Stability of diverse dodecagonal quasicrystals in T-shaped liquid crystalline molecules

TL;DR

This study explores the thermodynamic stability and formation criteria of diverse dodecagonal quasicrystals in T-shaped liquid crystalline molecules using self-consistent field theory, revealing new design principles for soft material quasicrystals.

Contribution

It introduces three self-similar dodecagonal tilings, including a novel pattern, and analyzes their stability and structural features in liquid crystalline molecules.

Findings

Identification of stable dodecagonal quasicrystals from tilings

Development of criteria to distinguish quasicrystals and approximants

Insights into design rules for stabilizing quasicrystals in soft materials

Abstract

Quasicrystals are intriguing ordered structures characterized by the lack of translational symmetry and the existence of rotational symmetry. The tiling of different geometric units such as triangles and squares in two-dimensional space can result in a great variety of quasicrystals that could be realized by the self-assembly of liquid crystalline molecules. In this study, we introduce three self-similar dodecagonal tilings, including a novel Diamond-Square-Triangle pattern, composed of triangular and quadrangular tiles and examine their thermodynamic stability by using the self-consistent field theory applied to T-shaped liquid crystalline molecules. Specifically, we detail the inflation rules for the construction of these dodecagonal tilings and analyze their self-similarity, and show that these tilings can be viewed as projections of higher-dimensional periodic lattice points with projection windows. Using these dodecagonal tilings as initial configurations of the SCFT results in solutions corresponding to quasicrystals that could form from the T-shaped liquid crystalline molecules. The relative stability of these aperiodic phases is analyzed to obtain design rules that could stabilize quasicrystals. Meanwhile, we provide two criteria for distinguishing three dodecagonal quasicrystals and their approximants by analyzing their diffraction peaks. These findings shed new lighten on the discovery of new quasicrystals in soft materials.