Extending the Maier-Saupe theory to cybotactic nematics

TL;DR

This paper extends the Maier-Saupe theory to describe thermotropic nematic liquid crystals with internally ordered clusters, predicting new phases and order behaviors influenced by cluster size.

Contribution

It introduces a generalized theory incorporating cluster internal order, predicting stable isotropic phases with internal order and cybotactic nematic phases.

Findings

Prediction of uniaxial nematic and isotropic phases with internal order

Order parameter and entropy change depend on cluster size

Cybotactic order persists above the transition temperature

Abstract

A theory of thermotropic nematic liquid crystals in which molecules form internally ordered clusters is presented. The formulation is based on the same mean field approximation and form of the anisotropic potential used in the Maier-Saupe theory. A uniaxial nematic and two macroscopically isotropic phases are predicted. One of the isotropic phases consists of thermodynamically stable clusters with internal orientational order. The nematic phase shows cybotactic order throughout its range of stability. This order persists above the transition temperature, either as a stable feature or as a pretransitional effect. The values of the order parameter and of the entropy change at the nematic to isotropic phase transition depend on the size of the clusters. The Maier-Saupe theory is obtained in the limit of extremely large or extremely small clusters.