Twisted quasiperiodic textures of biaxial nematics

TL;DR

This paper develops a systematic approach to classify and visualize complex quasiperiodic textures in biaxial nematic liquid crystals, revealing their geometrical, topological, and optical properties through numerical and Fourier analysis.

Contribution

It introduces a novel method to study biaxial nematic textures, including the derivation and numerical solution of simplified elastic energy models, and identifies quasiperiodic solutions with multiple characteristic periods.

Findings

Identification of quasiperiodic textures with multiple space periods

Visualization of textures revealing geometrical and topological features

Insights into optical properties of biaxial nematic textures

Abstract

Textures (i.e., smooth space non-uniform distributions of the order parameter) in biaxial nematics turned out to be much more difficult and interesting than expected. Scanning the literature we find only a very few publications on this topic. Thus, the immediate motivation of the present paper is to develop a systematic procedure to study, classify and visualize possible textures in biaxial nematics. Based on the elastic energy of a biaxial nematic (written in the most simple form that involves the least number of phenomenological parameters) we derive and solve numerically the Lagrange equations of the first kind. It allows one to visualize the solutions and offers a deep insight into their geometrical and topological features. Performing Fourier analysis we find some particular textures possessing two or more characteristic space periods (we term such solutions quasiperiodic ones because the periods are not necessarily commensurate). The problem is not only of intellectual interest but also of relevance to optical characteristics of the liquid-crystalline textures.