Mixtures in the frustrated spin-gas theory of reentrant polar liquid crystals

Mixtures of polar liquid crystals are studied microscopically via the development of the frustrated spin-gas theory, previously applied to single-component systems. Phase diagrams are calculated in the composition and temperature variables, with nematic, smectic-$A_d$, and smectic-$A_1$ phases joined in a variety of topologies, including multiple reentrances and bubbles. Thus experimentally observed topologies are reproduced and new topologies are presented. It is found that the doubly and quadruply reentrant phase diagrams, seen experimentally in mixtures of successive homologs such as the phenyl nitrobenzoyloxy benzoates, ${\mathrm{DB}}_{\mathrm{n}}$ ${\mathrm{ONO}}_2$, are obtained for molecules with steric hindrance increasing with tail length. These model mixtures also yield reentrant phase diagrams in the pressure-temperature plane that are similar to those seen experimentally.