Nematic ordering of a liquid crystalline homeotropic cell

Nematic ordering in a very thin system under the homeotropic anchoring condition is studied in the framework of the Maier-Saupe model. The first order transition disappears and continuous change of phase occurs at the system with thickness smaller than a certain critical thickness. To study the mechanism of the continuous change of phase, nonuniformity due to the boundary effect is described in terms of an effective field which is conjugate to the order parameter, and behaviour of the system is analysed by observing loci of the effective fields on the phase diagram of the bulk. It is found that the continuous change is mediated by an unstable state; a metasteble high-temperature phase changes to a metastable low-temperature one continuously via an unstable phase between them. This mechanism is an analogue of the phenomenon occurring in a freely suspended film of a certain chiral smectic material.