Fluctuations, scattering

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... 

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). 

Jerome [48] proposed that the -behavior of pA(I) could be caused by electron-spin fluctuation scattering. This approach can be viewed as an extension of electron-electron scattering to larger effective interaction strengths, which are perhaps caused by the lower dimensionality. The dominant process is scattering of electrons by collective excitations of the electron gas (the spin fluctuations) rather than first-order electron-electron scattering. 

The intensity fluctuations due to the Brownian motion lake place on a lime scale much faster than conventional photometers or the human eye can detect. The variation in the fluctuating scattered light intensity with time resembles a noise signal that can be analyzed in terms of its correlation function with respect to time. The usual practice is to measure the polarized intensity tiine correlation function that is related to the diffusion coefficient for monodisperse particles as follows... 

Fig. 5.2.6. Measured intensity of X-ray scattering at the Bragg angle versus temperature for cholesteryl myristate. The dashed line is the calculated diffuse scattering and fluctuation scattering contribution. The full lines represent the theoretical curves for the total intensity due to Bragg, diffuse and fluctuation scattering derived from (a) the simpler model potential and (b) the refined one. The theoretical intensity has been adjusted to be equal to the experimental value at the lowest temperature. (After McMillan." )...

Dynamics of the concentration fluctuations. Scattered light spectrum... 

The general, wavevector-dependent IRPA scattering function for pure concentration fluctuation scattering is given by [57,61]... 

Thus, in the thread limit PRISM with the R-MMSA closure reduces precisely to mean-field Flory theory The corresponding spinodal temperature is given by Eq. (5.2). The inverse osmotic compressibility, or concentration fluctuation scattering intensity, is nearly exactly given by the RPA form ... 

Fig. 4 SANS data taken from PE(M = 5000)-PEB(M = 8000) in decane at ambient temperature. The triangles show the scattering in core-contrast the circles the scattering in brush-contrast . The dashed and solid lines are the scattering contribution computed from the average structure. The inset shows the fluctuation scattering range using a linear intensity scale together with the decomposition as obtained by the spin-echo measurement plain solid line (computed average structure contribution), open diamonds dynamical brush fluctuations, solid diamonds static (frozen) brush fluctuations...

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