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 additional assumptions such as the biaxiality of the LC interactions. (C) 1996 American Institute of Physics.