Lamellar peaks semicrystalline polymers

Two new parametets for describing the SAS data from semictystalline polymers are introduced. These are the ellipticity of the trace of the lamellar peak-maxima, and the orientation parameter determined from the increase in the longitudinal width of the lamellar peak with the distance from the meridional axis. These two parameters along with Ae lamellar spacing, tilt-angle of the lamellar plane, the diameter and the coherence length of the lamellar stack, and the lamellar intensity completely describe the SAS data from oriented semiciystalline polymers. These parameters can be obtained by fitting the 2-D SAS from uniaxially oriented semicrystalline polymers in elliptical coordinates. 

Small-angle x-ray scattering (SAXS) probes structural features at the mesoscopic length-scale (Section 1.9.2). It can be used to measure the radius of gyration of polymers in solution, via Eq. (1.27), which can be up to hundreds of nanometres. Semicrystalline polymers form lamellae, which are layered systems with a layer period of the order of 10 nm. Such lamellar stacks diffract x-rays at small angles, indeed they are a one-dimensional lattice, and Bragg s law can be used to determine the layer period. Furthermore, the relative intensities of the peaks depend on the distribution of amorphous and crystalline material, and this can be analysed to provide a model of the electron density profile normal to the layers. 

In a good approximation, the morphology of a semicrystalline polymer can be described as a lamellar two-phase system consisting of crystalline and amorphous phases with different electron densities and with sharp boundaries between them. This structure gives rise to a peak in the scattering intensity... 

Modeling the Interface Distribution Function for a ID Lamellar Stack As demonstrated in the last section, the nonideality of a real semicrystalline polymer can lead to a broadening and overlapping of the peaks in K (z), which makes it difficult to extract the correct structure parameters simply from the peak positions. The one-dimensional paracrystalline stack has been suggested as an analytical model for the semicrystalline structure [2,13,16], We here present a procedure that allows simulating and modeling the measured IDF based on this model. A simulated IDF... 

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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