A three-dimensional monoclinic paracrystalline macrolattice is used to calculate the small angle X-ray scattering pattern of partially oriented polymers with rotational symmetry about the fiber axis. The influence of the crystallite size, the lattice parameters, the lattice distortions and the orientation relative to the fiber axis on the diffraction patterns is studied.

Abstract:The Small-angle X-ray scattering (SAXS) patterns of oriented LDPE 0-= 1 ... 5.7) were fitted by calculating the small-angle intensity for a structure consisting of a linear paracrystalline lattice built up by finite lamellar or cylindrical crystallites. The resulting data of the superstructure were compared with corresponding values from wideangle X-ray scattering. It is shown that it is impossible to get quantitative information about the superstructure of oriented polymers by using SAXS alone. Nevertheless, the qualitative transition of the crystals during orientation can be explained very well.

Three-dimensional small-angle intensity plots are calculated and discussed for a structure consisting of a linear paracrystalline lattice built up by finite lamellar or cylindrical crystallites, tilted with respect to the lattice direction. The lattice directions are distributed with respect to the fiber axis. The effects of different parameters (orientation, tilt angle, crystallite size, etc.) on the diffraction pattern are studied.

SummaryIt was possible to obtain film exposures of the WAXSdiagram (20 < 50 °) of a PE-fracdon (M = 2 000) in the temperature range from 10 K to 300 K by using a special low temperature Guinier-chamber. The crystallographic a-, band c-axis has been calculated from the positions of all reflexions. The different behaviour of their expansion coefficients can be explained by activation of rotational-and torsional-vibrations. If we take the number of net planes as constant and consider a temperature-independent part resulting from paracrystalline disorder (built up during crystallization), we can describe the linear increasing of the integral widths of the reflexions with decreasing temperature (10 ... 100%) with building up of inherent stresses inside the crystals. ZusammenfassungEine spezielle Tieftemperatur-Guinier-Kammer erm6g-lichte es, Filmaufnahmen der R6ntgenweitwinkelstreukurve (2t9~50 °) einer hochkristallinen Poly~ithylen-Fraktion (M = 2 000) im Bereich von ca. 10 K his 300 K zu erhalten. Das unterschiedliche Temperaturverhalten der Ausdehnungskoeffizienten der kristallographischen a-, b-und cAchse, berechnet aus der Lage aller auswertbaren Reflexe, kann durch Anregung von Torsions-und Rotationsschwingungen erkl~irt werden. Unter der Annahme konstanter Kristallitgr6f~en sowie eines temperaturunabh~ngigen parakristallinen Gitterst6rungsanteils (hervorgerufen durch Defekteinbau bei der Kristallisation), kann die starke Zunahme der integralen Breiten der Reflexe (bis ca. 100%) zu tiefen Temperaturen ;iuf Eigenspannungen in den Kristalliten zurfickgefiihrt werden.

The small‐angle x‐ray scattering (SAXS) intensity of highly‐oriented, low‐density polyethylene (LDPE) with fixed draw ratio has been investigated during several heating and cooling cycles. Using a three‐dimensional, monoclinic, paracrystalline superlattice to describe the superstructure of the sample, it has been possible to calculate the SAXS patterns completely. A very large irreversible variation of the superstructure during the first heating cycle, and a smaller reversible variation of the average size and distance of the crystallites during subsequent temperature cycles, could be obtained. These results can be explained using the thermodynamic theory of crystallization of polymer multicomponent systems of Kilian.