Polar biaxial liquid crystalline phases with fluidity in two and three spatial dimensions

We discuss the macroscopic properties of several classes of polar liquid crystalline phases, We focus on polar biaxial liquid crystalline phases made of achiral molecules with fluidity in two and three spatial dimensions. The classes we examine include polar biaxial nematic phases, orthogonal biaxial smectic phases with anisotropic in-plane fluidity and tilted polar biaxial smectic phases with in-plane fluidity, We show that many of the phases discussed are ferroelectric. In addition, we find that in each of the three classes discussed, there is one phase which has C-1 symmetry thus allowing spontaneous helix formation. Finally we investigate in detail the properties of a tilted phase with C-2 symmetry (C-B2),which is probably very important for liquid crystalline phases composed of banana-shaped molecules. (C) 2000 Elsevier Science Ltd. All rights reserved.