The classical theory
The continuum theory of liquid crystals is a variational theory in which a free energy functional is posited. The classical mathematical theory of liquid crystals is a continuum theory based on the works of C. W. Oseen, H. Zocher and F. C. Frank. This chapter traces the origins of Frank’s theory and explains its consequences, following mostly J. L. Ericksen’s work. The swarm theory Frank refers to regards a nematic liquid crystal as a collection of small droplets within which the orientation of the optic axis is constant, being generally different in different droplets. Oseen attempted to comprehend the molecular forces that give rise to liquid crystals. He described the orientation of each molecule through a vector of unit length which is directed along the axis of symmetry of the molecule. The chapter presents all the requirements that the energy density of both nematics and cholesterics is expected to satisfy.