Small-angle-X-ray scattering by crystalline polymer fibres 1. Experimental method and investigation of the linear paracrystalline model

Abstract

Hosemann's formula for X-ray scattering by a linear paracrystal is investigated using the distribution of intensity parallel to the fibre axis of oriented poly(butylene terephthalate). The formula was put into a form suitable for numerical analysis, and a stepping refinement procedure used to adjust the paracrystalline parameters so that the discrepancy between the calculated and measured intensity was minimised. The measured intensity had been corrected for the spread of scattering transverse to the fibre axis before making this comparison. The pin-hole collimation system was designed so that resolution was limited only by the linear position-sensitive detector, and was good enough not to distort the recorded scattering distribution. Although parasitic scatter could not be measured to the same accuracy, it was so small that negligible error was introduced when it was subtracted. “Top-hat”, Gaussian and Reinhold distribution functions for the lengths of the two phases all fitted well in the region of the main peak although detailed analysis suggested significant disagreement on the low-angle side. Only the asymmetric Reinhold function fitted around the third-order peak and beyond. The range of parameter values giving a good fit for this distribution were determined.