A Molecular-Based Q-Tensor Hydrodynamic Theory of Smectic Liquid Crystals

Abstract

The Doi–Onsager molecular theory is capable of providing a rather accurate description of the local behavior of molecules; however, its computation is extremely time-consuming, since some higher-dimensional variables are typically involved. Therefore, establishing a computable reduced model that can capture essential physical properties is an important issue. In this work, we derived a reduced Q-tensor hydrodynamic theory that described smectic phases with density variations from the Doi–Onsager molecular theory using the Bingham closure approximation. The coefficients in the tensor model were derived from those in the molecular model. The energy dissipation law was inherited from the tensor model. Some special cases for the model were also discussed.