Shape and position of middle-angle scattering peaks from smectic phases of polymers

Abstract

A method for the quantitative analysis of isotropic middle-angle X-ray scattering (MAXS) from segmented polymers, which are able to form liquid-crystalline (LC) phases, is proposed and applied to scattering curves from poly(ester imide) samples. Oriented material in the LC state shows MAXS fiber patterns with a meridional layer-line reflection, which sometimes is split, creating a four-point pattern. Comparing scattering data from oriented material with data from isotropic material, we can explain the asymmetry of the isotropic MAXS reflection by limited lateral correlation. Thus, for the LC state of segmented polymers, the notion of stacks built from alternating planar layers of smectic mesogens and spacers units is not generally applicable. Only in the limiting case of infinite flatness does the line profile become symmetric. A simple analytical expression for the shape of the line profile of MAXS reflections is deduced. The equation fitted to the MAXS peak of isotropic LC polymer samples in the smectic state results not only in the determination of a corrected long period but also in two additional parameters, the correlation height of the smectic stack and the flatness of its layers. Compared to established methods for line-profile analysis in small-angle scattering, the proposed method models the nanostructure with classical notions of a two-phase system in one direction only, whereas the lateral contribution to the scattering intensity is characterized by a short-range loss of correlation instead of a classical description by domain-phase boundaries. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 1749–1755, 2001