Maier-Saupe model for a mixture of uniaxial and biaxial molecules

TL;DR

This paper models a mixture of uniaxial and biaxial liquid-crystalline molecules using a Maier--Saupe lattice approach, revealing complex phase diagrams with multiple nematic phases and multicritical points.

Contribution

It introduces shape fluctuations in a lattice model for mixed uniaxial and biaxial molecules, analyzing their thermodynamics and phase behavior at the mean-field level.

Findings

Rich phase diagrams with uniaxial and biaxial nematic phases

Reentrant ordered regions identified

Multiple multicritical points discovered

Abstract

We introduce shape fluctuations in a liquid-crystalline system by considering an elementary Maier--Saupe lattice model for a mixture of uniaxial and biaxial molecules. Shape variables are treated in the annealed (thermalized) limit. We analyze the thermodynamic properties of this system in terms of temperature $T$, concentration $c$ of intrinsically biaxial molecules, and a parameter $\Delta$ associated with the degree of biaxiality of the molecules. At the mean-field level, we use standard techniques of statistical mechanics to draw global phase diagrams, which are shown to display a rich structure, including uniaxial and biaxial nematic phases, a reentrant ordered region, and many distinct multicritical points. Also, we use the formalism to write an expansion of the free energy in order to make contact with the Landau--de Gennes theory of nematic phase transitions.