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 th e smectic-A phase of a liquid crystal. These structures have been obse rved 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 conseque nce of a mismatch between layer thickness in the bulk and at the surfa ce. We use the covariant form of the Landau-de Gennes free energy expr essed in terms of the nematic director field n(r) and the smectic comp lex order parameter psi(r). The threshold condition for and evolution of the chevron and tilted structure are obtained as a function of liqu id crystal elastic properties, cell thickness, and surface orientation al anchoring strength. The threshold and amplitude evolution exhibit a lmost universal behavior as a function of a dimensionless chevron numb er 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 trans ition and discuss the case where the stress imposed by surface positio nal anchoring is partially relieved by incorporating a lattice of wedg e dislocations.