Scattering Methods Light, X-Ray, Neutron

The scattering intensity (for light scattering). Re, due to concentration fluctuations when extrapolated to zero angle [Rg] is inversely proportional to the second derivative of the free energy of mixing d Gm/ P h) expressed by the Zernike [125] equation  

Zimm plots represent a historical method, as the procedure today utilizes numerical methods to obtain the desired data. 

In polymer blends, the radius of gyration of a polymer molecule in a matrix of another polymer can be compared with the radius of gyration of in a matrix of molecules of the same composition. In order to achieve these comparisons, tagged molecules (deuterium) are usually required to achieve resolution and thus small angle neutron scattering employs the above noted procedure to assess the level of miscibility of polymer blends. 

For neutron scattering experiments, the Flory-Huggins interaction parameter can be obtained from the second virial coefficient from the expression  

Further details of scattering theory are beyond the scope of this book and specific reviews can be found in [130]. 

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In all studies involving methods based on absorption or scattering of light, X rays, or neutrons, the characteristic time scales on which radiation interacts with the substance are many orders of magnitude shorter than those of atomic motions. Therefore, it is not the motions themselves but the disordering which arises due to molecular dynamics that should be investigated. 

All three types of radiation scattering techniques light. X-ray and neutrons, have been used to measure the interaction parameters and study the phase equilibria. Using the relations derived for polymer solutions (see Eqs 2.31-2.36), the methods can be used to measure M, < s and Aj, thus Xj2 ... 

The experimental techniques for the study of conformational branched properties in solution are the same as used for linear chains. These are, in particular, static and dynamic light scattering, small angle X-ray (SAXS) and small angle neutron (SANS) scattering methods, and common capillary viscometry. These methods are supported by osmotic pressure measurements and, nowadays extensively applied, size exclusion chromatography (SEC) in on-line combination with several detectors. These measurements result in a list of molecular parameters which are given in Table 1. 

While rheological measurements are wonderfully quantitative, they are usually poor qualitative probes of fluid structure. This is because in rheological experiments, the structural changes responsible for the measured relaxation behavior remain hidden. Thus, rheometry is often most useful when supplemented by other experimental methods that characterize fluid structure and flow-induced structural changes. Some of the most useful methods are microscopy, light, x-ray, and neutron scattering, and polarimetry. 

Scattering methods are among the most powerful and widely used in the study of complex fluids. Light, x-rays, and neutrons can be scattered (Lindner and Zemb 1991). For light scattering, length scales of 2000 A to 100 p,m are probed, while both x-rays and neutrons can reach smaller length scales, from 10 to 1000 A for x rays and from 10 to 200 A for neutrons. 

Several methods may be applied to obtain the micellar size and shape of block-and-graft copolymers light scattering, small-angle X-ray scattering, small-angle neutron scattering. 

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