A unified continuum theory of liquid crystals

Abstract

A unified continuum theory is proposed governing physical behavior of all liquid crystals whose molecules are modelled with rigid directors. Balance laws and constitutive equations are given and thermodynamic restrictions are obtained. Chiral and nonchiral liquid crystals are shown to differ only in their symmetry groups and smectic liquid crystals in a constraint on twist elasticities. Dynamic constitutive equations include translation and gyration viscosities coupled with heat conduction. The theory is shown to give the director (Oseen-Frank) theory under special conditions valid for that theory.