A direct method to determine the degree of crystallinity and lamellar thickness of polymers: application to polyethylene☆

Abstract Time-resolved small-angle X-ray scattering (SAXS) and wide-angle X-ray scattering (WAXS) patterns have been simultaneously obtained during melting and crystallization of high-density polyethylene using a newly constructed camera at the SRS, Daresbury. The data have been analysed to yield the long spacing, the degree of crystallinity and the lamellar thickness in the context of the two-phase model. The long spacing was obtained from the peak in the Lorentz-corrected SAXS pattern. The degree of crystallinity was obtained from a combination of the SAXS invariant and the integrated WAXS intensity of the crystals. The invariant passes through a maximum at 50% crystallinity and the integrated WAXS intensity is a minimum for the melt. Thus two points in the linear relationship between the WAXS intensity and the degree of crystallinity are known, affording calibration. Calculation of the degree of crystallinity by solving the quadratic in the SAXS invariant gave good agreement with the WAXS result. The long spacing and the degree of crystallinity may be combined in the two-phase model to estimate the lamellar thickness, an important parameter in determining mechanical properties.