Molecular model for the simultaneous orientational and translational ordering in a two-dimensional liquid

We present a molecular-statistical theory of the phase transition from the two-dimensional isotropic liquid to the phase which has the elements of the orientational and translational order combined in a single order parameter. This phase possesses the glide symmetry, similar to the herringbone order in crystals, and is related to the mesophases observed in Langmuir monolayers. The microscopic definition of the herringbone order parameter is presented and the transition temperatures from the isotropic to the nematic, smectic, and the herringbone phases are expressed in terms of the direct correlation function of the two-dimensional isotropic fluid. The relative stability of these phases is discussed. The transition temperature into the herringbone phase is estimated using the simple model of hard discs interacting via the quadrupole-quadrupole potential that promotes the herringbone order. (C) 1998 American Institute of Physics.