Invited Lecture. Order-parameter theories of phase diagrams for antiferroelectric smectic-A phases

Abstract

Using exact relations between Landau and molecular approaches, the symmetryinduced topologies of phase diagrams are studied for antiferroelectric smectic-A phases. In particular, the tricritical points are found for a large class of orderparameter theories of nematic-smectic A (-A₁, -A_d) and -A₂ (NA) phase transitions. These include generalizations to antiferroelectric smectic-A phases of McMillan and Meyer-Lubensky mean-field theories and the Ramakrishnan-Youssouff(RY) density-functional approach. The use of these different approaches allows study of influence of various couplings between nematic (orientational) and smectic (translational) degrees of freedom and polarization field, P₁ (cos θ), on various NA and AA phase transitions. From the results, it is of interest that the coupling between orientational degrees of freedom (P₄(cos θ) and density waves can destabilize the smectic-A phase at low temperatures-pointing to the existence of a nematic-smectic-A-reentrant-nematic phase transition. A possible relation of this result to A_d, C₂, C_d and [ctilde] phases is discussed. Some relations between Fourier components of correlation functions and order parameters at tricritical points are derived from the RY density-functional theory. Despite some limitations, the theory presented here seems to provide the simplest approach to study topologies of phase diagrams in molecular theories.