Biaxial nematics and nematic-nematic demixing in polydisperse mixtures of hard board-like particle fluids

Abstract

We study the bulk phase behavior of a polydisperse liquid crystal fluid made of biaxial boards with restricted orientations using both fundamental measure theory and Monte Carlo computer simulations. The continuous polydispersity is included in the intermediate particle length of the boards via a truncated Schulz distribution. By calculating several phase diagrams across a range of polydispersity coefficients, we find that polydispersity (i) enhances demixing between two uniaxial nematic phases and (ii) expands the stability region of the biaxial phase. Although metastable with respect to non-uniform phases, we identify certain mixtures exhibiting two-phase coexistence paths involving uniaxial-uniaxial and uniaxial-biaxial phase separations. Whether these paths can be completed depends on the precise shape of the parent distribution function. Monte Carlo simulations performed for a representative case exhibit the same phase diagram topology predicted by theory, thereby validating the theoretical approach. The main difference between both approaches lies in quantitative agreement, with simulated phase transitions systematically occurring at higher packing fractions than those predicted theoretically. Our combined theoretical and simulation results may prove relevant to the design and interpretation of sedimentation experiments on colloidal suspensions of polydisperse anisotropic particles.