Measurement of Pole Figures and Orientation Functions for Polyethylene Films Prepared by Unidirectional and Oriented Crystallization

Abstract

The x-ray pole figure technique has been applied to the study of orientation in polyethylene. Wilchinsky-type orientation functions of the form 〈cos2φhkl, q〉 are determined as well as pole figures. These functions are shown to be related to the crystalline contributions to birefringence and infrared dichroism. A new method of presenting these functions on an equilateral triangle plot is introduced. Equations are presented for calculating the orientation functions for weakly diffracting [hkl] planes for materials of the orthorhombic, tetragonal, hexagonal, and cubic systems. The method of analysis is applied to various polyethylene samples, including a unidirectionally recrystallized sample (I) and to crosslinked film recrystallized at low orientation (II), and at higher orientation (III). The resulting data are interpreted in terms of various morphological models and are also correlated with birefringence. The data on (I) are consistent with a model of random orientation of a and c about the b axis. In (II) and (III) the row nucleation model and the a-axis orientation model are both inadequate. For (II) a diffusely oriented helix model is suggested; for (III) a screw dislocation model of crystal growth, with the screw axes parallel to the stretch direction, is proposed.