Effect of particle geometry on phase transitions in two-dimensional liquid crystals

TL;DR

This study uses density-functional theory to explore how particle shape affects phase transitions in two-dimensional liquid crystals, revealing differences in phase behavior between rectangles and discorectangles, and implications for biaxial phase stability.

Contribution

It introduces a combined theoretical approach to analyze phase diagrams of anisotropic particles, highlighting the impact of particle geometry on phase behavior and biaxial phase stability.

Findings

Hard rectangles exhibit bimodal orientational distributions with biaxial order.

Discorectangles show unimodal distributions, lacking biaxial order.

Shape perturbations may stabilize biaxial phases by destabilizing spatially ordered phases.

Abstract

Using a version of density-functional theory which combines Onsager approximation and fundamental-measure theory for spatially nonuniform phases, we have studied the phase diagram of freely rotating hard rectangles and hard discorectangles. We find profound differences in the phase behavior of these models, which can be attributed to their different packing properties. Interestingly, bimodal orientational distribution functions are found in the nematic phase of hard rectangles, which cause a certain degree of biaxial order, albeit metastable with respect to spatially ordered phases. This feature is absent in discorectangles, which always show unimodal behavior. This result may be relevant in the light of recent experimental results which have confirmed the existence of biaxial phases. We expect that some perturbation of the particle shapes (either a certain degree of polydispersity or even bimodal dispersity in the aspect ratios) may actually destabilize spatially ordered phases thereby stabilizing the biaxial phase.