Light scattering from fluctuations

Light Scattering from Fluctuations and the Structure Factor 65... 

In equation (4.51) of Chapter 4, the equal time structure factor, C (x), was defined. For light scattered from fluctuations in the dielectric properties of a material, it was shown that the light intensity was proportional to this quantity. In the problem of total intensity light scattering discussed in that chapter, the measurement is integrated over time and time-dependent fluctuations are not directly observed. When time-dependent fluctuations are... 

Fig. 4.4. Intensity (reflection side) of the light scattered from fluctuations ( i + n) trot s (bending mode) and from fluctuations ( , — n) 2GoG, -G,/ 3 (squeezing mode), where tf— 0 60°, 1.36, and X, =546 nm. (From Ref. 68, courtesy of Elsevier Scientific Publishing Company, Amsterdam.)...

Tnterest in the investigation of macromolecular diffusion phenomena in both dilute and concentrated solutions has received recent stimulus with the development of techniques vhich can conveniently and accurately identify the dynamic characteristics of light scattered from fluctuations in solute concentration. In dilute solution, part of this activity stems from the fact that the limiting value of the translational diffusion... 

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... 

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] ... 

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]. 

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. 

In solutions, part of the light scattering arises from fluctuations in refractive index caused by fluctuations in composition. The well-known equation for light scattering from solutions is based on these considerations... 

The intensity of light scattered from a small volume element of solution is not constant but it fluctuates in the manner shown in Figure 7-23 (Berne and Pecora 1976). The situation is like that of a short sighted person looking at an ants nest at some distance although individual ants cannot be discriminated, it can readily be seen whether the nest is quiet or in a state of hectic activity. 

The intensity I of the light scattered from a dilute macromolecular or supra-molecular solution is a fluctuating quantity due to the Brownian motion of the scattering particles. These fluctuations can be analysed in terms of the normalised autocorrelation function y1 ( t ) of the scattered electrical field Es, which contains information about the structure and the dynamics of the scattering particles [80]. 

In general, the source of light scattering from a polymer (or polyelectrolyte) solution is the existence of spatial and temporal fluctuations in refractive index in this scattering medium. The overall scattering intensity measured in an SLS experiment is proportional to the average of the square of refractive index fluctuations in the scattering volume,... 

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