Janusz Walasek

STATISTICAL THERMODYNAMICS OF POLYMER LIQUID CRYSTALS : COMPETITION BETWEEN ENERGETIC AND ENTROPIC EFFECTS

A system of linear polymer liquid crystal (PLC) macromolecules is considered in which each macromolecule constitutes an alternating copolymer of flexible and LC sequences. The distribution function of the system is factorized so that the Gibbs distribution is used for anisotropically interacting LC sequences while Dirac delta functions represent flexible polymer sequences modeled by linear chains of freely jointed statistical segments. A general formula for the Helmholtz function is derived for arbitrary types of anisotropic interactions between LC sequences; the formula of Maier and Saupe for monomer LCs is obtainable from it as a special case. The phase diagram of the system is obtained in the limit of the mean‐field approach. Types and orders of phase transitions that the system can undergo are defined and discussed in terms of the Landau classification; all transitions are of the first order. Formation of cholesteric phases in addition to isotropic and nematic or smectic is predicted without involving...

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

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 int...

Theory of thermotropic polymer liquid crystals

The thermal nematic system consisting of semiflexible polymer liquid crystal chains is considered. Orientational order for liquid crystal particles and for chain as a whole in addition to the chain anisotropy parameters at the nematic-to-isotropic transition and in the stable nematic phase are considered. Results are obtained by extension of the Maier and Saupe theory of thermotropic liquid crystals on systems of semiflexible macromolecules.

ORIENTATIONS AND PHASE TRANSITIONS IN UNCROSSLINKED AND CROSSLINKED POLYMER LIQUID CRYSTALS

A system of linear polymer liquid crystal (PLC) macromolecules is considered. Each macromolecule constitutes an alternating copolymer of flexible and LC sequences. The macromolecules can be either unconnected or else connected into a PLC network. The system is characterized with respect to local orientation. Competition between energetic effects of anisotropic orienting interactions between LC sequences and entropic effects determined mainly by flexible parts is considered. The Maier and Saupe mean-field approach is assumed for the representation of LC interactions. Types and orders of phase transitions that the system can undergo with respect to local order are discussed in terms of the Landau classification. All transitions are found to be of the first order. Thermodynamical and structural parameters of the system at phase transition points are represented by phase diagrams.

A statistical-mechanical model of polymer liquid crystals subjected to external deformations

We consider the nematiclike system of polymer liquid crystal (PLC) macromolecules represented by the Flory semiflexible chain model. Segments of the flexible (F) spacers are shorter than the LC hard-rod sequences. We investigate effects of imposition of external deformations. The behavior of LC sequences is largely governed by orienting interactions while for F spacers the short-range interactions determined by the chemical structure are the most important. The stress-strain relation is obtained in addition to the orientation-deformation relations. Orientational order phase transitions caused by the external deformations of the system are recognized and described.

Internal orientations in externally deformed nematic polymer liquid crystals

The system of linear polymer liquid crystal (PLC) macromolecules, each modeled by semiflexible chain of alternate connected flexible and stiff rodlike sequences, is externally deformed. As a result, two orientation phases for hard rods are generated. One of them is nematic N+ with orientation parameter s>0; this has the place in monomer liquid crystal (MLC) systems and in PLCs. The nematic N- phase with s>0 appears in deformed PLCs only. This causes the fact that orientation of PLC chains, as a whole, is generated also by the system deformation. A discussion of that effect is the main goal of this article. The change of orientation is also discussed dependent on changes of the system temperature and parameters of the chain structure, such as the liquid crystal component concentration, contour lengths of stiff and flexible parts, and internal interactions parameters. Average shape of PLC chain and the shape anisotropy are calculated and discussed.

Internal orientations and elastic properties of non-Gaussian nematic polymer network.

Elasticity of the polymer network, with nematic interactions between segments of all the system chains, is considered. The Maier and Saupe molecular mean-field is used for description of nematic interactions. Calculations are performed for non-Gaussian network containing chains of finite contour length. The network topological structure is taken into consideration via the system contraction coefficient. Values of thermodynamic parameters, necessary for the existence of the isotropic-nematic equilibrium, are calculated. The system free energy (Helmholtz function) is calculated for any direction of external elongation of the network. A relation between the deformation force and elongation ratio is obtained. The network can have isotropic as well as anisotropic elastic properties. It depends on the system internal orientations and chain lengths. For the network in isotropic phase, defined with respect to orientation of segments, elastic constants have the same values in any direction. It is independent of whether the chain length is finite or infinite. In the nematic phase, the network elastic constants have the same values for chains with infinite length, while they are many in various directions for finite length of chains. The problem of the nematic axis rotation under the system external deformation is considered.

Mechanisms of orientation of polymer liquid crystals (PLCs) in external fields

Abstract We analyze existing theories of behavior of polymer liquid crystals (PLCs) in external fields such as electric or magnetic. Against this background, we recall a fairly general theory of PLCs [77] and extend it to include effects of the external fields. We consider in particular phase transitions that PLCs undergo. In some cases the changes are qualitative only. However, we also observe significant quantitative modifications of phases caused by the presence of the fields.

The Influence of External Electric Field on Local Orientations and Phase Transitions in Polymer Liquid Crystals (PLCs)

Full Paper: The starting point is our previous study of influence of the internal molecular mean field of dipoledipole interactions on local orientation and phase transitions in polymer liquid crystal (PLC) systems of longitudinal chains. [1, 2] Electric dipoles are created by LC mesogen moieties. The longitudinal PLC is a macromolecule of consecutively copolymerized LC and flexible polymer sequences. We now amplify the model by inclusion of dipole-external electric field interactions. We find that the external fields can seriously modify the local orientational order of the system and affect phase transition parameters dependent on that order. In particular, the external fields induce the formation of disoriented nematic phases with negative values of the second order orientation parameter pP2P for LC sequences in the longitudinal PLCs while the first order parameter pP1P is positive. However, some rapid decreases in pP1P are observed at points of positiveto-negative transitions of pP2P; thus the LC disorientation manifests itself. The limiting case of the monomer liquid crystal (MLC) systems is included also.