A model for the orientational order in liquid crystals

Abstract

A model for the orientational-order parameter in liquid crystals from the microscopic viewpoint and in conformity with its current understanding well established in the field of phase transitions is proposed here. This model has a close resemblance with the original ideas of Maier and Saupe. However, it is independent of the nature of molecules, rigid or flexible, and enables us to describe a phase with a single-order parameter tensor $$\mathop S\limits^ \leftrightarrow$$ as expected. Moreover, an important advantage of this model in contrast to the prevailing ones is its, ability to separate the contributions of long-range order from local information inherent in any microscopic measurement such as by NMR and EPR techniques with some reasonable assumptions. All these are demonstrated here with the observed quadrupole splittings for different deuterium sites of long-chain molecules forming the uniaxial nematic phase. The role of molecular conformations on the observed splittings is also explicitly demonstrated by recovering quadrupole coupling constants and bond orientations at different molecular sites. These results are in reasonable agreement with available data.