Small angle X-ray scattering from finite sequence of lamellar stacks of crystalline polymers

Abstract

An analysis method using small-angle X-ray scattering (SAXS) of the lamellar stacks of crystalline polymers was examined. The scattering profile was expressed by a fitting function on the basis of a paracrystalline stacking model of finite sequence of parallel lamellae in a stack with border zones continuously connecting to the mean density in spherulites. The SAXS pattern of poly(butylene terephthalate) was able to be fitted to both the conventional model with infinite number of parallel lamellae in a stack and the present model with finite number. The SAXS pattern of polyethylene could not be fitted by the conventional model supposing an infinite sequence, and it was necessary to suppose a lower finite number; the best fit result was obtained with two crystalline layers. A lower number of parallel lamellae in a stack is consistent with the fact that polyethylene lamellar crystals are twisted in three-dimensional space, and cannot form an infinite sequence of simple stacked structure of lamellae oriented parallel to each other. For the finite sequence with lower number, the determination of crystalline lamellar thickness requires the consideration of border zones. It was also confirmed that an alternative method using triangular shape of a one-dimensional auto-correlation function could be acceptable with better level of agreement for narrower distributions of thickness.