Fluctuations scattering density

The correlation fiinction G(/) quantifies the density fluctuations in a fluid. Characteristically, density fluctuations scatter light (or any radiation, like neutrons, with which they can couple). Then, if a radiation of wavelength X is incident on the fluid, the intensity of radiation scattered through an angle 0 is proportional to the structure factor... 

In the next section we shall pursue the scattering by fluctuations in density. In the case of solutions of small molecules, it is the fluctuations in the solute concentration that plays the equivalent role, so we shall eventually replace 6p by 6c2. First, however, we must describe the polarizability of a density fluctuation and evaluate 6p itself. 

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]. 

The use of photon correlation spectroscopy to study the dynamics of concentration fluctuations in polymer solutions and gels is now well established. In bulk polymers near the glass transition there will be slowly relaxing fluctuations in density and optical anisotropy which can also be studied by this technique. In this article we review the development of the field of photon correlation spectroscopy from bulk polymers. The theory of dynamic light scattering from pure liquids is presented and applied to polymers. The important experimented considerations involved in the collection and analysis of this type of data are discussed. Most of the article focuses on the dynamics of fluctuations near the glass transition in polymers. All the published work in this area is reviewed and the results are critically discussed. The current state of the field is summarized and many suggestions for further work are presented. 

It is difficult to prepare bulk polymer samples which yield only intrinsic light scattering due to thermal fluctuations in density and optical anisotropy. The samples used were poorly characterized commercial materials. 

Another complication arises from the shape of the quasi-one-dimen-sional Fermi surface, which is typical of most organic conductors. This fact implies that important spin density fluctuations (scattering) can occur with wavevectors q 0 (forward scattering) and q = 2kF (backward scattering). 

Statistical Fluctuations. Thermodynamic systems in general present unordered random deviations from equilibrium referred to as statistical fluctuations. Even slight fluctuations are apt to give rise to experimentally accessible effects. Thus, as shown by Smoludiowski, local fluctuations in density in gases and liquids cause light scattering by optically transparent media. Attempts to raise the sensitivity of measuring devices are fmled by... 

When a binary mixture is quenched in the unstable coexistence region, by thermal treatment or pressure changes or simply by mixing the two macromolecules, fluctuations in density grow with time, and finally result in a complete phase separation. The dynamics of phase separation are generally divided into early, intermediate and late stages. The different stages can be described by means of the temporal evolution of the scattered intensity function.20-22... 

It should be noted, however, that some typically colloidal phenomena, such as light scattering, are exhibited (though very weakly) by systems in which the microheterogeneity arises from random kinetic fluctuations in density in an otherwise uniform system of small molecules such as a gas or a liquid, while in some cases (e.g. suspensions of relatively coarse solid particles) certain colloid-like properties may persist to particle sizes much larger than the above maximum. 

Fig. 2. Schematic variation of neutron scattering density for an object composed of a central sphere of RNA and a concentric outer shell of protein, i.e. a simple virus. The contrast difference dp is the difference between the scattering density of the solvent pg and the solute py. High positive and negative dp are seen in 0 and 100% H20. The protein shell is matched-out in 43% H20 and the RNA core is matched-out in 72% H20. Note that for reason of solvent H- H exchange, the average protein and RNA densities increase slightly on going from 0 to 100% H20. Solution scattering is observed where the solute and solvent densities are different. Note that the fluctuations in scattering densities pp(r) within each of the protein and RNA components do not disappear at their respective matchpoints. See Section 2.3 for a further explanation of the terms in dp, ps, Py and Pp(r).

The data of Fig. 3 and Tables 2 to 7 are discussed in three further levels of increasing detail below the contrast difference Ap (Section 2.3.3) the sensitivity of Pv to the ratio of H non- H atoms or electron-rich atoms in neutron or X-ray scattering (Section 2.3.4) scattering density fluctuations Pp(r) (Section 2.3.5). 

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