We present the macroscopic equations for polar nematic liquid crystals. We consider the case where one has both, the usual nematic director, $\widehat{\mathbf{n}}$, characterizing quadrupolar order as well as the macroscopic polarization, $\mathbf{P}$, representing polar order, but where their directions coincide and are rigidly coupled. In this case one has to choose $\mathbf{P}$ as the independent macroscopic variable. Such equations are expected to be relevant in connection with nematic phases with unusual properties found recently in compounds composed of banana-shaped molecules. Among the effects predicted, which are absent in conventional nematic liquid crystals showing only quadrupolar order, are pyro-electricity and its analogs for density and for concentration in mixtures as well as a flow alignment behavior, which is more complex than in usual low molecular weight nematics. We also discuss the formation of defect structures expected in such systems.

• Received 31 May 2006

DOI:https://doi.org/10.1103/PhysRevE.74.021713