Statistical thermodynamics of polymer liquid crystals: Competition between energetic and entropic effects

Abstract

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.

Mechanisms of Orientation of Polymer Liquid Crystals (PLCs) in External Fields

“…A variety of possible phases and phase transitions predicted by the theory is shown in Figures (2) and ( 3 ) . The phase diagram for u h vs. (2) and (3) leads to the conclusion that all types of the phase transitions in PLCs with dipole -dipole interactions are of the first order [77] in terms of the Landau classification [81]. More specifically, the typical behavior of uniparticle Helmholtz function shows that each change of s from a state in which global minima of A (s) have the same values (equilibrium) to a state €or which A(s) has only one minimum is of the jumping type.…”

“…The superposition of these probabilities gives a general formula for the probability of the whole PLC system. The general results in [77] are not constrained to any special type of orienting interactions between LC particles and/or with an orienting external field. Some special results are obtained for: 0 chains with long flexible parts; 0 induced dipole -dipole internal interactions between LC rods in the In the latter case the Helmholtz function 2 per particle is [77] Maier-Saupe mean-field theory limit [82,83].…”

“…Precisely this means in the Landau classification that the phase transition is of the first order. The general results of the theory [77] shortly sumarized here can be applied to PLCs in an external magnetic or electric field; see the next section.…”

“…However, experiments [72-761 and some theoretical results for biaxial orienting interactions [61-631 suggest possibilities of other types of transition such as from s = 0 to s < 0 or from s < 0 to s > 0. This situation behooved us to formulate a new approach [77] to the PLCs theory in which all phase transitions are predictable; the model so created is described in the following section.…”

“…The generalized theory [77] is based on a non-lattice approach. The system consists of Nch semiflexible chains; the structure of a chain is shown in Figure 1.…”