2D scattering pattern

In general, only a 2D scattering pattern will be available. In this case isotropization can only be performed if the pattern shows fiber symmetry and the fiber axis is contained in the scattering pattern. This symmetry axis must be known. Complete is the available information under these conditions only if SAXS data are evaluated. For WAXS data there are blind regions about the meridian (cf. Fig. 2.6 on p. 28), and missing information must be completed either by extrapolation or by extra experiments in which the sample is tilted with respect to the primary beam. 

A well-known device that performs a 2D projection of the scattering pattern is the Kratky camera. By integrating the intensity along the direction of the focus slit, it is collapsing the SAXS intensity on the plane that is normal to the slit direction. In general, 2D projections collapse the measured complete intensity not on a line, but on a plane. As in the case of the ID projections, the orientation of this plane can freely be chosen. The result of such a projection / 2 (Sj,Sk) is not a curve as was the case with the ID projection, but a 2D scattering pattern. Only in the case of 2D isotropy (i.e., / 2 (sjk) with sjk = Js2, + s ) the scattering pattern can be represented by a curve. 

Fig. 13 Effect of an electric field on the lamellar distance of a block copolymer solution, (a) 2D scattering pattern of a 50 wt% solution of SI51 dissolved in THF for different electric field strengths, (b) Dependence of the lamellar distance d of parallel (filled circles) and perpendicular (open circles) aligned lamellae, with respect to the electric field lines, on the electric field strength for the same solution, (c) Proposed chain stretching effect for lamellae aligned parallel to the field lines. Adapted with permission from Nature Materials [57]. Copyright (2008) Nature Publishing Group...

Parts with fiber symmetry, like fibers, rods or tubes, are not only of practical interest because they are ubiquitous in everyday life. Moreover, they appear paxticularly suited for investigation by means of scattering methods. As the part is rotated about its axis, the 2D scattering pattern does not change. Thus, there is no advantage to take patterns at different rotation angles as it would be for oriented materials with less symmetry. 

The recorded 2D scattering pattern of a fiber is oriented and contains all the accessible information on the structure of the sample. 

For the professional analysis of anisotropic 2D scattering patterns of polymer materials, there are no user-friendly standard computer programs because materials scientists do not carry out standard experiments e.g., protein crystallographers). Therefore some program modules must be adapted to the actual experiment every time in order to reflect the actual setup and the actual mode of operation. Such adaption requires computer programming skills. After adaption and the proper combination of modules, the data can be evaluated automatically. The other option is slow frame-by-frame manual evaluation that is prone to inconsistency or incompleteness. 

Fig. 2.27 Scattering curves for an electrospun fibre sample of (50/50) hydrogenous/perdueterated polystyrene collected onto a rotating collector. The data has been reduced to a ID plot of the differential scattering cross section as a function of Q, where the curves represent the scattering both parallel (solid line) and perpendicular (dotted line) to the fibre axis (vtutical on page) obtained from the 2D scattering pattern (inset). Inset runs from —0.05

Fig. 7.20 2D scattering patterns and orientation parameter ( P2 ) of vertically positioned PCL filaments prepared using different screw rotatirai velocities (a) 40 rpm, (b) 50 rpm and (c) 70 rpm... 

For instance, Fit2D is frequently used to extract slices from 2D scattering patterns, whereas either an azimuthal average or a projection would have been appropriate. Even such simple and inappropriate operation will turn into a nightmare, when Fit2D is operated by mouse clicks and many patterns are operated. Finally, noisy slices are extracted instead of low-noise integrated... 

Interpretation of Anisotropic 2D Scattering Pattern Polymer crystallization under external fields (e.g., shear or extensional flows, stretching of polymer solids) usually exhibits preferred orientation, which results in anisotropic scattering patterns. For example, a four-point SAXS pattern was seen during solid-state uniaxial deformation of an ethylene-propylene copolymer (both experimental data and fitted 3D plot are shown in Fig. 1.17) [108]. 

Selected 2D scattering patterns from PEE bristles (Arnitel EM400) are displayed in Figure 8. 

Considering TPEs under uniaxial load, Bonart [23] has proposed the study of two aspects of the nanostructure, called longitudinal and transverse structure. They can readily be extracted from the scattering pattern by projections [24]. In both cases, the result is a curve and, obviously, curves are analyzed with less computational effort than 2D scattering patterns. 

Figure 3 schematically sketches the different regions potentially present in the scattering curve of a polymer system. If the polymer is amorphous, WAXS would only show the amorphous halo (so named because of its appearance as a diffuse ring in 2D scattering patterns) and no crystalline peaks. SAXS peaks are observed only if the polymer system forms an ordered macrolattice, as discussed in detail in Section 2.12.6, which includes the semicrystalline lamellar stack in Figure 2 as a special case. 

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