LANDAU-DE GENNES THEORY OF THE CHEVRON STRUCTURE IN A SMECTIC-A LIQUID-CRYSTAL

We make a theoretical study of the chevron and tilted structures in the smectic-A phase of a liquid crystal. These structures have been observed to occur in cells in which the director is oriented in the plane of the wall. We examine the hypothesis of Limat and Frost [Liq. Cryst. 13, 101 (1993)] that the layer buckling and the tilting is a consequence of a mismatch between layer thickness in the bulk and at the surface. We use the covariant form of the Landau-de Gennes free energy expressed in terms of the nematic director field n(r) and the smectic complex order parameter psi(r). The threshold condition for and evolution of the chevron and tilted structure are obtained as a function of liquid crystal elastic properties, cell thickness, and surface orientational anchoring strength. The threshold and amplitude evolution exhibit almost universal behavior as a function of a dimensionless chevron number a. We give a possible explanation of the hysteresis effect observed in the liquid crystal 40.8 [4-octyl-n-(4'-butoxybenzylidene)aniline]. We estimate the energy barrier for the chevron-tilted-structure transition and discuss the case where the stress imposed by surface positional anchoring is partially relieved by incorporating a lattice of wedge dislocations.