Elliptical Small‐Angle X‐Ray Scattering Patterns from Aligned Lamellar Arrays

Abstract

Semicrystalline polymers aligned by drawing into films or fibers produce small-angle X-ray scattering patterns with two or four spots. Some liquid crystalline materials, cybotactic nematics, produce extremely similar patterns when oriented in magnetic fields. A structure of stacked lamellae, tilted for four point patterns, explain the basic features. However, the peak intensity positions of the broadened reflections lie not on a layer line or on the arc of a circle, but very close to an ellipse. Specific structural explanations of this feature have been suggested, but models using an equilibrium distribution of molecular orientations and lamellar tilts can predict elliptical shapes for the reflections. The model parameters are chosen by fitting the entire 2D intensity distribution of the scattering pattern. Assumptions required for modeling make some fitted parameters uncertain, but it is clear that the elliptical form can emerge from a statistical distribution of the properties of the stacks of lamellae, without a directly assignable structural cause.

Microstructural Evolution of Isotactic‐Polypropylene during Creep: An In Situ Study by Synchrotron Small‐Angle X‐Ray Scattering

“…During tertiary creep, the SAXS patterns change from slight ellipses to distinct ellipses. This transition indicates that lamellae are tilted and rotated . After that the SAXS patterns transform from a distinct ellipse into a “two‐spot” pattern, meaning that lamellae are preferentially aligned along the loading direction.…”

“…This transition indicates that lamellae are tilted and rotated. [38] After that the SAXS patterns transform from a distinct ellipse into a "two-spot" pattern, meaning that lamellae are preferentially aligned along the loading direction. What's more, a streak appears in the equatorial direction, which provides a hint that a highly oriented fibrillar structure is formed in this region.…”

“…However, the quantitative interpretation of the elliptical reflections is still an ongoing topic up to now. In the very recent work by Murthy and his co‐workers, models using an equilibrium distribution of molecular orientations and lamellar tilts are proposed which can predict elliptical reflections. Whereas the models require some assumptions, these make the physical background of the fitting parameters unclear.…”

Nanostructure of Unconventional Liquid Crystals Investigated by Synchrotron Radiation

“…These estimates should be considered as lower limits for the actual correlation lengths. In fact, measured values, especially in the transverse direction, are inevitably underestimated by the broadening of the low-angle reflections caused by orientational disorder [ 17 ].…”

“…Nanomaterials 2020, 10, x FOR PEER REVIEW 5 of 29 the transverse direction, are inevitably underestimated by the broadening of the low-angle reflections caused by orientational disorder [17]. Figure 4 shows the values of ξ and ξ so obtained as a function of temperature: values of ξand ξ of the order of one molecular length L (approximately 36 Å ) and a few (roughly three) intermolecular distances D (typical intermolecular distance approximately 4.5 Å ), respectively, are to be interpreted as indicative of very short-ranged correlations.…”