smoluchowski theory light scattering

The depolarization of light by dense systems of spherical atoms or molecules has been known as an experimental fact for a long time. It is, however, discordant with Smoluchowski s and Einstein s celebrated theories of light scattering which were formulated in the early years of this century. These theories consider the effects of fluctuation of density and other thermodynamic variables [371, 144]. 

Let us consider now behaviour of the gas-liquid system near the critical point. It reveals rather interesting effect called the critical opalescence, that is strong increase of the light scattering. Its analogs are known also in other physical systems in the vicinity of phase transitions. In the beginning of our century Einstein and Smoluchowski expressed an idea, that the opalescence phenomenon is related to the density (order parameter) fluctuations in the system. More consistent theory was presented later by Omstein and Zemike [23], who for the first time introduced a concept of the intermediate order as the spatial correlation in the density fluctuations. Later Zemike [24] has applied this idea to the lattice systems. 

The theory of thermodynamic fluctuations in the context of light scattering was introduced first by Smoluchowski and Einstein [12, 13]. Einstein considered that the scattering of light in a solution arises from local density and concentration fluctuations. However, it was only till the late 40s and early 50s that Brinkman and Hermans [14], Stockmayer [15], and Kirkwood and Goldberg [16] adopted this approach in the context of light scattering by poiymer solutions. Here, we summarize only the basic results for a binary mixture. 

Peter Debye in 1944 further extended the work of Rayleigh and the fluctuation theory of Smoluchowski and Einstein to include the measurement of the scattering of light by macromolecular solutions for determining molecular size. 

Here, an and a are the polarizabilities of the diatomic complex parallel and perpendicular to the internuclear separation, R12. A purely classical theory, which accounts for the electrostatic distortion of the local field by the proximity of a point dipole (the polarized collisional partner), suggests that )S(Ri2) 6ao/Ri2 with (Xq designating the permanent polarizability of an unperturbed atom. This expression is known to approximate the induced anisotropy of such diatoms fairly well. This anisotropy gives rise to the much studied pressure-induced depolarization of scattered light and to depolarized CILS spectra in general. The depolarization of light by dense systems of spherical atoms or molecules has been known as an experimental fact for a long time. It is, however, discordant with Smoluchowski s and Einstein s... 

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