Phase Diagram Behaviors for Rod/Plate Liquid Crystal Mixtures

Abstract

We present a simple theory of rod/plate liquid-crystal mixtures in which the angle-dependent pair interactions are assumed to be of second-rank form. Calculations are reported for varying relative anisotropies of the “rods” and “plates”. Temperature vs. mole-fraction phase diagrams show successive isotropic (I) → uniaxial ( U) and U → biaxial ( B) transitions which are first- and second-order, respectively. For each pair of species there exists a special composition ( x _rod*) for which cooling of the isotropic phase leads directly (and continuously) to a biaxial liquid. As X _rod approaches X _rod* from either side, the first-orderness of the I → U transition (i.e. discontinuities in volume, order parameter, etc.) becomes vanishingly small. Furthermore the transition temperature of the rod-(plate-) solvent is found to be depressed when “doped” by not-too-anisotropic plates (rods) and elevated when doped by sufficiently anisotropic plates (rods). These behaviors are explained in terms of simple excluded volume considerations and compared with recent experimental data on rod/plate mixtures.