Tilted lamellae in an affinely deformed 3D macrolattice and elliptical features in small‐angle scattering

Abstract

AbstractLamellar reflections in small‐angle X‐ray and neutron scattering patterns of uniaxially drawn semicrystalline polymers appear to fall on elliptical or hyperbolic arcs. We attribute this to a 3D lattice of tilted lamellae, a macrolattice. Affine deformation of this lattice, such as during uniaxial draw, moves and spreads the reflections along elliptical arcs, and nonaffine deformation, such as during rolling, moves and spreads the reflections along an arc that deviates from an ellipse. Discrete reflections are the product of two functions: the elliptical trace that is the Fourier transform of the affinely deformed lattice and the radial streak that is the Fourier transform of the individual lamella in the reciprocal space. Four‐point patterns are obtained if the lamellar‐surface normal is tilted away from the fiber‐axis, and two‐point patterns if it is not. This model is used to discuss the transformation between four‐ and two‐point patterns and other changes in lamellar morphology that occur during drawing and annealing of oriented semicrystalline polymers. The deformation of the macrolattice of crystalline lamellae, need not be correlated to the tilt of the lamellae. The tilt of the lamellae is shown to be important. It reflects the cross‐sectional area mismatch at the lamellar surface between crystalline stems and amorphous chains segments, and this indicates the internal strain in the interfibrillar amorphous regions. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1277–1286, 2006