Voronoi patterns in liquid crystal textures

Abstract

An inverse Voronoi tessellation algorithm is developed that can be applied to a large variety of liquid crystalline textures, yielding the seed positions of individual cells. The patterns formed via Voronoi tessellation describe those observed in the texture micrographs very well, with a similarity in excess of 80%, when employing a harsh numerical measure to describe the similarity between experimental and calculated patterns. This is shown for a number of very different liquid crystalline systems, such as nematics on polymer surfaces, chiral materials like frustrated Blue Phases and cholesteric defect structures, discotics, bolaamphiphiles with columnar phases and metallomesogens. Discrepancies between calculated Voronoi patterns and experimental textures are mainly due to inevitable temperature gradients and nucleation fluctuations, which can in principle not be accounted for by the Voronoi algorithm. The methodology can be used for example in materials optimisation, the construction of complex photonic or diffraction devices and even for electronics with molecular wires based on columnar phases.