MOLECULAR THEORY OF ORDER ELECTRICITY

The concept of order electricity has been employed by Durand, Barbero and colleagues to explain, in particular, the existence of equilibrium conical anchoring at liquid crystal interfaces. In this paper we exam ine this concept from a molecular point of view, using the density fun ctional theory of liquid crystals. We show that the long range nature of the electrostatic force between molecules with permanent quadrupole s creates formal problems with rather profound consequences on the lin k between microscopic and macroscopic formulations of liquid crystal t heory. One result is that the Landau-de Gennes gradient expansion must be employed with extreme caution in an inhomogeneous nematic. These f ormal problems have analogues in the theory of dielectrics and were ex plored by Ewald long ago. In addition we derive from a statistical mec hanical viewpoint the phenomenological relations used to describe orde r electricity, and explore in detail the consequences of order electri city at an isotropic-nematic interface and at a nematic-substrate inte rface.