Polydisperse polymer liquid crystals near the anisotropic-isotropic transition

Polydisperse systems of polymer liquid crystal (PLC) macromolecules consisting of LC and flexible sequences are considered, particularly at the phase transition LC-i from an anisotropic to the isotropic phase. The Flory and Matheson lattice model is used for formulation of the partition function; the orientation distribution function for LC orienting potential interactions introduced by Flory and Ronca is included. Using a Landau approach to calculating the Helmholtz function of the system as a function of the orientation parameter s, we obtain the formulae for parameters of the model in the vicinity of the LC-i transition. The critical values at the transition of s, of the strength of orienting interactions, the system temperature, and the anisotropy of LC sequences are calculated and discussed as functions of the polydispersity parameter d. Regions of d are found where polydispersity has a weak influence on the LC-i equilibrium parameters. There is also a region of d values in which the influence of polydispersity is quite pronounced.