The nematic to smectic-A transition: A theoretical overview

Abstract

The de Gennes model is used as a basis for a discussion of the properties of the nematic and smectic-A phases and the transition between them. Order parameter and director correlation functions and the Landau-Peierls destruction of long range order in the smectic phase are reviewed. A gauge transformation that restores long range order to the smectic phase is introduced. Anisotropic scaling with correlation length exponents, ν|| and ν┴ , is presented and shown to imply that the critical point in three dimensions with finite splay elastic constant must either be isotropic (ν|| = ν┴ ) and in the same universality class as the superconducting transition or anisotropic with ν|| = 2ν┴ . Predictions for the behavior of physically measurable quantities for these two universality classes are presented and compared with experiment. Predictions for both classes are in agreement with some but not all experiments.