SMALL-ANGLE X-RAY-SCATTERING OF DISTORTED LAMELLAR STRUCTURES

Small-angle x-ray scattering (SAXS) intensity for the lamellar structu re of polymeric materials has been formulated with consideration of st ructural defects such as the finiteness of the lamellar stack, the lam ellar bend, and the paracrystalline distortions. In particular, the ef fects of the lamellar bend on the SAXS profile have been elucidated on the basis of Vonk's formula gamma1 (x) = gamma1(0) (x)exp(-2x/d). Her e, the scattering profile due to the lamellar bend is shown to be expr essed by a Cauchy function. The integral breadth is equal to 2pi/d, be ing independent of the order of scattering. As an example of the SAXS analysis based on the theory, the characterization of the lamellar str ucture in the ''hard'' elastic polypropylene films is reported. The lo ng period and the lamellar thickness are evaluated from the correlatio n function, and the distortion length and Hosemann's g factor are esti mated according to the procedure presented here. On the basis of these structural parameters, the relationship between the manufacturing pro cess and the lamellar structure of the polypropylene films is discusse d. (C) 1993 John Wiley & Sons, Inc.