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.

Small-angle x-ray scattering by crystalline polymer fibers 2. Investigation of the linear paracrystalline model using various materials

“…Since the previous investigation [4] had shown that good agreement with experimental data was obtained for a model in which both crystalline and amorphous phase lengths were distributed according to the Reinhold [5] where y is a parameter controlling both the skew and the dispersion of the distribution, e = (Y> (1 -2 y r), and < Y> is the mean length. Provided 0 < y < 0.5, lengths less than e are not possible, since this would cause h(Y) to be negative.…”

“…More recently, Hall et al [4] have developed experimental techniques of recording the intensity distribution at a resolution sufficient to avoid distortion by instrumental effects. These use a linear position sensitive detector (LPSD) enabling the statistical uncertainty of the data to be determined, and Eq.…”

“…The average angular separation between two adjacent chanels (determinedin a separate calibration) was then used to express intensity as a function of scattering angle. Correction for the transverse spread of scattering was made by multiplying each intensity by the corresponding value of s (this assumes that the spread is mainly caused by variation in the inclination of the lamellae surfaces to the stack axes, and was previously shown to be the most appropriate correction [4], and the data was then scaled so that the maximum intensity was unity.…”

“…As in the previous study [4], CuKa radiation from the 0.1 mm square focus of a Maroni-Avionics GX-20 rotating anode x-ray generator was used with a Rigaku-Denki goniometer and an LPSD manufactured by Marconi-Avionics. Monochromatisation was achieved by nickel filtration and energy discrimination at the detector.…”

Structural Approaches of Polyethylene Environmental Stress-Crack Resistance

“…number-average and weight-average molar weights, M n and M w ; crystal weight fraction, X c ; most probable crystal thickness, L c ; thickness distribution parameter, γ; number of coherently scattering lamellae, N relevant equations for computing the SAXS intensity profiles have been already reported by several authors [22,23]. The disorder parameters were assessed from the best fitting of the model with experimental data, taking the L c and L a values as determined above, and assuming γ c = γ a = γ.…”