Landau theory of the nematic–smectic-Aphase transition under shear flow

Shear flow distorts the microstructure of fluids if the Deborah number scrD becomes comparable to 1. In complex fluids, exotic hydrodynamics effects are often seen in this regime. We compute within Landau theory the structure factor S(q) of a sheared nematic liquid crystal close to the nematic to smectic-A (N–Sm-A) phase transition. As a function of increasing Deborah number, the pretransitional smectic-A fluctuation clusters become increasingly geometrically restricted, evolving from their usual three-dimensional ellipsoidal shape for scrD≪1 to an extremely anisotropic one-dimensional shape for scrD≫1. We discuss the predictions of Landau theory for x-ray diffraction experiments for various orientations of the nematic director. The suppression of pretransitional critical fluctuations by shear flow is found to raise the transition temperature ${\mathit{T}}_{\mathit{N}–\mathrm{Sm}\mathrm{-}}$A, and peculiarly, ${\mathit{T}}_{\mathit{N}–\mathrm{Sm}\mathrm{-}}$A is found to depend on the orientation of the director. The presence of the microscopic fluctuation clusters under the shear flow is also reflected on the macroscopic level. The classical theory of the hydrodynamics of nematic liquid crystals, due to Ericksen, Leslie, and Parodi (ELP), is found to be incomplete. We compute the new fluctuation-induced forces that must be added to ELP nematic hydrodynamics and we discuss their consequence, in particular for large scrD, the analog of shear-thinning for liquid crystals.