Probing a non-biaxial behavior of infinitely thin hard platelets

TL;DR

This paper introduces a criterion to test non-biaxial behavior in thin hard platelets and applies it to simulate and analyze their nematic phases, revealing uniaxial nematic ordering regardless of shape anisotropy.

Contribution

It provides a new criterion based on order parameter tensors to identify non-biaxial behavior in platelet systems and applies it through Monte Carlo simulations.

Findings

All systems exhibited uniaxial nematic behavior.

Shape anisotropy did not induce biaxial nematic phases.

Theoretical and simulation effective diameters were compared.

Abstract

We give a criterion to test a non-biaxial behavior of infinitely thin hard platelets of $D_{2h}$ symmetry based upon the components of three order parameter tensors. We investigated the nematic behavior of monodisperse infinitely thin rectangular hard platelet systems by using the criterion. Starting with a square platelet system, and we compared it with rectangular platelet systems of various aspect ratios. For each system, we performed equilibration runs by using isobaric Monte Carlo simulations. Each system did not show a biaxial nematic behavior but a uniaxial nematic one, despite of the shape anisotropy of those platelets. The relationship between effective diameters by simulations and theoretical effective diameters of the above systems was also determined.