Stability of Biaxial Nematic Phase for Systems with Variable Molecular Shape Anisotropy

TL;DR

This paper investigates how molecular shape fluctuations affect the stability of the biaxial nematic phase, revealing that such fluctuations can either stabilize or destabilize the phase and lead to new phase diagram features.

Contribution

It generalizes the mean field model to include Gaussian shape anisotropy fluctuations, showing their impact on phase stability and diagram topology.

Findings

Shape fluctuations can stabilize the biaxial nematic phase.

Fluctuations lead to new phase diagram classes.

Splitting of the Landau point into two triple points.

Abstract

We study the influence of fluctuations in molecular shape on the stability of the biaxial nematic phase by generalizing the mean field model of Mulder and Ruijgrok [Physica A {\bf 113}, 145 (1982)]. We limit ourselves to the case when the molecular shape anisotropy, represented by the alignment tensor, is a random variable of an annealed type. A prototype of such behavior can be found in lyotropic systems - a mixture of potassium laurate, 1-decanol, and $D_2O$, where distribution of the micellar shape adjusts to actual equilibrium conditions. Further examples of materials with the biaxial nematic phase, where molecular shape is subject to fluctuations, are thermotropic materials composed of flexible trimeric- or tetrapod-like molecular units. Our calculations show that the Gaussian equilibrium distribution of the variables describing molecular shape (dispersion force) anisotropy gives rise to new classes of the phase diagrams, absent in the original model. Depending on properties of the shape fluctuations, the stability of the biaxial nematic phase can be either enhanced or depressed, relative to the uniaxial nematic phases. In the former case the splitting of the Landau point into two triple points with a direct phase transition line from isotropic to biaxial phase is observed.