Biaxial Field and Crossover between Homeotropic and Homogeneous Structures in the System Anchored by Biaxial Walls

Abstract

ABSTRACT Landau free energy with both of uniaxial and biaxial order parameters is derived in the framework of Maier-Saupe model, based on which a phase diagram in two types of external fields is obtained. The free energy is generalised to be applied to the thin system sandwiched by parallel boundary walls of biaxial anchoring, and nematic ordering occurring therein is studied, where the biaxiality is introduced by the fixed orientation of molecules on the boundary walls. The first order phase transition becomes critical behaviour at a critical thickness, and the system thinner than this has no transition as the case of homeotropic structure, and biaxiality dependence of the critical thickness is evaluated. A crossover between homeotropic and homogeneous structures is shown to occur at a certain biaxial condition, where the first order transition changes to the second order one as the thickness decreases.