Light scattering density fluctuations

K is a constant containing all the optical parameters for light, electron density fluctuations for X-rays and scattering length difference for neutrons. The exact definitions of K are given as ... 

The scattering techniques, dynamic light scattering or photon correlation spectroscopy involve measurement of the fluctuations in light intensity due to density fluctuations in the sample, in this case from the capillary wave motion. The light scattered from thermal capillary waves contains two observables. The Doppler-shifted peak propagates at a rate such that its frequency follows Eq. IV-28 and... 

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... 

Out of the five hydrodynamic modes, the polarized inelastic light scattering experiment can probe only the tliree modes represented by equation (A3.3.18), equation (A3.3.19) and equation (A3.3.20). The other two modes, which are in equation (A3.3.17), decouple from the density fluctuations diese are due to transverse... 

Rayleigh scattered light from dense transparent media with nonuniform density. If these nonuniformities are time-independent, there will be no frequency shift of the scattered light. If, however, time-dependent density fluctuations occur, as e. g. in fluids, due to thermal or mechanical processes, the frequency of the scattered light exhibits a spectrum characteristic of this time dependence. The type of information which can be obtained by determining the spectral line profile and frequency shift is described in an article by Mountain 235). 

If a S> 1, collective effects play an important role and the light scattering is no longer caused by individual electrons but by electron density fluctuations 280), Jn this case the spectrum shows a central line at Xq and two narrow lines located symmetrically about Xq, at a distance governed by the electron plasma frequency. The linewidth is smaller than in the case X < 1 and is determined rather by the thermal motion of the ions, not that of the electrons. The line shape depends on the ratio of electron to ion temperatures. Therefore, a measurement of the shape and width of this central line allows, under certain assumptions, a direct determination of the ion temperature. 

Light scattering from a solution is due both to the scattering from local density fluctuations and to the scattering from the solvent [9,18], This scattering may be described by the Rayleigh scattering ratio [9,18] ... 

In solutions and in mixtures of liquids, additional light scattering arises from irregular changes in density and refractive index due to fluctuations in composition. If the solution is dilute, the density fluctuations are essentially identical to those existing in the pure solvent [9]... 

As pointed out, the value gh must be selected properly. Roughly speaking it will have a value such that the density of a cell when one molecule is in the cell will be equal to the vapor density. In any case it seems to be possible to select this value so that the distribution will predict the existence of nuclei, that is, cells which have the proper density and energy to cause spontaneous growth of a new phase. The evaluation of the interaction term, W>, is unsatisfactory. However the fluctuation theory cannot be dismissed. Light scattering measurements are strong proof that the assumed fluctuations are very real. 

The scattered light intensity from a polymer solution arises from the fluctuations in both the solvent density and the polymer concentration. These fluctuations are considered as stable during the timescale of the measurement in the static mode of light scattering (for more details, see Evans (1972)). The light scattered from just the polymer (in excess of the light scattered from the pure solvent) is given by (Burchard, 1994)... 

Liquid solutions also scatter light by a similar mechanism. In the case of a solution, the scattering may be traced to two sources fluctuations in solvent density and fluctuations in solute concentration. The former are most easily handled empirically by subtracting a solvent blank correction from measurements of the intensity of light scattered from solutions. What we are concerned with in this section, then, is the remaining scattering, which is due to fluctuations in the solute concentration in the solution. 

Critical Behavior of Gels. In 1977, the critical phenomena were discovered in the light scattered from an acrylamide gel in water [18]. As the temperature was lowered, both the scattered intensity and the fluctuation time of the scattered light increased and appeared to diverge at —17 °C. The phenomenon was explained as the critical density fluctuations of polymer networks although the polymers were crosslinked [19, 20]. 

Polymer molecules in a solution undergo random thermal motions, which give rise to space and time fluctuations of the polymer concentration. If the concentration of the polymer solution is dilute enough, the interaction between individual polymer molecules is negligible. Then the random motions of the polymer can be described as a three dimensional random walk, which is characterized by the diffusion coefficient D. Light is scattered by the density fluctuations of the polymer solution. The propagation of phonons is overdamped in water and becomes a simple diffusion process. In the case of polymer networks, however, such a situation can never be attained because the interaction between chains (in... 

They also examined phase transition under external forces. Later, Tanaka et al. found a critical divergence of light scattering and a critical slowing down of the density fluctuations in polyacrylamide gels with lowering of the temperature... 

These circumstances may explain why it took ten years for the phenomenon to be experimentally observed after the prediction. In 1973, prior to this finding, Lon Hocker, George Benedek, and Tanaka realized that a gel scattered light, and the light intensity fluctuated with time [5]. They established that the scattering is due to the thermal density fluctuations of the polymer network and derived a theory that explained the fluctuation. These fluctuations are similar to... 

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. 

It has been established that the volume phase transition of gels is an universal phenomenon [17]. Dynamic light scattering studies indicate that the dynamic fluctuations of the density correlation diverges in the vicinity of the volume phase transition point of the gel. It has also been shown that the time scale of the density fluctuations become slow in the vicinity of the volume phase transition... 

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