Straley Model of Biaxial Nematics Extended

Abstract

In 1974 Straley [Phys. Rev. A 10, 1881 (1974)] presented the mean-field model of interacting particles similar to hard rectangular blocks. The orientation-dependent potential was built from the four basic functions composed from the standard rotation matrix elements with j = 2. As there is only one basic function composed from the standard rotation matrix elements with j = 3, it is interesting to find out whether it has any influence on the known phase diagrams. We show that the j = 3 term can enlarge the biaxial nematic phase range. The article also discusses an extension of the Romano model mimicking shape amphiphilicity [Phys. Lett. A 333, 110 (2004)]. It is showed that the j = 3 interaction term can create the tetrahedral phase with the second order transition to the isotropic phase. What is more, the first order transition from the biaxial nematic phase to the isotropic phase or to the tetrahedral phase is predicted. Finally, the possible presence of the j = 3 term in other theories is discussed.