SOLUBILITY AND MISCIBILITY IN TERNARY-SYSTEMS - POLYMER LIQUID-CRYSTAL PLUS FLEXIBLE POLYMER PLUS SOLVENT

We use the Matheson-Flory theory,11 with the orientational contribution represented by the Flory-Irvine term12 in the partition function. Polymer liquid crystal (PLC) molecules have a fraction theta of thermotropic sequences, with the remainder 1 - theta fully flexible. The excess Gibbs function of mixing for the ternary system is formulated, and chemical potentials of the components in the ansiotropic phase are derived; a set of rive equations defines the anisotropic-isotropic phase equilibrium. Calculated miscibility gaps have the usual base on the PLC + flexible polymer side, but unusual shapes (cusps) are predicted for values of the characteristic temperature of the mixture T* in certain intervals; such shapes appear for fully rigid rods as well as for theta < 1. Moving from the Gibbs triangle base toward the top (solvent), we find the LC order parameter s quite high, except in the immediate vicinity of pure solvent. As an example, s almost-equal-to 0.97 for the volume fraction of PLC in the anisotropic phase as low as 0.170. Thus, solvent molecules must be channeled by the thermotropic sequences, with perhaps unwilling flexible PLC sequences participating in the channeling. Available experimental data for one ternary system19 are compared with predictions from the theory.