Scattering patterns

These are plotted in Fig. 10.6, which shows the net intensity envelope in the xy plane as a solid line and represents the horizontally and vertically polarized contributions to the resultant by the broken lines. Since 0 is symmetrical with respect to the x axis, the three-dimensional scattering pattern is generated by rotating the solid contour around the x axis. 

Fig. 4. SmaH-angle x-ray scattering pattern from PVC plasticized with 20 parts per hundred resin of dioctyl phthalate (18).

Figure 3 Calculated X-ray diffuse scattering patterns from (a) a full molecular dynamics trajectory of orthorhombic hen egg white lysozyme and (b) a trajectory obtained by fitting to the full trajectory rigid-body side chains and segments of the backbone. A full description is given in Ref. 13.

X-ray diffraction has been used for the study both of simple molten salts and of binary mixtures thereof, as well as for liquid crystalline materials. The scattering process is similar to that described above for neutron diffraction, with the exception that the scattering of the photons arises from the electron density and not the nuclei. The X-ray scattering factor therefore increases with atomic number and the scattering pattern is dominated by the heavy atoms in the sample. Unlike in neutron diffraction, hydrogen (for example) scatters very wealdy and its position cannot be determined with any great accuracy. 

Complementary information about the structure of the smectic phases is contained in the X-ray scattering patterns, as in studies of real mesogens. The intermolecular scattering patterns calculated (see Sect. 3) for GB(4,4, 20,0, 1,1)... 

Fig. 9a,b. The intermoleailar scattering patterns calculated for a the smectic A b the smectic B phases of the mesogen GB(4.4, 20.0, 1, 1) with the scattering vector parallel to the layer normal. The scaled scattering vectors Q and Q range from -8n to 8n... 

All measured intensities can be put on absolute scale by proceeding as follows. At high angles the scattering pattern can be considered as arising from a collection of noninteracting gas molecules rather than from a liquid sample. 

C02-0042. Describe the scattering pattern that would have been observed in Rutherford s experiment if atoms were like chocolate chip cookies. 

In practice, commercially fabricated polymer items are generally oriented to some degree. The scattering patterns from such materials comprise arcs, which are parts of the full circles obtained from unoriented samples. The lengths and positions of these arcs reveal much about the orientation of crystallites within a sample. The shorter the arcs, the more oriented the sample. In cases of extreme orientation, as found in highly oriented fibers such as Kevlar , the scattering pattern can approach that of a single crystal. 

With the core contrast (Fig. 55a) a strong peak is observed as in the case of completely labelled stars [148], while with the average contrast (Fig. 55c) the peak is less intensive. With the shell contrast (Fig. 55b) the scattering pattern is quite different. Its most important feature is the intermediate minimum, which is observed at the same Q-value, where the maxima are found for the core and average contrast conditions. 

Figure 14 Most characteristic small-angle laser light scattering patterns (Hv) observed with linear polyethylene fractions. Reproduced by permission of The Royal Society of Chemistry from Ref. [224].

The application of X-ray scattering for the study of soft matter has a long tradition. By shining X-rays on a piece of material, representative structure information is collected in a scattering pattern. Moreover, during the last three decades X-ray scattering has gained new attractivity, for it developed from a static to a dynamic method. 

Classical X-ray diffraction and scattering is carried out in the subarea of wide-angle X-ray scattering (WAXS). The corresponding scattering patterns yield information on the arrangement of polymer-chain segments (e.g., orientation of the amorphous phase, crystalline structure, size of crystals, crystal distortions, WAXS crystallinity). 

In principle every scattering pattern can be recorded using the classical X-ray diffraction setup sketched in Fig. 2.2. In the detector the scattering intensity is measured in units of counts-per-second. 

The general case of scattering is less favorable. The decrease of the correlation function with increasing r depends both on the shape of the particle itself and on the arrangement of neighboring particles. In principle the maximum information of a scattering pattern is such correlation information. 

Polydispersity is one of the most frequent reasons that soft condensed matter does not show diffraction but scattering. Thus its consideration is of utmost importance. The general effect of polydispersity on scattering patterns is demonstrated in this section. 

From the observed correlation function the scattering pattern is obtained by Fourier transformation. As Eq. (2.31) is subjected to the Fourier transform, it will only act on the correlation function of the template because hu (a) is no function of r. With Eq. (2.29) we obtain the expected result... 

Meridian is the name for the principal axis found in the scattering patterns of uniaxial materials. 

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