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When we are dealing with semicrystalline polymers, we can presume a "paracrystalline lattice". This means that the crystalline lattice finds itself subjected to distortions of the second kind (distortions of the first kind describe a situation where the objects are still in a regular lattice but vary around their designated position as given with random thermal displacements): Starting from a chosen origin the next neighbors distance is not constant but varying. Different distributions for the distance function have been proposed in literature. Crist has shown that usually a symmetric or slightly skewed distribution is best suited to describe the actual SAXS data. (60, 61) We therefore used a Gaussian distribution for the next neighbor distance. The whole lattice builds on the varying distance principle; therefore, we loose all long-range order, and higher order reflections in scattering experiments are usually negligible. This can also be observed in semicrystalline polymers. A significant advantage of this model is that it can be analyzed analytically: the lattice factor can be directly calculated as the absolute squared of the Fourier transform of such a lattice. (38, 40, 48)
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A closer analysis of the simulations has shown that with increasing orientation the scattering profile of the complete orientation model and a simplified model without orientation on the meridian become similar. We can therefore ignore the scattering contribution of the radial part and use the simplified model for a faster fit of the parameters L, g, and H.
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A closer analysis of the simulations has shown that with increasing orientation the scattering profile of the complete orientation model and a simplified model without orientation on the meridian become similar. We can therefore ignore the scattering contribution of the radial part and use the simplified model for a faster fit of the parameters L, g, and H.
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