Analysis of polymeric X-ray diffraction profiles. I. Theory and application of the variance method

In the field of polymer physics, X-ray diffraction line profile analysis methods have yet to acquire the significance which they possess in the analysis of the fine structure of metals and alloys. The present paper attempts to put these methods on a solid theoretical basis and to introduce new concepts in the analysis of polymeric X-ray diffraction profiles. The theory of paracrystals has been used to calculate the expressions for integral line breadth and variance-range function of 0k0 diffraction profiles. The methodology is illustrated by an application of the integral breadth and variance methods to a polynosic viscose fibre, Tufcel, whose axial structure has been shown to be `paracrystalline'. Special emphasis is laid on the elimination of diffuse background scatter, the correction of profiles for angular variation factors, the problem of overlapping reflexions etc. and the superiority of the variance method over the integral breadth method in the analysis of polymeric X-ray diffraction profiles is established.