A Rigorous Derivation of Oseen-Frank Theory from Molecular Theory of Liquid Crystals

In this talk, we investigate the relationship between the molecular theory and the Oseen-Frank theory for nematic liquid crystals. In the framework of Onsager’s molecular theory for liquid crystal, we consider a molecular free energy that include the effects of nonlocal intermolecular interactions. By imposing the uniaxial boundary condition on the second moment of the distribution function, we prove the existence of non-trivial global minimizers. Moreover, we study the limit of small interaction distance and show that, the global minimizers will converge to a uniaxial distribution function predicted by the Oseen-Frank theory for uniaxial nematic liquid crystals with constant order parameter. This is a joint work with Wei Wang in Zhejiang University.