Structural Characterization SAXS Data

Important morphological parameters such as the long period (I), crystal thickness (Ic), and amorphous layer thickness (la) of semi rystalline polymer melts and blends can be determined using SAXS via two different approaches. In the first approach, standard models such as the Hosemarm-Tsvankin [23] and the Vonk-Kortleve [24,25] for lamellar stacks are fitted to data obtained for the SAXS profile. The second approach is based on performing a Fourier transform for the SAXS profile to produce a one-dimensional correlation function, y(z) (which is Fourier transform of the measured I(q) in SAXS) or an interphase distribution function (IDF) in real space. 

In scattering measurements, structural information from a three-dimensional (3D) system is often recorded in two-dimensional (2D) form, and hence an I(q) versus q data does not offer an ideal representation to extract meaningful structural details of the system. To resolve this issue, the data are multiplied by (f, which is termed the Lorentz-correction.  

Correlation Function (CF) Method This Lorentz-corrected SAXS profile (Iq versus q) is used to calculate the one-dimensional (ID) correlation function, y z), given by 

Interphase Distribution Function (IDF) Method The IDF, g (z), is equal to the second derivative of the correlation function, y(z), and is given by 

the morphological parameters can be deduced from the simple geometric analysis of y(z) and gj (z) and by locating their maxima and minima. 

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A PbS-PPX nanocomposite with 4.7 vol. % of PbS was investigated also by the small-angle X-ray scattering (SAXS) method, which characterizes different PbS inclusions in PPX matrix regardless of their internal structure. The size distribution of PbS inclusions calculated from SAXS data is similar to the WAXS crystallite size distribution on Figure 2.10. This result signifies that PbS nanoparticles do not aggregate in matrix but are distributed in PPX mostly as small crystallites [53]. 

Polyurethane elastomers based on ADMH. All samples of the polyurethane elastomers studied (for synthesis see Section 2.6.1) are amorphous, since the poly(tetramethylene oxide) used in their synthesis loses its recrystallization ability within the urethane-containing polymers. For this reason, the areas of heterogeneity existing in the bulk of polyurethane elastomers are domains of hard blocks. As it follows from the small-angle X-ray scattering (SAXS) data (Table 5), sample PU(H) 1/1, which is characterized by structural heterogeneity. 

The SAXS data also allow us to evaluate other very important characteristics of the heterogeneous structure. From these data the mean square of electron density fluctuation, Ap, may be obtained. This value is calculated using the experimentally determined value of the thickness of the interphase layer E, which is also a very important quantity characterizing the transition region between two separated phases. The method of calculating E is rather complicated and is described in detail [130]. The boimdary diffuseness p may be expressed as... 

We used the familiar dependence between the first excitonic absorption peak position and PbS QDs size [5] to estimate the particle sizes in our glasses from the optical data. On the other hand, another microscopic and structural methods are worthwhile to characterize this material. The SAXS technique has... 

Fig. 2.17 X- ray characterization of the nano-scale structure for example PUs, plotted as crystallinity index (y) versus SAXS peak areas filled symbols — data for MDl-based polymers open symbols — data for DBDl-based polymers [175]...

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