Scattering thermal density fluctuations

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... 

In this chapter the dilute particulate system, the nonparticulate two-phase system, and the periodic system are discussed in Sections 5.2, 5.3, and 5.5, respectively. Section 5.4 deals with scattering from a fractal object, which may be regarded as a special kind of nonparticulate two-phase system. The soluble blend system is dealt with in Chapter 6. The method discussed in Section 4.2 for determining, for a single component amorphous polymer, the thermal density fluctuation from the intensity I(q) extrapolated to q -> 0 can also be regarded as a small-angle technique. 

In order to describe the static structure of the amorphous state as well as its temporal fluctuations, correlation functions are introdnced, which specify the manner in which atoms are distributed or the manner in which fluctuations in physical properties are correlated. The correlation fimctions are related to various macroscopic mechanical and thermodynamic properties. The pair correlation function g r) contains information on the thermal density fluctuations, which in turn are governed by the isothermal compressibility k T) and the absolute temperature for an amorphous system in thermodynamic equilibrium. Thus the correlation function g r) relates to the static properties of the density fluctuations. The fluctuations can be separated into an isobaric and an adiabatic component, with respect to a thermodynamic as well as a dynamic point of view. The adiabatic part is due to propagating fluctuations (hypersonic soimd waves) and the isobaric part consists of nonpropagating fluctuations (entropy fluctuations). By using inelastic light scattering it is possible to separate the total fluctuations into these components. 

In equation 18, rcorr(s) is the intensity afte correction fix thermal density fluctuation, and t is the thickness cf the interphase (a region possessing an intermediate electron density between pc and Pa). Plotting ln(I corr(s) s ) vs. s, the scattering at large s is used to find the slope, rc t, from which fte interphase thickness is found (15). 

Incompressible melts of identical polymer chains show no thermal density fluctuations and therefore no diffraction occurs in the Q range of SANS. Therefore, the scattering cross section of eqn [24] must be zero and the following relationship holds... 

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... 

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. 

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... 

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