Biaxial nematic phase in the Maier-Saupe model for a mixture of discs and cylinders

TL;DR

This paper investigates the phase behavior of a Maier-Saupe lattice model with mixed oblate and prolate molecules, revealing conditions under which a biaxial nematic phase is stable or unstable.

Contribution

It introduces a model incorporating disorder degrees of freedom and analyzes the stability of biaxial nematic phases under different thermalization conditions.

Findings

Biaxial nematic phase exists with quenched disorder.

Thermalization of disorder destabilizes the biaxial phase.

Slight non-thermalization stabilizes the biaxial phase.

Abstract

We analyze the global phase diagram of a Maier-Saupe lattice model with the inclusion of disorder degrees of freedom to mimic a mixture of oblate and prolate molecules (discs and cylinders). In the neighborhood of a Landau multicritical point, solutions of the statistical problem can be written as a Landau-de Gennes expansion for the free energy. If the disorder degrees of freedom are quenched, we confirm the existence of a biaxial nematic strucure. If orientational and disorder degrees of freedom are allowed to thermalize, this biaxial solution becomes thermodynamically unstable. Also, we use a two-temperature formalism to mimic the presence of two distinct relaxation times, and show that a slight departure from complete thermalization is enough to stabilize a biaxial nematic phase.