Molecular theory of order electricity

Abstract

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 examine this concept from a molecular point of view, using the density functional theory of liquid crystals. We show that the long range nature of the electrostatic force between molecules with permanent quadrupoles creates formal problems with rather profound consequences on the link between microscopic and macroscopic formulations of liquid crystal theory. One result is that the Landau-de Gennes gradient expansion must be employed with extreme caution in an inhomogeneous nematic. These formal problems have analogues in the theory of dielectrics and were explored by Ewald long ago. In addition we derive from a statistical mechanical viewpoint the phenomenological relations used to describe order electricity, and explore in detail the consequences of order electricity at an isotropic-nematic interface and at a nematic-substrate interface.