SAXS data

Recently, a unique approach for using the correlation fiinction method has been demonstrated to extract morphological variables in crystalline polymers from time-resolved syncluotron SAXS data. The principle of the calculation is based on two alternative expressions of Porod s law using the fonu of interference fiinction [33. 36]. This approach enables a continuous estimate of the Porod constant, corrections for liquid scattering... 

Small-angle X-ray scattering (SAXS) data have made it possible to deduce the localisation of organic additives (pigments) in the bulk of isotactic polypropylene (iPP) [344]. This work has confirmed that the additives are located in the amorphous phase, in spite of their crucial influence on the formation of the crystalline phase of iPP. SAXS has also been used to study the 3D structure of different carbon-black aggregates, and silica-filled SBR rubber compounds [345]. 

For USAXS and SAXS data the tangent-plane approximation is valid and the relation between scattering angle and the units of reciprocal space are given by Eq. (2.7). If the scattering pattern is properly aligned with the vertical direction identical to a fiber axis or the polymer chain direction, then sy = 53. In similar manner the. vx-axis of the detector is related to the actual orientation of the sample with respect to the beam. 

Guinier s law exhibits two parameters, I (0) and R2, which describe structural aspects of the sample. The experimentalist should consider their determination, if the recorded SAXS data show a monotonous decay that is indicative for the scattering from uncorrelated1 particles. Particularly useful is the evaluation of Guinier s law, if almost identical particles like proteins or latices are studied in dilute solution (cf. Pilz in [101], Chap. 8). The absolute value of 1(0) is only accessible, if the scattering intensity is calibrated in absolute units (Sect. 7.10.2). 

Table 8.2. Long period from the isotropic SAXS data presented in Fig. 8.7 as determined in different ways. The bottom row method is most closely related to reality... 

Application in Materials Science. For simple fluids the amount of the density fluctuation background can be computed. Thus its measurement can be used for the calibration of SAXS data to absolute intensity [91,94], This method is convenient if liquid samples are studied. 

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. 

From experimental SAXS data of isotropic materials Q is determined by means of Eq. (7.25) (cf. p. 91). An interactive computer program (e.g., TOPAS) is very helpful, because several manual steps are involved. 

Visualization of Domain Topology from SAXS Data... 

The isotropic chord length distribution (CLD) is of limited practical value if soft matter with only short-range order is studied. Nevertheless, the related notions have been fruitful for the development of new methods for topology visualization from SAXS data. 

Fig. 7 Universal scaling function S(x) plot for the late stage of SD, calculated from the SAXS data of PET. The solid curve indicates the theoretical Eq. 2 [7]...

This problem is very important, but it is extremely difficult to make SAXS measurements at higher temperatures because the induction period becomes too short to observe the time evolution of SAXS intensities. For example, as was seen in Sect. 2.2, the induction period was only 100 s when the PET glass was crystallized even at 115 °C, 40 K higher than Tg, where a detailed analysis of the SAXS data was impossible. Of course, as the crystallization temperature approaches the melting temperature, the induction period is expected to become longer. However, as will be shown below, no characteristic peaks of SD could be detected in SAXS curves either. This is probably because the crystallization temperature was not in the unstable state, or the characteristic wavelength was much larger compared with the lower resolution limit of... 

Fig. 30 Comparison of cyclic PS-fc-PB and their linear PS-b-PB-b-PS analogue. Molecular weights were approx. 50kg/mol ps = 0.4. a TEM image cyclic PS-b-PB. b TEM image linear PS-b-PB-b-PS. c SAXS data, A cyclic PS-b-PB linear PS-b-PB-b-PS. From [100], Copyright 2003 American Chemical Society...

Fig. 37 Morphology of 4-miktoarm-star copolymers of PS(P2MP)3 type, a TEM images, b SAXS data. From [113]. Copyright 2003 American Chemical Society...

The TEM (Fig. 44) and SAXS data clearly indicate that the structure is lamellar to the first order but modified by channels in the PI layers, leading to a PL pattern. However, Fredrickson s theoretical results indicate that in the SSL this structure is not the most favourable one [123]. In the WSL, similar PLs are to occur for equal weight fractions, even though lamellae are expected in that region [124]. A similar behaviour has been observed in the case of PI2PS homopolymer blends for the PL morphology [15]. 

Figure 6. MaxEnt reconstruction of SAXS data from as-received Nafion equilibrated under (a) ambient humidity and (b) 100% RH. (Reprinted with permission from ref 63. Copyright 2000 American Chemical Society.)...

Using a novel, model-independent maximum entropy method to interpret the SAXS data, Elliott et al. presented a self-consistent morphological para-... 

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