Nematic-nematic demixing in polydisperse thermotropic liquid crystals

We consider the effects of polydispersity on isotropic-nematic phase equilibria in thermotropic liquid crystals, using a Maier-Saupe theory Z. Naturforsch. A 13A, 564 (1958)] with factorized interactions. A sufficient spread (approximately 50%) in the interaction strengths of the particles leads to phase separation into two or more nematic phases, which can in addition coexist with an isotropic phase. The isotropic-nematic coexistence region widens dramatically as polydispersity is increased, leading to reentrant isotropic-nematic phase separation in some regions of the phase diagram. We show that similar phenomena will occur also for nonfactorized interactions as long as the interaction strength between any two particle species is lower than the mean of the intraspecies interactions.