Orientations and phase transitions in liquid crystals consisting of short linear polymer chains

Abstract

The system of semiflexible linear polymer liquid crystal (PLC) macromolecules is studied. Each macromolecule constitutes an alternating chain of flexible (F) and rigid (LC) sequences. The distribution function of the chain conformations is factorized in three terms. The Gibbs distribution is used for anisotropically interacting LC sequences; products of the Dirac delta functions represent F sequences modeled by linear chains of freely jointed statistical segments; connections of LC and F sequences in a linear chain are controlled by the Dirac delta functions with a proper argument. The general formula for the Helmholtz function A for arbitrary types of anisotropic interactions between LC sequences and for an arbitrary number of statistical segments per flexible part of linear chain obtained by the present authors [J. Chem. Phys. 105, 4367 (1996)] is applied in numerical calculations performed for some special cases. The cases selected here are (a) the Maier and Saupe mean-field limit formula for LC+LC interactions; and (b) the linear approximation with respect to the inverse value of the total length of the chain flexible part. Mostly one deals with very large (infinite) chain length with Gaussian behavior and earlier we have done this also. In this work we investigate the non-Gaussian case with a finite number of statistical segments per chain. The resulting modifications of the phase diagrams and phase transition points are discussed taking also into account results of the numerical calculations.