Statistical models of mixtures with a biaxial nematic phase

TL;DR

This paper uses a statistical model to explore how disorder affects the stability of biaxial nematic phases in mixtures of rod-like and disc-like molecules, revealing conditions that promote or inhibit this phase.

Contribution

It introduces a two-temperature formalism to demonstrate how partial annealing can stabilize biaxial nematic phases in liquid mixtures.

Findings

Quenched disorder stabilizes biaxial nematic phase.

Full annealing prevents biaxial phase stability.

Partial annealing can stabilize the biaxial phase.

Abstract

We consider a simple Maier-Saupe statistical model with the inclusion of disorder degrees of freedom to mimic the phase diagram of a mixture of rod-like and disc-like molecules. A quenched distribution of shapes leads to the existence of a stable biaxial nematic phase, in qualitative agreement with experimental findings for some ternary lyotropic liquid mixtures. An annealed distribution, however, which is more adequate to liquid mixtures, precludes the stability of this biaxial phase. We then use a two-temperature formalism, and assume a separation of relaxation times, to show that a partial degree of annealing is already sufficient to stabilize a biaxial nematic structure.