Structural implications of the elliptical form of small-angle reflections in oriented semicrystalline polymers

The intensity maxima of lamellar reflections in small-angle scattering patt erns from uniaxially oriented polymers such as fibers do not generally fall on a straight layer line or on a circular are. The shape of the reflection can be analyzed by measuring the periodicity L-phi of the lamellar planes as a function of the angle phi between the reflection and z. L-phi is measu red parallel to the fiber axis z. The data give a straight line in a plot o f L-phi(2) vs tan(2) phi. This shows that the reflection is elliptical and provides a basis for fitting small-angle patterns in an elliptical coordina te system using few parameters. Further analysis of patterns that extend to large values of phi shows that an elliptical fit is not merely a convenien ce; it is also the best fit. Many possible structures could cause the lamel lar reflection to lie on a curve, but few models predict an ellipse. The si mplest is affine deformation of the lamellar structure. Recognizing that a single lamellar population will give reflections of an elliptical form allo ws populations of lamellae to be distinguished even when the reflections ov erlap strongly, with long spacings L-M different by only 2-8%. This permits a greater understanding of the processes of fiber drawing and annealing.