Adaptation of the Rietveld method to the characterization of the lamellar microstructure of polymers. 2. Influence of a tilt of chain axes versus the normal 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 crystals as found in semicrystalline polymers. In the present study, a new version of the model is described, which is designed to take into account the possible existence of a non-zero tilt angle (ψ) of the chain axes versus the large faces of the lamellar crystals. Fits of this model to the diffractograms 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 ψ = 0°. For the polymers, two equivalent solutions were found, one with thick lamellae and ψ = 0°, another with thinner lamellae and ψ = 20°. Models with and without chain tilt give similar goodness-of-fit parameters, indicating that results coming from other techniques than X-ray diffractometry are required in order fully to characterize the dimensions and shape of crystals in isotropic polymer samples. Comparing the present values with results obtained by such other techniques suggests the existence of a tilt angle for cold-crystallized PEEK samples.