Enhancement by polydispersity of the biaxial nematic phase in a mixture of hard rods and plates

TL;DR

This study investigates how polydispersity influences the stability of the biaxial nematic phase in mixtures of hard rods and plates, showing that sufficient polydispersity can stabilize this phase even at aspect ratios where it is normally unstable.

Contribution

It demonstrates that polydispersity can stabilize the biaxial nematic phase in mixtures of rods and plates, providing insights for experimental realization.

Findings

Polydispersity stabilizes the biaxial phase at κ=5.

Phase diagram at κ=15 remains similar regardless of polydispersity.

Polydispersity can be used to design experiments to observe the biaxial phase.

Abstract

The phase diagram of a polydisperse mixture of uniaxial rod-like and plate-like hard parallelepipeds is determined for aspect ratios $\kappa=5$ and 15. All particles have equal volume and polydispersity is introduced in a highly symmetric way. The corresponding binary mixture is known to have a biaxial phase for $\kappa=15$, but to be unstable against demixing into two uniaxial nematics for $\kappa=5$. We find that the phase diagram for $\kappa=15$ is qualitatively similar to that of the binary mixture, regardless the amount of polydispersity, while for $\kappa=5$ a sufficient amount of polydispersity stabilizes the biaxial phase. This provides some clues for the design of an experiment in which this long searched biaxial phase could be observed.