From Microscopic Theory to Macroscopic Theory: a Systematic Study on Modeling for Liquid Crystals

Abstract

In this paper, we propose a systematic way of liquid crystal modeling to build connection between microscopic theory and macroscopic theory. A new Q-tensor theory based on Onsager's molecular theory which leads to liquid crystals with certain shape has been proposed. Making uniaxial assumption, we can recover the Oseen-Frank theory from the derived $Q$-tensor theory, and the Oseen-Frank model coefficients can be examined. In addition, the smectic-A phase can also be characterized by the derived macroscopic model.