STUDY OF THE DISTRIBUTION OF MOLECULAR-ORIENTATION IN HIGHLY ORIENTED POLYETHYLENE BY X-RAY-DIFFRACTION

High-density polyethylene (HDPE) cylindrical rods produced by ram extrusion were studied by wide-angle X-ray diffraction. Even order <P(n)(cos chi)> coefficients of the Legendre polynomial series describing the orientation distribution of the 110, 200, 020, 011, 211, and 002 crystal planes were calculated from the X-ray data for n up to 32. It is shown that high order <P(n)(cos chi)> values can be used to characterize the evolution of the orientation at high draw ratios, whereas the commonly used "orientation function", <P2(cos chi)>, reaches a constant value close to unity at draw ratios over approximately 12. The <P(n)(cos chi)>c values describing the c axis or molecular orientation distribution were computed from the different planes: the correlation between the coefficients thus calculated is excellent. It is concluded that the molecular orientation may be calculated from any arbitrary reflection for uniaxially oriented samples. Finally, the average <P(n)(cos chi)>c coefficients are used to compare the experimental distributions with those calculated from the pseudoaffine deformation model and from Gaussian, Lorentzian, and "most probable" distribution functions.