Adaptation of the Rietveld method to the characterization of the lamellar microstructure of polymers. 2. Influence of a tilt of chain axes versus thenormal to basal planes of crystalline lamellae

In a previous paper [Dupont, Jonas & Legras (1997). J. Appl. Cryst. 30, 921 -931], a variant of the Rietveld method was applied to the characterization by X-ray scattering (powder diffractometry) of disordered and small crysta ls as found in semicrystalline polymers. In the present study, a new versio n of the model is described, which is designed to take into account the pos sible existence of a non-zero tilt angle (psi) of the chain axes versus the large faces of the lamellar crystals. Fits of this model to the diffractog rams of various samples of cold-crystallized PEEK [poly(ether-ether-ketone) ] and of a monodisperse PEEK oligomer are presented. For the oligomer, the fits converged only towards psi = 0 degrees. For the polymers, two equivale nt solutions were found, one with thick lamellae and psi = 0 degrees, anoth er with thinner lamellae and psi = 20 degrees. Models with and without chai n tilt give similar goodness-of-fit parameters, indicating that results com ing from other techniques than X-ray diffractometry are required in order f ully to characterize the dimensions and shape of crystals in isotropic poly mer samples. Comparing the present values with results obtained by such oth er techniques suggests the existence of a tilt angle for cold-crystallized PEEK samples.